Applied Science, Faculty of
Chemical and Biological Engineering, Department of
DSpace
UBCV
Migaybil, Hashim
Doctor of Philosophy - PhD
University of British Columbia
Conventional single-slope solar stills are essential for decentralized freshwater production, yet their performance optimization is limited by small datasets and the nonlinear dynamics of desalination. This doctoral thesis addresses these constraints by developing and evaluating data-efficient supervised machine learning frameworks to predict freshwater productivity (Pstd, L/m²·day). The study integrates a novel high-performance solar still design with two complementary learning paradigms: Transfer Learning (TL) and tailored Data Augmentation (DA). The research begins with the design and MATLAB/SIMULINK simulation of a photovoltaic-assisted single-slope solar still engineered for improved thermal performance. The hybrid system achieved a peak efficiency of 45%, and its 730-sample dataset served as the “source” domain for TL. The first paradigm introduces a cross-design TL framework. A source Artificial Neural Network (ANN) was pre-trained on the hybrid system simulation data, and its learned weights were transferred and fine-tuned to model a conventional solar still using only 365 experimental samples. The optimized TL-based ANN (5-64-64-1) outperformed both randomly initialized ANNs and Multiple Linear Regression (MLR), achieving an Overall Index of Model Performance (OIMP) of 0.872 and demonstrating superior predictive accuracy and generalization. The second paradigm develops a tailored DA strategy to directly expand the conventional still’s limited dataset. Gaussian noise–based jittering was applied to sequential inputs within a 7-day look-back window to generate synthetic training data for a one-dimensional Convolutional Neural Network (CNN-1D). The optimized CNN-1D model—comprising three 128-filter convolutional layers—substantially outperformed baseline CNN and Support Vector Regression (SVR) models, achieving an RMSE of 0.045 and an OIMP of approximately 0.97. A threshold-based classification method was also introduced to translate raw predictions into interpretable productivity categories. Overall, this thesis provides a comparative evaluation of TL and DA approaches, validating their effectiveness in addressing data scarcity in solar still modeling. Key contributions include a novel cross-design TL framework, a specialized DA technique for time-series solar still data, and highly accurate predictive models. The findings provide practical, cost-effective tools for optimizing conventional solar stills and underscore the broader potential of advanced machine learning in renewable energy–driven desalination.
Data-Efficient Deep Learning for Predictive Modelling of Conventional Single Slope Solar Stills: Leveraging Transfer Learning and Tailored Data Augmentation Strategies by Hashim Migaybil B.Sc., King Abdul-Aziz University, 2011 M.A.Sc, The University of British Columbia, 2021 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) November 2025 ©Hashim Migaybil 2025 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Data-Efficient Deep Learning for Predictive Modelling of Conventional Single Slope Solar Stills: Leveraging Transfer Learning and Tailored Data Augmentation Strategies submitted by Hashim Migaybil in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical and Biological Engineering Examining Committee: Dr. Bhushan Gopaluni, Professor, Chemical and Biological Engineering, UBC Supervisor Dr. Ryozo Nagamune, Professor, Mechanical Engineering, UBC Supervisory Committee Member Dr. Yankai Cao, Associate Professor Chemical and Biological Engineering, UBC Supervisory Committee Member Dr. Dana Grecov, Professor, Mechanical Engineering, UBC University Examiner Dr. Steven Weijs, Associate Professor, Civil Engineering, UBC University Examiner iii Abstract Conventional single-slope solar stills are essential for decentralized freshwater production, yet their performance optimization is limited by small datasets and the nonlinear dynamics of desalination. This doctoral thesis addresses these constraints by developing and evaluating data-efficient supervised machine learning frameworks to predict freshwater productivity (Pstd, L/m²·day). The study integrates a novel high-performance solar still design with two complementary learning paradigms: Transfer Learning (TL) and tailored Data Augmentation (DA). The research begins with the design and MATLAB/SIMULINK simulation of a photovoltaic-assisted single-slope solar still engineered for improved thermal performance. The hybrid system achieved a peak efficiency of 45%, and its 730-sample dataset served as the “source” domain for TL. The first paradigm introduces a cross-design TL framework. A source Artificial Neural Network (ANN) was pre-trained on the hybrid system simulation data, and its learned weights were transferred and fine-tuned to model a conventional solar still using only 365 experimental samples. The optimized TL-based ANN (5-64-64-1) outperformed both randomly initialized ANNs and Multiple Linear Regression (MLR), achieving an Overall Index of Model Performance (OIMP) of 0.872 and demonstrating superior predictive accuracy and generalization. The second paradigm develops a tailored DA strategy to directly expand the conventional still’s limited dataset. Gaussian noise–based jittering was applied to sequential inputs within a 7-day look-back window to generate synthetic training data for a one-dimensional Convolutional Neural Network (CNN-1D). The optimized CNN-1D model—comprising three 128-filter iv convolutional layers—substantially outperformed baseline CNN and Support Vector Regression (SVR) models, achieving an RMSE of 0.045 and an OIMP of approximately 0.97. A threshold-based classification method was also introduced to translate raw predictions into interpretable productivity categories. Overall, this thesis provides a comparative evaluation of TL and DA approaches, validating their effectiveness in addressing data scarcity in solar still modeling. Key contributions include a novel cross-design TL framework, a specialized DA technique for time-series solar still data, and highly accurate predictive models. The findings provide practical, cost-effective tools for optimizing conventional solar stills and underscore the broader potential of advanced machine learning in renewable energy–driven desalination. v Lay Summary Access to clean drinking water is a growing challenge worldwide. Solar stills offer a simple, eco-friendly way to purify water using the sun’s heat, but their efficiency is limited, and predicting their output is difficult when data are scarce. This research tackles that problem using computer modeling and artificial intelligence (AI). First, I designed and simulated a new solar still that uses solar panels (PV) to boost heating. The model reached up to 45% efficiency—much higher than traditional stills—and produced 730 data samples for AI training. Next, I used Transfer Learning, allowing an AI model trained on the large simulation dataset to make accurate predictions on a much smaller real-world dataset. Finally, I expanded the small experimental dataset using Data Augmentation and trained a 1D Convolutional Neural Network (CNN-1D) for improved accuracy. Overall, this work shows that AI can significantly enhance low-cost solar stills for clean water in remote communities. vi Preface The work presented in chapters 3, 4, and 5 have been published as research articles: For the research presented in chapter 3, I served as the primary investigator, leading conceptualization, data analysis, and modeling under the supervision of Professor Bhushan Gopaluni, with contributions to analysis and conceptual development from Dr. H.A. Maddah. The core findings have been disseminated through a journal paper publication: • H. H. Migaybil, H. A. Maddah, and B. Gopaluni, "Design and simulation of a novel solar photovoltaic system assisted single‐slope solar still distillation unit," Can. J. Chem. Eng., vol. 101, no. 6, pp. 3059-3073, Jun. 2023. The development of the models and the analytical work presented in Chapter 4 were primarily conducted by me, encompassing data analysis and initial modeling. Professor Bhushan Gopaluni provided supervisory guidance, contributed to concept formation, and oversaw subsequent manuscript revisions. This research has been accepted for publication: • H. H. Migaybil and B. Gopaluni, "A performance neural network model for conventional solar stills via transfer learning," Appl. Energy, vol. 375, p. 124118, Dec. 2024. I led the research design, data analysis, and modeling detailed in Chapter 5, serving as the principal investigator, with Professor Bhushan Gopaluni providing supervision as the secondary author for the ensuing manuscript. The manuscript detailing this research has been accepted for publication in the Energy Conversion and Management Journal: • H. H. Migaybil and B. Gopaluni, "Advancing Predictive Modeling in Conventional Solar Stills: A Deep Learning Approach Leveraging Data Augmentation and Convolutional Neural Networks," Energy Convers. and Manag., vol. 346, p. 120565, Dec. 2025. vii Throughout the execution of this doctoral research, numerous technical and analytical challenges were encountered and systematically addressed, each contributing to the substantive depth and scientific rigor of this dissertation. I extend my profound gratitude to my esteemed advisors, supportive colleagues, and family for their unwavering encouragement and invaluable support during this endeavor. In the preparation of this dissertation, generative AI, including ChatGPT and Grammarly, were used solely as a writing assistance tool for minor editorial refinement and for troubleshooting coding errors during method implementation. All core research activities, including conceptualization, experimental design, data analysis, interpretation of results, and intellectual contributions, are entirely the original work of the author. Research Ethics Ethics approval was not required for this research. viii Table of Contents Abstract .......................................................................................................................................... iii Lay Summary .................................................................................................................................. v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ viii List of Tables ............................................................................................................................... xiii List of Figures ............................................................................................................................. xvi List of Abbreviations ................................................................................................................. xxiv Nomenclature ............................................................................................................................ xxiv Acknowledgments....................................................................................................................... xxx Dedication.................................................................................................................................. xxxi Chapter 1: Introduction & Research Framework ........................................................................ 1 1.1 Motivation .................................................................................................................................... 1 1.2 Problem Statement ....................................................................................................................... 2 1.3 Study Objectives .......................................................................................................................... 4 1.4 Study Novelty ............................................................................................................................... 5 1.5 Scientific Contributions and Values ............................................................................................. 7 1.6 Research Limitations and Gaps .................................................................................................... 9 1.7 Thesis Outline and Structure ...................................................................................................... 10 1.8 Conclusion .................................................................................................................................. 13 ix Chapter 2: Literature Review: Integrating the Blue Economy and Supervised Machine Learning ....................................................................................................................................... 16 2.1 The Global Imperative for Sustainable Water Security .................................................................... 16 2.2 Saudi Arabia's Vision: The Blue Economy and Pioneering Sustainable Solutions .......................... 17 2.2.1 Scale and Strategic Focus of Saudi Arabia's Blue Economy .................................................................... 18 2.3 The Desalination Challenge: Conventional Methods and the Quest for Sustainability .................... 20 2.4 Solar Still Distillation: Principles, Advancements, and Persistent Hurdles ...................................... 21 2.5 The Transformative Role of Supervised Machine Learning in Optimizing Solar Stills ................... 23 2.6 Research Significance and Dissertation Contribution ....................................................................... 26 2.7 Background and Literature Review ................................................................................................... 28 2.7.1 Design and simulation of the novel hybrid solar still .......................................................................... 28 2.7.2 Artificial Neural Networks (ANNs) ..................................................................................................... 30 2.7.3 Multiple linear regression (MLR) ........................................................................................................ 33 2.7.4 Transfer Learning and Fine-Tuning ..................................................................................................... 34 2.8 Foundational Principles of CNN-1D and SVR for Sequential Numerical Data Analysis in Regression Tasks ..................................................................................................................................... 36 2.8.1 CNN-1D Conceptual Framework for Regression ................................................................................ 37 2.8.2 Core Operations and Mathematical Formulation ................................................................................. 38 2.8.3 Parameter Optimization for Regression ............................................................................................... 42 2.8.4 Support Vector Regression (SVR) Conceptual Framework ................................................................ 43 2.8.5 Core Operations and Mathematical Formulation ................................................................................. 44 2.8.6 SVR Key Hyperparameters .................................................................................................................. 47 2.8.7 Gaussian Noise Injection for Data Augmentation ............................................................................... 48 2.9 Conclusion and Dissertation Outlook ........................................................................................ 48 x Chapter 3: Design and Simulation of a Novel Solar Photovoltaic System Assisted Single-Slope Solar Still Distillation Unit .......................................................................................................... 50 3.1 Motivation .................................................................................................................................. 50 3.2 Introduction ................................................................................................................................ 50 3.3 Proposed Novel Solar Still Model .............................................................................................. 58 3.4 Methodology and Framework .................................................................................................... 60 3.4.1 Photovoltaic Process Modeling Technique .......................................................................................... 61 3.4.2 Solar Still Process Modelling Technique .................................................................................................. 64 3.4.2 Feed Tank Process Modeling Technique ............................................................................................. 69 3.4.3 Distillate Tank Process Modeling Technique ...................................................................................... 71 3.5 Results and Discussion ............................................................................................................... 73 3.6 Conclusion .................................................................................................................................. 84 Chapter 4: A Performance Neural Network Model for Conventional Single-Slope Solar Stills via Transfer Learning .................................................................................................................. 87 4.1 Motivation .................................................................................................................................. 87 4.2 Introduction ....................................................................................................................................... 87 4.3 Literature Review ....................................................................................................................... 93 4.4 Methodology and Framework .................................................................................................... 95 4.4.1 Developing the source ANN model ...................................................................................................... 96 4.4.2 Criteria of assessment for random initialization ANN model .............................................................. 99 4.5 Results and Discussion ............................................................................................................. 108 4.5.1 Optimization of pre-trained ANN model architecture ....................................................................... 108 4.5.2 Performance analysis of ANN RI and comparison with MLR ........................................................... 117 xi 4.6 Conclusion ................................................................................................................................ 131 Chapter 5: Advancing Predictive Modeling in Conventional Solar Stills: A Deep Learning Approach Leveraging Data Augmentation and Convolutional Neural Networks .................. 134 5.1 Motivations............................................................................................................................... 134 5.2 Introduction .............................................................................................................................. 134 5.3 Methodology and Framework .................................................................................................. 141 5.3.1 Developing Baseline CNN-1D model................................................................................................. 141 5.3.2 Criteria of evaluation for the Augmented CNN-1D model ................................................................ 145 5.3.3 Developing Baseline and Augmented SVR Models .......................................................................... 158 5.3.4 Criteria of Optimization for SVR Models .......................................................................................... 160 5.4 Results and Discussion ............................................................................................................. 163 5.4.1 Optimization of baseline CNN-1D model architecture ...................................................................... 163 5.4.2 Optimization of augmented CNN-1D model architecture .................................................................. 168 5.4.3 Performance analysis of CNN 1D and comparison with SVR ........................................................... 171 5.5 Recent Advancements and Insights.......................................................................................... 189 5.5.1 Performance Analysis ........................................................................................................................ 191 5.6 Conclusion ................................................................................................................................ 194 Chapter 6: Overall Conclusion, Recommendations, and Path Forward ................................. 197 6.1 Introduction ..................................................................................................................................... 197 6.2 Summary of Major Findings and Contributions.............................................................................. 197 6.2.1 Advancements through Transfer Learning (TL) ..................................................................................... 197 6.2.2 Advancements through Data Augmentation (DA) .................................................................................. 198 6.2.3 Overarching Contributions ...................................................................................................................... 199 6.3 Overall Conclusion .......................................................................................................................... 200 xii 6.4 Recommendations ........................................................................................................................... 201 6.4.1 For Practical Application and Industry .................................................................................................... 201 6.4.2 For Future Research ................................................................................................................................ 201 6.5 Path Forward: Integrating Solar Stills with Emerging Sustainable Technologies .......................... 202 6.5.1 Physics-Informed Neural Networks (PINNs) for Enhanced Model Robustness and Interpretability ..... 202 6.5.2 Integration of Solar Stills with Electrolyzers for Green Hydrogen Production ...................................... 203 6.5.3 Continued Exploration of Advanced Machine Learning Models ............................................................ 203 6.6 Concluding Remarks ....................................................................................................................... 204 Bibliography ............................................................................................................................... 205 Appendices .................................................................................................................................. 225 Appendix A: Mathematical Symbols Definition .................................................................................. 225 Appendix B: Tables including 3-D Results and Figures ....................................................................... 228 xiii List of Tables Table 2. 1 Illustrative Indicators of Saudi Arabia's Blue Economy and Desalination Focus. ...... 19 Table 2. 2 Illustrative Performance Metrics for ML-Integrated Solar Still Distillation (from Recent Literature). ........................................................................................................................ 26 Table 4. 1 Inputs and outputs parameters data sources. ................................................................ 99 Table 4. 2 Presenting the RI ANN model methodology in a pseudocode form. ........................ 106 Table 4. 3 Hyperparameters optimization for source (pre-trained) ANN model in sequence from minimum to maximum loss. ....................................................................................................... 112 Table 4. 4 Statistical parameters for assessing the performance of ANN and MLR models during training, testing, and validation stages. ....................................................................................... 120 Table 4. 5 Statistical parameters for assessing the performance of ANN and MLR models during training, testing, and validation stages. ....................................................................................... 129 Table 5. 1 Description of the input and output parameters for modeling the baseline conventional single-slope solar still system and their respective data sources. The input parameters include key meteorological variables from the NASA Power database and the operational input of saline water feed flow rate obtained from literature and experimental datasets. The output parameter, representing solar still productivity in terms of daily freshwater yield (L/day), was also derived from validated experimental studies. .......................................................................................... 145 Table 5. 2 Input and output matrix dimensions of the developed baseline and augmented CNN-1D and SVR models following time-series conversion (look-back window = 7) for solar still freshwater prediction. The augmentation process, applied only to the training set, generated six additional samples per original instance using Gaussian noise. For SVR models, the time-series xiv sequences were flattened to vectors of 35 features (7 × 5). The output across all models represents daily freshwater productivity as a univariate continuous target. ............................... 153 Table 5. 3 Pseudocode-based representation and mathematical formulation of the proposed augmented CNN 1D modeling pipeline. Each step describes the systematic workflow, including time series conversion, data augmentation, scaling, model definition, hyperparameter optimization, training, and evaluation. This framework integrates a Gaussian noise-based augmentation approach and employs hyperparameter tuning and early stopping to enhance model performance and generalization. ................................................................................................. 155 Table 5. 4 Hyperparameter configurations for the augmented SVR model obtained using the TPE algorithm over 100 optimization trials. The table presents the regularization parameter (C), epsilon-insensitive margin (ε), selected kernel type, and corresponding validation loss (MSE). The best-performing configuration achieved a minimum validation loss of 0.01289 using the RBF kernel with a relatively low regularization strength, indicating improved generalization due to data augmentation. .................................................................................................................. 162 Table 5. 5 Hyperparameter configurations for the baseline SVR model derived from 200 optimization trials using the TPE approach. All top-performing configurations utilized the RBF kernel with marginal variations in ε. The lowest validation loss was 0.01339, obtained at a considerably higher regularization strength (C = 116.801), indicating a greater reliance on penalizing deviations due to the limited diversity of the training data in the un-augmented dataset. ........................................................................................................................................ 162 Table 5. 6 Hyperparameter optimization results for the baseline CNN-1D model across 50 trials, arranged in ascending order of final loss values. The table reports the optimal combinations of convolutional layer size, number of dense units, filters, batch size, learning rate, and weight xv decay (λ). The best-performing configuration (trial 1) achieved the lowest loss of 0.006711 using a 3-layer CNN with eight dense units, 64 filters, and a learning rate of 0.01. ............................ 167 Table 5. 7 Hyperparameter optimization outcomes for the augmented CNN-1D model evaluated over 50 trials. The table presents the tuned values for convolutional layers, dense units, filters, batch size, learning rate, and weight decay, ordered by increasing loss. The optimal configuration (trial 1) achieved the lowest loss of 0.001359 using a 3-layer architecture with 128 filters, 128 dense units, and a batch size of 8, confirming the effectiveness of the augmentation-enhanced search space. ............................................................................................................................... 170 Table 5. 8 Comparative statistical performance of the CNN-1D and SVR models ‘’baseline and augmented configurations’’ evaluated across the training, validation, and testing phases. The augmented CNN-1D model achieved the highest accuracy and lowest error values in all phases, demonstrating superior learning efficiency and generalization ability. These findings validate the robustness and effectiveness of the proposed augmentation strategy in enhancing the performance of deep learning-based forecasting in solar desalination applications................... 181 Table 5. 9 Classification performance comparison of the CNN-1D and SVR models under both baseline and augmented configurations, using accuracy, precision, recall, and F1-score metrics. The augmented CNN-1D model achieved the highest overall performance, with an accuracy of 88% and an F1-score of 0.82, indicating enhanced feature learning and more balanced classification. In contrast, SVR models exhibited minimal improvement with augmentation, suggesting limited benefit from the added variability in feature space. ..................................... 187 Table 5. 10 Performance comparison of the proposed augmented CNN 1D model, benchmarked against recent studies in the field, including experimental setup, theoretical modelling, simulation, and machine learning applications. .......................................................................... 192 xvi List of Figures Figure 2. 1 Global map illustrating regions projected to face high to extreme water stress by 2050. (Adopted from [4]). ............................................................................................................. 16 Figure 2. 2 Conceptual diagram illustrating the interconnected sectors of Saudi Arabia's Blue Economy, highlighting desalination and renewable energy. (Adapted from information [9].) .... 18 Figure 2. 3 Simplified schematic diagram of a single-slope passive solar still, illustrating the basic principles of evaporation and condensation. (Adopted from [14])...................................... 22 Figure 2. 4 NEOM Adopts Pioneering Solar Dome Technology for Sustainable Desalination Project. (Adopted from [22]). ....................................................................................................... 23 Figure 2. 5 Developed schematic diagram for a solar photovoltaic system assisted a single slope solar still distillation unit. ............................................................................................................. 29 Figure 2. 6 A fundamental building block of the components of an artificial neuron, adopted and modified from [29]. ....................................................................................................................... 31 Figure 2. 7 Architecture of a one‐dimensional convolutional neural network (CNN-1D) model, adopted from [40]. ........................................................................................................................ 39 Figure 2. 8 Schematic illustration of Support Vector Regression (SVR) using the ε-insensitive loss function, adopted from [13]. In the input space x (left), SVR models non-linear relationships, while the application of a kernel function ϕ(x) (e.g., RBF) maps the data to a higher-dimensional feature space (right) where a linear regression function is fitted. The dashed margins represent the ε-tube within which errors are not penalized, and 𝜉 denotes the slack variables for data points falling outside the margin. This structure corresponds to the prediction function (Eq. 1), RBF kernel transformation (Eq. 2), and SVR objective loss formulation (Eq. 3)........................................................................................................................................................ 46 xvii Figure 3. 1 Proposed schematic diagram for a solar photovoltaic system-assisted solar still distillation unit. ............................................................................................................................. 60 Figure 3. 2 Photograph of the developed solar PV system design parameters and look-up tables “Solar Photovoltaic System Simulink Model Browser”. .............................................................. 62 Figure 3. 3 Photograph of the developed solar still distillation unit design parameters and cost analysis “Solar Still Distillation Unit Simulink Model Browser”. ............................................... 65 Figure 3. 4 Photograph of the created weather input parameters using the signal builder tool “Climatic Input Variables Simulink Model Browser”. ................................................................. 66 Figure 3. 5 Feed saline water tank model browser. ...................................................................... 70 Figure 3. 6 Distillate water tank model browser. .......................................................................... 72 Figure 3. 7 (A) solar still design area, Ast (m2) at different solar radiations, Is (15-20 MJ/m2.day) and solar still feed tank flow rate productivities, Pst (1-5 kg/day), (B-C) solar still glass cover area, Ag (m2) at solar radiations, Is (15 & 20 MJ/m2.day) respectively. ...................................... 74 Figure 3. 8 (A) Solar still designed area Ast (m2) at different feed tank productivities, Pst (kg/day), (B) photovoltaic cell total system area, At (m2), (C) solar still freshwater productivities without/ with black dye additives, Pstd (kg/m2.day), (D) temperature differences between water and basin glass cover, TW-Tg (oC). ................................................................................................ 77 Figure 3. 9 (A) Thermal load inside the solar still Qload (kW) at different flow rate productivities, Pst (kg/day), (B) evaporative heat transfer coefficient inside the solar still, hev (W/m2 oC), (C) solar still efficiency during the operational day, st (%), (D) solar still total capital cost, TCC ($/unit)........................................................................................................................................... 80 Figure 3. 10 (A) thermal load inside the still Qload (kW) at different solar radiations, Is (15-20 MJ/m2.day) and feed tank productions flow rate (1-5 kg/day), (B) total photovoltaic cell costs, xviii PVCt ($/module) at Tamb 25 oC against other solar radiations, Is (15-20 MJ/m2.day) and feed flow rate productivities, Pst (1-5 kg/day). .............................................................................................. 82 Figure 3. 11 Designed solar still efficiencies, st (%). .................................................................. 83 Figure 3. 12 Solar still and solar PV designed model system areas, A (m2). ............................... 84 Figure 4. 1 Flowchart for selecting and developing optimal pre-trained and target ANN models for accurately predicting distillate water productivity. ............................................................... 103 Figure 4. 2 Schematic diagram for applying the transfer learning technique on the conventional solar still system to accurately predict distillate water outputs Pstd, L/m2.day. ........................... 104 Figure 4. 3 A schematic block flow diagram for applying the transfer learning method on the conventional solar still system known as the random initialization (RI) ANN model to predict distillate water (Pstd, L/m2.day) outputs more accurately. The optimal source (pre-trained) ANN model was developed to produce the best-learned weights, freeze, and transfer them to the RI ANN network to further generate the target ANN model with minimal statistical errors. ......... 105 Figure 4. 4 ReLU and PReLU activation functions graph. ......................................................... 110 Figure 4. 5 Average contribution values of input node variables on distillate water outputs Pstd, L/m2.day. ..................................................................................................................................... 114 Figure 4. 6 Training loss vs. validation loss over the number of epochs: (A) for the source (pre-trained) ANN model and (B) for the RI ANN model, showing both models are approaching zero loss and being optimized by the desired number of Epochs. ...................................................... 116 Figure 4. 7 Optimal architecture of the developed source ANN model to predict distillate water...................................................................................................................................................... 117 xix Figure 4. 8 Comparison between observed vs. predicted distillate water values using source (pre-trained) ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation dataset. ................... 119 Figure 4. 9 Evaluation of the performance of pre-trained ANN and MLR models during all modeling processes. .................................................................................................................... 121 Figure 4. 10 Comparison between observed vs. predicted distillate water values using RI ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation datasets. ........................................ 125 Figure 4. 11 Comparison between observed vs. predicted distillate water values using target ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation datasets. .......................... 126 Figure 4. 12 Evaluation of ANN and MLR models' performance during the testing modeling process......................................................................................................................................... 130 Figure 4. 13 A histogram comparison of deviations between predicted and actual values for the RI ANN model vs. the target ANN model. ................................................................................. 130 Figure 5. 1 Methodological workflow for developing and validating the Augmented CNN-1D model architecture for distillate prediction in a conventional single-slope solar still. The flowchart outlines the data preparation process, which involves converting time series with a 7-day look-back window, applying Gaussian noise-based data augmentation, and scaling. Model development includes hyperparameter optimization using the Hyperopt algorithm, training with early stopping, and evaluation using statistical metrics. The procedure is benchmarked against baseline CNN-1D and SVR models to ensure robust performance assessment. ........................ 152 xx Figure 5. 2 Schematic representation of the optimal augmented CNN 1D model architecture denoted as 5-(128)3-1. The model begins with five input features processed through a time-series look-back window (k = 7), followed by three consecutive 1D convolutional layers, each comprising 128 feature maps and activated by the ReLU function. These are followed by a flatten layer that transforms the multidimensional outputs into a one-dimensional vector, then passes to a fully connected dense layer with 128 neurons. Lastly, a single output neuron predicts the daily distillate water yield (L/day). This architecture yielded the lowest prediction errors and highest performance metrics among all tested configurations, as highlighted in Table 5. ......... 154 Figure 5. 3 A block diagram showing the implementation of the proposed time series data augmentation strategy for training 1D CNN models, specifically applied to a conventional single-slope solar still distillation unit. The original dataset, consisting of 365 daily samples with five input features, was first converted using a look-back window (k = 7) to capture temporal dependencies. Two modeling paths were followed: a baseline CNN-1D model trained on the original data, and an augmented CNN-1D model trained on data enhanced with Gaussian noise. This augmentation process increased data diversity and improved model robustness. Both models were evaluated across training, validation, and testing phases to forecast daily freshwater output and assess generalization performance. ...................................................................................... 154 Figure 5. 4 Training and validation loss comparison across created models. (A) The loss progression of the baseline CNN-1D model across 120 epochs exhibits minor fluctuations in validation loss relative to training, indicating acceptable generalization but limited optimization stability. (B) The augmented CNN-1D model exhibits more consistent convergence across 200 epochs, with training and validation losses nearly overlapping throughout the training process. This indicates robust generalization and reduced overfitting due to the augmentation process and xxi optimized architecture. These plots support the improved learning stability and performance of the augmented model. ................................................................................................................. 170 Figure 5. 5 Comprehensive comparative analysis between baseline CNN and SVR models. Subplots (A–C) illustrate the temporal response patterns for the training, validation, and testing phases, comparing the observed distillate water output with predictions from baseline CNN and SVR models. Subplots (D–F) present regression plots showing the correlation between predicted and observed outputs across the three phases. The CNN model consistently exhibits higher alignment with the diagonal (ideal prediction line), suggesting better accuracy. Subplots (G–I) display residual distribution plots, where the baseline CNN model demonstrates a more compact residual spread, particularly in the testing phase, compared to SVR. Collectively, these results validate the superior predictive performance of the CNN baseline model over SVR in modeling freshwater output from solar stills. ............................................................................................. 174 Figure 5. 6 Comparative analysis of augmented CNN-1D and SVR models across all modeling phases. Subplots (A–C) illustrate the temporal prediction performance of the augmented CNN-1D and SVR models relative to actual observed distillate water output across the training, validation, and testing phases. Both models closely follow the actual trend, with the augmented CNN-1D model displaying improved alignment and reduced fluctuations, particularly during the testing phase. Subplots (D–F) present scatter plots of predicted versus observed distillate water values, indicating that the augmented CNN-1D model yields higher prediction accuracy, as evidenced by tighter clustering along the 1:1 reference line. Subplots (G–I) display residual plots, where the augmented CNN 1D model maintains a more compact and symmetrical residual distribution around zero, suggesting reduced prediction error and improved generalization. In contrast, the augmented SVR model exhibits more scattered residuals and greater deviation, xxii particularly in the testing phase. These results underscore the superior robustness and predictive accuracy of the augmented CNN-1D framework compared to the SVR approach for modeling solar still distillation output. ....................................................................................................... 178 Figure 5. 7 Residual heatmaps comparing prediction errors between the augmented CNN-1D and SVR models across training (A), validation (B), and testing (C) datasets. Each subfigure visualizes the relative error distribution, where lighter shades indicate smaller residuals and darker shades correspond to larger deviations from the ground truth. The CNN-1D model demonstrates more compact and consistent residuals across all phases, particularly in the training and testing stages, which highlights its superior generalization and error control. However, SVR exhibits broader and more scattered error patterns, featuring its limited ability to capture the nonlinear dependencies in the solar still desalination data. ........................................................ 182 Figure 5. 8 (A) Histogram and (B) Kernel Density Estimation (KDE) plots illustrating the deviation distribution of predicted values from actual values in the testing dataset for both the baseline CNN-1D and the augmented CNN-1D models. The augmented CNN-1D model exhibits a sharper concentration of errors around zero, indicating improved prediction accuracy and reduced output variance. Conversely, the baseline CNN-1D model shows a broader distribution of deviations, reflecting more significant prediction uncertainty. These findings highlight the effectiveness of time-series data augmentation in enhancing model precision and narrowing the error distribution. ........................................................................................................................ 183 Figure 5. 9 Radar plots comparing six statistical metrics—R², Efficiency Coefficient (EC), Overall Index of Model Performance (OIMP), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Variance (CV)—across training, validation, and testing phases for four models: augmented CNN-1D, augmented SVR, baseline CNN-1D, and baseline SVR. xxiii The augmented CNN-1D model demonstrates superior performance with higher accuracy and lower error dispersion, particularly in the testing phase, highlighting the effectiveness of data augmentation in enhancing model generalization and predictive reliability. ............................. 185 Figure 5. 10 : Comparative bar chart of testing phase metrics across four developed models. The diagram illustrates model accuracy and error using six statistical performance metrics. The Augmented CNN-1D model consistently outperforms all others, demonstrating superior accuracy and generalization with higher R², EC, and OIMP values, and lower RMSE, MAE, and CV. .. 186 Figure 5. 11 Confusion matrices for the four predictive models applied to the water output classification task. The classification was based on a stable thresholding approach, where both actual and predicted water output values were labeled as “Yes” if they exceeded 1.25× the mean actual value and “No” otherwise. Unlike percentile-based methods, this threshold-based strategy improves interpretability, ensures consistent labeling across datasets, and avoids distortions caused by skewed distributions or outliers. The impact of data augmentation is evident in the CNN model, which shows reduced misclassification rates, particularly in minimizing false positives and improving classification stability during the testing phase. .................................. 186 xxiv List of Abbreviations AI ⎯ Artificial Intelligence ALSS ⎯ Aluminum-based Solar Still ANN ⎯ Artificial Neural Network BL ⎯ Baseline CNN ⎯ Convolutional Neural Network CPL ⎯ Cost per Liter CV ⎯ Coefficient of variation DA ⎯ Data Augmentation 1D ⎯ One Dimensional DC ⎯ Direct Current EC ⎯ Efficiency coefficient GCC ⎯ Gulf Cooperation Council GDP ⎯ Gross Domestic Product GHG ⎯ Greenhouse Gases GJO ⎯ Golden Jackal Optimization GUI ⎯ Graphical User Interface KDE ⎯ Kernel Density Estimator KSA ⎯ Kingdom of Saudi Arabia L2 ⎯ Regularization Strength MAE ⎯ Mean Absolute Error xxv MAPE ⎯ Mean Absolute Percentage Error ME ⎯ Model Efficiency MENA ⎯ Middle East and North Africa ML ⎯ Machine Learning MOEP ⎯ Ministry of Economics and Planning MSE ⎯ Mean Squared Error NEPCMS ⎯ Nano-enhanced Phase Change Materials MLR ⎯ Multiple Linear Regression NOB ⎯ Number of Batteries NOM ⎯ Number of Modules OI ⎯ Overall index of model Performance OIMP ⎯ Overall index of model Performance PCM ⎯ Phase Change Materials PCSS ⎯ Polycarbonate-based Solar Still PV ⎯ Photovoltaic RE ⎯ Renewable Resources RF ⎯ Random Forest ReLU ⎯ Rectified Linear Unit R2 ⎯ Coefficient of determination RI ⎯ Random Initialization RMSE ⎯ Root mean square error RO ⎯ Reverse Osmosis xxvi SEC ⎯ Specific Energy Consumption SWCC ⎯ Saline Water Conversion Corporation SWRO ⎯ Sea Water Reverse Osmosis SVM ⎯ Support Vector Machine SVR ⎯ Support Vector Regression TL ⎯ Transfer Learning xxvii Nomenclature A ⎯ Short circuit currents, A Ac ⎯ Cell area, cm2 Adt ⎯ Distillate tank cross area, m2 Aft ⎯ feed tank cross area, m2 Ag ⎯ Glass cover area, m2 Am ⎯ Module area, m2 Ast ⎯ Solar still area, m2 At ⎯ Total photovoltaic system area, m2 BS ⎯ Battery storage, Wh Cp ⎯ Heat capacity at constant pressure, kJ/kg oC d ⎯ Solar still brine depth, cm dH ⎯ Water level inside the tanks, m dTw ⎯ Water temperature difference inside the still, oC FOB ⎯ Full overboard price, $/watt/module hc ⎯ Convection heat transfer coefficient between water and cover W/m2 oC hevp ⎯ Evaporative convective heat transfer coefficient between water and glass cover, W/m2 oC Ht ⎯ Feed tank total height, m Im ⎯ Maximum current, A Is ⎯ Solar Radiation, MJ/day Lh ⎯ Latent heat of distillate vapor evaporation, kJ/kg xxviii Pst ⎯ Saline water feed flowrate, L/day Pstd ⎯ Solar still productivity per unit area, kg/m2.day Pdye ⎯ Solar still productivity with black dye per unit area, kg/m2.day Pf ⎯ Feed tank pressure, KPa PVCt ⎯ Total photovoltaic cost, $/module Pw ⎯ Water vapor pressure, Pa Pg ⎯ Glass cover vapor pressure, Pa Qev ⎯ Evaporation heat transfer, kW Qload ⎯ Thermal load inside the still, kW RH ⎯ Relative humidity, % Tamb ⎯ Ambient temperature, oC TCC ⎯ Total capital cost, $/unit Tg ⎯ Glass cover temperature, oC Tw ⎯ Basin water temperature, oC Twi ⎯ Feed water temperature from the tank, oC V ⎯ Open circuit voltage, V Vf ⎯ Feed tank volume, m3 Vm ⎯ Maximum voltage, V Voldt ⎯ Distillate tank volume Voldt, m3 Vw ⎯ Wind speed, m/s b ⎯ Battery efficiency, % st ⎯ Solar still efficiency, % xxix List of Subscripts amb ⎯ Ambient b-w ⎯ Basin to water Ct ⎯ Cost dt ⎯ Distillate tank e ⎯ Evaporative ev ⎯ Evaporative ft ⎯ Feed tank g-amb ⎯ Glass cover to the ambient Greeks ∝ Absorptivity η Efficiency, % 𝜀 Emissivity 𝜎 Stephen-Boltzmann constant (W/m2 K4) 𝜏 Transmissivity xxx Acknowledgments In the name of Allah, the Most Merciful, the Most Gracious. With deep humility and gratitude, I commence this thesis. All recognition and glorification are due to the Almighty for guidance, provision, and unwavering support throughout every stage of this endeavor. It is with immense pleasure that I share the accomplishment of this doctoral research, a success made possible by the invaluable contributions of many individuals and institutions. First and foremost, I would like to extend my sincere gratitude and appreciation to my PhD supervisor, Professor Bhushan Gopaluni. He graciously provided me with the opportunity to join his esteemed research group, and his remarkable and steadfast support, insightful guidance, and mentorship throughout this project have been indispensable. His direction and dedicated time throughout my research, particularly his guidance in navigating the complexities of solar energy applications, have been instrumental to its progress. I would also like to express my sincere gratitude and appreciation to the Royal Saudi Government, particularly the Ministry of Education, for the prestigious scholarship that enabled me to pursue my doctoral studies. This support fulfilled my aspiration to pursue graduate research at the University of British Columbia and facilitated my adaptation to a new academic and cultural environment. Furthermore, I would like to acknowledge the crucial financial support provided by my sponsoring institution, King Abdulaziz University. Finally, I wish to convey my deepest and most special gratitude to my loving and kind parents. Their continuous support, unwavering belief in my capabilities, and comforting words during challenging times, despite the thousands of miles separating us, have been a constant source of strength. It is their encouragement that has consistently transformed obstacles and uncertainties into manageable endeavors. I sincerely hope this achievement brings them happiness and pride. xxxi Dedication To my parents for their endless support 1 Chapter 1: Introduction & Research Framework 1.1 Motivation The motivation for this doctoral research arises from the pressing challenges and opportunities related to sustainable water management. A primary concern is the escalating global water scarcity crisis, which is particularly severe in arid regions, such as the Kingdom of Saudi Arabia. In these areas, the demand for freshwater consistently exceeds the natural supply. Although conventional desalination has been a key component of the Kingdom's water strategy, its high energy consumption and environmental impact are fundamentally at odds with the sustainability objectives outlined in Saudi Arabia's Vision 2030. Specifically, the Vision—which incorporates a "blue economy" framework—calls for innovative, energy-efficient, and environmentally friendly solutions to enhance national water security. Solar distillation presents a promising alternative, utilizing the abundant renewable energy available in the region. However, a significant barrier to the widespread optimization and deployment of solar still systems is the inability to accurately predict their freshwater productivity. This forecasting challenge is intensified by the limited experimental data from real-world installations, which hinders efforts to optimize designs, dynamically control operations, and confidently assess economic viability. Without robust predictive capabilities, solar stills remain an under-optimized technology despite their potential. To address this critical predictive gap, the primary motivation of this dissertation is to demonstrate that advanced, data-efficient machine learning techniques can provide the essential tools needed to overcome this limitation. By systematically developing and validating novel frameworks in Transfer Learning and tailored Data Augmentation, this research seeks to unlock the full potential of solar distillation. The ultimate goal is to produce highly accurate, scientifically validated predictive models that empower engineers and policymakers to optimize 2 solar still performance effectively. By doing so, this research will directly contribute to Saudi Arabia's Vision 2030 sustainable water security objectives and provide scalable solutions for water-scarce regions worldwide. 1.2 Problem Statement Conventional single-slope solar stills are a vital technology for decentralized freshwater production. Optimizing their design and operation for enhanced water productivity (Pstd) is crucial for economic viability and resource maximization. This optimization relies heavily on accurate predictive models for Pstd. Furthermore, understanding and categorizing the performance levels based on these predictions can provide significant operational insights. However, developing such comprehensive modeling and analytical frameworks using supervised machine learning for conventional solar stills faces significant challenges: 1. Data Scarcity for Conventional Stills: Acquiring extensive, high-quality experimental datasets for conventional single-slope solar stills (like the available 365-sample dataset) is often resource-intensive, limiting the ability to train complex models from scratch and extract deeper insights from their outputs. 2. Leveraging External Knowledge for Conventional Stills (Transfer Learning Context): Separately, a prior study by the research group successfully designed and simulated a novel hybrid solar photovoltaic (PV) system assisted single-slope solar still, and an ANN model was developed based on this novel system. The problem addressed by the Transfer Learning component of this PhD is how to effectively transfer the learned features (weights) from this more complex source model to improve Pstd predictions for conventional single-slope solar stills using their distinct dataset. 3 3. Enhancing Limited Datasets for Conventional Stills (Data Augmentation Context): For the Data Augmentation component of this PhD, the challenge is how to effectively expand and enrich the existing dataset of 365 samples from a conventional single-slope solar still to improve the training, generalization, and subsequent analytical interpretation of deep learning models (like 1D CNNs) applied directly to this conventional system. 4. Model Generalization and Output Utility for Conventional Stills: Predictive models trained on moderately sized datasets may struggle to generalize well. Moreover, raw predictions require further interpretation to be operationally useful, highlighting the need for methods that can categorize performance reliably. 5. Complexity of Non-Linear Dynamics & Simulation Limitations: The thermal and mass transfer processes within any solar still are non-linear. While the simulation of the novel hybrid still (used as the source for TL) captured these, purely physics-based simulations can have limitations (e.g., restricted input ranges for solar radiation), underscoring the value of robust data-driven ML approaches that also facilitate nuanced output analysis. This PhD study addresses the development and validation of advanced, data-efficient supervised machine learning frameworks for conventional single-slope solar stills. It will employ two distinct but complementary strategies: a. Transfer Learning (TL): Leveraging a pre-trained ANN model from a novel hybrid PV-assisted solar still to initialize and fine-tune models for Pstd prediction in conventional stills. b. Data Augmentation (DA): Applying tailored augmentation techniques directly to the experimental dataset of a conventional single-slope solar still to enhance model training for Pstd prediction and enable more robust subsequent output analysis. The overall goal is to significantly enhance the accuracy, robustness, and generalizability of 4 predictive models for freshwater productivity in conventional single-slope solar stills distillation units, and to develop innovative methods for interpreting these predictions for practical applications. 1.3 Study Objectives The primary aim of this research is to develop, evaluate, and demonstrate the utility of robust predictive models for the freshwater productivity of conventional single-slope solar stills by independently investigating and applying Transfer Learning and Data Augmentation, including methods for enhanced output interpretation. The specific objectives are: 1. To Develop and Evaluate Transfer Learning-based Models for Pstd Prediction in Conventional Stills: • Investigate Transfer Learning by adapting the pre-trained source ANN model (from the novel hybrid PV-assisted solar still) to predict the Pstd of conventional single-slope solar stills using their dedicated dataset. • Optimize the fine-tuning process for conventional still Pstd prediction, comparing performance against models trained from scratch and traditional regression models. 2. To Develop and Evaluate Data Augmentation-enhanced Models for Pstd Prediction and Analysis in Conventional Stills: • Implement tailored data augmentation strategies (e.g., Gaussian noise injection with a look-back window) directly on the experimental dataset of a conventional single-slope solar still. • Develop and optimize deep learning architectures (e.g., 1D CNNs) trained on this augmented conventional still dataset to accurately forecast Pstd. 5 • Investigate methods for interpreting the outputs of these predictive models, such as threshold-based classification of productivity levels, to provide actionable insights. 3. To Conduct Comparative Performance Analysis of Predictive Models: • Rigorously compare the Pstd predictive performance of the TL-based models and the DA-enhanced models. • Benchmark these against each other and baseline models (e.g., MLR, SVR, standard ANNs/CNNs on original conventional still data) using comprehensive statistical metrics. 4. To Validate the Proposed Modeling and Analytical Frameworks for Conventional Stills: • Validate the most promising developed predictive models and associated output interpretation techniques using appropriate methods to ensure their practical applicability and robustness for conventional single-slope solar stills. 5. To Identify Key Parameters and Sensitivities for Conventional Stills: • Analyze the developed predictive models to understand the relative importance of input variables on Pstd predictions for conventional single-slope solar stills, further enriching the operational understanding derived from the models. 1.4 Study Novelty This PhD research presents novelty in several key areas, encompassing both predictive modeling advancements and innovative analytical approaches for conventional single-slope solar stills: 1. Pioneering Application of Transfer Learning in Solar Desalination for Conventional Stills: 6 • A core novelty is the utilization of Transfer Learning (TL) to build accurate predictive ANN models for freshwater productivity (Pstd) specifically in conventional single-slope solar stills, employing a pre-trained source ANN model from a novel hybrid PV-assisted solar still. • This research introduces and validates a specific target ANN model architecture (5-64-64-1) for conventional stills, enhanced through transfer learning. • The demonstrated superior Pstd prediction performance of this TL-enhanced target ANN model for conventional stills underscores its practical effectiveness. 2. Advanced Data Augmentation and Deep Learning Integration for Conventional Solar Still Time-Series Data: • This study presents a novel integration of Gaussian noise-based data augmentation (jittering) with a 1D Convolutional Neural Network (CNN-1D) to significantly enhance Pstd prediction accuracy for conventional single-slope solar stills, using their dedicated experimental dataset. • The meticulous development of an optimized CNN-1D model (5-128-128-128-1 structure) through comprehensive hyperparameter tuning is a novel aspect, designed to capture spatial-temporal patterns in conventional solar still data. 3. Methodological Advancements in Model Application and Output Interpretation: • The extensive benchmarking of the augmented CNN-1D model within the DA study demonstrates superior performance in predicting Pstd. • Critically, this research extends beyond mere prediction by introducing innovative analytical techniques, such as a pioneering threshold-based classification method, to reliably categorize freshwater outputs from conventional stills based on 7 meaningful productivity thresholds. This technique, offering enhanced interpretability and stability over traditional methods, represents a novel step in translating predictive outputs into actionable operational insights for conventional stills. 4. Practical Insights and Foundation for Future Advancements in Conventional Solar Still Technology: • Both the TL and DA studies provide valuable and practical insights directly relevant to real-world conventional single-slope solar desalination systems, not only for prediction but also for performance assessment. • Collectively, these distinct approaches and their findings, including methods for improved output interpretation, lay a robust groundwork for future advancements and cost-effective, reliable forecasting and performance management in conventional solar desalination technologies. 5. Addressing Limitations of Prior Simulation Work through ML for Conventional Stills: This research, through both TL and DA, proposes robust ML alternatives aimed at overcoming identified limitations of physics-based simulations, enabling more reliable predictions and analyses for conventional single-slope solar stills across a wider range of operational conditions. 1.5 Scientific Contributions and Values This research is anticipated to make the following significant scientific contributions and provide substantial value: 1. Enhanced Predictive Accuracy and Output Utility for Conventional Stills: The primary contribution will be the development of models for conventional single-slope solar 8 still Pstd with significantly higher accuracy and generalization, coupled with innovative methods for interpreting these predictions (e.g., performance classification) to enhance their practical utility. 2. Data-Efficient Modeling and Analytical Solutions for Conventional Stills: This study will provide and compare validated methodologies (TL leveraging an external source model, DA enhancing existing limited data) that address data limitations for modeling conventional stills, making advanced predictive modeling and subsequent sophisticated analysis more accessible. 3. Improved System Optimization, Design, and Operational Understanding for Conventional Stills: More accurate Pstd predictions, combined with clearer performance categorization, will enable better optimization of conventional still designs, operational strategies, and overall understanding of system behavior. 4. Demonstration of Effective Knowledge Transfer, Data Enhancement, and Advanced Analytics in Solar Desalination: The research will showcase how knowledge from complex systems can be transferred (TL), how limited data can be effectively augmented (DA), and how advanced analytical techniques can be applied to model outputs for deeper insights in the context of conventional solar stills. 5. Advancement of Machine Learning in Renewable Energy Desalination: The research contributes by applying and comparing powerful ML techniques and demonstrating their extension into practical analytical frameworks for solving prediction and interpretation problems in solar desalination. 9 6. Practical Tools for Water Resource Management: The developed models and analytical approaches will serve as valuable tools for assessing and managing the performance of conventional single-slope solar stills. 7. Methodological Insights for ML Application and Interpretation: The study will offer insights into the relative strengths of TL versus DA for Pstd prediction and demonstrate novel ways to process and understand the outputs from these complex models. 1.6 Research Limitations and Gaps Building upon the provided information, this PhD study aims to address the following limitations and gaps, related to both predictive modeling and the analytical interpretation of outputs for conventional single-slope solar stills: A. Gaps Addressed by the Transfer Learning Component: 1. Optimizing Knowledge Transfer for Conventional Still Pstd Prediction: Investigating optimal strategies for adapting the pre-trained ANN model (from the novel hybrid still) to effectively predict Pstd for conventional single-slope solar stills using their dedicated dataset. 2. Quantifying TL Benefit for Conventional Stills with Limited Data: Establishing the degree of improvement TL offers for Pstd prediction in conventional stills compared to models trained from scratch on limited data. B. Gaps Addressed by the Data Augmentation Component: 3. Systematic Application of DA for Conventional Solar Still Time-Series for Prediction and Analysis: Confirming the efficacy of Gaussian noise with a look-back window and exploring if other tailored DA techniques could further enhance model training for Pstd prediction and the robustness of subsequent output interpretations (like classification) using the conventional still's 365-sample dataset. 10 4. Boosting Deep Learning with Limited Conventional Still Data for Enhanced Insights: Demonstrating how DA enables practical training of deep learning models for accurate Pstd prediction and facilitates more reliable downstream analyses (performance categorization) even with a moderately sized dataset. C. Overarching Gaps Addressed by the PhD: 5. Comparative Efficacy of TL vs. DA for Conventional Still Pstd Prediction: Systematically comparing the effectiveness of TL versus DA for improving Pstd predictions of conventional single-slope solar stills. 6. Generalizability and Utility of Enhanced Models and Analytical Frameworks for Conventional Stills: Ensuring that the models for conventional stills (enhanced by TL or DA) and the associated analytical interpretations are robustly generalizable and practically applicable. 7. Robustness to Extreme Inputs for Conventional Still Prediction and Analysis: Investigating if the ML models for conventional stills can robustly handle critical input values for accurate Pstd prediction and reliable performance categorization, potentially overcoming limitations seen in some physics-based simulations. 8. Developing Interpretable Advanced Models for Conventional Stills: While predictive accuracy is key, this research aims to enhance the utility of these models by developing methods (like threshold-based classification) that make their outputs more directly interpretable and actionable for understanding conventional still performance. 1.7 Thesis Outline and Structure This dissertation is structured into six chapters to systematically address the research objectives and present the findings: 11 Chapter 1: Introduction, Problem Definition, and Research Framework This initial chapter establishes the comprehensive foundation for the dissertation. It begins by delineating the overarching context, emphasizing the global challenge of water scarcity, and situating the research within Saudi Arabia's strategic ambitions for the blue economy through a synthesis of pertinent background information, statistical data, and key performance indicators. Following this contextualization, the chapter articulates a detailed problem statement, identifying the specific challenges in accurately predicting the performance of conventional solar stills, particularly under conditions of data scarcity and complex system dynamics. Subsequently, the chapter explicitly defines the study objectives pursued in this research. The inherent novelty of the proposed methodologies and the anticipated scientific contributions to the fields of solar desalination and applied machine learning are then presented. Finally, this chapter provides a critical analysis of prevailing research gaps, inherent limitations in current approaches, and the challenges addressed by this doctoral work, thereby setting the stage for the research framework and methodologies detailed in subsequent chapters. Chapter 2: Literature Review and Foundational Machine Learning Principles This chapter provides a comprehensive and critical review of the relevant academic literature concerning solar distillation technologies and predictive modeling. Concurrently, it outlines the foundational tenets of machine learning methodologies germane to this investigation. This encompasses a detailed exposition of artificial neural networks (ANN), multiple linear regression (MLR), one-dimensional convolutional neural networks (CNN-1D), and support vector regression (SVR). Advanced concepts, including transfer learning methodologies and data augmentation techniques (such as jittering via Gaussian noise injection), are also explored. Core 12 mathematical formalisms and operational principles are presented to ensure a thorough comprehension of the diverse methodologies subsequently employed. Chapter 3: Design and Simulation of a Novel Hybrid Solar Still System This chapter details the systematic design and computational simulation of a novel solar photovoltaic-assisted single-slope solar distillation unit. Employing physics-based modeling and validated design equations within the MATLAB/SIMULINK environment, this chapter demonstrates the practical integration of renewable energy conversion and fundamental engineering principles. The focus is on establishing a high-performance source model based on simulated data, which serves as a foundation for subsequent transfer learning investigations. Chapter 4: Transfer Learning Framework for Enhanced Solar Still Performance Prediction This chapter introduces and evaluates a transfer learning framework designed to augment the predictive accuracy of performance models for conventional solar stills. A pre-trained Artificial Neural Network (ANN) model, developed from the simulation data of the novel hybrid solar still system detailed in Chapter 3, is strategically leveraged. The methodology involves transferring learned features and fine-tuning the model using an experimental dataset procured from a conventional single-slope solar still. The resultant target model's performance is rigorously benchmarked against a randomly initialized ANN and an MLR model, thereby providing empirical validation for the advantages conferred by transfer learning in terms of enhanced generalization and predictive precision. Chapter 5: Data Augmentation Strategies for Robust Predictive Modeling with 1D-CNN and SVR This chapter examines the effectiveness of data augmentation strategies in enhancing predictive models for conventional solar stills, particularly when working with limited experimental 13 datasets. One-dimensional Convolutional Neural Network (CNN-1D) and Support Vector Regression (SVR) models are employed. Comparative analyses are conducted utilizing both baseline (original) and augmented datasets (generated using techniques such as jittering) to assess the impact on model robustness and predictive accuracy quantitatively. The empirical results furnish evidence supporting the utility of data augmentation in ameliorating model performance and introduce a novel threshold-based method for interpreting productivity predictions. Chapter 6: Overall Conclusion, Recommendations, and Path Forward The final chapter consolidates the entire research, presenting the overarching conclusions derived from the preceding investigations. It critically synthesizes the principal findings, reiterates the significant scientific contributions to the field, and offers specific, actionable recommendations for both the practical implementation of the developed modeling frameworks and future research trajectories. Furthermore, this chapter outlines a "path forward," discussing the potential for building upon these findings to create more integrated, intelligent, and synergistic sustainable technology ecosystems, thereby underscoring the transformative impact of advanced computational intelligence on optimizing renewable energy technologies, such as solar stills, for global water and energy sustainability. 1.8 Conclusion This introductory chapter lays the foundation for a doctoral study that focuses on advancing predictive modeling and analytical capabilities for conventional single-slope solar still distillation units. The critical need for accurate Pstd forecasting and meaningful interpretation of performance levels has been highlighted, driven by the imperative to optimize design, enhance operational efficiency, and improve economic viability. However, developing such 14 comprehensive frameworks using machine learning is often constrained by data scarcity and the complexity of solar still dynamics. This research proposes to address these challenges through two distinct advanced machine learning strategies: Transfer Learning (TL), which leverages a pre-trained ANN model from a novel hybrid solar still, and Data Augmentation (DA), applied directly to the experimental dataset of a conventional solar still. The objectives are to develop, optimize, and rigorously evaluate TL-based and DA-enhanced predictive models for Pstd, and to investigate innovative methods, such as threshold-based classification, for interpreting these predictions to provide actionable insights. The problem statement has underscored the limitations of existing approaches, and this study's novelty lies in its pioneering application of cross-design TL, tailored DA for conventional solar still data, the meticulous development of specific model architectures, and crucially, the extension of modeling efforts to include innovative analytical techniques for enhanced output interpretation. This research aims to make significant scientific contributions by developing more accurate and data-efficient predictive tools, as well as more insightful analytical frameworks, for conventional solar stills. The findings are expected to overcome existing limitations, providing practical solutions for performance assessment and optimization, and thereby paving the way for more intelligent and efficient utilization of solar desalination technology. Having established the problem domain, objectives, novelty, and intended contributions of this research, including the multifaceted approach to both prediction and output interpretation, the subsequent chapter will delve into a comprehensive review of the existing literature. 15 Chapter 2 will critically examine previous studies related to solar still desalination, predictive modeling techniques (including traditional methods and various machine learning approaches), the theoretical underpinnings and applications of Transfer Learning, Data Augmentation strategies relevant to time-series data, and methods for analyzing and interpreting machine learning model outputs in engineering contexts. This review will provide a deeper context for the current study, further solidify the identified gaps that this PhD aims to address and justify the proposed comprehensive methodologies and their potential impact. 16 Chapter 2: Literature Review: Integrating the Blue Economy and Supervised Machine Learning 2.1 The Global Imperative for Sustainable Water Security The confluence of water security, sustainable development, and climatic resilience constitutes a defining global imperative for the 21st century. Escalating demographic pressures and evolving socio-economic landscapes are projected to significantly intensify freshwater demand, thereby imposing unprecedented stress on finite water systems and the ecosystems they sustain [1]. Current estimates indicate that global freshwater demand may exceed reliable supply by as much as 40% by 2050, with nearly half the world's population potentially facing severe water stress [2], a situation visually depicted in Figure 2.1 This challenge is particularly pronounced in arid and semi-arid regions, which are increasingly emerging as innovation hubs for sustainable water solutions. Ambitious undertakings, such as Saudi Arabia's NEOM project, exemplify this paradigm shift, aiming to harness cutting-edge technologies and abundant renewable energy resources to secure sustainable water supplies and redefine urban living in water-stressed environments [3]. Figure 2. 1 Global map illustrating regions projected to face high to extreme water stress by 2050. (Adopted from [4]). 17 2.2 Saudi Arabia's Vision: The Blue Economy and Pioneering Sustainable Solutions In response to these pressing global and regional challenges, Saudi Arabia is strategically repositioning itself as a worldwide leader in sustainable development through its ambitious Vision 2030 agenda. Central to this transformative vision is the “blue economy”—a comprehensive framework designed to leverage the Kingdom’s extensive marine resources for driving economic diversification, promoting environmental stewardship, and fostering technological innovation [5] [6]. This strategic approach is exemplified by initiatives such as the National Red Sea Sustainability Strategy, which aims to safeguard marine ecosystems and establish the Red Sea as a global benchmark for blue economy activities [6] [7]. Saudi Arabia’s blue economy encompasses traditional sectors such as shipping and port logistics, alongside emerging domains, including regenerative tourism, marine biotechnology, renewable energy, and, critically, zero-emissions desalination [5] [8], as conceptualized in Figure 2.2. These endeavors are buttressed by a robust research, development, and innovation (RDI) ecosystem, with the Research Development and Innovation Authority (RDIA) having substantially augmented competitive funding for R&D initiatives [5]. 18 Figure 2. 2 Conceptual diagram illustrating the interconnected sectors of Saudi Arabia's Blue Economy, highlighting desalination and renewable energy. (Adapted from information [9].) 2.2.1 Scale and Strategic Focus of Saudi Arabia's Blue Economy Saudi Arabia’s commitment to the blue economy is distinguished by its unprecedented scale and strategic investments, with a particular emphasis on sustainable water solutions. Key aspects of this focus include: • Investment Scale: Over USD 3.2 trillion is reportedly earmarked for blue economy initiatives by the end of this decade, targeting sustainable prosperity and robust protection of marine ecosystems [5]. • Coastline and Marine Resources: The Kingdom’s strategy leverages its extensive 2,640-kilometer coastline and over 300 islands as foundational assets [5] [6]. • Economic Context: Projected non-oil Gross Domestic Product (GDP) growth of 4.3–4.6% in 2025 is anticipated to be partly driven by diversification efforts, including significant contributions from blue economy projects. 19 • Project Pipeline: A substantial project pipeline, valued at approximately SAR 2.1 trillion (circa USD 560 billion) for 2025, encompasses infrastructure, water, tourism, and renewable energy sectors. • Desalination Innovation: Projects within NEOM, for example, are actively exploring advanced solar-powered desalination concepts aimed at achieving enhanced efficiency and environmental sustainability [3], [10]. • Investment Opportunities: More than 100 investment-ready opportunities have been identified across diverse blue economy sectors, prominently featuring desalination innovation and water reuse. • Sustainability Commitments: The Saudi Green Initiative’s target to protect 30% of marine and terrestrial territory by 2030 directly aligns water projects with overarching environmental conservation goals. Table 2.1 provides a synopsis of illustrative indicators that reflect the scale and focus of Saudi Arabia's blue economy, particularly in the context of desalination. Table 2. 1 Illustrative Indicators of Saudi Arabia's Blue Economy and Desalination Focus. Category of Indicator Specific Metric Illustrative Value/Statistic Associated Context / Potential Source Type Strategic Investment Total Blue Economy Investment USD 3.2 trillion (by 2030) [5], National Strategy Documents Projected Non-Oil GDP Growth (2025) 4.3–4.6% Economic Reports (e.g., IMF, National) National Project Pipeline (2025) SAR 2.1 trillion (c. USD 560 billion) Industry/Economic Outlook Reports 20 Identified Investment Opportunities 100+ Investment Authority Publications Geographic & Resources Coastline Length 2,640 km [5], [6], Official Geographic Data Number of Islands Over 300 [5], [6], Official Geographic Data Desalination Focus Desalination Cost Target (Advanced Solar) e.g., Aiming for < $0.40/m³ in pilot projects [10], Project-specific reports Sustainability Commitment Marine/Terrestrial Protection Target (SGI) 30% by 2030 Saudi Green Initiative Documents 2.3 The Desalination Challenge: Conventional Methods and the Quest for Sustainability Given its arid climate and limited renewable freshwater resources, Saudi Arabia has historically relied heavily on desalination technologies [11] [12]. Globally, established methods such as Multi-Stage Flash (MSF) distillation, Multi-Effect Distillation (MED), and Seawater Reverse Osmosis (SWRO) dominate large-scale freshwater production [13]. Thermal processes, such as MSF and MED, while historically dependable, are characterized by high specific energy consumption (SEC); older MSF plants, for instance, can require an electrical equivalent of 10-16 kWh/m³ [14]. Even modern MED plants, though more efficient, exhibit significant thermal energy demands. Consequently, the reliance on fossil fuels for these processes often leads to substantial carbon footprints, with CO₂ emissions potentially ranging from 5 to over 15 kg CO₂-equivalent (CO₂-eq)/m³ of produced water for certain thermal plants [15]. 21 SWRO technology presents a more energy-efficient alternative, with advanced plants achieving specific energy consumption (SEC) values below 3.0 kWh/m³. This efficiency is primarily attributable to high-efficiency pumps and energy recovery devices, which can reclaim over 95% of hydraulic energy [16], resulting in an energy reduction that often exceeds 50-70% compared to older thermal methods. Nevertheless, SWRO faces persistent challenges, including rigorous pre-treatment requirements, membrane fouling, limited membrane lifespan, and the environmental management of concentrated brine discharge [17]. Despite significant advancements in RO efficiency through innovations such as advanced membrane materials and sophisticated energy recovery systems [13], the escalating global deployment of desalination capacity means that overall energy consumption remains a critical concern. This highlights the need for further advancements in low-energy, sustainable water purification technologies [18]. 2.4 Solar Still Distillation: Principles, Advancements, and Persistent Hurdles In the pursuit of sustainable and environmentally benign desalination, solar distillation, which directly harnesses solar irradiance, offers a compelling alternative, particularly in regions like Saudi Arabia that are rich in sunlight [18]. This technology emulates the natural hydrologic cycle: solar energy heats saline water within an enclosure, promoting evaporation. The resultant vapor subsequently condenses on a cooler surface, yielding purified distillate while leaving behind salts and other contaminants [11], as illustrated in the basic schematic of Figure 2.3 Among various designs, single-slope solar stills are widely recognized for their operational simplicity, minimal capital and maintenance expenditure, and suitability for decentralized, off-grid water production in remote or resource-limited communities [19]. 22 Figure 2. 3 Simplified schematic diagram of a single-slope passive solar still, illustrating the basic principles of evaporation and condensation. (Adopted from [14]). Recent advancements have concentrated on enhancing the thermal performance and productivity of solar stills. Innovations include modified geometries (e.g., hemispherical, pyramidal designs), the integration of internal/external condensers, solar reflectors, advanced wick materials for enhanced evaporation, and the incorporation of phase-change materials (PCMs) for latent heat storage. These modifications have, in specific studies, collectively boosted daily yield by percentages reportedly ranging from 30% to over 90% compared to conventional single-basin designs [11], [20]. Furthermore, advancements in salt-rejection mechanisms and concepts such as floating solar receivers aim to enhance system longevity and output [20]. Ambitious large-scale concepts, such as integrated solar dome structures being explored in developments like NEOM, envision concentrating solar power for high-volume, carbon-neutral freshwater generation, potentially coupled with mineral recovery from brine, thereby embodying the circular economy principles central to the blue economy [10], [21]. 23 Figure 2. 4 NEOM Adopts Pioneering Solar Dome Technology for Sustainable Desalination Project. (Adopted from [22]). Despite these innovations, a primary impediment to the broader adoption and scalability of passive or direct solar stills remains their inherently variable and comparatively modest freshwater productivity per unit area. This is typically documented in the range of 2–5 L/m²·day under average meteorological conditions [19] [23]. Such output levels present a significant challenge for applications requiring larger, more consistent water volumes, thereby underscoring the critical need for robust predictive management and operational optimization strategies. 2.5 The Transformative Role of Supervised Machine Learning in Optimizing Solar Stills The integration of supervised machine learning (ML) models into the design, operation, and management of solar still distillation units represent a significant leap forward in enhancing the efficacy of these sustainable water treatment systems. Machine learning (ML) techniques are increasingly pivotal for accurately predicting performance, optimizing operational parameters, and ultimately improving the viability of solar stills, particularly in data-rich environments or through effective data augmentation in data-scarce scenarios [24]. 24 2.5.1 Predictive Accuracy and Model Performance Benchmarks Advanced supervised ML architectures, such as Artificial Neural Networks (ANNs), have demonstrated considerable success in modeling the complex, non-linear dynamics inherent in solar still operation. For instance, recent studies utilizing ANNs, often incorporating sophisticated feature engineering and hyperparameter optimization, have reported high coefficients of determination (R² > 0.95) and significantly low error metrics (e.g., Root Mean Square Error (RMSE) values consistently below 0.5 L/m²·day for daily yield prediction) when benchmarked against experimental data for various solar still designs [14] [25]. Furthermore, hybrid ML models, which synergistically combine ANNs with metaheuristic optimization algorithms (e.g., genetic algorithms or particle swarm optimization for tuning network parameters or feature selection), have shown further incremental improvements in predictive accuracy. These hybrid approaches have, in specific comparative studies, reduced Mean Squared Error (MSE) by an additional 10-15% over standalone ANN configurations [24] [26]. The ability of these models to accurately forecast freshwater yield based on fluctuating meteorological inputs (solar radiation, ambient temperature, humidity, wind speed) and operational parameters (feedwater characteristics, water temperature, water depth) is foundational to their practical utility. 2.5.2 Enhancing Productivity and Efficiency through ML-Driven Insights The capacity for accurate prediction directly translates into opportunities for enhanced operational efficiency and increased freshwater productivity. ML models can inform real-time control strategies, enabling dynamic adjustments to operational parameters to maximize output under prevailing environmental conditions [25]. Data-driven insights derived from ML simulations also facilitate the optimization of solar still design parameters, including geometry, 25 insulation, and the selection of advanced materials. Studies suggest that ML-guided design can contribute to productivity improvements ranging from 20% to potentially over 40% compared to empirically designed conventional units [24] [27]. Moreover, ML can play a crucial role in ensuring high-quality potable water by predicting and helping to manage factors that might affect purity, such as maintaining optimal Total Dissolved Solids (TDS) levels in the basin. 2.5.3 Addressing Data Challenges and Ensuring Scalability A significant challenge in applying ML to novel or site-specific solar still configurations are often the limited availability of extensive experimental datasets. To this end, techniques such as transfer learning are gaining traction. Transfer learning allows knowledge acquired from models pre-trained on larger, related datasets (e.g., from different still designs or similar thermal systems) to be adapted to new scenarios with significantly less site-specific data, thereby accelerating model development and enhancing robustness [28]. Concurrently, data augmentation strategies, which involve generating synthetic yet realistic data points from existing datasets (e.g., through methods compatible with time-series characteristics, such as noise injection or bootstrapping), are employed to expand training sets. This improves model generalization and reliability across diverse operational scenarios [24], [28]. These ML advancements are crucial not only for optimizing individual units but also for the design, simulation, and intelligent management of larger, interconnected arrays of solar stills. Predictive analytics derived from ML models further support proactive maintenance scheduling, early fault detection, and adaptive control systems, all of which are vital for ensuring the reliable, cost-effective, and scalable commercial deployment of solar distillation technology [25]. Table 2.2 presents illustrative performance metrics, drawn from recent literature, for solar still distillation systems integrated with ML techniques. 26 Table 2. 2 Illustrative Performance Metrics for ML-Integrated Solar Still Distillation (from Recent Literature). Performance Aspect Specific Metric Achieved Illustrative Value/Result Indicative Reference Type (from Recent Studies) Model Predictive Accuracy ANN Model R² (Yield Prediction) > 0.95 [14], [25], Peer-reviewed ML/Solar Energy Journals 2022-2024 ANN Model RMSE (Yield Prediction, L/m²·day) < 0.5 [14], [25], Peer-reviewed ML/Solar Energy Journals 2022-2024 MSE Reduction (Hybrid ML vs. Standalone ANN) ~10-15% [24], [26], Comparative ML studies on Solar Stills System-Level Impact Productivity Improvement (ML-guided) 20–40%+ (over conventional designs/operations) [24], [27], Studies on ML for Solar Still Optimization Product Water Quality (TDS from saline feed) < 50 ppm (from >6,000 ppm feed) General Solar Still Performance Literature 2.6 Research Significance and Dissertation Contribution The confluence of Saudi Arabia's strategic blue economy objectives, ongoing innovations in solar distillation technology, and the transformative potential of supervised machine learning 27 presents a unique and timely opportunity to advance sustainable water security. This research direction is significant as it: • Facilitates more predictable, efficient, and optimized freshwater production from an abundant renewable resource (solar energy), directly addressing pressing water scarcity challenges. • Contributes to minimizing the environmental footprint associated with conventional desalination by promoting energy-efficient, low-emission technologies. • Supports national goals of economic diversification within the blue economy framework and fosters domestic expertise in high-technology sectors such as artificial intelligence (AI) and renewable energy systems. • Possesses the potential to further position Saudi Arabia as a global leader in the development and deployment of sustainable water management solutions [6] [7] [9]. This dissertation aims to make a substantive contribution to this critical field by developing and rigorously evaluating an advanced predictive modeling framework specifically tailored for solar still freshwater productivity. The core of this research involves the novel application of one-dimensional convolutional neural networks (1D CNNs) enhanced by a tailored time-series data augmentation strategy utilizing Gaussian noise and a 7-day look-back window to improve forecast accuracy from limited datasets for single-slope solar stills operating under diverse Saudi Arabian climatic conditions. This study aims to demonstrate superior forecasting accuracy, robustness, and generalization capabilities compared to existing models, thereby providing a scientifically validated and practically valuable tool for enhancing the design, dynamic operation, and strategic scaling of solar distillation systems in Saudi Arabia and other arid regions worldwide. 28 2.7 Background and Literature Review This section covers the design and simulation of the novel hybrid solar still, as well as a literature review on the state-of-the-art for developing predictive solar desalination models using statistical techniques and machine learning tools. Transfer learning methods and fine-tuning were thoroughly explored and examined. This section thoroughly explains the previously designed and simulated novel solar still system employed to build the source (pre-trained) ANN model [3]. It provides basic concepts and definitions related to Artificial Neural Networks (ANNs), Multiple Linear Regression (MLR), and transfer learning and fine-tuning methods. Additionally, this part of the study will present a statistical comparison and performance analysis between the created ANN pre-trained model (source) and the MLR model throughout all modeling stages. 2.7.1 Design and simulation of the novel hybrid solar still In this study, a novel hybrid solar photovoltaic system, previously designed and simulated, was employed in conjunction with a single-slope solar still distillation unit to develop an optimal source ANN model for predicting distillate water production. Figure 2.5 illustrates a schematic diagram of a single-basin solar still unit equipped with a heating element located at the bottom of the basin within the still. The solar still unit was connected to a solar photovoltaic system, which absorbs solar energy (photons) directly from sunlight to generate a flow of electricity (DC) as a power load on the solar photovoltaic cell, thereby heating the coil. The supporting heating coil converts the electrical energy generated by the solar PV cell into thermal energy for heating purposes and facilitating evaporation and condensation processes within the collector. The driving force of heat transfer, expressed as the temperature difference (Tw - Tg) between hot water and the glass cover inside the basin, causes evaporation and condensation processes. Brackish water is introduced to the still from the feedwater tank and desalinated to yield treated 29 water. The distillates correspond to the release of the latent heat of condensation produced when impure water evaporates by sunlight shining through the transparent basin. The vapor condenses on the top glass cover. The condensed water film on the inclined glass cover will then be collected by gravity in the distillate water compartment inside the basin through a collecting trough before being discharged into the distillate water tank and storage [29]. MATLAB/SIMULINK software was used to design and simulate the novel solar still system, utilizing graphical user interface (GUI) applications for support. This project design aims to develop and simulate a novel hybrid solar desalination system at a commercial scale, capable of producing 3-4.6 kg/m².day purified water. Figure 2. 5 Developed schematic diagram for a solar photovoltaic system assisted a single slope solar still distillation unit. The study's results revealed that the solar desalination standalone unit had an efficiency 22% lower than that of the solar still assisted with a solar photovoltaic system. The system achieved a freshwater productivity of 3-4.6 L/m²/day at 1-hour intervals, with a design basin area of 11 m² and an efficiency of 45% at peak time, while integrating into the PV system [30]. It is worth mentioning that the designed novel solar still system was considered a base/ pre-trained model. 30 Knowing input and output measurements enables the creation of the most prevalent mathematical algorithm, known as the forward-backward propagation algorithm, which ultimately leads to selecting an ideal source ANN model configuration with fine-tuned hyperparameters and trained network weights. The transfer learning technique was applied since the base (reference) ANN model on the base datasets and functions was being trained. Afterward, the learned weights (intelligence) from the pre-trained ANN model were repurposed (reused) in a second ANN, namely the random initialization ANN model, to be trained on new datasets and functions. Subsequently, the latest target ANN model was generated from the transfer learning process as a third model to forecast distillate water outputs, Ps [31]. As stated, the study aims to assess the target ANN as a favorable model and compare it to the random-initialized ANN and MLR models to determine which model provides better performance based on the minimum statistical errors and high accuracy measures. 2.7.2 Artificial Neural Networks (ANNs) ANNs are computational machine learning algorithms designed to mimic the behavior of biological nervous systems, which consist of neurons. The interrelationships between associated parameters are utilized to develop mathematical prediction models. These parameters symbolically specify these neurons or nodes, which act as interconnected processing neurons of the human brain cells [32]. Each layer consists of a specific number of small, individual, and interconnected processing units, known as nodes or neurons. Signals are transmitted through neurons connected via communication links with connection weights attached. Each node provides a single output signal that can be propagated to other nodes after taking several inputs from different nodes, based on their connection weights [1]. Figure 2.6 illustrates a simple schematic diagram of the components of an artificial neuron, which serves as a standalone 31 computational processor featuring a summing junction operator and an activation or transfer function. Weights and biases are made from the connections between inputs, neurons, and outputs [2]. Figure 2. 6 A fundamental building block of the components of an artificial neuron, adopted and modified from [29]. The most used ANN type for modeling and predicting results is a multi-layer perceptron (MLP). The general mathematical equation of the ANN model can be expressed as follows [33] [4] : 𝛶𝑦 = 𝐹 ( ∑ 𝑤𝑦𝑗 𝐹 ( ∑ 𝑤𝑗𝑘 𝐹 ( ∑ 𝑤𝑘𝑖𝑛𝑖=1𝑥𝑖 + 𝑏𝑘)𝑝𝑘=1+ 𝑏𝑗)𝑚𝑗=1+ 𝑏𝑦) (2.1) Where Υ𝑦 represents output variables identified as distillate water. 𝑤𝑦𝑗 are the weights between 2nd hidden and output layers, 𝑥𝑖 are input variables, including meteorological conditions and feed water flow rate. 𝑤𝑗𝑘 indicates the weights between the 1st and 2nd hidden layers, 𝑤𝑘𝑖 are weights between the input and first hidden layers, 𝑚 is the number of neurons in the 1st hidden layer, 𝑝 is the number of neurons in the 2nd hidden layer, 𝑛 is the number of neurons in the input layer, 𝑏𝑘 𝑏𝑗 𝑏𝑦 are the bias values of the neurons in the 1st hidden layer, 2nd hidden layer, and output layer, respectively, and 𝐹 is the activation function. This study used sigmoid, hyperbolic tangent, and ReLU as transfer/activation functions. The sigmoid transfer function (SIG) for any variable Z was [8]: 32 𝐹(𝑍) = 11 + 𝑒𝑥𝑝(−𝑍) (2.2) The hyperbolic tangent transfer function (TANH) for any variable 𝑍 was: 𝐹(𝑍) = 1 − 𝑒𝑥𝑝(−2𝑍)1 + 𝑒𝑥𝑝(−2𝑍) (2.3) Also, the relu function for any variable Z was expressed as the following [9]: 𝐹(𝑍) = { 0, 𝑓𝑜𝑟 𝑧 < 0𝑧, 𝑓𝑜𝑟 𝑧 ≥ 0 (2.4) Where Z = 𝑥𝑖𝑤𝑖 + 𝑏 , and the ANN model can be formulated by an algebraic equation as follows [10]: 𝛶𝑦 = 1 − 𝑒𝑥𝑝[(𝐹1𝑤1 + 𝐹2𝑤2 + 𝐹3𝑤3 + … ) + 𝑏]1 + 𝑒𝑥𝑝[(𝐹1𝑤1 + 𝐹2𝑤2 + 𝐹3𝑤3 + … ) + 𝑏] (2.5) Where 𝐹1, 𝐹2 and 𝐹3 … 𝐹𝑛 are hidden units that are computed according to number of neurons in the hidden layers 𝑘, 𝑗 and 𝑦 respectively as follows: 𝐹𝑛 = 1 − 𝑒𝑥𝑝[(𝑥1𝑤𝑘1 + 𝑥2𝑤𝑘2 + 𝑥3𝑤𝑘3 + … ) + 𝑏𝑘 ]1 + 𝑒𝑥𝑝[(𝑥1𝑤𝑘1 + 𝑥2𝑤𝑘2 + 𝑥3𝑤𝑘3 + … ) + 𝑏𝑘] (2.6) 𝐹𝑛 = 1 − 𝑒𝑥𝑝[(𝑥1𝑤𝑗1 + 𝑥2𝑤𝑗2 + 𝑥3𝑤𝑗3 + … ) + 𝑏𝑗 ]1 + 𝑒𝑥𝑝[(𝑥1𝑤𝑗1 + 𝑥2𝑤𝑗2 + 𝑥3𝑤𝑗3 + … ) + 𝑏𝑗] (2.7) 𝐹𝑛 = 1 − 𝑒𝑥𝑝 [(𝑥1𝑤𝑦1 + 𝑥2𝑤𝑦2 + 𝑥3𝑤𝑦3 + … ) + 𝑏𝑦 ]1 + 𝑒𝑥𝑝 [(𝑥1𝑤𝑦1 + 𝑥2𝑤𝑦2 + 𝑥3𝑤𝑦3 + … ) + 𝑏𝑦] (2.8) The trial and error is the most effective method to determine the optimal number of nodes in the hidden layer. The optimal neurons for the network's hidden layer were found through trial -and- error. The data are automatically normalized to a range of -1 to 1 before the modeling process. 33 The normalization process is crucial for enhancing the network's generalization capabilities and accelerating training [8]. In general, the following is an outline of the procedure used in the establishment of the ANN model [12]: i. Define the matrix sizes of the novel and commercial solar stills datasets, [730 x 6] and [365 x 6], respectively. ii. Divide and create a network configuration for the ANN's hidden layers that must be processed through three modeling stages: training, testing, and validation sub-datasets. iii. Normalize the curated datasets to the range of [-1, 1] before beginning the modeling process. 𝑋𝑛 = (𝑋0 − 𝑋𝑚𝑖𝑛 𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛 ) (2.9) Where 𝑋𝑛 is the normalized value, 𝑋0 is the original values of input and output variables, and 𝑋𝑚𝑖𝑛 and 𝑋𝑚𝑎𝑥 are minimum and maximum values of input and output variables, respectively. iv. Fine-tune the hyperparameters of the created ANN regressor, such as the gradient descent method (optimizer), number of iterations, learning rate, batch size, number of neurons, activation function, and regularization strength during the training process. v. Determine the optimal number of neurons using the trial-and-error method. vi. Train the feedforward neural network using the backpropagation algorithm. vii. Create a feedforward neural network. viii. Unnormalize the output values when the modeling process is completed. ix. Generate distillate water output values (Pstd, L/m2.day). x. Check the neural network’s performance by comparing the actual (observed) values with predicted (target) values through correlations and error analysis. 2.7.3 Multiple linear regression (MLR) 34 MLR is used to model the linear relationship between each dependent variable, such as solar still productivity as an output parameter, and one or more independent variables (input variables) during the saline water desalination process. MLR determines which technique provides better prediction results in all modeling phases, categorized as training, testing, and validation. A broad MLR model formula can be written as follows [10]: 𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + ⋯ + 𝛽𝑛𝑥𝑛 (2. 10) Where 𝑦 is the predicted parameter, 𝛽0 is the intercept, 𝛽𝑖(𝑖 = 1,2, … , 𝑛) are the coefficients of the predictors, and 𝑥𝑖(𝑖 = 1,2, … , 𝑛) are the predictors. Since the MLR method is based on least squares, the model is fitted to minimize the sum of squares of the differences between the observed and predicted values. 2.7.4 Transfer Learning and Fine-Tuning Learning a new activity more effectively is enhanced by transferring knowledge from a previously mastered task. The transfer learning method is an area of machine learning research topic that depends on the ability to retain learned knowledge (intelligence) while using it to solve one problem and then use it to address a different but related one. It is proposed to develop a source model known as the pre-trained ANN model and optimize it to forecast freshwater productivity. The datasets of the designed novel hybrid solar still system was obtained and used to train the model for water prediction instead of predicting the same output parameter using long and complicated design equations dedicated to various solar still configuration systems [11]. The ANN model's last hidden layer (known as the head) must be reworked to fit our number of variables to work. In the training process, artificial neural networks use the most 35 prevalent mathematical tool called the back-propagation algorithm, which backpropagates the error from the output to the input nodes. Here, the head's role is to decode these data into predictions for each of our variables. During transfer learning, a new head with a random initialization technique will be created, preserving the input and first hidden layers (also referred to as the model's backbone), neurons, and weights already pre-trained in the source model. First, we will freeze the body weights and train only the head to convert the evaluated features into predictions for our data, probably using differential learning rates. Following that, we will unfreeze the backbone layers and fine-tune the entire model [12]. It is important to clarify the following terms that pertain to specific techniques for creating and optimizing the ANN models via transfer learning: ▪ Freezing: This term refers to maintaining specific layers of the pre-trained (source) ANN model that are unaltered during the initial stages of transfer learning. Applying the freezing technique to these layers prevents their weights from being updated throughout the training process on the new datasets. This enables us to utilize the pre-existing learned features from the pre-trained ANN model, which are expected to be advantageous for the target task. ▪ Unfreezing: Following an initial training phase where some layers are frozen, we progressively release/unfreeze these layers to enable fine-tuning. This method entails adjusting the weights of previously frozen layers using the new dataset, which enhances the ability of the pre-trained ANN model to adapt to the specific attributes of the target task efficiently. 36 ▪ Frozen: When a layer is described as "frozen," it indicates that its weights remain unchanged and are not updated during the training process. As mentioned earlier, this is a component of the freezing process. This study employed these strategies to create the most effective target ANN model to precisely predict purified water outputs in solar stills. The procedure involved freezing specific layers of the pre-trained ANN model, known as the source ANN network, and fine-tuning the hyperparameters to improve performance. Subsequently, the performance of the optimized target ANN model was compared to a random initialization ANN model to emphasize the advantages of transfer learning. Fine-tuning a pre-trained ANN model entails removing the final hidden layer and replacing it with a new one. All the layers below the head (or at least part) were frozen and could not be altered. By taking the backbone layers of our model out of the frozen state, unfreezing enables us to select which layers of our ANN model to train at any given time. Fine-tuning the ANN's network is essential to be considered after applying the transfer learning method because the early layer of our built ANN model will already be well-trained at identifying patterns and gradients. On the contrary, the last layers were focused more on our goal, such as producing distillates requiring further training [13]. It is essential to highlight that fine-tuning pre-trained networks enhances their ability to recognize datasets (or variables) that they were not initially trained on during the first trial. Moreover, this method can outperform the training ANN model from scratch using a particular algorithm in terms of mean square error (MSE) and an overall index of model performance (OI). 2.8 Foundational Principles of CNN-1D and SVR for Sequential Numerical Data Analysis in Regression Tasks 37 This supplementary document presents a clear and comprehensive overview of the fundamental principles underlying one-dimensional Convolutional Neural Networks (CNN-1D) and Support Vector Regression (SVR). The chosen input variables—daily solar radiation (Is), ambient temperature (Tamb), wind speed (Vw), relative humidity (RH), and saline water feed flow rate (Pst), have been identified as critical factors influencing the performance of solar stills. This highlights their importance in predictive modeling for a continuous numerical target variable, specifically daily freshwater productivity (Pstd, L/day). In addition to discussing CNN-1D architectures, the document introduces both baseline and augmented SVR models, highlighting their methodological construction and theoretical foundations. The aim is to equip readers with a robust conceptual and mathematical understanding of these models, covering essential formulations, kernel functions, loss objectives, and optimization procedures. Special emphasis is placed on applying these models to sequential or vector-based numerical datasets derived from operational measurements of solar stills. This framework is intended to inform model selection, feature engineering, and data-driven performance tuning in regression-based forecasting applications. 2.8.1 CNN-1D Conceptual Framework for Regression One-dimensional Convolutional Neural Networks (CNN-1D) are a specialized subset of deep neural networks derived from traditional multi-dimensional Convolutional Neural Network (CNN) architectures. They are specifically designed for the automated extraction and hierarchical learning of patterns from one-dimensional input data, such as time series and sequential datasets, to enable continuous numerical predictions in regression tasks. A defining characteristic of CNN-1D is its utilization of learnable convolutional filters (or kernels) that traverse the temporal dimension of the input. Each convolutional layer performs a linear 38 transformation followed by a non-linear activation function, which increases the model's expressiveness. This operation enables the detection of localized features and recurring patterns across different temporal scales, which are essential for effectively modeling and forecasting the associated continuous target variables [18] [39]. 2.8.2 Core Operations and Mathematical Formulation In the context of time-series regression utilizing CNN-1D models, each sample in the input dataset is structured as a three-dimensional matrix with the dimensions [n, k, f], where n represents the number of sequences, k denotes the look-back window (number of time steps), and f indicates the number of input features. As shown in Figure 2.7, the architecture of the CNN-1D model for regression tasks consists of an input layer, several convolutional layers, a flattening operation, and one or more fully connected (dense) layers, often enhanced with dropout for regularization, followed by a final output layer. This model is designed to automatically identify local temporal patterns in sequential numerical inputs by utilizing learnable filters across time steps. The convolutional layers convert raw input features into hierarchical feature maps, which are subsequently flattened and fed into dense layers to capture global dependencies. This architecture enables effective learning from time-dependent data, such as multivariate sensor signals or environmental measurements, allowing for efficient learning from complex data sets. The diagram elucidates the foundational computational workflow and structural design of the CNN-1D models utilized in this study. It is included in the supplementary materials for conceptual clarity and was not derived from the empirical results presented in the main manuscript. 39 Figure 2. 7 Architecture of a one‐dimensional convolutional neural network (CNN-1D) model, adopted from [40]. This figure illustrates the structural layout and functional flow of a CNN-1D model designed for time-series regression tasks. The architecture begins with an input layer that receives sequential numerical features. This is followed by several convolutional layers that learn local temporal patterns from the input data. The output from these convolutional layers is then passed through a flattening layer, followed by a dense layer that may include optional dropout regularization. Finally, an output layer generates the predicted results. This pipeline efficiently extracts patterns from temporally dependent inputs while also controlling for overfitting, making it suitable for small to medium-scale datasets with limited samples. The primary computational operation involved is 1D convolution, which can be mathematically defined as: Z(l)[i, j] = ∑ w(l) [k, j] ∙ A(l−1)[i + k] + b(l)[j]K−1k=0 (2.11) Where w(l)and b(l) denotes the weights and bias for the lth layer, and K is the kernel size. With a stride S = 1 and padding set to ‘same’, the output retains the input length Lout = Lin, achieved by applying P = [K−12] Padding on each side. The Rectified Linear Unit (ReLU) activation 40 function, defined as f(x) = max(0, x) , is used to introduce non-linearity [41] [42]. Mathematically, the input to the first layer is represented as A(0) = x, where x denotes the input sequence matrix. The linear output of the lth convolutional layer is expressed as Z(l)[i, j]. This output is then passed through the ReLU activation function to create the activation map A(l)[i, j] defined by: A(l)[i, j] = max(0 , Z(l)[i, j]) and A(0) = x (2.12) This piecewise non-linearity enhances the network's capacity to recognize intricate patterns by selectively activating relevant features while preserving the flow of gradients. The ReLU function is widely favored due to its computational efficiency and its effectiveness in addressing vanishing gradient issues, making it a vital component in the hierarchical representation learning process of CNN-based regression models. Following the final convolutional layer, a flatten operation is applied to transform the multi-dimensional output tensor (A(l)) ϵ ℝM into a one-dimensional vector f = Flatten (A(l)) ϵ ℝM , where M = T × m , and T denotes the temporal dimension. This flattened representation is then passed to a fully connected dense layer that performs the non-linear transformation using the ReLU activation function, defined as [43]: hm = max (0 , ∑ WmnMi=1 . fn + bm) , for m = 1, … , M (2.13) Where: 41 • hm: Output from the m-th neuron in the dense hidden layer after applying the ReLU activation function. • max(0, . ): ReLU activation function, which returns the input if positive, and zero otherwise. • Wmn: Weight connecting the n-th feature from the flattened layer to the m -th neuron in the dense hidden layer. • fn: n-th input value from the flattened layer (i.e., output from the previous convolutional layer). • bm: Bias term associated with the m-th neuron in the dense hidden layer. • M: Total number of neurons in the dense hidden layer (e.g., 128). This operation enables hierarchical feature abstraction and interaction across all time steps and channels. Finally, the model outputs the scalar prediction ?̂?ϵ ℝM, corresponding to each input sequence, through a linear output layer defined as [44]: ?̂? = ∑ wm(0)Mi=1 . hm + b(0) (2.14) • ?̂?: Predicted scalar output value from the network (i.e., estimated water productivity). • wm(0): Weight connecting the m-th neuron in the dense hidden layer to the output layer. • b(0): Bias term in the output layer. The linear output layer is optimized during training to regress the continuous target variable associated with solar still freshwater productivity. The model's output is a single continuous 42 variable per sequence, optimized to minimize a regression loss function, typically Mean Squared Error (MSE). 2.8.3 Parameter Optimization for Regression Hyperparameter optimization for the CNN-1D regression models was conducted using the Hyperopt library, employing the Tree-structured Parzen Estimator (TPE) as the search algorithm. The tuned hyperparameters included the number of convolutional layers, filter size, kernel size, batch size, learning rate, batch size, number of dense units, regularization strength (L2), and number of training epochs. These parameters were sampled from well-defined discrete or continuous search spaces, depending on their characteristics (e.g., the learning rate is continuous, and the number of layers is discrete). The optimization process focused on minimizing the validation loss, typically measured by the Mean Squared Error (MSE), to enhance the model's generalization capabilities. The batch size determines the number of training samples used to estimate the gradient in each iteration, playing a crucial role in the stability and speed of the training process. The number of epochs indicates how many times the entire training dataset is processed by the network, which directly influences the model's convergence. To mitigate overfitting, an early stopping criterion with a patience parameter was implemented, which halted training when the validation loss failed to improve over a predetermined number of consecutive epochs. The trainable parameters of the CNN-1D model, including convolutional kernels, biases, and dense layer weights, were updated iteratively using gradient-based optimization algorithms, such as the Adam optimizer, which is an adaptive variant of stochastic gradient descent (SGD). The fundamental update rule for the model parameters θ (weights and biases) follows the form: θt+1 = θt − η ∇θℒ (θt) (2.15) 43 Where: • θt denotes the parameter vector at iteration t • η is the learning rate • ∇θℒ is the gradient loss function ℒ with respect to the parameters. This process is applied to minimize a predefined loss function, such as the Mean Squared Error (MSE) or Mean Absolute Error (MAE), calculated over the training set, while also evaluating the same loss on the validation set to assess generalization performance [45] [46]. This comprehensive framework facilitated a systematic exploration of architecture-performance trade-offs (space), resulting in reproducible and robust model configurations [47] [48]. 2.8.4 Support Vector Regression (SVR) Conceptual Framework Support Vector Regression (SVR) is a robust machine learning algorithm that adapts the principles of Support Vector Machines (SVM) for regression tasks involving continuous numerical outputs. Unlike traditional regression models that aim to minimize prediction errors across all data points, SVR introduces the concept of an ε-insensitive margin, within which errors are not penalized. The algorithm seeks to identify a regression function that fits the data while maximizing the margin around it. Data points that lie outside this margin are referred to as support vectors, which play a crucial role in defining the regression solution. This design allows SVR to be resilient to outliers and effective in situations with limited data availability. SVR is particularly well-suited for non-linear regression problems, utilizing a kernel trick to implicitly transform the input space into a higher-dimensional feature space without requiring the explicit computation of the transformation. In this context, the Radial Basis Function (RBF) kernel was chosen for its ability to effectively model nonlinear relationships in time series and environmental datasets [49]. 44 2.8.5 Core Operations and Mathematical Formulation The primary goal of SVR is to estimate a continuous-valued function 𝑓(𝑥) such that the predicted output does not deviate from the actual target 𝒴𝑖 by more than a threshold 𝜀 for each training data point 𝑥𝑖, while simultaneously maintaining the function as flat as possible. This formulation is optimized by solving a convex quadratic programming (QP) problem known as the dual optimization problem, with the prediction function defined as: ?̂? = ∑(𝛼𝑖 − 𝛼𝑖∗) 𝐾(𝑥𝑖 , 𝑥) + 𝑏 𝑁𝑖=1(2.16) Where: • ?̂? 𝜖 ℝ is the predicted continuous value, • 𝛼𝑖 , 𝛼𝑖∗ are the dual Lagrange multipliers, • 𝐾(𝑥𝑖 , 𝑥) is the kernel function that measures similarity between input vectors, • 𝑏 is the model bias, and • 𝑁 is the total number of training instances. To capture non-linear relationships, SVR employs the RBF kernel, which maps input vectors into a high-dimensional feature space without explicit transformation: 𝐾(𝑥𝑖, 𝑥) = 𝑒𝑥𝑝(−𝛾 ‖𝑥𝑖 − 𝑥‖2) (2.17) Here γ is the kernel coefficient that defines the influence radius of each data point in the transformed feature space. This "kernel trick" enables SVR to operate in a high-dimensional space without explicitly computing the mapping 𝜙(𝑥), allowing for efficient modeling of nonlinear regression surfaces. 45 The learning objective of SVR loss combines model complexity minimization, which is achieved through L2 regularization with prediction tolerance using an ε insensitive loss function, into a unified cost function. This dual objective ensures both flatness of the regression function and tolerance for small deviations within an ε margin: ℒSVR = 12 ‖w‖2 + C ∑ max(0, |𝒴i − ?̂?i| − εNi=1 (2.18) Where: • w is the weight vector in the induced feature space, • C > 0 is the regularization parameter controlling the trade-off between model flatness and tolerance for deviations beyond ε. • ε defines the width of the margin (tube) around the regression function within which errors are not penalized. • 𝒴i and ?̂?i are the actual and predicted values, respectively. Figure 2.8 visually represents the theoretical foundation of SVR. The left plot depicts a non-linear regression scenario in the original input space, where the model seeks to fit a function within a defined ε-insensitive margin. This margin allows for some tolerable deviations (ξ) from the actual values. The right plot shows the same problem transformed into a high-dimensional feature space using a kernel function 𝜙(𝑥), where the regression function becomes linear. In this high-dimensional space, SVR aims to identify a hyperplane that minimizes both prediction error and model complexity through regularization. This illustration clarifies how SVR effectively handles non-linear regression by utilizing kernel methods and an ε-insensitive loss function. Like Figure 1, this diagram is included in the supplementary material for explanatory purposes only and was not derived from the dataset or results used in the core analysis of the manuscript. 46 Figure 2. 8 Schematic illustration of Support Vector Regression (SVR) using the ε-insensitive loss function , adopted from [13]. In the input space x (left), SVR models non-linear relationships, while the application of a kernel function ϕ(x) (e.g., RBF) maps the data to a higher-dimensional feature space (right) where a linear regression function is fitted. The dashed margins represent the ε-tube within which errors are not penalized, and 𝜉 , denotes the slack variables for data points falling outside the margin. This structure corresponds to the prediction function (Eq. 1), RBF kernel transformation (Eq. 2), and SVR objective loss formulation (Eq. 3). Slack variables that account for violations occurring outside the ϵ-insensitive tube are implicitly managed through the dual Lagrange multipliers 𝛼𝑖 𝛼𝑖∗ in the SVR formulation, which streamlines the optimization process. Alternatively, the primal form explicitly captures these violations using slack variables 𝜉𝑖 , 𝜉𝑖∗ penalizes them in the objective function to ensure a balance between model complexity and prediction tolerance. Unlike neural networks, SVR does not rely on gradient descent or backpropagation for training. Instead, the solution is achieved through convex optimization solvers that guarantee global optimality within a well-defined dual quadratic programming (QP) framework. This characteristic, along with the sparsity of solution, where only support vectors contribute to predictions, makes SVR particularly robust and efficient in dealing with high-dimensional, noisy, or small-sample datasets. Equations (6) – (8) and the dual- 47 based training mechanism are fundamental to the SVR algorithm and are widely cited in the literature [50] [51] [52] [50]. 2.8.6 SVR Key Hyperparameters In Support Vector Regression (SVR), the effectiveness of the model is significantly influenced by the thoughtful selection and tuning of key hyperparameters, specifically the regularization parameter C, the kernel coefficient 𝛾 for non-linear kernels (such as the RBF), and the width of the ε-insensitive tube. The parameter C regulates the trade-off between minimizing training error and maintaining a smooth model structure. Higher values of C result in models that tightly fit the training data, which can lead to reduced generalizability, while lower values allow for a wider margin with increased tolerance for error. The 𝛾 parameter in the RBF kernel function determines the influence each training example has. A high 𝛾 value leads to a model that fits the training data closely, thereby increasing the risk of overfitting, whereas a low 𝛾 value yields a smoother function. Meanwhile, the ε parameter establishes the width of the margin of tolerance, within which no penalty is applied for prediction errors. Proper tuning of this parameter enables the model to disregard minor deviations, thereby improving its robustness in the presence of noise. Hyperparameter optimization for SVR typically employs systematic search strategies, including grid search, random search, or Bayesian optimization, often guided by cross-validation performance. In this study, we utilized a TPE approach through the Hyperopt library to explore a defined search space and minimize validation loss (MSE). This approach ensured an efficient and reproducible convergence to optimal configurations. It is essential to note that these hyperparameters are problem-specific and should be optimized in conjunction with the dataset's characteristics and the regression objectives [53]. 48 2.8.7 Gaussian Noise Injection for Data Augmentation In this study, we employed a controlled Gaussian noise injection strategy, commonly referred to as jittering, as a data augmentation technique specifically for the training datasets of both the CNN-1D and SVR models. This approach involves perturbing each input feature vector 𝒳 𝜖 ℝ5 by adding noise sampled from a zero-mean Gaussian distribution 𝒩(0, σ2), while preserving the original target output intact. By artificially introducing statistically consistent variability, jittering enhances the effective training distribution, enabling the model to better generalize to unseen patterns and mitigate the risk of overfitting. The rationale behind this technique lies in its ability to simulate plausible variations within the physical limits of the system being modeled, specifically, solar still freshwater productivity, without violating domain realism. Notably, the augmentation was limited to the input space and applied solely to the training portion (70%) of the dataset, resulting in six perturbed replicas for each original instance. This process significantly enriched the training set while preserving the integrity of the validation and test distributions. Existing empirical evidence highlights the effectiveness of Gaussian noise augmentation in enhancing the robustness and predictive reliability of models, particularly in regression scenarios involving sparse data with continuous numerical inputs [54]. 2.9 Conclusion and Dissertation Outlook Saudi Arabia’s profound commitment to its blue economy, coupled with the imperative for sustainable water solutions, creates a fertile environment for innovations that integrate advanced solar distillation technologies with the analytical power of supervised machine learning. By systematically harnessing data-driven optimization, leveraging novel designs, and capitalizing on abundant renewable energy resources, a clear pathway exists to not only address intrinsic national water challenges but also contribute significantly to global best practices in water 49 management, environmental stewardship, and knowledge-based economic development. This dissertation will explore a specific aspect of this synergy, focusing on the development of a highly accurate 1D CNN-based predictive model for solar still output, augmented by specialized time-series techniques. The overarching aim is to deliver novel insights and practical methodologies that can further empower this transformative agenda. The subsequent chapters will delineate the theoretical underpinnings and specific methodology employed, present a comprehensive analysis of the experimental results and model performance, discuss the broader implications of these findings, and conclude with recommendations for future research trajectories and practical deployment strategies. 50 Chapter 3: Design and Simulation of a Novel Solar Photovoltaic System Assisted Single-Slope Solar Still Distillation Unit 3.1 Motivation Freshwater scarcity remains a pressing global challenge, particularly in arid and semi-arid regions where conventional freshwater sources are limited. While fossil fuel-based seawater desalination technologies have traditionally played a central role in addressing water demand, their environmental and economic drawbacks necessitate the exploration of sustainable alternatives. Solar desalination has emerged as a viable, eco-friendly solution by harnessing renewable solar energy. This chapter introduces the development and simulation of an innovative hybrid solar desalination system that integrates photovoltaic (PV) technology with a conventional single-slope solar still. The aim is to enhance freshwater productivity while reducing system costs and dependence on non-renewable energy sources. The chapter begins by outlining the design methodology and performance benchmarks, followed by a detailed analysis of distillate output, energy efficiency, and economic viability under variable operating conditions. Through the integration of a solar PV-driven heating element, the proposed system demonstrates significant improvements in thermal performance and freshwater output, establishing a foundation for scalable, high-efficiency solar distillation technologies. 3.2 Introduction Water is widely recognized as the most vital component on Earth and the critical source of life. Water is considered the central element of Earth's hydrosphere, which covers 71% of its surface area. It is an essential fluid for all biological processes and living organisms. Moreover, water scarcity is a significant global challenge, particularly in the Middle East and North Africa (MENA) and Gulf Cooperation Council (GCC) regions. Nowadays, 2.2 billion people lack 51 access to safe and fresh water. Additionally, 4.2 billion people require enhanced competencies and capabilities to manage sanitation services safely. Over the past two decades, freshwater demand has drastically increased [55]. For instance, Saudi Arabia is experiencing a population growth from 25 million in 2007 to approximately 34 million in 2022, with an average annual growth rate of 3% [56]. Therefore, the desalination process is a suitable choice and strategic solution to address the phenomenon of freshwater shortage in the Kingdom of Saudi Arabia (KSA), particularly in remote areas, as the country lacks sufficient fresh and potable water sources, such as rivers, springs, and rainwater. As a result, methods for seawater conversion, wastewater treatment, and water desalination must be developed, specifically for desert and arid regions such as Gulf countries and Saudi Arabia [57]. In the industrial sector, industrial water is essential for the industrial process and its utilities. The demand for treated water in industrial fields has risen and reached 900 million m³ in 2014, compared to 550 million m³ in 2000[58]. The desalination process is the most strategic and effective solution for Saudi Arabia's freshwater needs. The total production capacity of desalinated water in Saudi Arabia is 41% of GCC states, with a total global output of 18% [59]. Seawater desalination through energy-intensive thermal processes, such as reverse osmosis (RO) and multi-stage flash (MSF) distillation, is one of KSA's major strategic plans to meet its water needs. However, these traditional processes have some drawbacks, including long-term adverse environmental effects, hazardous pollutant releases, and control problems. Moreover, high-capacity purified water production remains energy-intensive, with a specific power consumption of 3-4 kWh/m³. They must be integrated with renewable sources, such as solar energy. Furthermore, these types of water treatments and plants emit a substantial amount of greenhouse gases (GHGs), primarily CO2 and NO2 [60]. 52 Therefore, an alternative source of friendly and renewable energy, such as solar, should be considered, besides the compactness considerations that could be suitable for small groups of people (tribes), army units, and tourist spots. Ironically, KSA has a high potential for solar energy because it is blessed with vast areas of arid desert, which primarily features a rich source of heat energy. Standard solar radiation in KSA ranges from 2,200 to 2,400 kWh/m2/year, and the number of sunshine hours is approximately 3,600 per year. This enormous amount of solar insolation energy corresponds to thermal collection efficiencies from 25% to 60% [61], [62]. Even though the desalination system entails a large capacity of thermal storage, the facility necessities to operate continuously. Thence, solar radiation is a crucial choice to be combined with desalination/distillation processes, especially for low-scale capacities such as solar still units. For example, Arunkumar and Kaiwalya Ra presented a review study to improve solar still productivity by more than 5 L/ m2/day of fresh water. As stated, conventional solar stills can only produce a capacity range of 2–5 L /m2/day, which is an insufficient amount of freshwater and does not meet the demand for an individual to live a decent life. Their study aimed to classify various solar still designs to increase the yield of distillate water by more than 5 L/m2/day. Moreover, a comprehensive review is conducted to identify such efficient stills with high productivity and explore some novel modifications along with heat transfer techniques to benefit future researchers in developing solar still designs for production with high efficiency and performance [63], [64]. Noe I. Santos performed another study to predict the solar still yield of distillate water from multiple commercial stills, which continuously functioned for a year and a half. His study objective is to determine the efficacy of modeling solar still freshwater production through artificial neural networks (ANNs) and local climatic data such as daily average ambient 53 temperature, daily total solar radiation, daily average wind speed, direction, etc. These input weather variables are critical and impact the solar still’s performance. Noe I. Santos and his team evaluated ANN prediction models using various input parameter patterns to determine the minimum volume required to accurately model the solar still's performance. The study revealed that ANN model predictions achieved 31 – 78% and were within 10% of the output concerning the designated input variables. Besides, it was concluded that the ANN model calculated 93 – 97% of the variance using the determination coefficient. The analysis claims that to attain at least 60% of the model predictions that fall within 10% of the actual yield, around half to two-thirds of the available long-term data is desired. The study's favorable results for the two dissimilar solar stills suggest that the ANN method could be extended to predict the performance of other solar still designs in diverse climate regimes, provided sufficient input data is available [65]. Maddah investigated the feasibility of exploiting great water production from solar distillation systems. His study attempted to design and test a solar still with altered brackish waters. The experiment was conducted under solar radiation from March to April in Los Angeles. The 3D shape prototype of the still was created over AutoCAD with an inner surface area of around 12.7 cm × 12.7 cm and a maximum volume of 322.6 cm3. The performance of the designed model was assessed theoretically and experimentally, presenting a good harmonization between experiment and theory. It was concluded from the study that the highest attained efficiency was 20.54%, which is equivalent to 384.4 mL/day.m2 (6.2 mL/day) of purified water production. It is worth mentioning that the increase in experimental performance from 6% to 18.3% resulted from reducing the quantities of feed from 120 to 30 mL/day, owing to the rapid decline in the heat of vaporization; though, the rate of freshwater discharge decreased from 446.4 to 341 mL/day.m2 (7.2 to 5.5 mL/day). Other factors were considered in the proposal to improve the solar still 54 performance, for instance, blackened basins and walls, and polystyrene insulation thickness. The still critical design factors, including the rate of solar radiation, construction materials, and tilt angle of the glass cover, were influential in boosting solar absorption, maintaining the high temperature inside the basin, and reducing heat loss to the surrounding [66]. Consequently, Maddah conducted another analytical study to evaluate one of these factors and determine its potential impact on still efficiency and performance. He aims to select a highly efficient still insulation material and downscale it to achieve high freshwater productivity in single-basin solar stills, thereby facilitating experimentation. Maddah designed a mini-passive polystyrene (PS)- based single slope solar still in Los Angeles (34°01'13.6"N, 118°17'45.1"W) for saline water treatment. Experimental computations and mathematical models were employed to determine the still performance and heat transfer coefficient. The experimental results were extracted to create training models using the supervised machine learning regression paradigm. It is worth noting that by replacing the polystyrene insulator with another insulator, the resulting built model can marginally predict the still’s performance with F ≤ 30 mL/day. Results displayed that the water-glass temperature gradient (Tw-Tg) increased when the feed saline water decreased, and evaporative heat transfer coefficients (hewg) enhanced the rate of evaporation/condensation processes. The model accuracy was perceived through a good correspondence between theoretical and experimental outcomes. It was found that the maximum efficiency that the still can accomplish is 18.33%, corresponding to several operational parameters such as radiative water-glass coefficient (qrwg) = 0.188 W/ m2 at 15:00 time, (Tw-Tg) = 4.6 °C, hewg = 21.11 W/m2 °C, and feed flow rate, F = 30 mL/day. NASA insolation data is then fitted versus hourly measured solar still outputs, presenting successful operational results, and obeying similar patterns. Other fine insulator materials such as PU and Silica, with low thermal conductivity 55 Kins, were subjected to maximize the productivity of distillate water. The study opens up broad prospects towards sustainability to maintain the still-absorbed solar incident through insulators with low thermal conductivity, such as thin film foil [67]. Considerable studies have been conducted in the field of water production and treatment by making use of such chemical addition. For instance, A.S. Nafey and M.A. Sharaf demonstrated a study to drastically promote boiling heat transfer in a small-scale unit of the solar water distillation process. Their study investigates the effect of small concentrations of surfactant additives such as sodium lauryl sulfate (SLS) in water. The experiment results showed that the top brine temperature (TBT) increased when small dosages of surfactant additives were placed in the processing unit, thus increasing freshwater productivity. According to the experimental findings, with surfactant concentrations equivalent to 50, 100, 200, and 300 ppm, the distillate water productivity improved by 0.7%, 2.5%, 4.7%, and 7%, respectively. Nevertheless, boosting the subject additive concentration beyond 400 ppm will reduce the water productivity by 6% [68]. It was clear from the literature that the optimal productivity per unit area of the solar still was 384.4 mL/day.m2 (6.2 mL/day) of distilled water. However, this study aims to present a novel hybrid system that utilizes a solar PV system as the primary source of generated electrical power to enhance the solar still unit performance by more than 45% and boost its productivity from 3.6 to 4.6 kg/day.m2. The mathematical system model was built based on the design technique of modeling, where the target productivity, Pst (discharged saline water from a feed tank to a solar basin), is assigned as an input (5-20 kg/day). The design aspects will remain outputs such as the solar still area, the total capital cost of the entire system, and thermodynamic properties, including heat transfer coefficients (W/m2.oC) and the temperature difference between water and 56 glass cover (Tw-Tg), etc. The primary objective of this study is to design, simulate, and evaluate the performance of an innovative hybrid solar desalination system that combines a photovoltaic (PV) module with a conventional single-slope solar still. By integrating a PV-powered electrical heater into the basin, the system aims to enhance thermal energy input, thereby increasing the rate of water evaporation and overall freshwater productivity. This study aims to evaluate the system's technical feasibility under varying environmental conditions, specifically solar radiation, while also seeking to minimize associated capital and operational costs. Furthermore, a significant focus is placed on generating a high-quality, physics-based dataset through simulation, which will serve as a foundational resource for future data-driven modeling efforts, including training artificial neural networks (ANNs) and applying transfer learning techniques in predictive modeling for solar desalination systems. The main contributions and innovations presented in this work are as follows: • This study introduces a newly designed hybrid desalination system that combines a photovoltaic (PV) module with a conventional single-slope solar still. The addition of a PV-powered electric heater enables active thermal enhancement, representing a significant advancement over traditional passive configurations. • A comprehensive, physics-based model was developed in MATLAB/Simulink, grounded in fundamental principles of heat and mass transfer. This simulation provides a detailed understanding of the system's behavior under varying climatic conditions and component parameters, serving as a powerful tool for predictive performance analysis. • The hybrid system achieved a maximum thermal efficiency of approximately 45%, exceeding the typical efficiency range of 20-35% reported for passive solar stills. This 57 improvement underscores the potential of PV-assisted systems to significantly enhance freshwater productivity in solar desalination. • An initial simulated dataset comprising 100 diverse samples was generated using the Signal Builder in Simulink. To enrich the learning process for transfer learning, this dataset was expanded by a factor of 7.3, resulting in 730 curated samples. The resulting data not only supports performance evaluation but also serves as a physics-informed "source domain" for training a pre-transfer ANN model in subsequent AI-based modeling. • The study assesses the economic feasibility of the proposed design, demonstrating that the addition of PV heating can boost freshwater productivity without disproportionately increasing capital and operational costs. This affirms the design’s potential viability for implementation in off-grid, water-scarce, or decentralized rural settings. The subsequent section of this chapter provides an in-depth development and simulation of the proposed hybrid solar desalination system. Section 3.3 presents a comprehensive description of the processes involved in this innovative hybrid system. In Section 3.4, the methodology begins with the conceptual design, focusing on the integration of a photovoltaic (PV) panel with a single-slope solar still to create a hybrid configuration. A detailed mathematical model is then established, incorporating energy and mass transfer equations that govern thermal behavior, solar energy input, heat losses, and evaporation dynamics. These governing equations are implemented in MATLAB/Simulink to simulate the system's performance under realistic climatic and design conditions. The results discussed in Section 3.5 examine the system's freshwater productivity, thermal efficiency, and cost-effectiveness, supported by sensitivity analyses on key design parameters such as basin dimensions, PV power input, and the 58 incorporation of black dye to enhance solar absorption. Finally, Section 3.6 concludes by emphasizing the significant performance improvements achieved through PV-assisted heating, particularly regarding freshwater yield and system efficiency. This demonstrates the system's potential for low-cost, sustainable, and decentralized freshwater production in arid and remote regions. 3.3 Proposed Novel Solar Still Model A schematic diagram for the developed novel system is shown in Figure 3.1. The design system is proposed to model and simulate a hybrid PV system (heating element) integrated into a single-slope solar still unit for performance enhancement of more than 45% and improved distillate water productivity from 3.6 to 4.6 kg/day.m2. The proposed system consists of a solar still unit, including the basin connected to a photovoltaic system, a feed saline water tank as an input to the basin, and a distillate water tank for freshwater production and storage. The solar still is supported by a heating coil at the bottom of the basin, linked to a solar PV system to utilize solar thermal energy for heating purposes. A solar PV cell allows photons absorbed directly from sunlight to knock electrons free from atoms, generating a flow of electricity (DC) as a power load on the photovoltaic cell, which is then used to heat the coil. The supported heating element converts the electrical energy transformed by the photovoltaic cell into thermal energy for heating purposes and initiates evaporation and condensation processes inside the basin. When saline water is introduced to the still from the feed saline water tank, it evaporates, and the water vapor condenses on the glass cover, yielding distillate water and the latent heat of condensation. The condensed water film on the inclined glass cover will then be collected by gravity in the distillate water compartment inside the basin through a collecting trough and further discharged into the distillate water tank storage. The solar 59 distillation process involves three modes of heat transfer. There is heat transfer by conduction through the transparent cover glass, as well as the bottom and side walls. An insulation material with a high thickness and a relatively low thermal conductivity k-value is also considered in this model design, which is necessary to minimize heat loss from the solar still to the ambient environment. The other mode of heat transfer is from the basin liner to the saline water by convection; however, the thermal energy of the hot saline water layer is transferred by convection and radiation mode through the evaporation process. Evaporation occurs when there is a temperature difference between the basin water (high) and the glass cover (low). Similarly, the inclined glass cover scatters the heat transfer to the ambient by convective and radiative modes of heat transfer. It is worth mentioning that the various modes of heat transfer inside the solar still include mass transfer. Subsequently, the design code and energy balance analysis equations have established the correlation between the convective and evaporative heat transfer coefficients from hot water to a transparent glass cover. Moreover, adding the black dye inside the basin is considered part of the modeling to determine the effect and behavior of the still productivity, Pstd (kg/m2.day). 60 Figure 3. 1 Proposed schematic diagram for a solar photovoltaic system-assisted solar still distillation unit. 3.4 Methodology and Framework In this study, a survey is designed and set up to assess the importance of operating the entire proposed design system using MATLAB/SIMULINK software. As solar desalination processes contain various interactive units, employing these units can generate large-scale process configurations. Many flow sheeting problems can be addressed and manipulated using such software or programs. These programs are based on the mathematical computations and modeling capabilities of certain commercially available programs [69]. Implementing the validation results is achieved through various techniques. Accordingly, a developed software package (photovoltaic cell assisted with single slope solar still) is launched to model/design and simulate an active single slope solar still desalination unit accompanied by a solar photovoltaic system. Additionally, a comparison is performed with another type of passive solar still (excluding photovoltaic cells) for design and cost analysis. The design model of the proposed 61 system setup that is simulated using the MATLAB/SIMULINK program comprises the following components: 1. Solar photovoltaic system. 2. Single slope solar still (basin with a glass cover). 3. Feed and distillate water tanks. 3.4.1 Photovoltaic Process Modeling Technique Industrial plants involve several integrated process units. To comprehend the performance of various process units with different operational conditions, reliable and flexible software programs such as SIMULINK are crucial. Therefore, many flow sheeting problems can be well analyzed and organized using these subject computer programs. The scope of work here is to focus on the design problems of the system, rather than its performance and optimization issues. In design problems, certain design parameters such as areas, dimensions, voltage, current, number of cells, and feed variables are left unspecified and become unknown quantities to be determined, unlike the superpower of the photovoltaic module, which is primarily the broader streams of the processing unit and is usually identified. Several actual data points are taken from the absolute manufacturing manual of each module type to simulate and predict the characteristics of different PV systems. The design limits are expected to be calculated by identifying the output power from the system application. The PV system is designed and modeled based on actual data presented through hundreds of collected data points, which serve as inputs from manufacturing manuals and literature papers. SIMULINK browser is utilized to model and visualize the PV and solar still system program. Figure 3.2 shows a photograph of the software library that represents the PV design models and parameters. 62 Figure 3. 2 Photograph of the developed solar PV system design parameters and look-up tables “Solar Photovoltaic System Simulink Model Browser”. The design limits for the photovoltaic cell can be summarized as follows: 1. The open circuit voltage (V) and the short circuit current (A). 63 2. The maximum voltage (Vm) and current (Im). 3. The module and cell efficiencies (%). 4. The number of cells and modules of the system. 5. The module and PV system weights (kg), dimensions (m3), and areas (m2). 6. The module area and total system area, m2. In this work, the range of operating the PV module type is from 5 to 280 watts. Each module type can compute the module specification based on data inserted in the table. Regarding the module power, the following code can be designed and calculated. Based on the total power THP module power Pm, and the number of PV modules NOM, can be computed as follows [70] , [71]: 𝑁𝑂𝑀 =𝑇𝐻𝑃𝑃𝑚 (3.1) The module area Am (m2), can be calculated based on the module power and efficiency [72]: 𝐴𝑚 =(100 ∗ 𝑃𝑚)(𝐼𝑠 ∗ 𝐸𝑀) (3.2) The total system area At (m2) can be estimated based on the number of modules and module area as follow [72]: 𝐴𝑡 = 𝐴𝑚 ∗ 𝑁𝑂𝑀 (3.3) The cell area Ac (cm2), is calculated based on the number of cells (NC) and module area Am [72]: 𝐴𝑐 =𝐴𝑚 ∗ 103𝑁𝐶 (3.4) 64 The battery costs Cb, ($/module), and the full overboard costs (FOB) of the module’s price, ($/Watt/module), are used to determine the PV system total costs, PVCt ($/ module) [72]: 𝑃𝑉𝐶𝑡 = (𝑇𝐻𝑃 ∗ 𝐹𝑂𝐵𝑐) + (𝐶𝑏 ∗ 𝑁𝑂𝐵) (3.5) Since the FOB price ($/watt/module) contains the connections, cables, inverter unit, maintenance costs, and workers’ time, the number of batteries can be calculated based on the maximum voltage Vm and the battery voltage Vb as follows [72]: 𝑁𝑂𝐵 = 𝑉𝑚 ∗ (𝑁𝑂𝑀𝑉𝑏) (3.6) 3.4.2 Solar Still Process Modelling Technique The solar still model system is designed and simulated through the same platform. A visual library is inserted into the Simulink browser, supported by graphical user interface (GUI) modeling. Figure 3.3 depicts the software library photograph, which represents the solar still design models and parameters. 65 Figure 3. 3 Photograph of the developed solar still distillation unit design parameters and cost analysis “Solar Still Distillation Unit Simulink Model Browser”. The mathematical model could be correlated based on the data points stored in the table model. The signal builder tool, utilized from the library browser, is dragged and dropped into the environment model browser. A hundred data points for each input parameter, such as solar radiation, ambient temperature, the productivity flow rate from the saline water tank to the still’s basin, and wind speed, are manually extracted and fitted by the curve fitting tool field using the signal builder tool [72]. The subject’s input values are taken within the daytime pattern between 9:00 a.m. and 6:00 p.m. The meteorological conditions datasets were retrieved and collected from SolarGIS [73] and NASA POWER [74]. Figure 3.4 illustrates the photograph of the solar still library under the climatic input variables Simulink model browser using the signal builder tool. 66 Figure 3. 4 Photograph of the created weather input parameters using the signal builder tool “Climatic Input Variables Simulink Model Browser”. Regarding the solar still system, the design limits can be summarized as follows: 1. The system dimensions, areas, and efficiency: ▪ Solar still area, Ast (m2). ▪ Glass cover area, Ag (m2). 2. Brine depth, d (cm), and freshwater productivities, Pstd (kg/m2.day). 3. Basin water temperature, Tw (oC), and temperature differences between water and glass cover, Tw-Tg (oC). 4. Thermal load inside the still, Qload on photovoltaic cell (kW). The curve-fitting toolbox fits the data points. The design code of the solar still needs to align with the analysis block of the basin by double-clicking the photograph itself. The model is 67 presented and correlated as a function of the solar still according to the following major design equations: Solar still productivity based on still area, Pstd (kg/m2.day) is determined [75]: 𝑃𝑠𝑡𝑑 = (0.244 ∗ 𝐻𝑠) − (0.0294 ∗ 𝑇𝑎𝑚𝑏) − (0.0073 ∗ 𝑉𝑤) − 0.01222 (3.7) Where Hs is solar radiation in MJ/m2.day, Tamb is ambient temperature, oC, and Vw is wind speed, m/s. Solar still productivity with black dyes based on still area, kg/m2.day [76]: 𝑃𝑑𝑦𝑒 = 1.2122 ∗ (𝑃𝑠𝑡𝑑)1.0467 (3.8) Solar still area, Ast (m2), may be computed as follows [76]: 𝐴𝑠𝑡 =𝑃𝑠𝑡𝑃𝑠𝑡𝑑 (3.9) Where 𝑃𝑠𝑡 (kg/day) is the saline water feed tank productivity and basin input flow rate. The glass cover area, 𝐴𝑔 (m2) of the solar still [77]: 𝐴𝑔 = 𝐴𝑠𝑡 ∗ 𝐴𝑟 (3.10) Where Ar is the area dimensionless ratio = 1.5. Solar still efficiency can be estimated as the following expression [77]: 𝜂𝑠𝑡 =(𝑃𝑠𝑡𝑑 ∗ 2.43 ∗ 100)𝐻𝑠 (3.11) Thermal load inside the still, Qload (kW) [78]: 68 𝑄𝑙𝑜𝑎𝑑 =(𝐻𝑠 ∗ 1000 ∗ 𝐴𝑠𝑡 ∗ 𝜏𝑔 ∗ 𝛼𝑤)(𝑂𝐻 ∗ 3600 ∗ 𝑃𝐶) (3.12) Since, Glass transmissivity 𝜏𝑔 = 0.90. Water absorptivity 𝛼𝑤 = 0.85. Correction factor product 𝑃𝐶 = 0.85. Water temperature difference inside the still, 𝑑𝑇𝑤 (oC) [77]: 𝑑𝑇𝑤 =(𝑄𝑙𝑜𝑎𝑑 ∗ 1 ∗ 3600)(𝜌(𝑇𝑤𝑖 , 𝑆𝑓) ∗ 𝑉𝑜𝑙𝑠𝑡 ∗ 𝑓𝐶𝑝(𝑇𝑤𝑖 , 𝑆𝑓)) (3.13) Since, 𝐶𝑝 (kJ/kg oC) is the specific heat capacity of seawater at constant pressure. 𝜌 (kg/m3) is the saline water density based on feed water temperature 𝑇𝑤𝑖 at 30 oC and feed salinity 𝑆𝑓 at 5000 ppm. The water temperature inside the basin, 𝑇𝑤 (oC) [79]: 𝑇𝑤 = 𝑑𝑇𝑤 + 𝑇𝑤𝑖 (3.14) 𝑇𝑤𝑖 (oC) is the feed water temperature from the tank. Evaporative convective heat transfer coefficient between water and basin glass cover, hev (W/m2) [79]: 69 ℎ𝑒𝑣 =(16.273 ∗ 𝑒𝑥𝑝(−3) ∗ ℎ𝐶 ∗ (𝑃𝑤 − 𝑃𝑔))(𝑇𝑤 − 𝑇𝑔) (3.15) 𝑃𝑤 , 𝑃𝑔 are vapor pressures of water and glass cover, respectively, Pa. The vapor pressures (bar) of the water and basin glass cover can be estimated, respectively as follows [77]: 𝑃𝑤 = 0.01677 ∗ 𝑒𝑥𝑝(0.04133 ∗ 𝑇𝑤) (3.16) 𝑃𝑔 = 0.01677 ∗ 𝑒𝑥𝑝(0.04133 ∗ 𝑇𝑔) (3.17) Total capital cost, TCC ($/unit) of solar still distillation unit that should be computed based on solar still area, glass cover cost ($/m2), concrete construction costs ($/m2), and land cost ($/m2) with an interest rate of 15 % and 25 years plant lifetime [77]: 𝑇𝐶𝐶 = (𝐴𝑠𝑡 ∗ 𝐶𝑐𝑜𝑛𝑐 + 𝐴𝑔 + 𝐶𝑔𝑙𝑎𝑠𝑠 + 𝐶𝑙𝑎𝑛𝑑 ∗ 𝐴𝑠𝑡) + 0.15 ∗ (𝐴𝑠𝑡 ∗ 𝐶𝑐𝑜𝑛𝑐 + 𝐴𝑔 ∗ 𝐶𝑔𝑙𝑎𝑠𝑠 + 𝐶𝑙𝑎𝑛𝑑 ∗ 𝐴𝑠𝑡) (3.18) 3.4.2 Feed Tank Process Modeling Technique The feed tank represents the upstream unit in which saline/ brackish water is retained before it is introduced to the solar still. Figure 3.5 demonstrates the design analysis to model the tank with respect to its location and dimensions. The most critical parameter for seawater is its density and specific heat capacity 𝐶𝑝 relationship, which is a function of feed salinity (ppm) and water temperature (°C). 70 Figure 3. 5 Feed saline water tank model browser. The following design equations are considered in modeling the feed tank [80]: Feed tank cross-sectional area (m2) where Dft is the feed tank diameter (m): 𝐴𝑓𝑡 = (𝜋4) ∗ (𝐷𝑓𝑡2) (3.189) The water level inside the tank, dH (m) can be expressed as follow, where Mft (kg/day) is water production from the still: 𝑑𝐻 =𝑀𝑓𝑡(𝜌 ∗ 𝐴𝑓𝑡) (3.190) The following formula, which uses 𝐴𝑡𝑢𝑏𝑒 as the pipe's cross-sectional area (m2) and Dt as the tube diameter, yields the flow velocity, Vf (m/s) out of the feed water tank: 𝐴𝑡𝑢𝑏𝑒 = (𝜋4) ∗ 𝐷𝑡2 (3.21) 71 𝑉𝑓 =(𝑀𝑓𝑡𝑂𝐻 ∗ 3600)(𝜌 ∗ 𝐴𝑡𝑢𝑏𝑒) (3.22) Feed tank pressure, kPa, and volume (m3) are as follows: 𝑃𝑓𝑡 =𝜌 ∗ 9.81 ∗ (𝐻𝑡 −𝑉𝑓2(2 ∗ 9.81))1000 (3.23) 𝑉𝑜𝑙𝑓𝑡 = 𝐴𝑓𝑡 ∗ 𝑑𝐻 (3.24) Where 𝜌 is saline water density (kg/m3), 𝐴𝑓𝑡 is feed tank cross area (m2), and 𝐻𝑡 is the total height (m). 3.4.3 Distillate Tank Process Modeling Technique The distillate tank acts as the system's downstream unit and last component. It receives the freshwater product directly from the solar sill through a pipe. As presented in Figure 3.6, the distillate tank design parameters comprise but are not limited to the water level inside the tank and tank dimensions, including tank diameter and cross-sectional area. The level change in the tank depends on distillate water production and density. As explained in feed tank design analysis, the water density and specific heat capacity Cp are functions of water temperature (oC) and salinity, ppm. Therefore, basin water temperature Tw is considered a major parameter that affects the level change inside the distillate tank. 72 Figure 3. 6 Distillate water tank model browser. The following design equations are considered in modeling the distillate tank [81]: Distillate tank cross-sectional area Adt (m2) where Ddt is distillate tank diameter (m): 𝐴𝑑𝑡 = (𝜋4) ∗ (𝐷𝑑𝑡2) (3.25) The water level inside the tank dH, m can be expressed as follow where Mdt (kg/day) is the water production rate from the solar still, and 𝐴𝑑𝑡 is distillate tank cross area (m2): 𝑑𝐻 =𝑀𝑑𝑡(𝜌 ∗ 𝐴𝑑𝑡) (3.26) Distillate tank volume, Voldt (m3), is a function of the distillate tank cross-sectional area and the water level inside the tank as follows: 𝑉𝑜𝑙𝑑𝑡 = 𝐴𝑑𝑡 ∗ 𝑑𝐻 (3.27) 73 3.5 Results and Discussion While validating the system performance, the state-of-the-art claims the design parameters, such as still area and dimensions, capable of enhancing the system's efficiency and performance (feed saline water tank outlet, 𝑃𝑠𝑡𝑑= 5 𝑘𝑔 𝑚2⁄ . 𝑑𝑎𝑦). Figure 3.7 (A) exhibits the design solar still area at altered ranges of solar radiations, Is (MJ/m2.day) concerning the design still productivities 𝑃𝑠𝑡= 1-5 kg/day. As illustrated, the solar still area Ast (m2) is directly proportional to the required system’s productivity 𝑃𝑠𝑡 (kg/day), and that area will be augmented to 2 m2 when raising the system’s productivity to 5 kg/day, but with the lower value of the solar intensity 16 MJ/m2.day. As solar radiation increases, the rate of the brine water evaporation process inside the still increases with the ambient temperature. Thus, lowering the required area for the solar still below 1.5 m2 to maintain the desired productivity at a given exposed solar radiation, Is > 17 (MJ/m2.day). Another critical output design parameter is the solar still glass cover area, Ag (m2). As shown in the following 3-D mesh Figure 3.7 (B-C), while the still productivity, kg/day accents, the glass cover area Ag increases to 3 m2 with rising the still ambient temperature Tamb 45 oC and diminishing the solar radiation, Is 15 (MJ/m2.day). In contrast, the highest value of solar radiation, Is 20 (MJ/m2.day), is desirable concerning the solar still ambient temperature Tamb ranging between 25 – 45 oC. Accordingly, the solar still required the lowest design area of 2 m2, which will save on design and construction costs. It can be summarized that it is crucial to lower the surface temperature, Tg (oC) of the glass cover to improve the distillate water production 𝑃𝑠𝑡𝑑 of the still. The basin glass cover's ability to absorb roughly 4.75% of the solar incident from the sun is the underlying cause, leading to an increase in the cover glass's temperature, Tg (oC). Moreover, the 74 condensation of water beneath the glass cover builds a water film, resulting in a partially opaque glass cover and an increase in the glass cover’s temperature. Hence, the temperature difference between the surface of the brine water inside the still and the condensed water in the glass cover will be reduced. Figure 3. 7 (A) solar still design area, Ast (m2) at different solar radiations, Is (15-20 MJ/m2.day) and solar still feed tank flow rate productivities, Pst (1-5 kg/day), (B-C) solar still glass cover area, Ag (m2) at solar radiations, Is (15 & 20 MJ/m2.day) respectively. Figure 3.8 (A) can also be established to demonstrate the solar still design areas at different productivity ranges (saline water feed tank outlet), starting from 5 to 10 kg/day (blue legend) and from 15 to 20 kg/day (orange legend). As depicted, the area required to design a solar still 75 system is almost 11 m2 when the needed solar still productivity is between 15-20 kg/day. On the other hand, it entails around a 3 m2 still area to design the model system when the productivity is from 1 to 5 kg/day. Logically, increasing access to freshwater production during the daytime requires a larger area for the solar still to accommodate the high amount of brine water inside the still to be processed (refer to Eqn 3.9). The solar still area curve is experiencing a downward trend. It reaches almost 5 m2 when the solar energy, Is (MJ/m2.day), increases as it converges to the afternoon time, meaning that the rate of evaporation of saline water inside the still will be boosted due to the high value of solar radiation at peak time. Additionally, it shows almost steady until 4:00 p.m.; then, it rose again when solar intensity decreased. Consequently, low amounts of water are evaporated and condensed inside the basin; hence, low freshwater productivities per unit area, 𝑃𝑠𝑡𝑑 (kg/m2.day). Regarding the photovoltaic total system area, Figure 3.8 (B) displays the same behavior at different still productivities, 𝑃𝑠𝑡 (kg/day). Photovoltaic total system area, At (m2), includes the constructed modules and cell areas. It is necessary to allocate almost 185 m2 total area to accommodate the photovoltaic cell and its auxiliaries when considering 15-20 kg/day distillate water production. In contrast, only 50 m2 is adequate to design a solar PV model with a still productivity of 1-5 kg/day (basin input). Referring to the PV design equations, it can be concluded that the PV total area is directly proportional to the module area, which is a function of the module power. Therefore, the required input power to efficiently operate the module will rise when it converges to nocturnal time. Thus, the high demand for module power, Pm (watts), necessitates a large module and PV total system area, Am and At (m2), respectively. Figure 3.8 (C) shows the distillate water production per still area, which significantly rose to 3.6 kg /m2.day when the solar radiation energy, Is > 15 MJ/m2.day mainly increased throughout the 76 peak period (14:00 time). Otherwise, it declines due to the lower amount of water evaporation process inside the basin 𝑃𝑠𝑡𝑑< 2.5 kg/m2.day. Hence, the rate of access to freshwater is reduced. Solar radiation energy is considered the most critical factor in producing distilled water. The more solar incident received from sunlight (15 - 20 MJ/m2.day), the higher the amount of distilled water yielded from the still, 𝑃𝑠𝑡𝑑 > 3.5 kg/m2.day and vice versa. It is worth mentioning that the black dye addition proved to have a significant effect on solar still performance. The causative factor behind this is that solar radiation incident is absorbed in a very thin upper layer (2 cm); hence, increasing the surface temperature of the brine, Tw (oC), and the rate of water evaporation will be promoted. Therefore, the productivity of the distillate water will rise sharply 𝑃𝑠𝑡𝑑 > 4.5 kg/m2.day. Solar still can offer great potential for generating almost 5 kg/m2.day of freshwater during the peak. Another important thermodynamic parameter that influences solar still performance is the temperature gradient (Tw-Tg) between the water level inside the basin and the glass cover, or the driving force of heat transfer. As predicted, the obtained results remarkably confirmed that brine water temperature is always greater than the glass cover temperature to attain the evaporation/ condensation process. Figure 3.8 (D) illustrates the temperature variation between water and the basin glass cover throughout the day. It can be explicitly observed that increasing the temperature difference (Tw-Tg) by > 12 °C will promote evaporation, thereby boosting water output and improving system performance. Likewise, the water temperature Tw and glass cover temperature Tg experienced an upward trend at the beginning. It achieves its greatest temperature at 50 oC and 39 oC, respectively, during peak hours, when the water production rate is at the maximum value, 3.6 (kg /m2.day). Both temperature differences (Tw-Tg) then decreased 77 substantially over time due to the low rate of absorbed solar incident, reducing the desalination process and freshwater output, 𝑃𝑠𝑡𝑑= 2 (kg/m2.day). Figure 3. 8 (A) Solar still designed area Ast (m2) at different feed tank productivities, Pst (kg/day), (B) photovoltaic cell total system area, At (m2), (C) solar still freshwater productivities without/ with black dye additives, Pstd (kg/m2.day), (D) temperature differences between water and basin glass cover, TW-Tg (oC). It is evident from the following Figure 3.9 (A) that the thermal load, Qload (kW) on PV, is directly related to the volume of water retained inside the still. Logically, the thermal load grows sharply, Qload > 3.5 kW, through the course of the period at different still’s productivities 𝑃𝑠𝑡 , 15 -20 (kg/day), understanding that as the design requirement demands a high freshwater production rate, the still desires a higher thermal load on PV. The reason behind that is while the solar 78 energy, Is (MJ/m2.day), decreased primarily during the nocturnal hours, the load on PV will be augmented as a power to make up for the lack of absorbed solar intensity and satisfy the freshwater demand by rising the rate of evaporation/ condensation process inside the basin; thereby, maintaining the distillate water production rate. One of the most fundamental thermodynamic properties that must be considered in the still design is the evaporative heat transfer coefficient, hev (W/m2 oC). This parameter is critical since it is attributed to the rates of water evaporation and condensation processes that occur inside the basin, which should be kept high enough to obtain as much freshwater output as feasible in the downstream unit. It can be deduced from Figure 3.9 (B) that the evaporative heat transfer coefficient experienced an upward trend of 0.1 W/m2.day in the forenoon period but showed a stable trend through noon. It then drops dramatically towards the end of the period. The reason for this overt trend is that as the depth of the brine water rises, more water fills the still, increasing its thermal inertia and slowing its rate of evaporation in the process. The findings also show that the wind speed, Vw (m/s), has a negligible association with the evaporative heat transfer coefficient, hev, between water and glass cover for a given ambient temperature, Tamb, and water temperature, Tw (oC). As was previously noted, the design limits and thermodynamic property evaluations represent the still performance, which is enhanced by more than 45% at peak time and corresponds to the still distillate water output per unit area, as shown in Figure 3.9 (C). The findings show that the suggested study exhibits the improvement of a solar distillation unit that achieved high efficiency when integrated into a solar photovoltaic system and increased distillate water output 𝑃𝑠𝑡𝑑 to 3.6 kg/m2.day. It can be concluded that a greater distillate water demand, 𝑃𝑠𝑡 (kg/day), necessitates the designer/investor spending more money on the system's design and construction. Regarding the effect of ambient temperature, it has been observed that PV costs significantly more (around 79 $1400/module) as the ambient temperature outside the solar still rises (Tamb > 25 oC). This is due to the low ambient temperatures, which cause the glass cover of the still to cool faster, increasing the temperature difference between the brine water layer and the still’s glass cover (Tw-Tg). As a result, the evaporation/condensation process is promoted, and treated water production will increase at a reasonable price. It is apparent from Figure 3.9 (D) that the total capital cost, TCC ($/unit), for the solar still is considerably higher when the productivity 𝑃𝑠𝑡 required for a design is greater than that for a low distillate water productivity from the still. When the solar incidence is at its optimum at 14:00, the TCC for solar still productivity (𝑃𝑠𝑡 =15 – 20 kg/day) substantially decreases to below $1500/unit. However, if it was decided to design and construct a solar still distillation unit with a total production of less than or equal to 5 kg/day, the total capital cost would be no more than $500/ solar still unit by the end of the day. 80 Figure 3. 9 (A) Thermal load inside the solar still Qload (kW) at different flow rate productivities, Pst (kg/day), (B) evaporative heat transfer coefficient inside the solar still, hev (W/m2 oC), (C) solar still efficiency during the operational day, st (%), (D) solar still total capital cost, TCC ($/unit). As the solar still design unit is combined with a solar photovoltaic system, the thermal load Qload, kW inside the solar still is a critical parameter to demonstrate. It is primarily affected by solar radiation, Is (MJ/m2.day), and solar still area, Ast (m2), rather than by ambient temperature, Tamb (oC). As explained earlier, the thermal load within the still is introduced to the photovoltaic cell in the form of total input power and module power, which are necessary to estimate the PV number of modules (NOM) and total PV system area, At (m2). Figure 3.10 (A) illustrates that at a constant ambient temperature, Tamb 25 (oC), the thermal load on PV experienced an upward 81 trend of 0.8 kW when the still productivity, 𝑃𝑠𝑡 3-5 (kg/day) and still area increase, whereas it experienced a downward trend < 0.8 kW when the solar radiation, Is 15-20 (MJ/m2.day) rise. The total photovoltaic costs per module are a key factor that should be considered in the design model, especially when coupled with a passive solar still unit. The PV's total system area depends on several factors, including the total power input into the cell through the load on PV, PV full overboard costs, FOB ($/watt/module), the number of batteries, and battery costs per module (refer to design cost analysis). The following mesh Figure 3.10 (B) illustrates this point, showing how the total cost of the photovoltaic cell, PVCt ($), rises sharply throughout the still’s production (𝑃𝑠𝑡 up to 5 kg/day). It is worth mentioning that increasing the amount of solar energy absorbed, Is (MJ/m2.day), effectively enhances the rate at which water vaporizes inside the basin. As a result, increasing the amount of freshwater discharged per unit area, 𝑃𝑠𝑡𝑑 (kg/m2.day). Therefore, the total cost will decrease even when solar radiation energy keeps rising to its peak value at 20 MJ/m2.day. Accordingly, the lowest PV costs per module may be identified, even though the feed tank's daily mass production is only about 1 kg/day. 82 Figure 3. 10 (A) thermal load inside the still Qload (kW) at different solar radiations, Is (15-20 MJ/m2.day) and feed tank productions flow rate (1-5 kg/day), (B) total photovoltaic cell costs, PVCt ($/module) at Tamb 25 oC against other solar radiations, Is (15-20 MJ/m2.day) and feed flow rate productivities, Pst (1-5 kg/day). Likewise, it is shown in the below contour Figure 3.11 that the design productivities of the solar still (outlet feed tank fed to still basin), 𝑃𝑠𝑡= 1 to 5 kg/day have no effect on the solar still efficiency st, (%), since all of them exhibit the same results (refer to Eqn. 3.13) and the still efficiency is directly proportional to the amount of distillate water produced 𝑃𝑠𝑡𝑑 (kg/m2.day). Therefore, boost the efficiency of the whole system. Although the solar still can attain up to 50% efficiency when the ambient temperature is relatively low at 25 oC (see Eqn. 3.8) and the solar radiation is quite high, Is ~ 45 MJ/m2.day, it is genuinely hard to accomplish. It can be concluded that optimal solar still efficiency >= 45% is reached when the ambient temperature varies between 25 and 34 oC and solar radiation energy sharply increases to 45 MJ/m2.day. 83 Figure 3. 11 Designed solar still efficiencies, st (%). A comparison of the design areas for each component of the developed model system is shown in Figure 3.12 below. In terms of the systems area, it can be observed that the solar still area (blue bar) features compact, minimal dimensions and can accommodate not more than 3 m2 at a designed system with purified feed water flow rate productivity, 𝑃𝑠𝑡, not exceeding 5 kg/day as an input mass flow rate to the basin. On the other hand, designers/ investors must consider the photovoltaic cell design area (orange bar). The standalone system necessitates a larger construction zone of around 30 m2 to accommodate its utilities, such as modules, cells, and batteries. The gray bar represents the combined system areas, including the solar still distillation unit and solar photovoltaic system, which demand much more space and costs to install in an appropriate plant > 30 m2 when intended to design and generate > 5 kg/day. In summary, PV cell 84 still takes up more space than the solar distillation unit, even though the latter does not have to contend with these utilities. As a result, solar requires far less space and construction expenses. Figure 3. 12 Solar still and solar PV designed model system areas, A (m2). 3.6 Conclusion This chapter provides a thorough investigation into the systematic design and computational simulation of a novel hybrid solar photovoltaic (PV) assisted single-slope solar still, aimed at enhancing freshwater productivity through the effective utilization of renewable energy resources. The study’s findings elucidate that the proposed system offers substantial performance and economic advantages over conventional passive solar stills. A comprehensive design analysis, conducted using the MATLAB/SIMULINK environment, substantiates the viability of this integrated approach for achieving targeted freshwater yields in a cost-effective manner. The primary outcome of this research is the demonstrable enhancement in performance achieved by integrating a solar PV system, connected to an internal heating element, with a conventional solar still. Simulation results revealed a marked increase in thermal efficiency, with the hybrid system attaining a maximum efficiency of approximately 45% during peak solar insolation. This 85 represents a substantial improvement over conventional passive solar stills, which exhibited an efficiency approximately 22% lower under identical conditions. This enhanced performance can be attributed to the synergistic effect of direct solar thermal heating of the brine, combined with the supplementary indirect heating provided by the PV-powered element, which effectively converts electrical energy into thermal energy within the basin. Moreover, the design analysis established that a basin area of only 3 m² is sufficient to achieve a targeted daily freshwater productivity of up to 4.6 kg/m² per day under optimal solar radiation conditions (~ 17 MJ/m²·day). This level of productivity significantly exceeds that typically achieved by passive stills of similar footprint. The integration of black dye was identified as a crucial factor, promoting increased solar radiation absorption at the surface of the brine, thereby elevating the surface temperature, and accelerating the evaporation rate. From an economic perspective, the feasibility analysis demonstrates that the proposed hybrid system is not only more productive but also more cost-effective. The estimated total capital cost for the photovoltaic-assisted solar still is approximately $1,500/unit, representing a significant decrease from the $2,600/unit cost of a conventional still designed to achieve comparable levels of productivity, though with a larger footprint or lower efficiency. This finding challenges the prevailing assumption of a trade-off between cost and performance in decentralized solar desalination systems. In conclusion, the design and simulation framework developed in this chapter affirms the concept of a PV-assisted hybrid solar still as a technically robust and economically viable solution for decentralized freshwater production. This work establishes a clear pathway for maximizing solar energy utilization through the integration of photovoltaic and thermal processes. 86 The outcomes of this study not only provide a detailed design for a high-performance solar still but also form a foundational dataset for the development of advanced machine learning models discussed in subsequent chapters of this dissertation. The findings from Chapter 3 underscore the potential of hybrid solar photovoltaic-assisted distillation units to enhance freshwater productivity through systematic design, energy efficiency analysis, and economic assessment. While these simulations provided critical insights into the thermophysical behavior and design viability of solar still systems, they did not address the potential of advanced computational tools for predictive modeling. As the complexity of solar still performance increases with variations in design parameters and environmental conditions, integrating artificial intelligence becomes essential for accurate forecasting. To address this, the subsequent chapter explores a novel application of transfer learning to develop supervised artificial neural network (ANN) models capable of predicting freshwater productivity using knowledge from prior hybrid still designs. This approach bridges the gap between data-driven modeling and theoretical design, setting the stage for a new generation of intelligent solar desalination prediction tools. 87 Chapter 4: A Performance Neural Network Model for Conventional Single-Slope Solar Stills via Transfer Learning 4.1 Motivation Predictive modeling in solar desalination has increasingly benefited from the adoption of machine learning and artificial intelligence techniques, particularly in forecasting water productivity under diverse operational and design scenarios. However, building reliable models that generalize well across various solar still configurations remain a significant challenge due to limited datasets and model variability. In this chapter, a transfer learning framework is proposed to enhance the accuracy of ANN-based regression models for predicting freshwater yield in single-slope solar stills. The methodology leverages a pre-trained source ANN model developed from a previously simulated hybrid solar still configuration and fine-tunes it using experimental datasets from literature-reported solar stills. The goal is to establish a robust target model that outperforms both the randomly initialized ANN and traditional regression baselines. Through comparative analysis and residual error evaluation, this chapter demonstrates the effectiveness of transfer learning in improving predictive precision and model generalization for solar desalination applications. 4.2 Introduction Globally, water scarcity is a significant challenge and entails thoroughly exploring all available possibilities for maintaining present water supplies while investigating new alternative sources. The abundance of saline water inspires substantial prospects for recovering vast amounts of water that demand treatment from this water source [82]. There is an urgent and severe necessity to acquire fresh water from the saline/brackish or polluted water on or within the earth owing to the stability of accessible fresh water, estimated to be about 1%. Its demand is increasing daily 88 due to the rapidly expanding industry and population growth increase [83] [84]. Desalination processes are feasible and of interest for potable water consumption; thus, they raise distillate water production, resulting in lower water consumption. The overproduction of industrial wastewater has never been as high as it is now owing to the rising demand for consumer goods and technology from various industrial and water-related manufacturing processes [85]. Hence, finding alternative approaches to pricy and energy-intensive separation methods such as: (multi-stage flash, multiple effects, solvent extraction, membrane filters, and reverse osmosis via emerging solar distillation may, therefore, contribute to fulfilling the world's increasing need for pumping purified and industrial water to the desired location [86] [87]. According to Cuce et al. [88], solar distillation systems can be classified into two groups: (i) direct systems, which use directly absorbed solar radiation energy like in solar stills. In addition, (ii) indirect systems use energy converted from solar to thermal or photovoltaic systems, such as thermal and membrane systems. The intriguing water distillation technique known as "solar stills" was found to have promise as a less costly substitute for the high-priced membrane technology [89]. This technology had been discovered in the late 19th century and had just recently entered the market for manufacturing and delivering water. Leveraging an environmentally friendly solar desalination process, offered by solar intensity energy, is a breakthrough since no wastes/emissions are created. Also, no additional energy is required, potentially lowering the costs of employing solar stills for desalination [90] [91]. Water solar distillation replicates the natural manner of "rain" through water's recurring evaporation/ condensation process [77]. The distilled and treated water produced is typically potable and of valuable high-quality owing to the complete removal of inorganic and organic pollutants and total dissolved solids (TDS) [92]. 89 In terms of solar distillation unit design aspect, direct passive solar stills are common practice due to their simplicity and capacity to improve water production in single slope solar stills via solar radiation absorption, basin thermal insulation, and energy storage medium [92] [93] [94]. Similarly, for the optimization of solar still freshwater productivity, some critical factors that must be taken into consideration comprise but are not limited to solar radiation, ambient temperature, wind speed, desired feed water flowrate (maximum permissible water levels inside the saline water tank), feed water temperature (the difference in water/glass temperature), air humidity, basin surface area, inclination angle for the top cover, and glass transparency for solar radiation [89]. The direct passive solar still's performance was shown to be significantly impacted by a number of these factors, including the solar incident, the ambient, water, and vapor temperatures, the brine depth (2-2.5 cm), and the wall insulating film thickness (1–5 cm). Previously, these parameters have been experimentally investigated, and mathematical models were used to correlate them to the performance with high prediction accuracy [95]. A total water productivity of 2,197.4 mL/week was found to be possible from the passive design with the sensible medium energy storage, according to research by Cuce et al. [7], who developed a novel non-insulated solar distillation unit through a sensible medium for energy storage coupled with a passive supporter reflector. Yet, the thermal insulation and cooling for the aperture glazing and exterior structure, which would drive up rates of the condensation-evaporation process via decreasing heat losses and improving convective coefficients, were the only factors affecting water productivity. Furthermore, Wang et al. [96] discovered that for forecasting productivity in tubular solar stills, seawater temperature, basin temperature, and solar radiation were among the most fundamental indicators, with 40.87%, 32.43%, and 18.2 %, respectively. The single-slope solar still was shown to be more efficient than a pyramid-shaped still in terms of the design 90 aspect, with a 30% greater output in winter due to the reduced escape of absorbed solar intensity energy from the substantial surface cover [97]. Due to the relatively low conversion rates and high installation costs, solar radiation employment for solar stills or power conversion still needs to be extensively industrialized. Supervised machine learning (ML) and cross-validation (CV) techniques should be the subject of more innovative research. Inventing unique technical technologies capable of in-depth assessing the patent outputs and literature datasets that are now available would aid in solar harvesting, material selection, and solar desalination application [98]. These newly developed algorithms can make it easier for large-scale solar stills to be commercialized and progress in solar-desalination technologies, which will benefit the creativities' community, business fields, and technical R&D facilities [99] [100]. Even though the inherent problem of solar still is its low water distillate productivity, it utilizes a sustainable and renewable energy source (pollution-free) to yield high-quality treated water. It is vital to select solar still systems wisely based on their productivity, which is considered a prime design goal to maintain design simplicity and operation feasibility. However, this is challenging due to various measurements and multiple heat transfer calculations [101]. There is a rising trend toward using ML/AI algorithms to build numerical models or complicated computational simulators capable of handling engineering problems. As a result, developing mathematical models is a valuable means and practical tool for estimating solar still productivity and evaluating system performance. These created mathematical models, embodied in ML models, play a primary role in optimizing and simulating solar still productivity, resulting in efficient and economical design [102]. 91 Moreover, it would be easy to build strategies to harness this new purified water source after the solar desalination process to service numerous industrial sectors by predicting and knowing solar still productivity. In contrast, the classical mathematical models used to implement these computations remain complex. These algorithms necessitate a lengthy computational time, a large processing capacity, and the solution of multiple complicated equations [103]. In this work, we developed a framework to establish a mathematical model that predicts how productive single-slope solar still would be using artificial neural networks (ANNs). In addition, the performance of the developed random initialization ANN model was evaluated through a statistical comparison of the results of solar still productivity derived from the constructed ANN model (predicted results) and previous experimental findings (observed results). Regarding the suitability for forecasting solar still productivity, transfer learning was applied to the random initialized ANN model. Fine-tuning via transfer learning allowed us to obtain the target ANN model by unfreezing the input layer nodes and freezing at least one hidden layer neuron per the learned weights. The learned networks are then transferred from the built pre-trained ANN model (novel solar still source model) to the random initialization ANN model for the conventional solar still model, ultimately yielding the target ANN model. The generated ANN latter model was then compared to the pre-trained ANN and multiple linear regression (MLR) models. Lastly, the ANN target model was contrasted with random initialization ANN and MLR models to compare the models’ accuracies in predicting water productivity in a single-basin solar still. This study highlights multiple novel and significant contributions: • The study utilizes transfer learning to build accurate predictive ANN models for freshwater productivity in solar stills, which is a unique application of solar desalination systems. Employing a pre-trained source ANN model improves prediction accuracy. 92 • The study introduces a unique target ANN model with a specific 5-64-64-1 architecture. The model has been enhanced through transfer learning and is designed to improve the accuracy of water productivity predictions in solar stills, distinguishing it from conventional ANN models. • The established target ANN model performs well in predicting purified water outputs, outperforming the random initialization ANN and MLR models developed in the study. This was evaluated using improved statistical performance metrics. • The study demonstrates the practical effectiveness of the ANN model by confirming its generalization and capability to accurately predict distillate water production under various conditions. • This research article provides valuable insights into solar desalination systems and suggests cost-effective, practical solutions for addressing significant industrial challenges. These discoveries form the basis for future advancements in solar desalination technologies and pave the way for potential practical applications, instilling a sense of hope in the reader about the future of the field. The subsequent sections of this chapter were organized as follows. Section 4.3 presents the essential literature review and discusses related work to identify the research gap. Section 4.4 introduces a supervised learning-based ANN methodology and framework for developing a pre-trained ANN model. Additionally, we investigate the application of transfer learning on the random initialization ANN model to generate the optimal target ANN model, describing the main building blocks, including network architecture, and shedding light on their criteria for evaluation. Moving on to section 4.5, we extensively discuss the implementation details for our proposed study with a performance analysis of the RI ANN compared to MLR models and an 93 exploration of hyperparameter optimizations. Finally, this chapter culminates with a discussion of closing remarks in section 4.6, emphasizing the potential prospects that lie ahead. 4.3 Literature Review Knowledge-based machine learning (ML) has emerged as a powerful tool in solar-desalination systems, offering rapid and accurate predictions and cost-effective designs by leveraging existing frameworks that have been proposed in the past. Using and implementing artificial neural network models in the solar still desalination process could attain desirable results that are difficult to obtain with conventional design equations. This might be attributed to the revolution in computer technology and innovative mathematical modeling techniques [104]. In a recent study, Murugan et al. [27] aimed to improve freshwater production using solar stills, focusing on performance in diverse climatic conditions. They utilized machine learning models to enhance yield predictions, addressing the limitations of traditional forecasting methods. The research involved evaluating several machine learning models, including linear regression, decision trees, random forest, support vector machines, and multilayer perceptron, employing metrics such as Mean Absolute Error (MAE), cross-validation, and parameter tuning techniques. The decision tree model emerged as the most effective predictor, achieving MAEs of 5.43 and 5.74 through random and grid search methods, respectively. This approach significantly enhances the accuracy of solar still output predictions, thereby contributing to optimizing solar still designs and solar energy conversion mechanisms. The study concluded that machine learning, particularly the decision trees model, offers a robust solution for forecasting distillate outputs in single basin single slope solar stills, enabling more efficient and sustainable water production. Future research avenues involve refining the model, integrating additional data, and further 94 exploring advanced techniques such as deep learning to improve predictive accuracy and performance across diverse solar still designs. In a study by S. Nazari et al. [105], accurate models for predicting the energy efficiency, exergy efficiency, and water productivity of a single-slope solar still were developed using ANN and an ANN optimized with the Imperialist Competition Algorithm (ICA). These models were trained using empirical data, with various environmental and operational parameters such as time, ambient temperature, solar radiation, glass temperature, basin temperature, and water temperature considered. The neural network with five hidden neurons demonstrated the best performance. Implementing the ICA significantly improved ANN performance, reducing Mean Absolute Error (MAE) by 54.30%, 40.11%, and 53.35% for water productivity, energy efficiency, and exergy efficiency, respectively. Furthermore, the ANN-ICA achieved root mean square error (RMSE) values of 15.77, 1.37, and 0.29 for predicting these metrics. The results highlighted that the ICA-enhanced ANN provided superior predictions compared to traditional ANN models. This study emphasizes the potential of integrating neural networks with optimization algorithms to enhance predictive accuracy in solar still performance metrics. Another advanced research conducted by H. A. Maddah [106], established precise supervised predictive machine learning models based on experimental results from the literature to estimate double slope solar still productivity and some key thermodynamic properties. Training collected datasets were created using previous inputs and outputs variables from different designed active or passive solar stills ( ~ 42%) for treating wastewater or brackish water with a TDS content of 45%. The difference in water and glass temperatures (Tw - Tg) was shown to be semi-proportionally correlated with the water distillate with the most minor statistical errors. According to the proposed relationship, the highest distillate would be produced at 14:00 with an 95 increase in both basin temperature (TB) and (Tw - Tg). In double slope still designs, the regression models (FGSVM, SEGPR, and EBoT) had the lowest attained root mean square error (RMSE) of 138, suggesting their reliability in precisely forecasting the distillate quantities. The remarkable accuracy of the SEGPR-trained model (R2 = 1) and very low RMSE < 8 demonstrated the model's capability to predict performance in comparable solar-desalination systems. Nevertheless, it was revealed that the stepwise linear regression (SLR) performed better predicting the TB pattern than the FGSVM did predict the (Tw - Tg) against the water distillate. For more precise predictions, H. A. Maddah [106] claimed that built models could be further optimized by utilizing inputs such as feed water flow rate, environmental conditions, and insulator properties. Such theoretical models would point us in the right direction for tuning the parameters linked to the convective, evaporative, and radiative coefficients for boosting the distillate-water outputs in double-slope solar stills. 4.4 Methodology and Framework In this work, we developed a framework to establish a mathematical model that predicts how productive single-slope solar still would be using artificial neural networks (ANNs). Moreover, the performance of the developed RI ANN model was evaluated through statistical metrics and comparison of the solar still productivity results derived from the constructed ANN model (predicted results) and previous experimental findings (observed results). The transfer learning method was employed for the RI ANN model based on its suitability for forecasting water outputs. Fine-tuning via transfer learning allowed us to generate the target ANN model by unfreezing the input and first hidden layers neurons and freezing at least one hidden layer neuron inherent to the learned weights. Therefore, to get the target ANN model with a more accurate prediction of treated water, the optimal learned networks (intelligence) were obtained, frozen, 96 and transferred from the developed pre-trained (source) ANN model to the RI ANN model. The source model was established from the novel solar still system datasets. Finally, the target ANN model was contrasted with RI ANN and MLR models to compare the models’ accuracies in predicting water productivity in a single-basin solar still system. 4.4.1 Developing the source ANN model The source datasets were collected from a novel hybrid solar still system designed and simulated using MATLAB/SIMULINK. The simulation software was used to accurately model system behavior with the aid of a graphical user interface (GUI) modeling tool [30]. This GUI application integrates a visual library into the Simulink browser, enhancing detailed and dynamic modeling capabilities. The initial datasets comprised operational variables of the solar still such as feed flow rate, meteorological conditions (sourced from NASA POWER) [107], water temperatures, salinity, and water distillates measured hourly from 9:00 to 18:00. These parameters were selected due to their critical impact on the efficiency and productivity of the solar still. The original data collected over several simulation runs was expanded by 7.3-fold using the MATLAB curve fitting toolbox through the signal builder tool to increase the dataset size from 100 to 730 data points for input parameters accompanied by distillate water output. This augmentation process involved adding controlled noise to the data to introduce non-linearity and prevent overfitting, which is essential for enhancing machine learning model training. For the development of the ANN base model, the expanded dataset was divided into training (70%), testing (20%), and validation (10%) sets. Several iterations of random selection and partitioning were performed in multiple rounds to ensure the generalizability and robustness of the results. This method was iterated ten times to address potential biases from a single partitioning. Following each iteration of partitioning, we conducted separate training and 97 evaluation of the models. The results obtained from these repeated iterations (runs) were averaged to evaluate the model's effectiveness comprehensively. This methodology facilitates attaining more reliable and comprehensive outcomes by considering the variations in the data splits. In the training phase, the ANN is trained to predict an output, specifically distilled water in the novel solar still system. During the testing phase, the ANN model is used to forecast a single output value (Pstd) to examine the validity and reliability of the machine learning models and to determine whether the training should stop or continue. The ANN is validated during the validation phase to ensure its performance on new cases [102]. A supervised machine learning technique, such as the ANN model, was chosen and compared with a multiple linear regression (MLR) model on labeled datasets in the training, testing, and validation phases to compare and select the best modeling stage for superior prediction outcomes. ANN and MLR models were constructed using a hold-out strategy of 32 random states, controlling the shuffling process in the train-test-split. The source ANN model was developed using Collab notebook/Python software and the widely used feed-forward/back-propagation algorithm [108]. Solar stills undergo energy gains and losses influenced by selected weather input variables [103]. The recorded daily operational feed water volume was included as an input into the ANN model. The feed water flow rate was considered in the neural network analysis as it is related to the constant factor of the basin area. When operating solar stills, users will likely utilize the feed water volume to determine the water quantity needed for flushing and operation [103]. The chosen input variables—daily solar radiation (Is), ambient temperature (Tamb), wind speed (Vw), relative humidity (RH), and saline water feed flow rate (Pst)—were identified as primary 98 influencers of solar still performance. The dependent variable, water productivity (Pstd), was then correlated with these inputs that emphasis our machine learning analysis. It is worth noting that the input parameters for our model were chosen based on their substantial influence on the performance of solar stills and their capability to forecast freshwater productivity precisely. Multiple factors justified the omission of the inlet water temperature. Initially, the inlet temperature of the basin was consistently maintained, leading to minimal fluctuations in its level. The initial investigation found that this parameter did not significantly improve the model's ability to predict water productivity accurately. Including it would have extended the model's complexity without yielding substantial benefits. Therefore, our attention was directed toward the five most influential operational variables to optimize the model and enhance its efficiency and interpretability. Critical decisions in the model training process included selecting 92 iterations based on a batch size of 8 samples, determined to be optimal through hyperparameter tuning. The Adam optimizer's regularization strength and learning rate were set at 0.001 and 0.0003, respectively, to ensure robust training while minimizing overfitting. Early stopping with a patience value of 20 was employed to halt training if the validation loss did not improve, thus preserving model generalization. A single epoch occurs when an entire dataset is only once passed through the neural network forward and backward. This detailed approach to dataset preparation and model training highlights the systematic methodology for developing a reliable and accurate ANN model for predicting solar still performance. Table 4.1 demonstrates the collected input and output parameters data sources for both solar stills configuration systems. 99 Table 4. 1 Inputs and outputs parameters data sources. Solar Still Design Configurations Input Parameters Data Source Output Parameters Data Source Novel solar still system (Pretrained model) Operational Variable: Saline water feed flowrate, L/day. Literature/ experimental datasets [28]. Solar still productivity Water distillate (L/day). Literature/ experimental datasets [103]. Conventional solar still system (Random Initialization model) Meteorological Conditions: Solar radiation, MJ/m2.day Ambient temperature, oC Wind speed, m/s Relative humidity, % NASA Power [107]. 4.4.2 Criteria of assessment for random initialization ANN model For evaluating the long-term performance of the conventional single-slope solar still, 365 numerical datasets were manually extracted from preceding experimental results found in the literature and were conducted by Santos [103]. The compiled datasets initially involved direct measurements of feed water volumes and daily average distillate productions between February 2006 and August 2007 using a rectangular basin still with an area of 0.976 m2 [109]. They then were tabulated with corresponding daily recorded weather data as input variables, including solar incidents retrieved from NASA power webs [107]. The random initialization ANN model was built with feed water volumes and daily average weather data as inputs and the total freshwater production as the output variable (Pstd, L/m2.day). 100 The earlier study [103] intended to predict single-basin solar still distillate production comprising some water physical properties of the feed and distillate. For instance, density and specific heat capacity are functions of feed salinity and initial water temperature since these factors were critical for assessing the water safety criteria for safe human consumption [110]. Likewise, as applied to the source model, the trained models used to forecast distillate water in the conventional solar still were employed in the testing analysis for both ANN and MLR models. The training datasets (70% of the curated data) comprised six matrices of [256 x 1], with each matrix representing an input parameter or water productivity as an output. This defined matrix size is also comparable to that a one [256 x 6] matrix was curated considering the inputs as mentioned earlier and the distillate water output. The same inputs were used in the testing datasets, extracted as 20% of the curated data to predict the known freshwater productivity for verifying trained model accuracy. Lastly, the 10% curated data were utilized to check the performance of new datasets and get a model that can generalize better on unseen or future datasets. It is typical to evaluate the predictive performance for the developed ANN and MLR model using a variety of statistical metrics, such as coefficient of determination (R2), root mean square error (RMSE), mean square error (MSE), mean absolute error (MAE), the overall index of model performance (OI), and residual, which were calculated using their mathematical computations in eqns. (4.1- 4.7), respectively [111]. 𝑅𝑀𝑆𝐸 = √∑ (𝑥𝑜,𝑖 − 𝑥𝑝,𝑖)𝑛𝑖=02𝑛 (4.20) 𝑅2 =(∑ (𝑥𝑜,𝑖 − ?̅?𝑜)(𝑥𝑝,𝑖 − ?̅?𝑝)2)𝑛𝑖=0∑ (𝑥𝑜,𝑖 − ?̅?𝑜)2 × ∑ (𝑥𝑝,𝑖 − ?̅?𝑝)2𝑛𝑖=0𝑛𝑖=0 (4.21) 101 𝑀𝐴𝐸 =∑ |𝑥𝑜,𝑖 − 𝑥𝑝,𝑖|𝑛𝑖=0𝑛 (4.22) 𝑀𝐸 = 1 − ∑ (𝑥𝑜,𝑖 − 𝑥𝑝,𝑖)𝑛𝑖=02∑ (𝑥𝑜,𝑖 − ?̅?𝑜)2 𝑛𝑖=0 (4.23) 𝑂𝐼 = 12 (1 − (𝑅𝑀𝑆𝐸 𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛) + 𝑀𝐸) (4.24) 𝐶𝑅𝑀 = (∑ 𝑥𝑝,𝑖 − ∑ 𝑥𝑜,𝑖𝑛𝑖=0𝑛𝑖=0 )∑ 𝑥𝑜,𝑖𝑛𝑖=0 (4.25) 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 = 𝑥𝑜,𝑖 − 𝑥𝑝,𝑖 (4.26) Knowing that the observed value is denoted by 𝑥𝑜,𝑖. 𝑥𝑝,𝑖 is symbolized as the predicted value by the ML models. ?̅?𝑜 is the averaged observed or mathematically obtained values; ?̅?𝑝 refers to the predicted values or theoretically estimated from averaging; the minimum and maximum observed values denoted by 𝑥𝑚𝑖𝑛 and 𝑥𝑚𝑎𝑥 respectively, and 𝑛 indicates the number of observations or dataset size. The lower 𝑅𝑀𝑆𝐸 and 𝑀𝐴𝐸 values determine the more accurate prediction results, and their values range from 0 to ∞. On the other hand, the higher 𝑅2 value demonstrates the more remarkable similarities between the trendlines of both observed and predicted samples (an identical pattern is reached when 𝑅2 = 1) [112]. A perfect fit between observed and forecasted results is generated when 𝑀𝐸 value is 1. In contrast, a zero value implies that a mean value would have produced the same level of accuracy [113] [114]. The latter metric could produce a negative value −∞ if the mean observed value ?̅?𝑜 102 is a better predictor than the simulated value, which indicates unacceptable performance. The 𝑂𝐼 value of 1 expresses an optimal fit between observed and predicted outputs. The 𝐶𝑅𝑀 values are near ±1. Better model accuracy is achieved when the 𝐶𝑅𝑀 value is close to zero. For ideal data modeling, 𝑅𝑀𝑆𝐸, 𝑀𝐴𝐸 and 𝐶𝑅𝑀 measures, which were obtained from the different trained models, need to be closer to zero, but 𝑅2, 𝑀𝐸 and 𝑂𝐼 values should converge to 1 as much as possible [115]. Figure 4.1 demonstrates a flow chart illustrating the selection and development of the optimal ANN source and target models for precisely predicting distillate water productivity, Pstd. Based on the statistical metrics presented in Table 4.2, the optimum ANN architecture was chosen through a trial-and-error technique by determining whether the R2 was greater than 0.75 and predicting the distillate water (Pstd) from the testing datasets. Selected models that only satisfied the previous criteria were retained for further analysis to compare their predicted response patterns and residuals (from the testing datasets) to the actual experimental results (from the training datasets). The ideal chosen architecture of the source ANN model represented in trained network weights was employed to be repurposed (reused) in the random initialization ANN model and trained on new datasets and functions based on minimum measures of errors. Hence, as illustrated in Figure 4.2, it was attempted to fine-tune the latter model by training only the first hidden layer, leaving the other frozen, and developing a predictive mathematical algorithm to obtain the target model from patterns that had been trained. 103 Figure 4. 1 Flowchart for selecting and developing optimal pre-trained and target ANN models for accurately predicting distillate water productivity. 104 Figure 4. 2 Schematic diagram for applying transfer learning technique on the conventional solar still system to accurately predict distillate water outputs Pstd, L/m2.day. These algorithms compute solar still freshwater productivity based on experimental findings from a previous study using ANN models [103]. This machine learning technique is identified as a transfer learning method, which was implemented in the conventional solar still base model to generate the final target model. random initialization ANN model was created as a first step in the conventional single slope solar still without applying the transfer learning method. Then, it was compared to the developed optimal target ANN model. In this research, we focused on developing an ANN regression model to forecast continuous numerical variables associated with water productivity in solar stills. Unlike binary classification problems that generally utilize hard-limit transfer functions [0,1], our ANN regression model employs non-linear transfer functions such as ReLU to capture the complex relationships within continuous data. By 105 integrating these non-linear transfer functions into our feedforward neural network, we can more effectively model and predict continuous values than using linear or hard-limit functions. It is important to note that graphical and statistical comparisons were used to evaluate the performance of all developed ANN and MLR models. Finally, it was aimed to study and emphasize whether the target ANN model generated by learned (frozen) weights would provide better prediction than the random initialization model based on their accuracies and minimum statistical errors. As illustrated in Figure 4.3, repurposing the pre-trained (source) model was applied to the random initialization model to predict target output data (distillates) in the future using the trained network model (transferred knowledge) and to evaluate overall long-term system performance in single slope solar still. Figure 4. 3 A schematic block flow diagram for applying the transfer learning method on the conventional solar still system known as the random initialization (RI) ANN model to predict distillate water (Pstd, L/m2.day) outputs more accurately. The optimal source (pre-trained) ANN model was developed to produce the best-learned weights, freeze, and transfer them to the RI ANN network to further generate the target ANN model with minimal statistical errors. 106 Table 4. 2 Presenting the RI ANN model methodology in a pseudocode form. S/N Step Pseudocode Explanation 1 Input Datasets (70% training, 20% testing, 10% validation) X: Input features dataset (2D array). Y: Distillate water variable dataset (1D array). X_train, X_test, X_val: Split X into training, testing, and validation datasets (2D arrays). y_train, y_test, y_val: Split y as an output variable into training, testing, and validation datasets (1D arrays). 2 Data Normalization Import necessary libraries (numpy, sklearn.model). Define MinMaxScaler objects for input and target variables. Fit MinMaxScaler on training datasets. Normalize the training, validation, and test data using the fitted scalers (Scaler Fit. transform). 3 ANN Model Creation Import necessary libraries (numpy, keras, sklearn.model and tensorflow). Create a sequential neural network model. First Hidden Layer Create the first hidden layer with 16 units, input dimension 5, using ReLU activation function, and normal weight initialization. Second Hidden Layer Create the second hidden layer with 32 units, using ReLU activation function, and normal weight initialization. Output Layer Create the output layer with 1 unit, representing a single fully 107 connected node, using normal weight initialization. Compile the model Compile the RI ANN model using mean squared error as the loss function and Adam optimizer with a learning rate of 3e-4. 4 Fitting the ANN to the Training Dataset Train the model on the training data (X_train, y_train) with a batch size of 20, 500 epochs, and validation data (X_val, y_val). 5 Early Stopping Apply early stopping during training to monitor the validation loss and restore the best weights when patience exceeds 20 epochs. 6 Hyperparameter Optimization Define a set of hyperparameter values for tuning (see Table 4.3). Use techniques such as grid search or random search to find the optimal hyperparameters with a maximum evaluation of 100 trials. Train the model using the optimal hyperparameter values. 7 Statistical Metrics Train the model on the training datasets. Evaluate the model on the validation and test datasets. Calculate statistical metrics such as Root Mean Squared Error (RMSE), R-squared, OI, etc. Print or store the metrics results for analysis and comparison. 108 4.5 Results and Discussion This chapter explains the development of an optimal pre-trained (source) ANN model architecture to get the best-learned network (weights). The ideal trained weights will then be repurposed (reused) in the random initialization (RI) ANN model to generate the target ANN model and predict daily water outputs. This part of the study will present a statistical comparison and performance analysis between the created random initialization ANN, the target ANN model, and the MLR model. 4.5.1 Optimization of pre-trained ANN model architecture The ANN and MLR regression models used to estimate distillate water outputs for both solar still configuration systems were covered in this study. The statistics of the pre-trained ANN model's performance with various hidden layer neuron/node numbers and activation functions are displayed in Table 4.3. Based on the network hyper-parameters / gradient descent optimization algorithm shown in Table 4.3, the optimum ANN architecture, 5-64-64-1, for the novel solar still was chosen through a rigorous optimization process using a trial-and-error method with a maximum evaluation of 100 trials aiming to balance between the model’s complexity and predictive accuracy. It was observed that the best neurons for the source ANN model's hidden layer were selected through trial and error (examined from 16 to 128 neurons) with a batch size ranging from 8 to 64. Each hidden layer's activation function varied and switched between sigmoid, ReLU, and Tanh. Despite the seemingly large number of parameters, our approach validated the model's generalization capabilities. Moreover, the empirical results confirmed that the chosen architecture 5-64-64-1 was optimal for the given data that minimized validation loss and enhanced predictive accuracy, and the use of techniques such as regularization and early stopping effectively mitigated overfitting. Although a higher number of 109 neurons, this configuration was the most effective at capturing our dataset's complexities and non-linear relationships. Additionally, the number of neurons in the hidden layers plays a crucial role in the model's capability to effectively learn from and generalize the data. While fewer neurons may simplify the model and reduce computational demands, they can also limit the model's ability to generalize and represent the underlying data patterns precisely. In our scenario, the architecture with 64 neurons in each hidden layer balanced model complexity and predictive performance, ensuring robust and accurate predictions. Certain literature presents empirical formulas to choose the number of neurons in neural network models. However, our study examined the number of neurons, ranging from 16 to 128, for forecasting distillate water productivity in solar stills using an ANN model. Instead of solely relying on existing empirical methods and guidelines, empirical assessment was carried out to optimize the architecture of the ANN model. This decision has been made after considering various factors. While empirical formulas provide a useful framework, they may not always generate the best configuration for a specific dataset. Fine-tuning the architecture of the ANN model through empirical testing can ensure that it fits the dataset's characteristics, leading to improved performance. The range of neurons from 16 to 128 has been selected to balance computational efficiency and model complexity, making it a widely preferred option. Fine-tuning the ANN within this range notably enhanced prediction accuracy and reliability as well as boosted learning and convergence efficiency. Several gradient descent methods optimizers, such as RMSprop, Adagrad, Adam, and SGD, have also been employed and tuned in the optimization process. Regularization strength, namely lambda, was also assessed between 0.001 and 0.1 to calibrate ANN models and to reduce the adjusted loss function; thus, avoid overfitting or underfitting (see Table 4.3). Trials were initiated 110 using 16 neurons in the input hidden layer as the starting point for optimizing the ANN base model architecture. It was noted that fixing the number of neurons to 64 resulted in a clear and remarkable improvement in the ANN model performance, particularly for the ReLU function. This transfer function provided the best network performance since R2, RMSE, MAE, ME, and OI values for the testing datasets were 0.996, 0.098, 0.074, 0.993, and 0.991, respectively. Figure 4.4 demonstrates the ReLU activation function graph and compares the denoising results of ReLU and PReLU activation functions in the pre-trained ANN model. It was observed that both transfer functions were very close in shape in terms of denoising capabilities, and the mean squared error, MSE values (ReLU = 0.0111 and PReLU = 0.0102) were similar, with the only difference being a slight slope for negative values in the PReLU curve. This behavior suggests that both activation functions performed similarly in fitting the training data and generalizing it to the validation data. Figure 4. 4 ReLU and PReLU activation functions graph. The optimization strategy primarily motivates the decision to utilize the ReLU activation function in our ANN model during training. By normalizing the input data to a range from -1 to 111 1, the ReLU function is optimized, leading to improved performance and model convergence speed. While the sigmoid transfer function is constrained to the interval [0,1], its efficacy was evaluated alongside other functions, including ReLU and Tanh, during the hyper-parameter optimization method. This examination helped us identify our regression task's optimal activation function. Ultimately, the ReLU function emerged as the most suitable choice for the dense layers of our ANN model due to its outstanding performance observed during training. It is essential to understand that in hyperparameter optimization, the output range of the activation functions does not necessarily have to match the normalization range of the input data. Irrespective of the activation functions being evaluated, it is advantageous to normalize the data in the training phase to a range from -1 to 1. In many practical applications, this slight difference may be insignificant. Moreover, ReLU is more computationally efficient than PReLU because it does not require additional learnable parameters, making it advantageous for resource-constrained environments. Its simplicity and robustness contribute to ReLU's viability as a reasonable option. It can be emphasized that the choice of activation is merely one component of the entire modeling pipeline, in which other factors, such as network architecture and hyperparameter tuning, also contribute to the overall performance. As shown in Table 4.3, the produced hyper-parameters optimization trials also revealed that having 16, 32, and 128 neurons with 4, 4, and 5 hidden layers, respectively, would harm ANN model performance with a more excellent loss value than one. Additionally, the ReLU function outperformed the Tanh function in most trials, with the smallest lambda (weight decay) value of 0.001 in predicting Pstd. Another hyper-parameter considered in the training process is the number of epochs, which specifies how often the learning algorithm will run 112 through the entire training dataset. Moreover, the learning rate values for the Adam optimizer and momentum were adjusted to maintain a constant value of 0.0003 and 0.99, respectively. Having too many epochs can result in an overfit model while having too few can lead to an underfitting of the training dataset. Consequently, an early stopping strategy, supported by a callback function, was considered while building the model that enables us to define an arbitrarily large number of training epochs (e.g., 500 epochs) and terminate training whenever the model performance on a holdout validation datasets halt improving. This technique can be accomplished by passing the validation dataset to the fit function during model training and allowing us to identify the performance indicator to monitor to stop training. The loss on the validation dataset will then be made available under the term "validation loss" with a minimum value. Stopping training at the first sign of no further improvement is usually not the most excellent option. The early stopping event while training the datasets may occur because the model may reach a plateau of little progress or perhaps slightly deteriorate before improving significantly. We may adjust for this possible behavior by adding a delay to the trigger based on how many epochs we want to observe no improvement. Adding delay to the trigger while fitting the ANN to the training set can be achieved by specifying the "patience" parameter with a value of 20 [116]. Table 4. 3 Hyperparameters optimization for source (pre-trained) ANN model in sequence from minimum to maximum loss. Trial number Hidden layer size No. hidden layers Activation function Batch size Optimizer Lambda (Weight decay) Loss 1 64 2 ReLU 8 Adam 0.001 0.000621 2 32 2 ReLU 8 Adam 0.001 0.00063 3 32 2 ReLU 8 Adam 0.001 0.000723 4 128 2 ReLU 16 Adam 0.001 0.000727 113 5 32 2 ReLU 16 Adam 0.001 0.000734 ... ... ... ... ... ... ... ... 96 32 2 ReLU 64 Adagrad 0.005 0.17612 97 64 5 ReLU 64 Adagrad 0.001 0.255997 98 32 4 ReLU 32 Adagrad 0.05 1.080505 99 16 4 Tanh 32 Adagrad 0.1 1.750207 100 128 5 Tanh 32 Adagrad 0.01 1.939331 Visualizing the performance of any ANN model is a simple approach to making sense of the data coming out of the model and creating a knowledgeable choice about the adjustments that need to be applied to the hyperparameters that influence the ANN model. It is vital to comprehend how to visualize data using the Matplotlib library and combine it with the ANN model to make an enlightened decision and enhance the ANN model. One of the main challenges of any ANN model is generalizing the model so that it can predict good results for new data and data that has already been trained. Figure 4.5 illustrates the average contribution of each input variable to the output within the optimal ANN model architecture. These values demonstrate the comparative significance of each input parameter in the training process of the developed RI ANN model. 114 Figure 4. 5 Average contribution values of input node variables on distillate water outputs Pstd, L/m2.day. Moreover, this analysis of contributions can provide insights into the relative importance of variables by identifying those with the highest contribution values relative to other inputs. Based on the conducted analyses, it was observed that the variable with the least significant impact is wind speed, with a contribution score of 0.04. On the other hand, relative humidity and feed water flow rate exhibit moderate effects on the predicted distillate water, with contribution scores of 0.061 and 0.075, respectively. The variables that indicate the most significant contributions to the distillate water output are solar radiation (0.135) and ambient temperature (0.122). These parameters are typically the most influential factors impacting the distillation process, primarily due to their involvement in the transfer of energy through radiant and convective mechanisms within the solar still system and their role as energy sources. The findings of this study are consistent with prior research [110] [111], which indicated that solar radiation and ambient temperature significantly affect the quality of treated water. 115 Visualizing the validation loss vs. training loss over the number of epochs (385, 235) for both the pre-trained and RI models, respectively, might help to decide whether the model has been appropriately trained. An ideal fit, as plotted in Figure 4.6, or a model that does neither overfit nor underfit, is specified when both the validation and training losses fall and stabilize at specific points. This approach is critical to avoid overfitting the ANN model and underfitting it to the point that it begins memorizing the training data, thus reducing its predictive accuracy [117]. Based on the learning curve analysis, the ANN model's performance appears balanced and does not exhibit clear signs of high variance, high bias, or overfitting. 1- Loss reduction: Both training and validation losses decrease as the number of epochs increases, indicating that the model is effectively learning from the data and improving its predictions. 2- Minimum plateau: Both training and validation losses reaching a minimum plateau suggest that the model has converted to a point where further training does not significantly reduce the losses. This behavior indicates that the model is not overfitting the training data. 3- Convergence of curves: Both curves meet and become steady as the number of epochs increases, indicating that the model's performance on both the validation and training sets has stabilized. This means the model has found a balance between fitting the training data and generalizing it to unseen data. 4- Absence of high variance or overfitting: Since the curves are steady and meet, there is no evident gap between training and validation losses, which suggests that overfitting is not a significant concern. Overfitting typically indicates a growing gap between training and validation losses as the model overlearns the training data. 116 5- Absence of underfitting or high bias: There is no indication of high bias either, which would manifest as both training and validation losses remaining high and not decreasing. High bias implies that the ANN model should be more complex to capture the underlying patterns in the datasets. Figure 4. 6 Training loss vs. validation loss over the number of epochs: (A) for the source (pre-trained) ANN model and (B) for the RI ANN model, showing both models are approaching zero loss and being optimized by the desired number of Epochs. Considering the optimal water distillates prediction and lowest error (the minimum RMSE, CRM, and MAE; and the largest R2, ME, and OI), the most appropriate ANN model was 5-64-64-1 with a ReLU activation function (bolded in Table 4.3). Figure 4.7 schematically illustrates the ideal generated source ANN model architecture 5-64-64-1. 117 Figure 4. 7 Optimal architecture of the developed source ANN model to predict distillate water. 4.5.2 Performance analysis of ANN RI and comparison with MLR Figure 4.8 shows multiple plots illustrating the comparison between the actual (observed) and predicted distillate water (Pstd, L/m2.day) values using source (pre-trained) ANN and MLR models during training, testing, and validation modeling processes with their obtained relative errors (residuals). The pre-trained ANN model, from which learned networks were transferred, was developed to apply transfer learning to the RI ANN model. The optimal learned weights (intelligence) were repurposed from the source model, and their hyper-parameters were fine-tuned to generate the target ANN model with more precise predictions of freshwater productivities. Across all modeling phases—training, validation, and testing—the pre-trained ANN model consistently outperformed the MLR model in terms of predictive accuracy and generalization capability. The ANN model, enhanced by transfer learning from a physics-based source model, demonstrated superior capacity to capture both linear and nonlinear relationships inherent in the data. This was evidenced by tighter clustering of predicted versus observed values around the 5-64-64-1 Architecture 118 ideal 1:1 reference line in scatter plots, indicating minimal deviation from actual values. On the other hand, the MLR model, while yielding high R² values due to the underlying linear trends in the dataset, showed comparatively larger deviations from the 1:1 line, especially during the testing phase. Furthermore, residual analysis revealed that the ANN model maintained consistent variance and lower error magnitudes across all data partitions, with no discernible patterns or bias, suggesting a well-generalized model. Meanwhile, the MLR model exhibited broader residual spreads and occasional systematic error patterns, particularly in the test set, underscoring its limited ability to capture the more complex interactions present in the system. These findings affirm the robustness and adaptability of the pre-trained ANN in modeling solar still behavior, justifying its selection as the core architecture in the proposed transfer learning framework. The source ANN model in this transfer learning framework was trained on a curated dataset comprising 730 samples, each generated from deterministic, physics-based equations implemented in MATLAB/Simulink. These equations simulate idealized operating conditions of the hybrid solar still by modeling mass and energy transfer mechanisms in a highly structured and repeatable manner. As a result, the input variables exhibit strong linear relationships with the water output variable. Additionally, daily aggregation of the data further smooths short-term fluctuations, reducing noise and reinforcing these correlations. To simulate a slightly more realistic scenario, controlled low-level noise was added without disrupting the physical consistency of the data. Consequently, both the pre-trained ANN and MLR models achieved exceptional predictive performance, with R² values exceeding 99%. This high R² is not only expected but essential, particularly in the context of transfer learning. The effectiveness of knowledge transfer depends on the fidelity of the source model. Transferring weights from a poorly trained or underperforming ANN would propagate inaccuracies to the target model 119 trained on the conventional solar still. Therefore, the high R² confirms that the source model accurately captures the physical behavior of the system and serves as a reliable foundation for downstream learning. Figure 4. 8 Comparison between observed vs. predicted distillate water values using source (pre-trained) ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation dataset. Table 4.4 summarizes the evaluation of pre-trained ANN and MLR models' performance during the training and validation modeling stages. The assessment criteria were based on the calculated 120 statistical errors for the applied ANN regression models to predict distillate water outputs. The results revealed that the source-trained model was more reliable for Pstd forecasting. In contrast, the MLR models predicted almost a similar pattern (superposition) for distillate water, suggesting that both models were valid to consider when predicting freshwater output values in single basin solar still systems. As shown in Figure 4.9, the source ANN and MLR models presented the highest possible model accuracy with minor root mean square errors. These remarkable outcomes indicate the reliability of these built ML models (optimal networks) to be utilized for transfer learning applications to precisely predict future datasets obtained from single-slope active or passive solar stills. Table 4. 4 Statistical parameters for assessing the performance of ANN and MLR models during training, testing, and validation stages. Statistical Parameters Testing Models Training Models Validation Models Pretrained ANN MLR Pretrained ANN MLR Pretrained ANN MLR R2 0.9960 0.9893 0.9971 0.9912 0.9963 0.9910 RMSE 0.0981 0.1285 0.1010 0.1171 0.0976 0.1047 MAE 0.0749 0.0846 0.0820 0.0933 0.0746 0.0805 CRM 0.0002 -0.0032 - 0.0024 0.0 0.0016 -0.0004 ME 0.9956 0.9810 0.9967 0.9908 0.9960 0.9907 OI 0.9912 0.9782 0.9923 0.9907 0.9912 0.9906 Note: R2: coefficient of determination, RMSE: root mean square error, MAE: mean absolute error, ME: model efficiency, OI: overall index of model performance. 121 Figure 4. 9 Evaluation of the performance of pre-trained ANN and MLR models during all modeling processes. Figure 4.10 compares the observed results, ANN, and MLR predictions for the training, testing, and validation datasets. The ANN prediction values for random initialization models were closer to the observed values than the MLR prediction values. The proportionate agreement between predicted and actual values evidences the predictive power and reliability of the built ANN model for predicting distillate water productivity Pstd, L/m2.day. Figure 4.10 (A) demonstrates that the values predicted by the developed random initialization (RI) ANN model fit precisely with the observed values during training. As shown in Table 4.5, some statistical analyses were employed to evaluate the overall performance of the ANN and MLR models. As revealed in Figure 4.10 (B), most of the values predicted by the ANN models were equally and tightly distributed around the 1:1 plotted line. The coefficient of determination, R2 (0.80) score for the RI ANN model, was partly close to one. The RI ANN model had an RMSE value of less than one (specifically, 0.743 L/m2.day), as presented in Table 4.5. Model efficiency, ME, and an overall index of model performance, OI-related values were 0.80 and 0.832, respectively, which draw near one. The coefficient of residual mass, CRM, was extremely near zero at - 0.0024 122 L/m2.day, but the mean absolute error, MAE, was somewhat diverged from zero at 0.607 L/m2.day. Furthermore, Figure 4.10 (B) illustrates that multiple points acquired by applying the MLR model during the training stage were positioned above and below the 1:1 slope line. Table 4.5 also presents the MLR statistical performance metrics. The created RI ANN model relatively outperformed the MLR's accuracy during the training phase, with an R2 value of 4% higher. The RMSE and MAE values were 0.5 and 0.43 times higher than their ANN model values. The OI value for the MLR model is reduced by roughly 1.8% compared to the value for the ANN model, and the ME value for the MLR model (0.771) was slightly far from one. The relative errors of the forecasted Pstd values using the RI ANN and MLR models are shown in 4.10 (C). Residuals were often in the proximity of 2% throughout the training process for the ANN model. In contrast, as stated in 4.10 (C), the MLR model's residuals were more significant than those using the RI ANN model, indicating that the developed RI ANN model was adequately accurate. Moreover, 4.10 (D) also indicates how the RI ANN and MLR models were employed to investigate the link between the observed and predicted distillate values during the testing process. As was the case during the training phase, the built ANN model outperformed the MLR model regarding the agreement between observed and predicted values. Most of the freshwater output values for the ANN model, as stated in 4.10 (E), followed the 1:1 line during the testing process. As a result, the predicted and observed values were relatively close. Table 4.5 shows the statistical parameters R2, ME, OI, RMSE, CRM, and MAE used to examine the agreement between the actual and predicted values by the ANN and MLR models using the testing datasets. During the testing process, the R2, ME, and OI values were near to one using the 123 established RI ANN model, demonstrating high agreement between the observed and predicted variables using the developed RI ANN model. On the other hand, the MLR model utilizing the testing datasets had R2, ME, and OI values of 2.3, 2, and 3.1 %, respectively, and hence was less accurate than the constructed RI ANN model. It can be seen from Table 3 that the values of RMSE, CRM, and MAE are high for the distillate water predicted by the MLR model and low for the Pstd forecasted by the RI ANN model. The created RI ANN model's RMSE (0.721 L/m2.day) was more than double that of the MLR model (0.750 L/m2.day). In comparison to the CRM value for the MLR model, the CRM value for the RI ANN model was closer to zero. Similarly, the CRM value for the MLR model was one time greater than that of the generated RI ANN model. The MAE value (0.602 L/m2.day) for the developed RI ANN model was about 1% lower than those from the MLR model (0.615 L/m2.day). The residuals during the testing process are plotted as illustrated in Figure 4.10 (F). With relative errors (90% of the values) largely falling between -1% and +1 %, the ANN RI model was closer to zero and can be utilized to predict Pstd. Nevertheless, using the MLR model, the residual values that fall within 1% imply less than 90% of the total error values during the testing process. Regarding the validation datasets, Figure 4.10 (G) compares the observed Pstd outputs, including ANN RI, forecasted results, and MLR prediction results. During the validation process for the established RI ANN model, Figure 4.10 (H) demonstrates that the distillate water typically followed a 1:1 line, suggesting a great match between actual and predicted values. As was the case during the training and testing processes, the constructed RI ANN model outperformed the 124 MLR model based on the agreement between observed and predicted data. R2 was close to 0.80 according to the ANN RI model prediction result. Table 4.5 displays that while the R2, ME, and OI values were comparatively close to one, the RMSE and MAE values were relatively low. The CRM value (-0.001) was also very near zero. The generated RI ANN model exhibited a higher R2 value than the MLR model, which was 4.7% less accurate. About 1.02 times as much RMSE was present in the MLR model (0.837 L/m2.day) compared to the ANN RI model. Furthermore, the developed RI ANN model had a ME value of approximately 5% more accurately than the MLR model. The MLR model's OI value (0.816) was not very close to one compared to the RI ANN model, with a value of 0.841. The MAE value of 0.728 for the MLR model rose by 97.02% from that of the RI ANN model. The validation datasets for both RI ANN and the MLR model's relative errors of the forecasted Pstd values are shown in Figure 4.10 (I), with an average relative error of 1.5 % for the MLR model when utilizing the validation datasets. This figure shows the discrepancies between the findings of the two models. It highlights the slight underestimation of the predicted distillate water. As evidence of the insignificant underestimation in the predicted distillates, the comparable value for the built RI ANN model was lower at 0.5% for the validation datasets. 125 Figure 4. 10 Comparison between observed vs. predicted distillate water values using RI ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation datasets. It is worth noting that when the plots illustrated in Figure 4.11 (A-I) were examined for the training, testing, and validation datasets using the transfer learning method, the predicted distillate water results using the developed target ANN model appeared too close to the observed values. The target ANN model was generated by repurposing the transferred learned weights from the source ANN model. In corresponding to the built target ANN model, the results obtained using the RI ANN and MLR models revealed a more significant deviation from the 126 actual values for all modeling processes. Based on the preceding, it was possible to conclude that the generated target ANN model was precisely trained and presented consistency in predicting freshwater productivity. Figure 4. 11 Comparison between observed vs. predicted distillate water values using target ANN and MLR models during modeling stages with their acquired residuals: (A-C) from training datasets; (D-F) from testing datasets; (G-I) from validation datasets. Likewise, it provided better predictions using the same statistical performance indicators, as demonstrated in Table 4.5, with 0.832 ME and RMSE value of 0.618, than the RI ANN model, 127 which scored a higher value with an increment of 0.103. These findings strengthen the reliability of the developed ANN models, particularly for ANN as a promising target model. Moreover, it was verified that the developed latter model effectively forecasted Pstd without requiring further experimental work, which consumes more time and involves higher expenses. To sum it up, the target ANN model performed much better than both RI ANN and MLR models during all modeling phases, namely training, testing, and validation sets. The evaluation criteria were in terms of OI with a unique value (0.872) relatively close to 90% compared to RI ANN and MLR models, which attained less overall performance with reduced values of 0.834 and 0.803, respectively. It was observed that the prime criteria for assessing the performance of the developed ANN and MLR models were during testing datasets based on statistical analysis results, as presented in Figure 4.12 Moreover, these outcomes for treated water predictions were comparatively in conformity with the studies of [118]. It is worth mentioning that the current study involved a comparative analysis of the performance of ANN and MLR models. This comparison is important for several reasons. Firstly, it serves as a foundational benchmark to assess the improvements offered by ANNs. While ANNs are known for their advanced predictive capabilities, particularly in capturing non-linear data relationships, MLR provides a simpler, more traditional model for comparison. Secondly, the analysis demonstrates the advantages of using more complex models like ANN in practical scenarios, such as solar desalination. By showcasing the superior performance of ANN over MLR, the study highlights the effectiveness of ANNs in addressing the inherent complexities of the dataset. Lastly, the inclusion of MLR in the study enhances the reliability and robustness of the findings, ensuring that the observed improvements with ANN are substantive and well-supported. This 128 comprehensive approach contributes to a more nuanced understanding of the value of ANNs in predictive modeling tasks related to solar desalination applications. H. A. Maddah et al. [84] developed precise supervised machine-learning regressions to generate trained models based on experimental outcomes. The suggested methodology aims to enhance the precision of prediction models by employing dimensional analysis and expanding datasets through in-between randomization. The constructed models were utilized to forecast the thermal efficiency (ηth) when substituting polystyrene with an alternative wall insulation material. The water glass difference temperature (Tw–Tg) and evaporative heat transfer coefficients (hewg) were correlated with the solar still outputs using the stepwise linear regression (SLR) method, which yielded minimal statistical errors (R2 = 1) and a root mean square error (RMSE) value < 0.016. Another comparable state-of-the-art study by M. Safa et al. [118]was focused on investigating irrigated and dryland wheat fields in Canterbury. The research involved comprehensive data collection methods. The study aimed to identify several direct and indirect parameters contributing to developing an ANN model for forecasting energy consumption in wheat production. The ultimate model could forecast energy consumption by considering various factors such as the size of the crop area, farmers' social considerations, and energy inputs. This model revealed a predictive accuracy for energy usage, with a margin of error of ±12% (equivalent to ±2900 MJ/ha). Moreover, a comparative analysis between the ANN model and the MLR model showed that the ANN model has superior predictive capabilities for energy consumption compared to the MLR model, specifically within the designated training and validation datasets. The ultimate ANN model can forecast energy consumption by considering various factors such as farm conditions, farmers' social considerations, and energy inputs. This model exhibited a margin of error of 129 ±2900 MJ/ha when predicting energy usage. Comparatively, the ANN model demonstrates superior predictive accuracy in estimating energy consumption compared to the MLR model. Figure 4.13 displays an illustrative residual histogram of the ANN models employed in the context of the conventional solar still. The study's findings indicate that the ANN modeling can yield test results wherein approximately 80% and 85% of the predictions fall within a 20% to 25% deviation from the actual value for the RI ANN and target ANN models, respectively. The average standard deviations for the relative errors of the optimal ANN predictions for distillate water were 0.46 and 0.50 for the RI ANN and target ANN models, respectively. The residual plots consistently exhibited a minor rightward skew, suggesting a slightly elevated occurrence of overestimations. Table 4. 5 Statistical parameters for assessing the performance of ANN and MLR models during training, testing, and validation stages. Statistical Parameters Testing Models Training Models Validation Models ANN-RI ANN-TL MLR ANN-RI ANN-TL MLR ANN-RI ANN-TL MLR R2 0.803 0.835 0.786 0.801 0.831 0.761 0.797 0.816 0.748 RMSE 0.721 0.618 0.750 0.743 0.622 0.783 0.822 0.708 0.837 MAE 0.602 0.523 0.615 0.607 0.545 0.649 0.685 0.575 0.728 CRM -0.035 -0.001 -0.034 - 0.0024 -0.002 -1.228 -0.001 -0.0026 -0.068 ME 0.801 0.832 0.782 0.798 0.831 0.771 0.795 0.813 0.746 OI 0.834 0.872 0.803 0.832 0.871 0.814 0.841 0.851 0.816 Note: R2: coefficient of determination, RMSE: root mean square error, MAE: mean absolute error, ME: model efficiency, OI: overall index of model performance. 130 Figure 4. 12 Evaluation of ANN and MLR models' performance during the testing modeling process. Figure 4. 13 A histogram comparison of deviations between predicted and actual values for the RI ANN model vs. the target ANN model. 131 4.6 Conclusion This research paves the way towards creating novel statistical tools for developing precisely accurate predictive supervised ANN models for freshwater productivity in conventional single slope solar stills using the transfer learning method. Due to the significant capital costs associated with solar distillation, which include the cost of land and equipment, the use of solar still technology for saltwater water desalination would demand an optimization process. Therefore, for the entire process to successfully optimize expenses and enhance water production, precise forecasting of the solar still's predicted productivity remains essential. An ANN model was presented in this study to forecast the water productivity (Pstd, L/m2.day) of solar still desalinating saline water. The primary objective of this work was to apply the transfer learning technique to the RI ANN model for conventional solar still. This method can be achieved by employing the best-learned weights acquired from the developed source ANN model to ultimately generate the optimum ANN model that has the potential to outperform the training ANN model from scratch. The generated ANN was studied and emphasized as a promising target model compared to the created RI and MLR models. The pre-trained ANN model was established from which learned weights (intelligence) were transferred. Several neural network architectures were trained with varying numbers of neurons in the hidden layers. Their hyper-parameters were tuned using the trial-and-error technique to determine which source ANN model offered the best performance and ensure the selection of the best-learned network. The chosen ideal pre-trained ANN model had a 5-64-64-1 architecture with a ReLU transfer function. A feed-forward back-propagation algorithm was utilized to build ANN models, and their applicability for Pstd prediction was investigated. 132 The transfer learning method predominantly enhances the predictive performance of neural networks, which enables the model to begin with a more informed state rather than learning from scratch. This approach is achieved by leveraging a pre-trained model to perform similar tasks. This method more effectively captures complex patterns and relationships in the selected variables. Furthermore, transfer learning frequently results in improved generalization and faster convergence, particularly when the training datasets are limited. Conversely, the inherent distinctions in the capabilities of the transfer learning-enhanced ANN models over MLR can be attributed to their superiority. The linear nature of MLR renders it incapable of capturing non-linear relationships and interactions between input variables, which neural networks, particularly those with transfer learning, can efficiently model. Therefore, ANN can make more precise predictions in complex scenarios like solar desalination systems It was concluded that when employing the transfer learning method, the target ANN model outperformed the RI ANN and MLR models in all phases of the modeling process, including training, testing, and validation, based on the highest recorded OI of 0.872 and lowest RMSE of 0.618 respectively. These findings suggest that the optimal target ANN model may be employed effectively in diverse solar still configuration systems, which desalinates brackish water, to forecast distillate water productions after the solar desalination process. The results also confirmed the developed ANN model's accuracy and generalization capability. Finally, a major contribution of this research implicates an evaluation of the ANN modeling techniques during the saltwater solar desalination process, which adds a new perception and guides us towards tunning key parameters correlated to some design aspects, such as solar still surface area and glass cover area, heat transfer energies, including evaporative, radiative, and convective 133 coefficients, to maximize purified water productions in various configurations of solar still desalination systems. The previous chapter demonstrated the utility of transfer learning for improving the generalization and predictive power of supervised ANN models applied to solar desalination systems. By leveraging pre-trained models developed on hybrid still configurations, the transfer learning approach significantly reduced forecast errors for freshwater productivity across diverse datasets. However, despite the improvements in model accuracy, the overall performance of deep learning frameworks can still be hindered by limited data availability—an inherent constraint in solar still experiments. To address this challenge, the next chapter introduces a novel data augmentation methodology integrated within a CNN-1D framework. This strategy aims to synthetically expand training datasets while maintaining temporal coherence, ultimately enhancing the learning capacity and robustness of deep models for solar still productivity prediction. 134 Chapter 5: Advancing Predictive Modeling in Conventional Solar Stills: A Deep Learning Approach Leveraging Data Augmentation and Convolutional Neural Networks 5.1 Motivations Accurate prediction of freshwater productivity from solar stills is critical for optimizing design and improving the economic viability of solar desalination technologies, especially in data-scarce environments. This chapter presents a comprehensive modeling approach that incorporates data augmentation into a CNN-1D deep learning framework to mitigate the limitations imposed by small datasets. A Gaussian noise-based jittering technique is applied to sequential input features within a defined look-back window, enabling the generation of additional training samples without compromising temporal dependencies. The proposed CNN-1D architecture is carefully optimized and benchmarked against a conventional support vector regression (SVR) model to assess its accuracy and generalizability. By doing so, this chapter highlights the transformative role of data augmentation in enabling more robust, scalable, and high-performing predictive models for solar desalination applications. 5.2 Introduction The escalating global water crisis, intrinsically linked to climate shifts and unsustainable resource management practices, poses a significant threat to ecological integrity, food security, and socioeconomic development in the 21st century [63]. With the world's population projected to reach 9.7 billion by 2050, the demand for freshwater is expected to surge by over 55%, exacerbating the existing pressure on already strained water resources [119]. Over 2.2 billion people globally lack access to safely managed drinking water services, while nearly 4 billion experience severe water scarcity for at least one month annually [120]. The available freshwater 135 constitutes only about 2.5% of global water resources, with less than 1% readily accessible for human consumption [121]. This predicament is particularly acute in arid and semi-arid regions, such as substantial portions of the Middle East and North Africa (MENA). In response, these regions are pioneering ambitious initiatives. For instance, Saudi Arabia's NEOM project aims to become a paradigm of sustainable living by developing advanced, large-scale water solutions predominantly powered by renewable energy sources, thereby establishing new benchmarks for efficiency and environmental stewardship in water production [122]. To mitigate the freshwater deficit, various desalination technologies have been developed and widely implemented worldwide. The most established methodologies for large-scale applications include Multi-Stage Flash (MSF) distillation, Multi-Effect Distillation (MED), and Seawater Reverse Osmosis (SWRO) [123]. MSF and MED, as mature thermal processes, have historically exhibited high energy consumption. The specific energy consumption (SEC) for older MSF desalination plants typically ranges from 10 to 16 kWh/m³. In contrast, modern MED plants, particularly those equipped with waste heat recovery systems, consume approximately 2.5 to 5 kWh/m³ of electrical energy or 60 to 70 kWh/m³ of thermal energy [124]. Older thermal facilities can have a considerable carbon footprint, with CO₂ emissions exceeding 10 to 15 kg CO₂ equivalent per cubic meter of water produced [125]. SWRO offers a more energy-efficient alternative, operating at less than 3 kWh/m³ and achieving a 50-70% decrease in energy consumption compared to older methods. However, SWRO encounters challenges such as extensive pre-treatment, issues with membrane fouling, and environmental concerns related to brine discharge. While innovations like energy recovery devices have enhanced efficiency, global energy demand for desalination continues to rise, underscoring the need for further advancements in sustainable water purification technologies [126] [127]. 136 In this framework, solar distillation, which harnesses solar irradiance to purify water, represents a compelling and environmentally sustainable alternative, particularly in regions abundant in solar resources [128]. Technologies like single-slope solar stills are noteworthy for their operational simplicity, low capital and maintenance costs, and inherent suitability for decentralized, off-grid water production in remote or resource-limited communities [129]. Despite these advantages, a primary obstacle to their widespread adoption is their relatively modest freshwater productivity, which typically ranges from 2 to 5 L/m². day under average climatic conditions [130]. This output, while valuable for specific applications, contrasts sharply with the notable throughput capacities of conventional desalination plants. Therefore, enhancing solar stills' efficiency and predictive management is essential to augmenting their contribution to sustainable freshwater generation, rendering them a more viable component within diverse and resilient water security frameworks. Researchers have explored various experimental modifications to enhance the performance of solar stills. Hammoodi et al. [131] conducted a study on the performance of pyramid solar stills enhanced with wick and reflective materials under the climatic conditions of Iraq. Incorporating wick materials increased evaporation and heat absorption, resulting in a remarkable 122% productivity boost and achieving a thermal efficiency of 53%. Introducing reflectors also augmented productivity by 170%, although the efficiency remained constant at 48%. Mohammed et al. investigated the use of phase change materials (PCMs) to enhance the productivity of a single-slope solar still in Qena. The study assessed the energy storage behavior of RT42 PCM placed inside the basin area in quantities of 2 kg, 4 kg, and 6 kg to improve performance during both day and night. The findings indicated that the configuration with 4 kg of PCM outperformed the other setups, resulting in productivity increases of approximately 137 18.6% compared to the 2 kg configuration and 27.7% compared to the 6 kg configuration. Additionally, this configuration achieved an average daily efficiency of 66.7%, representing a 29.7% improvement in freshwater yield over a conventional solar still without PCM. Using PCMs raised the basin water temperature and supported increased water production during nighttime due to enhanced thermal energy storage. The produced water met acceptable quality parameters, making it suitable for domestic applications [132]. Machine learning (ML) integration has introduced new possibilities for modeling, performance prediction, and real-time control of solar stills. Wang et al. developed and evaluated machine learning models to accurately predict the hourly production performance of tubular solar stills using experimental data. The models compared included artificial neural networks (ANN) and random forests (RF), both with and without Bayesian optimization, in addition to traditional multilinear regression. Before optimization, the RF model outperformed the ANN and multilinear regression, achieving a coefficient of determination (R²) of 0.9758 and a mean absolute percentage error (MAPE) of 5.21%. In contrast, the ANN and multilinear regression recorded R² values of 0.9614 and 0.9267, respectively, with MAPE values of 7.697% and 10.911%. Notably, applying Bayesian optimization significantly improved the prediction accuracy of the ANN by 35%. However, the RF model demonstrated superior robustness and less sensitivity to hyperparameter tuning. Overall, the study concluded that the RF model, owing to its accuracy and stability, is a highly effective and practical tool for forecasting the performance of tubular solar stills [133]. Ghandourah et al. investigated the thermal performance of two solar still designs, utilizing a hybrid artificial intelligence model optimized via the Golden Jackal Optimizer (GJO). The study compared an aluminum-based solar still (ALSS) with a polycarbonate-based solar still (PCSS), 138 which included modified absorber plates featuring air cavities. The proposed ANN-GJO model demonstrated superior performance in predicting overall heat transfer coefficients, energy efficiency, exergy efficiency, and distillate yield compared to conventional ANN, ANN-GA, and ANN-PSO models. Experimental results revealed that ALSS performed exceptionally well, achieving a maximum distillate output of 3.80 L/m²/day and an energy efficiency of 48.8%, in contrast to PCSS, which produced 3.40 L/m²/day and had an energy efficiency of 42.4%. These findings underscore the effectiveness of ANN-GJO in thermal modeling and confirm that the choice of material has a significant impact on solar still productivity [96]. Recent advancements in solar desalination technologies have increasingly focused on hybridization and intelligent modeling approaches to overcome the intrinsic limitations of conventional systems. Shoeibi et al. explored the enhancement of solar still performance by integrating porous media, nano-enhanced phase change materials (NEPCMs), and nano-coated absorbers. Their system utilized anthracite as a porous medium to enhance solar absorption, while paraffin wax infused with CuO and Al₂O₃ nanoparticles (at concentrations of 0.1% and 0.3% by weight) served as the NEPCM to improve thermal energy storage. These NEPCMs were situated within copper pipes above the anthracite layer, which were further coated with CuO-dispersed black paint to enhance thermal conductivity. The study revealed that the NEPCMs with 0.3% CuO and Al₂O₃ increased freshwater productivity by 55.8% and 49.5%, respectively. Additionally, including nano-coated pipes alone contributed to a 5.7% increase in productivity. Moreover, the incorporation of CuO and Al₂O₃ nanoparticles effectively lowered the melting point of the PCM by 2.1 °C and 1.8 °C, respectively, thereby enhancing its thermal responsiveness. The cost per liter (CPL) for distilled water was reduced to $0.10 and $0.104, confirming the economic viability of these enhancements. These findings highlight the 139 significant impact of improved thermal conductivity, enhanced latent heat storage, and optimized absorption on the efficiency and cost-effectiveness of solar stills [134]. Collectively, these studies highlight the potential of combining experimental enhancements and machine learning techniques, mainly when guided by evolutionary optimization algorithms, to maximize freshwater productivity, enhance modeling reliability, and improve operational efficiency in solar still systems. This body of research underscores the need for advanced predictive modeling techniques to address the shortcomings of conventional solar stills. In this context, the present study introduces a one-dimensional convolutional neural network (CNN-1D) model, augmented with Gaussian noise-based time series data expansion, to enhance forecasting accuracy under limited data conditions. The proposed model, trained on key meteorological variables and feed water flow, aims to surpass traditional nonlinear regression methods in predictive precision and generalization, thereby facilitating intelligent design and operational planning for solar desalination systems. This research study highlights multiple novel and significant contributions: ▪ This research presents a novel integration of Gaussian noise-based data augmentation (jittering) with CNN-1D and SVR models, significantly enhancing prediction accuracy for freshwater productivity in solar stills. This methodology effectively addresses data scarcity, improving model robustness and generalization compared to conventional techniques. ▪ Comprehensive hyperparameter tuning resulted in the meticulous development of an optimized CNN-1D model with the 5-(128)3-1 architecture. This carefully structured model effectively captures the spatial and temporal patterns inherent in solar still data, leading to significantly improved prediction accuracy compared to baseline models. 140 ▪ The study extensively benchmarks the augmented CNN and SVR models against their baseline counterparts, clearly demonstrating the superior performance of the augmented CNN-1D model across several key statistical metrics. This thorough validation underscores the practical advantages and enhances predictive accuracy achieved through data augmentation. ▪ A pioneering threshold-based classification method was introduced to reliably categorize freshwater outputs based on meaningful productivity thresholds. This technique mitigates the influence of outliers, providing enhanced interpretability and stability compared to traditional quartile-based approaches. ▪ The research presents practical insights with immediate relevance to real-world solar desalination systems. By illustrating the clear benefits of merging data augmentation with CNN-1D modeling, this study lays the groundwork for cost-effective and reliable forecasting in solar desalination technologies, potentially shaping future developments toward sustainability. The subsequent sections of this chapter are structured as follows. Section 5.3 outlines the proposed data augmentation framework, along with the equations incorporated into the CNN-1D and SVR models, emphasizing essential elements such as time-series processing, model architecture, and hyperparameter tuning. Section 5.4 provides a comprehensive description of the implementation procedures, model evaluation, and a comparative analysis of the augmented and baseline models. In section 5.5, we explore recent advancements and insights, address existing challenges, and conduct performance analysis within the field. Finally, this chapter culminates with a discussion of closing remarks in section 5.6, exploring potential avenues for future research. 141 5.3 Methodology and Framework In this study, we established a novel framework for modeling and predicting the freshwater productivity of a conventional single-slope solar still unit using a one-dimensional Convolutional Neural Network (CNN-1D). The performance of the baseline CNN-1D model, trained on the original un-augmented dataset, was assessed using various statistical metrics. Then, it was compared to the performance of the augmented CNN-1D model that benefited from augmented datasets through a noise-based data augmentation technique known as jittering. The latter model leveraged the increased diversity and robustness of the augmented dataset, resulting in improved prediction accuracy. The preprocessing step involved transforming the conventional solar still dataset into time series data using a seven-day look-back window. The data was then split into training, validation, and testing sets while maintaining consistent scaling. The augmentation process was then applied to the training data only by introducing random Gaussian noise to the input features, generating multiple variations of each training sample. Moreover, the Support Vector Regression (SVR) was employed as a benchmark to compare the predictive performance of both the baseline and augmented CNN-1D models. We analyzed the impact of data augmentation on predictive accuracy by evaluating statistical metrics across these models. This study investigates the predictive capabilities of the CNN-1D architecture in estimating freshwater productivity by analyzing time-series data derived from a solar still system. Notably, this investigation deliberately omits a focus on the physical or geometric characteristics of the system. 5.3.1 Developing Baseline CNN-1D model To assess the long-term performance of the conventional single-slope solar still, a total of 365 numerical continuous datasets were manually extracted from previous experimental findings 142 documented in the literature, specifically those conducted by Santos[135]. The compiled datasets encompassed direct measurements of feed water volumes and daily average distillate production, recorded between February 2006 and August 2007, using a rectangular basin still with an area of 0.976 m² [66]. Data accompanied these datasets corresponding to daily meteorological conditions, including solar incidents obtained from NASA power webs[109], which served as input variables. A baseline one-dimensional Convolutional Neural Network (CNN-1D) model was developed with feed water volumes and daily average weather data as inputs. At the same time, the total freshwater production was designated as the output variable (Pstd, L/day). The earlier study [107] aimed to predict the distillate production of single-basin solar stills, considering various physical properties of both the feed water and the distillate; for instance, key factors such as density and specific heat capacity were dependent on feed salinity and initial water temperature, as these elements are crucial for evaluating the water safety criteria necessary for safe human consumption[66]. To develop the baseline CNN-1D model, the original dataset, which comprised 365 samples with five input features and one output related to freshwater productivity, was transformed/reshaped into a time series format using a look-back window of 7. This transformation yielded a structured dataset suitable for time-series forecasting. The data was then divided into training (70%), testing (20%), and validation (10%) sets using a hold-out strategy with a fixed random state of 42 to ensure reproducibility. The baseline CNN-1D model was trained solely on the original dataset, omitting any augmentation. The resulting input data matrix had a shape of [359 × 7 × 5], derived from applying a look-back window of size seven across the 365-day sequence. As shown in Table 5.2, the target output was formatted as a [359 × 1] vector, representing the daily freshwater 143 yield. The training set was scaled to normalize the feature values, and the same scaling parameters were applied to the validation and testing sets to maintain consistency. A series of rounds involving random selection and partitioning was conducted to enhance the generalizability and robustness of our findings. This process was repeated ten times to minimize potential biases associated with a single partitioning. Following each iteration, we performed separate training and evaluation for the models, and the results from these iterations were averaged to provide a comprehensive assessment of the models' effectiveness. This methodology enhances reliability by considering the variations in data splits. In the training phase, the CNN-1D was trained to predict an output, precisely, distilled water in a conventional single-slope solar still system. During the validation phase, the model's performance on unseen data was assessed to monitor for overfitting and to ensure its generalizability. The testing phase involved evaluating the model's capability to forecast a single output value (Pstd, L/day), which facilitated the evaluation of the model’s validity and reliability and helped determine whether training should continue or be halted. Our analysis employed a supervised machine learning approach, specifically the CNN-1D model. We compared this model against a Support Vector Regressor (SVR) using labeled datasets throughout the training, testing, and validation phases. This comparison aimed to identify the optimal modeling approach for superior prediction outcomes. The CNN-1D and SVR models were constructed using a hold-out strategy that involved 42 random states, which regulated the shuffling process during the train-test split. The baseline CNN-1D model was developed using a Colab notebook and Python software, employing the widely utilized feed-forward/backpropagation algorithm. 144 Solar stills experience various energy gains and losses influenced by specific weather variables. Our study used the recorded daily operational feed water volume as input for the CNN-1D model. The feed water flow rate was included in the analysis due to its relationship with the constant factor of the basin area. Users typically reference the feed water volume when determining the necessary amounts for flushing and operating solar stills. It is essential to highlight that these input parameters were selected due to their significant impact on solar still performance and their effectiveness in accurately predicting freshwater productivity. It was decided to exclude the inlet water temperature for several reasons. The inlet temperature of the basin exhibited a consistently stable pattern, resulting in minimal fluctuations. Preliminary investigations indicated that this parameter did not significantly enhance the model's predictive accuracy concerning water productivity. Incorporating it would complicate the model without providing substantial advantages. Therefore, we focused on the five most influential operational variables to optimize the model, thereby enhancing its efficiency and interpretability. Throughout the model training process, several pivotal decisions were made to enhance the efficacy of the CNN-1D. A total of 50 iterations were selected, employing a batch size of 8 samples, which was determined to be optimal through rigorous hyperparameter tuning. The Adam optimizer was implemented, with a regularization strength of 0.1 and a learning rate of 0.0001, to promote robust training while mitigating the risk of overfitting. To further enhance the model's generalization capabilities, early stopping was employed, incorporating a patience value of 20; this mechanism halted training if no improvement in validation loss was observed over 20 consecutive epochs. It is pertinent to define an epoch as a complete pass of the entire dataset through the convolutional neural network, encapsulating both forward and backward propagation processes. 145 This systematic methodology for dataset preparation and model training underlines the development of a reliable and accurate CNN-1D model tailored for predicting the performance of solar stills. Furthermore, Table 5.1 elucidates the sources of input and output parameter data relevant to both configurations of solar still systems, thereby providing a comprehensive framework for understanding the variables involved in this study. Table 5. 1 Description of the input and output parameters for modeling the baseline conventional single-slope solar still system and their respective data sources. The input parameters include key meteorological variables from the NASA Power database and the operational input of saline water feed flow rate obtained from literature and experimental datasets. The output parameter, representing solar still productivity in terms of daily freshwater yield (L/day), was also derived from validated experimental studies. Solar Still Design Configurations Input Parameters Data Source Output Parameters Data Source Conventional Single-Slope Solar Still System (Baseline model) Meteorological Conditions: Solar radiation, MJ/m2.day Ambient temperature, oC Wind speed, m/s Relative humidity, % NASA Power [110]. Solar still productivity Water distillate (L/day). Literature/ experimental datasets [107]. Operational Variable: Saline water feed flowrate, L/day. Literature/ experimental datasets [66]. 5.3.2 Criteria of evaluation for the Augmented CNN-1D model In this study, the predictive performance of an augmented CNN-1D model was investigated to forecast the distillate water productivity of a conventional solar still. The augmentation process 146 was applied exclusively to the training dataset to enhance model robustness by introducing variability in the input features. This approach ensured the integrity of the validation and testing datasets, enabling an unbiased assessment of the model's predictive capabilities. The dataset, comprising numerical continuous values, was preprocessed to separate the input features—solar radiation, ambient temperature, wind speed, relative humidity, and feedwater flow rate—from the target output, distillate water productivity. Subsequently, the data was transformed/reshaped into a time-series format using a look-back window of 7, which was determined as optimal through iterative experiments during preprocessing using Python code. This configuration effectively captured the temporal dependencies critical for accurate modeling. To ensure a reliable evaluation of performance and prevent data leakage, the data augmentation process—specifically, the injection of Gaussian noise—was applied exclusively to the training set. This strategy enhances the model's generalization by introducing additional variability during training, enabling the model to learn stronger and more resilient representations. Notably, the ground truth labels corresponding to the training samples, denoted as ?̃?train[i, j], were preserved without modification throughout the augmentation process to maintain accurate supervision. Meanwhile, both validation and testing sets were intentionally excluded from augmentation, preserving their integrity as unbiased benchmarks. Altering these sets could lead to artificially inflated performance metrics by exposing the model to synthetic patterns that it might encounter during training. Therefore, restricting augmentation to the training phase upholds methodological rigor and supports a valid assessment of the model's true predictive capabilities. For the augmented CNN-1D model, the training dataset, representing 70% of the curated data, was expanded by generating six additional augmented samples for each original instance through 147 a jittering process. To enhance model generalization and address data scarcity, Gaussian noise statistically defined as 𝒩(0, 𝜎2), was systematically injected into the input features during the augmentation phase. As illustrated in Table 5.2, this process generated 1506 synthetic raining samples, each with a dimensionality of [7 × 5], representing seven consecutive days and five input variables. These augmented samples were subsequently concatenated with the original 251 unaltered sequences, yielding a total input training dataset of shape [1757 × 7 × 5]. Correspondingly, the output vector comprising the distillate water productivity values was structured as a [1865 × 1] matrix, inclusive of both augmented and non-augmented labels. Each dataset instance was further structured into time-series submatrices of dimensions [7 × 6], wherein each row captured the temporal progression of six key parameters. The selection of the look-back window (7 days) and the augmentation factor (sixfold increase applied to the training set) was guided by preprocessing experiments and empirical evaluations, aiming to maximize the model’s ability to capture short-term dependencies in continuous numerical datasets. It is worth mentioning that the selection of the look-back window size (7 days) and the number of augmentations per training instance (6) was established through extensive empirical experimentation. Multiple trials were conducted to evaluate various window lengths and augmentation scales, with performance assessed using validation metrics such as RMSE and R². A 7-day look-back window was ultimately chosen, as it consistently captured the temporal dependencies in the daily freshwater productivity data without introducing excessive redundancy or overfitting. Similarly, generating six Gaussian noise-augmented samples for each original training point provided a significant increase in data diversity, thereby enhancing model generalization while maintaining computational efficiency. Consequently, these hyperparameters were adopted as the optimal configuration for all augmented models in this study. 148 The CNN-1D model architecture was refined using hyperparameter optimization. This process adjusted critical parameters such as the number of convolutional layers, dense units, kernel size, batch size, learning rate, and regularization strength to achieve optimal predictive performance. Early stopping with a patience threshold of 20 epochs was implemented during training to prevent overfitting. While the training data was augmented to improve learning diversity, the validation dataset (10% of the curated data) and the testing dataset (20%) were left unaltered to ensure unbiased evaluation. The testing dataset was used to predict known freshwater productivity values to verify accuracy, while the validation dataset was used to monitor generalization performance. The augmented CNN-1D model was assessed using statistical metrics, including the coefficient of determination (𝑅2), root mean square error (RMSE), mean absolute error (MAE), coefficient of variation (CV), efficiency coefficient (EC), overall index of model performance (OIMP), and residual as defined in Equations (5.1–5.7) [29] [111]. Additionally, the predictive performance of the CNN-1D model was benchmarked against an SVR model using identical datasets and evaluation criteria, demonstrating the advantages of data augmentation in enhancing accuracy and robustness. 𝑅2 = 1 −∑ (𝒴𝑜,𝑖 − 𝒴𝑝,𝑖)2𝑛𝑖=0∑ (𝒴𝑜,𝑖 − ?̅?𝑜)2 𝑛𝑖=0 (5.1) 𝑅𝑀𝑆𝐸 = √1𝑛∑ (𝒴𝑜,𝑖 − 𝒴𝑝,𝑖)2𝑛𝑖=0 (5.2) 𝑀𝐴𝐸 =1𝑛∑ |𝒴𝑜,𝑖 − 𝒴𝑝,𝑖|𝑛𝑖=0 (5.27) 149 𝐶𝑉 =𝑅𝑀𝑆𝐸?̅?𝑜 × 100 (5.4) 𝐸𝐶 = 1 − ∑ (𝒴𝑜,𝑖 − 𝒴𝑝,𝑖)𝑛𝑖=02∑ (𝒴𝑜,𝑖 − ?̅?𝑜)2 𝑛𝑖=0 (5.5) 𝑂𝐼𝑀𝑃 = 1 − (𝑅𝑀𝑆𝐸 𝒴𝑚𝑎𝑥 − 𝒴𝑚𝑖𝑛 ) ∙ (1 − 𝐸𝐶) (5.6) 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 = 𝒴𝑜,𝑖 − 𝒴𝑝,𝑖 (5.7) Knowing that the observed value is represented as 𝒴𝑜,𝑖 the predicted value generated by the machine learning models is denoted as 𝒴𝑝,𝑖. The average observed value is indicated by ?̅?𝑜, and the average predicted value, obtained through theoretical estimation, is referred to as ?̅?𝑝. The minimum and maximum observed values denoted as 𝒴𝑚𝑖𝑛 and 𝒴𝑚𝑎𝑥 , respectively, and 𝑛 represents the number of observations or dataset size. Lower values of RMSE and MAE signify more accurate predictions, as both metrics range from 0 to ∞. In contrast, a higher 𝑅2 value indicates a more remarkable similarity between the trendlines of the observed and predicted samples, achieving an identical pattern when 𝑅2 = 1 [134]. A perfect fit between observed and forecasted results occurs when the EC value equals 1. Conversely, an EC value of zero indicates that a mean value would yield the same level of accuracy [85] [113]. The latter metric can sometimes even result in a negative value (−∞) if the mean observed value ?̅?𝑜 is a better predictor than the simulated value, indicating unacceptable performance and extremely poor model predictions. The OIMP value 1 denotes an optimal fit between observed and predicted outputs. The RMSE values should ideally be close to ±1, while better model accuracy is achieved when the RMSE value approaches zero. For effective data 150 modeling, the RMSE, MAE, and CV measures derived from the different trained models should be as close to zero as possible. Simultaneously, metrics such as R², EC, and OIMP should converge towards one, indicating improved performance [114]. A CV, expressed as a percentage, serves as a normalized measure of data dispersion, representing the variability of the prediction error relative to the average observed value ?̅?𝑜. Lower CV values (closer to 0%) reflect less mean variability, which is advantageous for achieving accurate predictions [115]. Figure 5.1 presents a flow chart depicting the selection and development process of the augmented CNN-1D model, specifically designed to predict distillate water productivity precisely, denoted as Pstd. Using the statistical metrics expressed in equations (5.1-5.7), the optimal CNN-1D architecture was systematically determined through a trial-and-error methodology, ensuring that the R² value exceeded 0.75 when predicting Pstd using the testing datasets. Only those models meeting this criterion were retained for further comparative analysis, focusing on the predicted response patterns and residuals derived from the testing datasets, in comparison with the actual experimental results obtained from the training datasets. The augmented CNN-1D model was formulated by implementing a data augmentation technique with a look-back window of 7, following the transformation and reshaping of the dataset into a time-series format. Six augmented instances were generated by introducing Gaussian noise for each original training sample, thereby significantly expanding the training dataset. The augmented CNN-1D model was subsequently trained on this enriched dataset to enhance predictive performance by learning from a more diverse representation of input data variability. As illustrated in Figure 5.2, the streamlined architecture and optimized hyperparameters of the augmented CNN-1D model, including the number of convolutional layers, filters, kernel size, learning rate, dense units, and regularization strength, were meticulously fine-tuned to improve 151 generalization and performance across all modelling phases. Additionally, the model incorporated non-linear transfer functions, such as ReLU, to effectively capture the complex relationships inherent in continuous numerical data associated with solar still freshwater productivity, Pstd. It is essential to note that graphical and statistical comparisons were used to rigorously evaluate the performance of both the baseline and augmented CNN-1D models. Metrics such as R², RMSE, MAE, and the OIMP were used to assess the predictive accuracy and reliability of these models. The augmented CNN-1D model framework was implemented through a structured pipeline, as summarized in the corresponding pseudocode Table 5.3, aiming to enhance predictive accuracy and generalization in modeling solar still productivity. This study ultimately underscores the effectiveness of the augmented CNN-1D model, trained on the expanded training dataset, in delivering superior predictions and achieving lower statistical errors compared to the baseline model. Figure 3 demonstrates the implementation of a time-series data augmentation framework for developing and evaluating baseline and augmented CNN-1D models. By employing a 7-day look-back window on the original dataset, we effectively captured temporal dependencies. The augmented model was trained on data enhanced with Gaussian noise, aiming to improve prediction robustness and generalization compared to the baseline model, which was trained exclusively on the original samples. This methodology highlights the significant role of data augmentation in enhancing the predictive capabilities of CNN-1D models while concurrently addressing the challenges associated with limited experimental data in solar still studies. 152 Figure 5. 1 Methodological workflow for developing and validating the Augmented CNN-1D model architecture for distillate prediction in a conventional single-slope solar still. The flowchart outlines the data preparation process, which involves converting time series with a 7-day look-back window, applying Gaussian noise-based data augmentation, and scaling. Model development includes hyperparameter optimization using the Hyperopt algorithm, training with early stopping, and evaluation using statistical metrics. The procedure is benchmarked against baseline CNN-1D and SVR models to ensure robust performance assessment. Table 5.2 presents the structured input and output shapes for all developed models, utilized for time-series prediction of freshwater productivity in a solar still system. Each model was trained on sequences derived from a fixed 7-day look-back window, transforming the original 365 daily samples into 359 tailored time-series instances. For the augmented CNN 1D and SVR models, the 70% training set was expanded sixfold through Gaussian noise-based data augmentation, significantly increasing sample diversity and size. The CNN models maintained the 3D temporal-spatial structure of the input as samples × time steps × features, while the SVR models required each time-series sequence to be flattened into a 1D vector. This uniform framework 153 ensured consistent evaluation across models, facilitating robust benchmarking. The comprehensive structure outlined in Table 5.3 validates the consistency of the preprocessing procedures. It supports a comparative performance analysis of the models in forecasting solar distillation outputs under varying environmental conditions. Table 5. 2 Input and output matrix dimensions of the developed baseline and augmented CNN-1D and SVR models following time-series conversion (look-back window = 7) for solar still freshwater prediction. The augmentation process, applied only to the training set, generated six additional samples per original instance using Gaussian noise. For SVR models, the time-series sequences were flattened to vectors of 35 features (7 × 5). The output across all models represents daily freshwater productivity as a univariate continuous target. Model Input Shape Output Shape Remarks Baseline CNN-1D [359 × 7 × 5] [359 × 1] Sliding window; standard time-series sequence Augmented CNN-1D [1757 × 7 × 5] Train [36 × 7 × 5] Val [72 × 7 × 5] Test [1865 × 1] 251× 6 = 1506 Augmented 251 original set (36 Val + 72 Test) = 108 Baseline SVR [359 × 35] [359 × 1] Time-series sequences flattened 7 × 5 = 35 Augmented SVR [1757 × 35] Train [36 × 35] Val [72 × 35] Test [1865 × 1] Same logic as CNN 1D flattening input after 6× augmentation 154 Figure 5. 2 Schematic representation of the optimal augmented CNN-1D model architecture denoted as 5-(128)3-1. The model begins with five input features processed through a time-series look-back window (k = 7), followed by three consecutive 1D convolutional layers, each comprising 128 feature maps and activated by the ReLU function. These are followed by a flatten layer that transforms the multidimensional outputs into a one-dimensional vector, then passes to a fully connected dense layer with 128 neurons. Lastly, a single output neuron predicts the daily distillate water yield (L/day). This architecture yielded the lowest prediction errors and highest performance metrics among all tested configurations, as highlighted in Table 5. Figure 5. 3 A block diagram showing the implementation of the proposed time series data augmentation strategy for training 1D CNN models, specifically applied to a conventional single-slope solar still distillation unit. The original dataset, consisting of 365 daily samples with five input features, was first converted using a look-back window (k = 7) to capture temporal dependencies. Two modeling paths were followed: a baseline CNN-1D model trained on the original 155 data, and an augmented CNN-1D model trained on data enhanced with Gaussian noise. This augmentation process increased data diversity and improved model robustness. Both models were evaluated across training, validation, and testing phases to forecast daily freshwater output and assess generalization performance. This research focused on developing a CNN-1D regression model to forecast continuous numerical variables related to water productivity in solar still systems. Unlike binary classification tasks that rely on discrete labels [0,1], our regression framework leverages non-linear activation functions, specifically ReLU, to effectively capture complex, non-linear dependencies in time series data. This design enables the CNN-1D architecture to learn subtle patterns and relationships across multiple environmental input features, improving predictive accuracy and robustness in modeling continuous distillate water production. Table 5. 3 Pseudocode-based representation and mathematical formulation of the proposed augmented CNN 1D modeling pipeline. Each step describes the systematic workflow, including time series conversion, data augmentation, scaling, model definition, hyperparameter optimization, training, and evaluation. This framework integrates a Gaussian noise-based augmentation approach and employs hyperparameter tuning and early stopping to enhance model performance and generalization. Step Modelling Name Pseudocode Explanation/ Mathematical Representation 1 Import Libraries import Pandas, NumPy, train_test_split, MinMax Scaler, Keras layers, Early Stopping, hyperopt 2 Slice Solar Still Datasets 𝑋𝑑𝑎𝑡𝑎 = 𝑆𝑜𝑙𝑎𝑟𝐷𝑎𝑡𝑎. 𝑖𝑙𝑜𝑐[: , ∶ −1]. 𝑣𝑎𝑙𝑢𝑒𝑠 𝒴𝑑𝑎𝑡𝑎 = 𝑆𝑜𝑙𝑎𝑟𝐷𝑎𝑡𝑎. 𝑖𝑙𝑜𝑐[: , −1]. 𝑣𝑎𝑙𝑢𝑒𝑠 3 Time Series Conversion 𝐹𝑜𝑟 𝑖 𝜖 {1,2, . . . , 𝑁 − 𝑙𝑜𝑜𝑘 𝑏𝑎𝑐𝑘}: where, 𝑙𝑜𝑜𝑘 𝑏𝑎𝑐𝑘 = 7 156 𝑋𝑡𝑠[𝑖] = [𝑋 [𝑖]𝑋 [𝑖 + 1]… 𝑋 [𝑖 + 𝑙𝑜𝑜𝑘𝑏𝑎𝑐𝑘 − 1] ] 𝒴𝑡𝑠[𝑖] = 𝒴[i + lookback − 1] 4 Datasets Split Two stages split into 70% training, 10% validation, 20% testing sets: (𝑋𝑡𝑟𝑎𝑖𝑛 , 𝑋𝑣𝑎𝑙 𝑡𝑒𝑠𝑡,, 𝒴𝑡𝑟𝑎𝑖𝑛 , 𝒴𝑣𝑎𝑙 𝑡𝑒𝑠𝑡) = 𝑡𝑟𝑎𝑖𝑛_𝑡𝑒𝑠𝑡_𝑠𝑝𝑙𝑖𝑡(𝑋𝑡𝑠 , 𝒴𝑡𝑠, 0.7) (𝑋𝑣𝑎𝑙 , 𝑋𝑡𝑒𝑠𝑡,, 𝒴𝑣𝑎𝑙 , 𝒴𝑡𝑒𝑠𝑡) = 𝑡𝑟𝑎𝑖𝑛_𝑡𝑒𝑠𝑡_𝑠𝑝𝑙𝑖𝑡(𝑋𝑣𝑎𝑙 𝑡𝑒𝑠𝑡, 𝒴𝑣𝑎𝑙 𝑡𝑒𝑠𝑡 , 0.67) 5 Augmentation (Training Data Only) 𝐹𝑜𝑟 𝑖 𝜖 {1,2, . . . , 𝑀𝑡𝑟𝑎𝑖𝑛 }, 𝑗 𝜖 {1, 2, . . . , 6 }: ?̃?𝑡𝑟𝑎𝑖𝑛[𝑖, 𝑗] = 𝑋𝑡𝑟𝑎𝑖𝑛[𝑖] + 𝒩(0, σ2), ?̃?𝑡𝑟𝑎𝑖𝑛[𝑖, 𝑗] = 𝒴𝑡𝑟𝑎𝑖𝑛[𝑖] 6 Scaling 𝑋𝑠𝑐𝑎𝑙𝑒𝑑 = 𝑋 − 𝑋𝑚𝑖𝑛𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛 , 𝒴𝑠𝑐𝑎𝑙𝑒𝑑 = 𝒴 − 𝒴𝑚𝑖𝑛𝒴𝑚𝑎𝑥 − 𝒴𝑚𝑖𝑛 7 Define CNN-1D Model (Conv Layers) CNN1D Model = Conv1D ⟶ Flatten ⟶ Dense Units ⟶ Output For 𝑙 = 1, 2, 3: 𝑍(𝑙)[𝑖, 𝑗] = ∑ 𝑤(𝑙) [𝑘, 𝑗] ∙ 𝐴(𝑙−1)[𝑖 + 𝑘] + 𝑏(𝑙)[𝑗]𝐾−1𝑘=0, 𝐴(𝑙)[𝑖, 𝑗] = max (0 , 𝑍(𝑙)[𝑖, 𝑗]) and 𝐴(0) = 𝑥 , ReLU activation 𝑃 = [𝐾 − 12] ( 𝐹𝑜𝑟 ′𝑝𝑎𝑑𝑑𝑖𝑛𝑔 = 𝑠𝑎𝑚𝑒′) 𝐸𝑛𝑠𝑢𝑟𝑒𝑠 𝐿𝑜𝑢𝑡 = 𝐿𝑖𝑛 , 𝑆 = 1 8 Flatten Layer 𝑓 = 𝐹𝑙𝑎𝑡𝑡𝑒𝑛 (𝐴(3)) 𝜖 ℝ𝑀 , 𝑤ℎ𝑒𝑟𝑒 𝑀 = 𝑇 × 128 9 Dense Layer ℎ𝑚 = max (0 , ∑ 𝑊𝑚𝑛𝑀𝑖=1 . 𝑓𝑛 + 𝑏𝑚) , 𝑚 = 1, … ,128 157 10 Output Layer ?̂? = ∑ 𝑤𝑚(0)𝑀𝑖=1 . ℎ𝑚 + 𝑏(0) , ?̂?𝜖 ℝ𝑀 11 Early Stopping 𝐸𝑎𝑟𝑙𝑦𝑆𝑡𝑜𝑝𝑝𝑖𝑛𝑔 (𝑚𝑜𝑛𝑖𝑡𝑜𝑟 = "𝑣𝑎𝑙𝑙𝑜𝑠𝑠" , patience = 20) 12 Hyperparameter Optimization 𝑂𝑝𝑡𝑖𝑚𝑖𝑧𝑒: 𝑓𝑖𝑙𝑡𝑒𝑟𝑠 𝜖 {8, 16, 32, 64, 128} , 𝑘𝑒𝑟𝑛𝑒𝑙 𝑠𝑖𝑧𝑒 𝜖 {2, 3, 5 } , 𝑑𝑒𝑛𝑠𝑒 𝑢𝑛𝑖𝑡𝑠 𝜖 {8, 16, 32, 64, 128 } , 𝑙𝑒𝑎𝑟𝑛𝑖𝑛𝑔 𝑟𝑎𝑡𝑒, 𝜂 𝜖 [10−4, 10−2], 𝑏𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒 𝜖 {8, 16, 32, 64}, 𝑟𝑒𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ, λ 𝜖 [10−4, 10−2] 13 Model Training 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑙𝑜𝑠𝑠: Loss: 𝑀𝑆𝐸 =1𝑀 ∑ (𝑀𝑖=1 𝒴𝑜,𝑖[𝑖] − 𝒴𝑝,𝑖[𝑖])2 𝑇𝑟𝑎𝑖𝑛: 𝐴𝑑𝑎𝑚 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑟, 𝑀𝑆𝐸 𝑙𝑜𝑠𝑠 , 𝑀𝐴𝐸 𝑚𝑒𝑡𝑟𝑖𝑐 14 Model Evaluation (Key Metrics) 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙 𝑀𝑒𝑡𝑟𝑖𝑐𝑠 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑛 𝑡𝑒𝑠𝑡 𝑠𝑒𝑡: 𝑅𝑀𝑆𝐸 = √1𝑛 ∑(𝑛𝑖=1𝒴𝑜,𝑖[𝑖] − 𝒴𝑝,𝑖[𝑖])2 𝑅2 = 1 −∑ (𝒴𝑜,𝑖 − 𝒴𝑝,𝑖)2𝑛𝑖=0∑ (𝒴𝑜,𝑖 − ?̅?𝑜)2 𝑛𝑖=0 𝑀𝐴𝐸 =1𝑛∑ |𝒴𝑜,𝑖 − 𝒴𝑝,𝑖|𝑛𝑖=0 158 5.3.3 Developing Baseline and Augmented SVR Models During the data preprocessing stage for the baseline and augmented SVR models, the datasets underwent a systematic transformation designed explicitly for time-series regression. For the augmented SVR model, which employed the same preprocessing pipeline as the augmented CNN-1D models, the original training data (70% of the complete dataset) was enhanced through a Gaussian noise-based augmentation strategy. This approach introduced zero-mean Gaussian noise, represented as 𝒩(0, σ2), to each of the five input features, generates six synthetic variations for every original instance. As a result, the augmented SVR training samples were subsequently concatenated with the original 251 unaltered sequences to total input training dataset dimensions [1757 × 35], with each row containing five predictors—solar radiation, ambient temperature, wind speed, relative humidity, and feed water flow rate—and one output variable, distillate water productivity. Correspondingly, the output vector comprising the distillate water productivity values was structured as a [1865 × 1] matrix, inclusive of both augmented and non-augmented labels. In contrast, the baseline SVR model was trained solely on the original dataset, omitting any augmentation. The resulting input data matrix had a shape of [359 × 7 × 5], derived from applying a look-back window of size 7 across the 365-day sequence. The target output was formatted as a [359 × 1] vector, representing the daily freshwater yield. It is crucial to understand that the input matrix dimension of [359 × 7 × 5] in the baseline CNN-1D and SVR models was derived by employing a sliding look-back window of size seven on the original dataset, which contains 365 consecutive daily observations. This time-series transformation technique segments the data into overlapping sub-sequences, with each input instance consisting of 7 consecutive days used to forecast the output for the next day. As a result, the number of effective sequences is determined by the formula 365 - 7 + 1 = 359, producing an 159 input matrix of shape [359 × 7 × 5] and a corresponding output vector of [359 × 1], representing the daily freshwater yield. This preprocessing strategy—utilizing a uniform look-back window of 7—was applied uniformly across all four developed models, including both the baseline and augmented variants of the CNN-1D and SVR architectures, thereby ensuring a standardized and equitable framework for comparative evaluation. To adequately account for temporal dependencies, all instances were reorganized into time-series submatrices of size [7 × 6]. The 7-day look-back window was fine-tuned through various empirical evaluations. This configuration enabled the SVR models to integrate historical context, effectively transforming each time-windowed matrix into a one-dimensional vector of length 42, suitable for the SVR architecture. These preprocessing steps ensured uniformity across baseline and augmented SVR models while facilitating a fair comparison with the CNN-1D model in subsequent predictive performance evaluations. In addition to developing the CNN-1D model, the present study employed SVR models in both baseline and augmented configurations to predict freshwater productivity derived from conventional solar stills. The initial phase involved constructing a baseline SVR model using the original dataset without augmentation. A comprehensive hyperparameter tuning process was implemented through the TPE algorithm, facilitated by the Hyperopt library. This process aimed to optimize critical model parameters, specifically the regularization parameter (C), the epsilon-insensitive loss parameter (ε), and the selection of the kernel type (linear, polynomial, RBF, or sigmoid). After completing 100 optimization trials, the most effective hyperparameters were determined to construct the final baseline SVR model as shown in Table 5.4. Subsequently, an augmented SVR model was devised by training it on a considerably expanded dataset generated through Gaussian noise-based data augmentation (jittering). A parallel hyperparameter 160 optimization procedure comprised 100 trials to thoroughly investigate the parameter space. The optimized augmented SVR model prominently employed the RBF kernel function, facilitating nonlinear mapping of inputs into a higher-dimensional feature space, thereby enhancing predictive accuracy. Both SVR models underwent rigorous evaluation across training, validation, and test datasets, employing consistent statistical metrics that were also utilized to assess the CNN-1D model. A comparative analysis of the two SVR implementations yielded significant insights into the efficacy of data augmentation techniques, highlighting their influence on the predictive reliability and robustness of the SVR modeling framework. 5.3.4 Criteria of Optimization for SVR Models The SVR models underwent thorough hyperparameter optimization using the TPE algorithm. For the augmented SVR model, as shown in Table 1, optimal hyperparameters were identified within 100 optimization trials, yielding a minimal validation loss of 0.01289. The best configuration included a regularization parameter (C) of 1.657, an epsilon (ε) value of 0.135, and the use of an RBF kernel. In contrast, the baseline SVR model required up to 200 optimization trials to achieve its lowest validation loss of 0.01339, as illustrated in Table 5.5 its optimal configuration featured a substantially higher regularization parameter (C = 116.801) while maintaining a similar epsilon (ε = 0.135) and kernel type. The extended trial count for the baseline SVR model was empirically driven by its slower convergence behavior, likely due to the limited data variability in the absence of augmentation. This contrasts with the augmented SVR, which benefited from the enriched training dataset, allowing faster convergence and improved generalization with a lower C value. The notable disparity in regularization strength (C) highlights the influence of augmentation, as the augmented dataset enabled the SVR model to generalize effectively with a considerably 161 lower regularization parameter, thereby showcasing improved robustness and stability. These trial limits were not arbitrarily selected but reflect the distinct convergence characteristics of the two models, ensuring a fair and robust comparison under consistent optimization protocols. The consistent use of the RBF kernel in both scenarios highlights the inherent nonlinear relationships within the solar still dataset, underscoring the need for nonlinear modeling approaches to accurately predict freshwater productivity. A comparative analysis of the baseline and augmented SVR models reveals consistent yet marginal enhancements in predictive performance attributable to the implementation of the data augmentation technique. Specifically, the augmented SVR model demonstrates a slightly elevated testing R² of 0.853 compared to the baseline’s 0.848, alongside an improved OIMP of 0.877 versus 0.874. Additionally, there are marginal reductions in RMSE (0.101 vs. 0.102), MAE (0.087 vs. 0.088), and CV (0.226 vs. 0.228), indicating a decrease in residual dispersion and an improvement in predictive precision. These subtle improvements were similarly observed throughout the validation and training phases. Notably, the augmented model achieved a best validation loss of 0.0129 with a regularization parameter of C = 1.657, which is significantly lower than the baseline model’s C = 116.80, resulting in a higher loss of 0.0134. This considerable reduction in regularization strength reflects improved model generalization, suggesting that the augmented SVR model may attain comparable or superior accuracy utilizing a simpler decision function. Collectively, these results highlight the stabilizing effect of data augmentation within the SVR framework, which enhances robustness, reduces model complexity, and ultimately improves the reliability of forecasting freshwater productivity in solar still systems. 162 Table 5. 4 Hyperparameter configurations for the augmented SVR model obtained using the TPE algorithm over 100 optimization trials. The table presents the regularization parameter (C), epsilon-insensitive margin (ε), selected kernel type, and corresponding validation loss (MSE). The best-performing configuration achieved a minimum validation loss of 0.01289 using the RBF kernel with a relatively low regularization strength, indicating improved generalization due to data augmentation. Trial Number Reg. Strength C Epsilon ε Kernel Loss 1 1.6570 0.1350 rbf 0.01289 2 23.2988 0.1369 rbf 0.013199 3 19.0919 0.1453 rbf 0.013780 4 14.5340 0.1463 rbf 0.013871 5 55.6788 0.1358 poly 0.014284 ... ... ... ... ... 6 136.7895 0.1365 poly 0.014291 7 53.3907 0.1359 poly 0.014295 8 1.5817 0.1510 rbf 0.014308 9 28.4521 0.1404 poly 0.014498 10 16.6311 0.1549 rbf 0.014686 Table 5. 5 Hyperparameter configurations for the baseline SVR model derived from 200 optimization trials using the TPE approach. All top-performing configurations utilized the RBF kernel with marginal variations in ε. The lowest validation loss was 0.01339, obtained at a considerably higher regularization strength (C = 116.801), indicating a greater reliance on penalizing deviations due to the limited diversity of the training data in the un-augmented dataset. Trial Number Reg. Strength C Epsilon ε Kernel Loss 1 116.801 0.1350 rbf 0.013390 2 20.5278 0.1356 rbf 0.013394 163 3 135.8546 0.135674 rbf 0.013398 4 352.3807 0.135674 rbf 0.013398 5 102.5012 0.135629 rbf 0.013403 ... ... ... ... ... 6 399.6159 0.135630 rbf 0.013403 7 39.7102 0.135768 rbf 0.013407 8 401.6382 0.135870 rbf 0.013421 9 123.0069 0.135994 rbf 0.013424 10 7.0628 0.136426 rbf 0.013448 5.4 Results and Discussion This section focuses on developing and optimizing a CNN-1D model using data augmentation to enhance prediction accuracy for daily water outputs. Two models were designed and assessed: the baseline CNN-1D, which is non-augmented, and the augmented CNN-1D. A statistical comparison and performance analysis were performed between these models to illustrate the effects of data augmentation on the models' generalization capabilities and accuracy in predicting water outputs. Furthermore, the results included a benchmark of the CNN-1D model against a support vector regression (SVR) model for additional validation. 5.4.1 Optimization of baseline CNN-1D model architecture This study employed CNN-1D and SVR regression models to predict the output of purified water from a conventional single-slope solar still. The performance statistics of the baseline CNN-1D model, which employed various convolutional filters, kernel sizes, dense units, and learning rates, are summarized in Table 5.6. Through a rigorous optimization process involving a maximum of 50 trials, the optimal architecture for the baseline CNN-1D model was selected. This architecture consists of three convolutional layers, each with 64 filters and a kernel size of 3 164 and complemented by a dense layer containing eight units. The optimization aimed to find the optimal combination of hyperparameters to balance the model's complexity and predictive accuracy. During the optimization process, the batch size varied from 8 to 64, and the ReLU activation function was consistently utilized due to its effectiveness in mitigating the vanishing gradient problem and facilitating efficient training. Despite having a seemingly large number of parameters, the chosen architecture demonstrated strong generalization capabilities. Empirical results confirmed that this configuration minimized validation loss and improved predictive accuracy. Techniques such as L2 regularization (with a regularization strength of 0.0001) and early stopping (with a patience of 20 epochs) were effectively employed to address the issue of overfitting. Incorporating three convolutional layers with a kernel size of three was essential for capturing spatial and temporal features from the input data. Using 64 filters in each layer struck an optimal balance between extracting meaningful features and maintaining computational efficiency. The dense layer, containing eight units, further consolidated the learned representations, thereby enhancing the model's ability to accurately predict distillate water output. The choice of filters, kernel size, and dense units within the baseline CNN-1D model was crucial for its learning and generalization capabilities. While fewer filters or reduced kernel sizes might lessen computational demands, they could also hinder the model's capacity to capture underlying patterns in the data. On the other hand, larger architectures could increase computational complexity without delivering significant improvements in predictive accuracy. Thus, the selected optimal configuration—64 filters, a kernel size of 3, and 8 dense units—effectively balanced these trade-offs, ensuring robust and accurate predictions. The optimization demonstrated the model's ability 165 to generalize effectively across the augmented training and untouched testing datasets. The results indicate that this architecture was particularly effective in capturing the complexities and non-linear relationships in the dataset, ensuring reliable predictions of treated water output for the conventional solar still. Early stopping was implemented with a patience of 20 epochs to prevent overfitting. The ReLU activation function was applied across all layers due to its simplicity and effectiveness in enhancing the model's predictive performance. Through rigorous optimization, the baseline CNN-1D model achieved the best validation loss of 0.006711 during training and demonstrated substantial predictive accuracy on the testing datasets, with a test RMSE of 0.1, MAE of 0.08, and R² of 0.86. The Adam optimizer was employed in the optimization process due to its computational efficiency and adaptability in adjusting learning rates during training, which enabled smoother and quicker convergence. In contrast to optimizers like SGD, Adagrad, and RMSprop, Adam incorporates momentum and adaptive learning rate adjustments, making it particularly suitable for managing the high-dimensional, non-linear relationships inherent in the freshwater water output dataset. Other gradient descent methods, such as SGD, which relies on a constant learning rate, were excluded because of their slower convergence and higher sensitivity to hyperparameter tuning. While Adagrad can be helpful in sparse datasets, it is prone to diminishing learning rates over time, which is not ideal for this regression task. The ReLU activation function was exclusively chosen for all layers because it alleviates the vanishing gradient problem, a common issue in deep neural networks. Its simplicity and computational efficiency make it a preferred choice for regression tasks. Alternative activation functions, such as sigmoid and Tanh, were ruled out due to their slower training performance and 166 tendency to saturate gradients for large input values, which can lead to slower convergence. The combination of ReLU and batch normalization contributed to a more stable training process and improved overall model performance. The optimization process systematically evaluated the number of convolutional filters, kernel sizes, dense units, and batch sizes. While existing empirical guidelines can provide a starting point for hyperparameter selection, this study employed an empirical assessment tailored to the dataset's characteristics. This approach ensured that the chosen architecture was well-suited to predicting the complexity of the treated water output. By evaluating a range of hyperparameters and leveraging the computational efficiency of the Adam optimizer alongside the robustness of the ReLU activation function, the selected baseline CNN-1D model architecture achieved a balance between computational efficiency and predictive performance. One key hyperparameter considered during the training process is the number of epochs, which indicates how often the learning algorithm will traverse the entire training dataset. Additionally, the learning rate for the Adam optimizer and the momentum were fine-tuned to maintain fixed values of 0.01 and 0.9, respectively. Having too many epochs can result in an overfit model, while having too few can lead to underfitting of the training dataset. To address this, we can implement an early stopping strategy supported by a callback function during model training. This approach allows us to define an arbitrarily large number of training epochs (for example, 120 epochs) and terminate the training process whenever the model's performance on a holdout validation dataset stops improving. To attain this technique, we pass the validation dataset to the fit function during training, enabling us to identify a performance indicator to monitor for stopping criteria. The loss on the validation dataset is referred to as "validation loss," which aims to achieve a minimum value. However, stopping training at the first indication of no further 167 improvement is not always the best strategy. During training, the early stopping event may occur if the model reaches a plateau with little progress, or it may even experience slight deterioration before making significant improvements. We can introduce a delay before triggering the stop to accommodate this potential behavior. This is accomplished by specifying the "patience" parameter, which allows us to observe no improvement for a certain number of epochs—in this case, we can set it to 20 [134]. Table 5. 6 Hyperparameter optimization results for the baseline CNN-1D model across 50 trials, arranged in ascending order of final loss values. The table reports the optimal combinations of convolutional layer size, number of dense units, filters, batch size, learning rate, and weight decay (λ). The best-performing configuration (trial 1) achieved the lowest loss of 0.006711 using a 3-layer CNN with eight dense units, 64 filters, and a learning rate of 0.01. Trial number Conv. layers size Dense Units Filters Batch size Learning rate Lambda (Weight decay) Loss 1 3 8 64 64 0.01 0.0001 0.006711 2 4 128 8 8 0.0001 0.001 0.013344 3 1 128 16 8 0.0001 0.001 0.013849 4 3 128 64 64 0.001 1 0.014300 5 1 128 64 32 0.0001 0.1 0.030448 ... ... ... ... ... ... ... ... 46 3 16 32 32 0.0001 0.1 0.030752 47 2 64 16 64 0.00001 0.01 0.667131 48 4 8 128 8 0.1 0.001 0.795904 49 4 8 16 8 0.00001 1 1.430148 50 2 128 16 32 0.00001 0.1 5.537681 168 5.4.2 Optimization of augmented CNN-1D model architecture The augmented CNN-1D model was developed based on the foundational structure of the baseline CNN 1D model, significantly enhanced through systematic data augmentation and rigorous hyperparameter optimization. Gaussian noise injection was employed to effectively expand the training dataset, which facilitated improved generalization capabilities of the model. The final architecture comprises three convolutional layers, each containing 128 filters with a kernel size of 3, followed by a flatten layer and a fully connected dense layer with 128 neurons. L2 regularization (λ = 0.1), a batch size of 8, and a learning rate of 0.0001 were implemented to address the overfitting challenges and stabilize the training process. These hyperparameters were optimized through a comprehensive search methodology, as outlined in Table 5.7, where the optimal configuration, highlighted in the first row, attained the lowest loss value of 0.001359. This architecture demonstrated an exceptional capacity for capturing intricate temporal patterns within the augmented time-series data, resulting in enhanced predictive performance for freshwater output. Visualizing the validation loss and training loss across the number of epochs (118, 200) for both the baseline and augmented models, respectively, is instrumental in assessing the adequacy of the model's training process. As depicted in Figure 5.4, an optimal model fit is characterized by the simultaneous reduction and stabilization of validation and training losses at specific points. This methodology is critically essential for mitigating the risks of overfitting the CNN-1D model and preventing underfitting, which can result in the model merely memorizing the training data and subsequently diminishing its predictive accuracy [136]. 169 Through the analysis of the learning curves, it can be observed that the performance of the CNN- 1D model is well-balanced, showing no discernible indications of high variance, high bias, or overfitting. The following key observations can be highlighted: 1. Loss Reduction: Training and validation losses consistently decrease as the number of epochs increases, indicating that the model is successfully learning from the data and enhancing its predictive capabilities. 2. Minimum Plateau: The training and validation losses reach a minimum plateau, indicating that the model has converged to an optimal point, as further training yields minimal additional reductions in loss. This behavior provides evidence against the occurrence of overfitting. 3. Convergence of Curves: The convergence and stabilization of both loss curves as the number of epochs progresses suggest that the model's performance on the training and validation datasets has become consistent. This implies that an appropriate balance between fitting the training data and generalizing to unseen data has been achieved. 4. Absence of High Variance or Overfitting: The steady convergence of the curves indicates a lack of significant disparity between training and validation losses, suggesting that overfitting is not a pressing concern. In typical scenarios, overfitting is evidenced by an increasing gap between training and validation losses, as the model excessively adapts to the training data. 5. Absence of Underfitting or High Bias: There is no indication of high bias, which would manifest as sustained high values for training and validation losses without decline. High bias suggests that the ANN model lacks complexity and cannot adequately capture the underlying patterns present within the datasets. This comprehensive analysis indicates that the model has been adequately trained, achieving a predictive performance in equilibrium. 170 Figure 5. 4 Training and validation loss comparison across created models. (A) The loss progression of the baseline CNN-1D model across 120 epochs exhibits minor fluctuations in validation loss relative to training, indicating acceptable generalization but limited optimization stability. (B) The augmented CNN-1D model exhibits more consistent convergence across 200 epochs, with training and validation losses nearly overlapping throughout the training process. This indicates robust generalization and reduced overfitting due to the augmentation process and optimized architecture. These plots support the improved learning stability and performance of the augmented model. Table 5. 7 Hyperparameter optimization outcomes for the augmented CNN-1D model evaluated over 50 trials. The table presents the tuned values for convolutional layers, dense units, filters, batch size, learning rate, and weight decay, ordered by increasing loss. The optimal configuration (trial 1) achieved the lowest loss of 0.001359 using a 3-layer architecture with 128 filters, 128 dense units, and a batch size of 8, confirming the effectiveness of the augmentation-enhanced search space. Trial number Conv. layers size Dense Units Filters Batch size Learning rate Lambda (Weight decay) Loss 1 3 128 128 8 0.0001 0.1 0.001359 2 3 128 128 8 0.0001 0.1 0.001446 3 3 16 128 8 0.0001 0.1 0.001610 4 3 8 128 8 0.0001 0.1 0.001745 5 3 128 64 8 0.0001 0.001 0.001785 ... ... ... ... ... ... ... ... 171 46 3 128 128 8 0.0001 0.001 0.001791 47 3 16 128 8 0.001 0.1 0.001888 48 3 16 128 8 0.1 0.1 0.002163 49 3 128 128 16 0.0001 0.001 0.002238 50 4 128 64 8 0.0001 0.01 0.002324 5.4.3 Performance analysis of CNN 1D and comparison with SVR Figure 5.5 presents a comprehensive comparative analysis of the baseline CNN-1D and baseline SVR models across the training (A, D, G), validation (B, E, H), and testing (C, F, I) phases. During the training phase (Figure 5.5 A), the CNN-1D model demonstrates a notably stronger alignment with observed distillate water output values than the SVR model, as its predictions closely reflect the temporal trends evident in the actual data. This close correlation highlights the CNN-1D model's superior learning capacity and stability. In contrast, the SVR model exhibits significant deviations, particularly in regions of peak output. The CNN-1D model achieves a high R² of 0.907 and efficiency coefficient (EC) of 0.907, indicating that the model explains approximately 90.7% of the output variance. By contrast, the SVR model attained lower values (R² = 0.875, EC = 0.875), reflecting a 3.5% reduction in explained variance. The CNN-1D model also demonstrated improved stability, with a coefficient of variation (CV) of 0.177 compared to SVR’s higher CV of 0.205, denoting a 15.8% increase in prediction variability. Moreover, the CNN’s error metrics were notably lower (RMSE = 0.081 L/m²·day, MAE = 0.065 L/m²·day) relative to SVR (RMSE = 0.094, MAE = 0.082), corresponding to 13.8% and 20.7% reductions, respectively. Regression plots, illustrated in Figure 5.5 D, further substantiate these observations; the predicted values generated by the CNN-1D model are tightly clustered around the 45° reference 172 line, indicating perfect concordance with the observed outputs. In contrast, the SVR model exhibits a broader distribution of points, especially at both extremes, reflecting diminished predictive accuracy. The residual plot depicted in Figure 5.5 G corroborates this trend, revealing that ~ 90% of the residuals from the CNN-1D model fall within ±2%. However, the SVR residuals display better dispersion and skewness, indicative of higher variability in prediction errors. In the validation phase (Figure 5.5 B), the CNN-1D model retains superior performance, consistently aligning closer to actual output values across the entire time series. It achieves an R² = 0.872, EC = 0.872, OIMP= 0.911 and CV = 0.219, while the SVR model recorded R² = 0.809, EC = 0.809, OIMP= 0.840 and CV = 0.268. These values reflect a 7.2% improvement in variance explanation and an 18.3% reduction in relative variability for CNN-1D over SVR. Error metrics again favored CNN-1D (RMSE = 0.095, MAE = 0.078) over SVR (RMSE = 0.115, MAE = 0.098), indicating reductions of 17.4% and 20.4% in MAE for the CNN-1D model. The regression plot in Figure 5.5 E confirms that CNN-1D predictions adhere more closely to the 1:1 reference line, whereas SVR predictions oscillate above and below. Residual analysis (Figure 5.5 H) further supports this observation, with CNN-1D residuals remaining compact and centered around zero, while SVR residuals exhibit more erratic and skewed patterns. During the testing phase (Figure 5.5 C), the CNN-1D model exhibits superior generalization capabilities, producing predicted outputs that closely align with the observed distillate water values. The model attained an R² = 0.862, EC = 0.862, and CV = 0.218, outperforming the SVR model (R² = 0.848, EC = 0.848, CV = 0.228). These results represent a 1.4% improvement in explained variance and a 4.4% reduction in prediction variability. The CNN-1D also produced 173 lower error metrics (RMSE = 0.097, MAE = 0.077) than SVR (RMSE = 0.102, MAE = 0.088), reflecting a reduction of 4.9% and 12.5%, respectively. As depicted in Figure 5.5 F, CNN-1D predictions aligned more closely with the diagonal reference line. In contrast, SVR predictions fluctuated significantly above and below this line, indicating more variability and inconsistencies in generalization. Residuals in Figure 5.5 I reinforce this distinction, with CNN-1D residuals predominantly contained within ±2%. On the other hand, the SVR residuals demonstrate a broader and less symmetric distribution, indicating a higher degree of uncertainty in predictions. 174 Figure 5. 5 Comprehensive comparative analysis between baseline CNN-1D and SVR models. Subplots (A–C) illustrate the temporal response patterns for the training, validation, and testing phases, comparing the observed distillate water output with predictions from baseline CNN-1D and SVR models. Subplots (D–F) present regression plots showing the correlation between predicted and observed outputs across the three phases. The CNN-1D model consistently exhibits higher alignment with the diagonal (ideal prediction line), suggesting better accuracy. Subplots (G–I) display residual distribution plots, where the baseline CNN-1D model demonstrates a more compact residual spread, particularly in the testing phase, compared to SVR. Collectively, these results validate the superior predictive performance of the CNN-1D baseline model over SVR in modeling freshwater output from solar stills. Figure 5.6 presents an integrated performance analysis of the augmented CNN-1D and SVR models, elucidating the significant advancements attained by implementing the proposed time 175 series data augmentation strategy. In the training phase (Figure 5.6 A), the augmented CNN-1D model exhibited near-perfect learning behavior, with predicted outputs overlapping seamlessly with the observed values. It achieved an outstanding R² of 0.986, an EC of 0.994, and an OIMP of 0.987, indicating that 99.4% of the output variance was explained. By comparison, the augmented SVR model yielded lower values (R² = 0.879, EC = 0.879, and OIMP of 0.893), reflecting an 11.5% drop in predictive efficiency. The CV for CNN was just 0.045, compared to 0.202 for SVR—a 77.7% reduction in prediction variability. Additionally, the CNN-1D achieved significantly lower errors (RMSE = 0.031, MAE = 0.023 L/day) compared to SVR (RMSE = 0.092, MAE = 0.084), translating to 66.3% and 72.6% reductions, respectively, and a 12.2% enhancement in R² for the augmented CNN model. The regression plot in Figure 5.6 D reveals that CNN-1D predictions are tightly aligned along the 45° reference line, while SVR predictions are broadly scattered. Residual analysis in Figure 5.6 G confirms that over 95% of CNN-1D residuals fall within ±1%, whereas SVR residuals are more dispersed and asymmetric. During the validation phase (Figure 5.6 B), the augmented CNN-1D model sustained superior performance, with R² = 0.971, EC = 0.981, OIMP of 0.971, and CV = 0.087, indicating that only 1.9% of variance remained unexplained. Conversely, the augmented SVR model achieved an R² = 0.813, EC = 0.810, OIMP of 0.841, and a much higher CV of 0.267, reflecting a 67.6% increase in variability over the CNN-1D. The CNN-1D also maintained lower error values (RMSE = 0.045, MAE = 0.035) compared to SVR (RMSE = 0.114, MAE = 0.098), with improvements of 60.5% in RMSE and 64.3% in MAE, accompanied by a 19.4% increase in R² in favor of the CNN-1D model. Notably, the CNN’s OIMP score demonstrated a 15.4% improvement over SVR, underscoring its more substantial overall predictive reliability and ability to capture complex nonlinear relationships within the augmented time-series data. Figure 176 5.6 E clearly illustrates the alignment of CNN predictions with the 1:1 diagonal line, in contrast to the significant deviations noted in the SVR results. As shown in Figure 5.6 H, ~90% of CNN-1D residuals remained within ±1%, whereas SVR residuals display a more erratic and widely scattered residual pattern. In the testing phase (Figure 5.6 C), the augmented CNN-1D demonstrated outstanding generalization capabilities, maintaining R² = 0.971, EC = 0.979, CV = 0.079, and OIMP of 0.9696. These values affirm the model’s ability to sustain predictive accuracy across unseen data. By comparison, the augmented SVR recorded R² = 0.853, EC = 0.852, CV = 0.226, and OIMP of 0.877, which reflect a 13.8% drop in explained variance, a 13.7% reduction in efficiency, and a 65.1% increase in output variability relative to CNN-1D. Additionally, the CNN-1D model achieved a 9.1% improvement in OIMP over SVR, highlighting its superior overall performance and robustness in capturing the nonlinear patterns in the data. The CNN-1D model also produced much lower errors (RMSE = 0.045, MAE = 0.035) than SVR (RMSE = 0.101, MAE = 0.087), with corresponding error reductions of 55.4% and 59.8%, respectively. Figure 6F illustrates a tight distribution of CNN-1D predictions along the 45° slope line, while SVR predictions exhibit a more dispersed trend. Residual plots in Figure 6I further validate this difference: approximately 92% of CNN-1D residuals fall within ±1%, while only ~75% of SVR residuals do, underscoring CNN’s greater consistency and reduced prediction uncertainty. In conclusion, the aggregate evidence derived from Figures 5.5 and 5.6, in conjunction with the detailed statistics outlined in Table 5.8, unequivocally demonstrates that the augmented CNN-1D model consistently outperforms all other configurations, exhibiting the highest accuracy, lowest error magnitudes, and strongest generalization. It achieved near-perfect agreement with the observed data, as indicated by its consistently high R² values (~0.97), (EC ≥ 0.97), and OIMP ≈ 177 0.97, while maintaining exceptionally low error dispersion with CV values ranging from 0.045 to 0.087. In contrast, the SVR models, particularly in their baseline form, exhibited weaker performance with lower R² and EC values (≤ 0.875), lower OIMP scores (as low as 0.84), and higher CVs (up to 0.268), reflecting greater variability and reduced reliability. The OIMP analysis further emphasizes the superiority of the augmented CNN-1D model, with an improvement of over 9% compared to the augmented SVR and more than 15% over the baseline SVR, thereby reinforcing its capability to effectively balance accuracy and error minimization. The regression plots further emphasized these differences, with CNN-1D predictions tightly following the 45° reference line and SVR predictions diverging more noticeably. Residual plots revealed that more than 90% of the augmented CNN-1D residuals consistently fell within ±1%, compared to only 75–80% for SVR, highlighting the augmented CNN's superior calibration and error control. Collectively, these findings validate the effectiveness of the proposed augmentation strategy and confirm the augmented CNN-1D model as the most robust and accurate framework for forecasting daily freshwater output in solar still systems. 178 Figure 5. 6 Comparative analysis of augmented CNN-1D and SVR models across all modeling phases. Subplots (A–C) illustrate the temporal prediction performance of the augmented CNN-1D and SVR models relative to actual observed distillate water output across the training, validation, and testing phases. Both models closely follow the actual trend, with the augmented CNN-1D model displaying improved alignment and reduced fluctuations, particularly during the testing phase. Subplots (D–F) present scatter plots of predicted versus observed distillate water values, indicating that the augmented CNN-1D model yields higher prediction accuracy, as evidenced by tighter clustering along the 1:1 reference line. Subplots (G–I) display residual plots, where the augmented CNN-1D model maintains a more compact and symmetrical residual distribution around zero, suggesting reduced prediction error and improved generalization. In contrast, the augmented SVR model exhibits more scattered residuals and greater deviation, particularly in the testing phase. These results underscore the superior robustness and predictive accuracy of the augmented CNN-1D framework compared to the SVR approach for modeling solar still distillation output. 179 Figure 5.7 displays the residual heatmaps for the augmented CNN-1D and SVR models across the training, validation, and testing phases, offering a clear visualization of relative error magnitudes. The augmented CNN-1D model consistently shows lighter and more uniform color intensities, particularly during the testing phase, indicating its superior generalization ability and reduced residual dispersion. In the training phase (Figure 5.7 A), the relative error range for the CNN-1D model spans approximately from 0.25 (light) to 1.75 (dark). In contrast, the validation (Figure 5.7 B) and testing (Figure 5.7 C) phases demonstrate narrower error ranges of 0.2 to 1.2 and 0.2 to 1.4, respectively. These lighter and more homogeneous patterns highlight the CNN-1D model's ability to produce tightly bound residuals across all phases. On the other hand, the SVR model exhibits darker and more scattered heatmaps, with pronounced color bands that suggest more prominent and more frequent prediction errors, especially during the validation and testing phases. The corresponding MAE values further validate these visual findings. The augmented CNN-1D achieved low MAE values of 0.023 for training, 0.035 for validation, and 0.035 for testing, which indicates consistent and minimal prediction errors. Conversely, the SVR model yielded higher MAE values of 0.084 (training), 0.098 (validation), and 0.087 (testing), which aligns with the increased residual variance observed in the heatmaps. Additionally, the CNN-1D model outperformed the SVR in overall performance metrics, achieving a lower test RMSE of 0.0814 and a higher R² of 0.903, compared to the SVR’s test RMSE of 0.112 and R² of 0.841. These quantitative results and visual residual patterns demonstrate that the augmented CNN-1D model, enhanced through data augmentation and architectural optimization, provides more accurate predictions. Also, it maintains superior stability and generalization across all modeling phases compared to the SVR model. 180 The deviation histograms and kernel density estimation (KDE) plots presented in Figure 5.8 for the testing dataset provide a valuable analysis of prediction accuracy and consistency across the various models. The histogram for the Augmented CNN-1D model demonstrates a concentrated and symmetric distribution of deviations, with the highest frequency reaching 14 and deviation values closely clustered between -0.23 and 0.82. In contrast, the Baseline CNN-1D model exhibits a broader and more dispersed distribution, peaking at a frequency of only 7.9, while displaying a wider range of deviations from 0.25 to 1.22. This increased spread indicates a higher error variance and a greater frequency of significant deviations in the baseline model. Similarly, the KDE plots reinforce the superior generalization capabilities of the augmented CNN-1D model. Its distribution features a sharp, dominant peak with a maximum density of 1.8, suggesting that most predictions closely align with the actual values, with deviations ranging from -0.70 to 1.21. Conversely, the Baseline CNN-1D model reveals a flatter curve with a lower peak density of 1.25 and a broader range of deviations spanning from -0.75 to 1.5. These differences underscore the augmented model's ability to produce more consistent and less biased predictions, with fewer extreme errors, thereby highlighting its enhanced predictive stability and accuracy. 181 Table 5. 8 Comparative statistical performance of the CNN-1D and SVR models ‘’baseline and augmented configurations’’ evaluated across the training, validation, and testing phases. The augmented CNN-1D model achieved the highest accuracy and lowest error values in all phases, demonstrating superior learning efficiency and generalization ability. These findings validate the robustness and effectiveness of the proposed augmentation strategy in enhancing the performance of deep learning-based forecasting in solar desalination applications. Stage Training Model / Metric R2 RMSE MAE CV EC OIMP CNN-1D Baseline 0.907 0.081 0.065 0.177 0.907 0.913 CNN-1D Augmented 0.986 0.031 0.023 0.045 0.994 0.987 SVR Baseline 0.875 0.094 0.082 0.205 0.875 0.891 SVR Augmented 0.879 0.092 0.084 0.202 0.879 0.893 Stage Validation Model / Metric R2 RMSE MAE CV EC OIMP CNN-1D Baseline 0.872 0.095 0.078 0.219 0.872 0.911 CNN-1D Augmented 0.971 0.045 0.035 0.087 0.981 0.971 SVR Baseline 0.809 0.115 0.098 0.268 0.809 0.840 SVR Augmented 0.813 0.114 0.098 0.267 0.810 0.841 Stage Testing Model / Metric R2 RMSE MAE CV EC OIMP CNN-1D Baseline 0.862 0.097 0.077 0.218 0.862 0.883 CNN-1D Augmented 0.971 0.045 0.035 0.079 0.979 0.9696 SVR Baseline 0.848 0.102 0.088 0.228 0.848 0.874 SVR Augmented 0.853 0.101 0.087 0.226 0.852 0.877 Note: R2: coefficient of determination, RMSE: root mean square error, MAE: mean absolute error, CV: coefficient of variance, EC: efficiency coefficient, OIMP: overall index of model performance. 182 Figure 5. 7 Residual heatmaps comparing prediction errors between the augmented CNN-1D and SVR models across training (A), validation (B), and testing (C) datasets. Each subfigure visualizes the relative error distribution, where lighter shades indicate smaller residuals and darker shades correspond to larger deviations from the ground truth. The CNN-1D model demonstrates more compact and consistent residuals across all phases, particularly in the training and testing stages, which highlights its superior generalization and error control. However, SVR exhibits broader and more scattered error patterns, featuring its limited ability to capture the nonlinear dependencies in the solar still desalination data. 183 Figure 5. 8 (A) Histogram and (B) Kernel Density Estimation (KDE) plots illustrating the deviation distribution of predicted values from actual values in the testing dataset for both the baseline CNN-1D and the augmented CNN-1D models. The augmented CNN-1D model exhibits a sharper concentration of errors around zero, indicating improved prediction accuracy and reduced output variance. Conversely, the baseline CNN-1D model shows a broader distribution of deviations, reflecting more significant prediction uncertainty. These findings highlight the effectiveness of time-series data augmentation in enhancing model precision and narrowing the error distribution. The integrated analysis of Figure 5.9 and Figure 5.10 presents a comprehensive comparative evaluation of four developed models: augmented CNN-1D, augmented SVR, baseline CNN-1D, and baseline SVR. This evaluation is predicated upon six critical statistical metrics assessed during the testing phase. The augmented CNN-1D exhibited the most consistent and superior performance across all identified metrics among the examined models. As illustrated by both figures, it attained the highest accuracy-related scores—R² = 0.97, EC = 0.98, and OIMP = 0.97—indicative of nearly perfect concordance between predicted and observed values and a highly efficient model structure. In stark contrast, the baseline SVR model recorded the lowest values across these metrics (R² = 0.85, EC = 0.85, OIMP = 0.87), underscoring its limited capability to generalize and accurately capture the underlying patterns within the data. The radar 184 plots vividly represent these distinctions, where the augmented CNN-1D model delineates the largest and most balanced polygon. On the contrary, the SVR model demonstrates a considerably smaller and irregular shape, reflecting diminished predictive power and more significant variability. Further validation of these findings is provided through the error-based metrics. The augmented CNN-1D achieved the lowest RMSE (0.04) and MAE (0.04), indicating a significant reduction of approximately 60% in RMSE and 55% in MAE compared to both baseline models. Conversely, while exhibiting improvements relative to its baseline counterpart, the augmented SVR still manifested significantly higher error values (RMSE = 0.10, MAE = 0.09) and greater variability (CV = 0.23). Unlike the augmented CNN-1D, it maintained a substantially lower CV of 0.08, signifying more stable and less dispersed predictions. The radar plots also illustrated these discrepancies, where the augmented CNN-1D model exhibited tight clustering and minimal distortion along the error axes. Meanwhile, the SVR-based models displayed considerable asymmetry and extended error regions. Collectively, the histogram and radar plots provide robust evidence that the augmented CNN-1D model achieves the highest predictive accuracy and demonstrates the most robust and reliable performance during the testing phase. These results underscore the efficacy of the proposed time series data augmentation strategy and further substantiate the CNN-1D architecture as a highly suitable and generalizable framework for forecasting freshwater output in solar still desalination systems. 185 Figure 5. 9 Radar plots comparing six statistical metrics—R², Efficiency Coefficient (EC), Overall Index of Model Performance (OIMP), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Variance (CV)—across training, validation, and testing phases for four models: augmented CNN-1D, augmented SVR, baseline CNN-1D, and baseline SVR. The augmented CNN-1D model demonstrates superior performance with higher accuracy and lower error dispersion, particularly in the testing phase, highlighting the effectiveness of data augmentation in enhancing model generalization and predictive reliability. 186 Figure 5. 10 : Comparative bar chart of testing phase metrics across four developed models. The diagram illustrates model accuracy and error using six statistical performance metrics. The Augmented CNN-1D model consistently outperforms all others, demonstrating superior accuracy and generalization with higher R², EC, and OIMP values, and lower RMSE, MAE, and CV. Figure 5. 11 Confusion matrices for the four predictive models applied to the water output classification task. The classification was based on a stable thresholding approach, where both actual and predicted water output values were labeled as “Yes” if they exceeded 1.25× the mean actual value and “No” otherwise. Unlike percentile-based methods, this threshold-based strategy 187 improves interpretability, ensures consistent labeling across datasets, and avoids distortions caused by skewed distributions or outliers. The impact of data augmentation is evident in the CNN-1D model, which shows reduced misclassification rates, particularly in minimizing false positives and improving classification stability during the testing phase. Table 5. 9 Classification performance comparison of the CNN-1D and SVR models under both baseline and augmented configurations, using accuracy, precision, recall, and F1-score metrics. The augmented CNN-1D model achieved the highest overall performance, with an accuracy of 88% and an F1-score of 0.82, indicating enhanced feature learning and more balanced classification. In contrast, SVR models exhibited minimal improvement with augmentation, suggesting limited benefit from the added variability in feature space. Model/ Metric Accuracy Precision Recall F1-Score Augmented CNN-1D 88% 0.78 0.88 0.82 Baseline CNN-1D 78% 0.61 0.92 0.73 Augmented SVR 78% 0.62 0.83 0.71 Baseline SVR 78% 0.62 0.83 0.71 The classification results in Figure 5.11 highlight the effectiveness of data augmentation in enhancing model performance, particularly within CNN-based architectures. Table 5.9 shows that the augmented CNN-1D model achieved the highest accuracy (88%) and F1-score (0.82), demonstrating improved generalization and a reduced false positive rate, which is crucial for the reliable classification of water output. Furthermore, its recall (0.88) demonstrates strong sensitivity in identifying high-output instances while maintaining better precision than other models. On the other hand, the baseline CNN-1D model, although it achieved a slightly higher recall (0.92), exhibited lower precision (0.61) and accuracy (78%), resulting in a greater number of misclassifications. This underscores the role of augmentation in refining decision boundaries and enhancing classification reliability. Both SVR models (Augmented and Baseline) produced identical outcomes (accuracy: 78%, F1-score: 0.71, recall: 0.83, precision: 0.62), indicating that 188 Gaussian noise had a negligible effect on their performance. This suggests that SVR's dependence on support vectors and kernel transformations renders it less sensitive to minor variations introduced by Gaussian noise. Unlike CNNs, which adaptively refine feature extraction using augmented data, SVR is built around support vectors and margin maximization, making it inherently less responsive to small perturbations. These findings reinforce the advantages of CNNs in processing augmented time-series data, demonstrating their potential to enhance predictive accuracy in solar still performance analysis. The comparative evaluation of the developed CNN-1D and SVR models was primarily conducted using the testing dataset, with performance assessed through a comprehensive statistical analysis, as shown in Figure 5.10. The results for freshwater prediction indicate that the CNN-1D model surpasses the SVR model in terms of accuracy, robustness, and generalization capability. This distinction is particularly significant when modeling complex, nonlinear interactions among meteorological inputs and distillate output, which are frequently encountered in solar desalination systems. This study highlights the importance of comparing these models for several reasons. First, SVR, while recognized for its non-linear regression capabilities, serves as a valuable benchmark for evaluating the enhanced ability of the deep learning model to capture temporal and spatial dependencies. Second, using CNN-1D enables hierarchical feature learning from time-series data, allowing it to capture intricate dynamics that are often oversimplified or overlooked by kernel-based methods, such as SVR. Lastly, validating the performance of the CNN-1D model against SVR strengthens the robustness of the proposed framework, as the observed improvements are not only statistically significant but also practically applicable to real-world solar still forecasting tasks. These findings are consistent with previous research studies [117] [102], demonstrating that deep 189 learning architectures, including ANNs, outperform traditional machine learning approaches like MLR through the transfer learning approach in predicting distillate outputs. 5.5 Recent Advancements and Insights Recent innovations in solar desalination have concentrated on improving thermal performance and predictive accuracy through experimental modifications and machine learning techniques. These advancements offer valuable insights into cutting-edge technologies, underscoring their importance in developing next-generation solar desalination solutions. Several experimental investigations have explored thermal enhancement strategies and their effects on freshwater yield, providing context for these breakthroughs. For instance, Issaq et al. [137] explored performance enhancement strategies for single-inclination solar stills through controlled trials focused on basin water depth, sensible heat storage, and inner glass surface treatment. Their findings revealed that thermal efficiency exceeded 40% under favorable weather without modifications, providing a strong baseline for comparison. However, increasing water depth beyond 6 cm significantly reduced yield and efficiency. Similarly, adding black gravel beyond a 2% gravel-to-water mass ratio showed negligible thermal improvements, while treating the inner glass surface with waxy materials led to a marked decline in performance. These results emphasize the sensitivity of solar still output to subtle design and material adjustments. Mahala et al. [138]thoroughly evaluated the performance enhancement of pyramid solar stills by incorporating rectangular fins, phase change material (PCM), and gravel. They developed and tested two configurations: a conventional solar still (CSS) and a modified solar still (MSS), along with variations that included gravels (CSS + G and MSS + G). This study, conducted under actual climatic conditions in Greater Noida, India, provided insights into improvements in productivity, energy, and exergy efficiency, as well as the impact of economic and 190 environmental factors. The findings revealed that the MSS + G configuration delivered superior performance, achieving an impressive 84% increase in daily freshwater output, along with enhancements in energy and exergy efficiency of 81.1% and 273%, respectively, compared to the CSS. The MSS + G configuration also led to a 29.2% reduction in cost per liter and a 29% shorter payback period. Environmentally, it resulted in a 76% increase in carbon credit gains and mitigated 19.14 tons of CO₂ emissions. These significant findings underscore the effectiveness of integrating thermal and material enhancements in developing cost-efficient and sustainable solar desalination systems. Complementing these efforts, Elsheikh et al. conducted a study to evaluate the thermal and predictive performance of a stepped solar still equipped with a copper corrugated absorber plate, comparing it to a traditional single-slope design. The research focused on key thermal parameters, such as convection, evaporation, radiation heat transfer coefficients, and energy and exergy efficiencies. The experimental findings highlighted that the stepped solar still significantly enhanced freshwater production, achieving approximately 128% more output than the conventional system. To forecast hourly freshwater yield, the authors implemented a Long Short-Term Memory (LSTM) neural network, trained on time-series data from field experiments. They assessed the predictive accuracy of the LSTM model against that of the traditional ARIMA model. The results revealed that the LSTM model exhibited remarkable forecasting precision, with coefficients of determination of 0.97 for the conventional still and 0.99 for the stepped design. These findings underscore the advantages of combining innovative absorber designs with deep learning models to optimize real-time prediction and performance in solar distillation systems [139]. 191 The studies reviewed indicate that integrating advanced materials, design optimizations, and AI-based models significantly boosts the performance of solar stills. These findings emphasize the crucial role of data-driven approaches, such as the proposed augmented CNN-1D model, in shaping the future of sustainable desalination technologies. 5.5.1 Performance Analysis The performance comparison in Table 5.10 elucidates the significant advancements accomplished by the proposed augmented CNN-1D solar still model when benchmarked against a diverse range of recent experimental and machine learning-based studies. This table consolidates various desalination configurations, including pyramid stills with wick materials, systems enhanced by external condensers or phase change materials (PCM), and alternative geometrical designs such as tubular and hemispherical stills. Furthermore, it reflects the growing adoption of predictive modeling, wherein artificial neural networks and hybrid optimization algorithms are employed to forecast system performance. This transition towards data-driven methodologies complements traditional thermal enhancements and often yields superior results. A distinctive feature of the proposed CNN-based model is its utilization of time series data augmentation, which facilitates high prediction accuracy without requiring physical modifications to the system. This comparative analysis exemplifies the potential of intelligent modeling techniques in solar desalination and advocates for their implementation as scalable and cost-effective solutions for optimizing freshwater production. These findings offer crucial insights for researchers and engineers aiming to improve the efficiency, adaptability, and long-term sustainability of solar still technologies. 192 Table 5. 10 Performance comparison of the proposed augmented CNN 1D model, benchmarked against recent studies in the field, including experimental setup, theoretical modelling, simulation, and machine learning applications. Study Type / Design Achieved Efficiency / Productivity Methodology Ref. Pyramid Solar Still (Wick Type with Reflectors) 55.3% Efficiency, 1476 mL/m²·d Productivity; up to 136.6% improvement Experimental [140] Wick Material Solar Still with External Condenser 27.13% Efficiency, Productivity improved by up to 75% Experimental + CFD Simulation [141] Pyramid Solar Still (PSS) 45.7% Efficiency (implied), 2.585 kg/m² Productivity Optimization (ANN+RSM) Models [142] Single-Slope Solar still (Modified with External Heater) PCM: Prod. increase ~30.6%, Vaporizer: 415% yield increase Experimental (HFU Vaporizer + PCM capsules) [143] Hemispherical Solar Distillers (Sponge-Enhanced) Exergy and Energy Efficiencies were improved ~512.87 ,70.53%, respectively. Experimental (Material Enhancement) [144] Passive Solar Thermal Desalination 32.9% Efficiency, 0.5 kg/m²·h Productivity; achieved 168 h (7 days). Experimental (continuous salt-free operation) [145] Wick Solar Still (Conventional & developed) ~50% Productivity Increase; ANN-TSA model achieved up to R2=0.99 ML (ANN + Tree–Seed Algorithm) [146] 193 Active Solar Still with Condenser 53.21% productivity increased at a fan speed of 1350 rpm. ML (ANN + Harris Hawks Optimizer) [147] Tubular Solar Still Distiller (Case III) 83.69% Energy Efficiency, 242.45% Exergy Efficiency, 79.88% Productivity increase Experimental [148] Novel Solar Desalination 65.48% Energy Efficiency, 6.67% Exergy Efficiency, 20.95 L/m². day Productivity Experimental (Heat Pump + Evacuated Tube) [149] Tubular Solar Still (Double-Trough) 58.5% Thermal Efficiency, 36.1% Productivity Improvement Experimental (Multi-Evaporator Design) [150] Tubular Solar Still (TSS) Fresh water production overall cost $0.0061-$0.2 per kg water Theoretical Review: Economic Analysis [151] Hemispherical Solar Still (HSS-GB) 25.75% Thermal Efficiency increase, 26 % more distilled water with 6.30 L/m2 yield Experimental (Glass Bottle) [152] Hemispherical Solar Still (HSS-N) Daily increase 6.8 L/m2 with 76.6% Productivity Improvement Optimization (Best Modification) [153] Solar Still with hybrid Nanofluid (MSS) 27.2% daily enhanced productivity in summer, 29.6 % CO2 reduction in winter Theoretical +Experimental [154] Conventional Single Slope R2 = 97.1%, OIMP = ~97%, RMSE ML-Data Augmentation Current 194 Solar Still = 0.045, MAE = 0.035, (Aug. CNN 1D Testing Phase) (CNN + SVR Models) Study 5.6 Conclusion This research has led to the development and thorough validation of a robust predictive modeling framework designed to estimate freshwater productivity in conventional single-slope solar stills. This was accomplished through integrating one-dimensional convolutional neural networks (CNN-1D) and strategic time-series data augmentation using Gaussian noise, based on inputs structured with a 7-day look-back window. Given the significant capital investment required for solar desalination, this accurate forecasting tool is essential for optimizing water production and resource management, particularly by improving model generalization from limited experimental datasets. The optimized CNN-1D architecture, which features three sequential convolutional layers, each with 128 filters and ReLU activation, was carefully determined through systematic hyperparameter tuning. This architecture was trained using a feed-forward backpropagation algorithm, leveraging proficiency in autonomously extracting important spatial and temporal features from input sequences, effectively learning the complex, non-linear relationships between environmental parameters and daily freshwater yield. Empirical evaluations demonstrated the superiority of the enhanced CNN-1D model over the SVR benchmark across a comprehensive range of statistical metrics. During the rigorous testing phase, the CNN-1D model achieved an EC of 97.9%, an OIMP of 0.9696, an RMSE of 0.045, an MAE of 0.035, and a CV of 0.079. These results highlight the model's exceptional predictive accuracy, strong generalization, and compact residual distribution, confirming its practical applicability for real-world solar desalination forecasting. 195 Notably, the support vector regression model utilized an RBF kernel—selected through a thorough optimization process involving linear, polynomial, and nonlinear kernels—to model the solar still system's nonlinear dynamics effectively. Despite its improved performance over simpler regression methods, the SVR model was consistently outperformed by the augmented CNN-1D model in all modeling phases. This disparity highlights the superior ability of deep learning models, particularly when enhanced with dataset augmentation, to capture complex, high-dimensional relationships within environmental systems. In summary, the combined use of tailored time-series data augmentation with deep learning, as demonstrated by the augmented CNN-1D, represents a robust, scalable, and data-efficient approach to enhancing predictive capabilities in solar still systems. The developed model showcased outstanding forecasting performance and outperformed traditional non-linear methods such as SVR. This research underscores the critical role of sophisticated data-driven modeling in promoting intelligent design, enabling performance monitoring, and facilitating operational optimization within solar desalination technologies, ultimately contributing to more effective and sustainable water resource management. Building on the successful integration of tailored data augmentation with deep learning methodologies, Chapter 5 demonstrated the enhanced predictive power and generalizability of CNN-1D models for estimating freshwater productivity from conventional solar stills. These findings reinforce the viability of data-efficient strategies in addressing real-world challenges of limited experimental datasets and system variability. With both transfer learning and data augmentation approaches now rigorously explored and benchmarked, the thesis reaches its culmination. The final chapter shifts focus from detailed model development to a broader synthesis of insights, summarizing the key contributions, evaluating their practical implications, 196 and proposing future research pathways to further advance sustainable solar desalination technologies. 197 Chapter 6: Overall Conclusion, Recommendations, and Path Forward 6.1 Introduction This doctoral research embarked on a comprehensive investigation to advance the predictive modeling capabilities for conventional single-slope solar still distillation units, a critical technology for decentralized freshwater production. Driven by the need for enhanced operational efficiency, optimized design, and improved economic viability of these systems, this thesis addressed the prevalent challenges of data scarcity and the complexities of modeling non-linear thermal dynamics. Through the systematic development, application, and evaluation of advanced machine learning strategies—namely Transfer Learning (TL) and tailored Data Augmentation (DA)—this work has sought to provide robust, accurate, and data-efficient predictive tools. This final chapter synthesizes the major findings of the research, draws overall conclusions, offers recommendations for practical application and further research, and delineates a compelling path forward for continued innovation in the domain of solar desalination modeling and integrated sustainable technologies. 6.2 Summary of Major Findings and Contributions This research has yielded several significant findings and contributions, fundamentally enhancing the approach to modeling freshwater productivity (Pstd) in conventional single-slope solar stills: 6.2.1 Advancements through Transfer Learning (TL) • Successful Knowledge Transfer from a Novel Hybrid System: A key finding, as detailed in the Transfer Learning study (referencing Study #1 conclusion), was the successful application of TL by adapting a pre-trained Artificial Neural Network (ANN) model—originally developed from simulation data of a novel hybrid solar photovoltaic (PV) 198 assisted single-slope solar still—to accurately predict the Pstd of conventional single-slope solar stills. This demonstrated the feasibility and benefit of leveraging knowledge from more complex, higher-performance source domains to improve modeling for simpler, widely deployed target systems, especially when direct data for the target is limited. • Superior Performance of TL-Enhanced Models: The TL-enhanced target ANN model (specifically the 5-64-64-1 architecture) significantly outperformed ANN models trained from random initialization and traditional Multiple Linear Regression (MLR) models in all modeling stages (training, testing, and validation). This was evidenced by superior statistical metrics, such as a higher Overall Index (OI) of 0.872 and lower Root Mean Square Error (RMSE), confirming the efficacy of TL in initializing models with more informed parameters (Study #1 Conclusion). • Improved Generalization and Accuracy: The TL approach led to models with sufficient accuracy (residuals of forecasted distillate values around 1%) and robust generalization capabilities, making them reliable tools for predicting freshwater outputs in diverse conventional single-slope solar still configurations (Study #1 Conclusion). This addressed a critical need for models that can perform well across varied operational contexts. 6.2.2 Advancements through Data Augmentation (DA) • Effective Mitigation of Data Scarcity: The Data Augmentation study (referencing Study #2 conclusion) successfully demonstrated that tailored DA strategies, specifically the application of Gaussian noise (jittering) to time-series inputs using a 7-day look-back window, can effectively address data scarcity for conventional solar stills. This synthetic expansion of the training dataset significantly enhanced the training of deep learning models. 199 • Superior Performance of Augmented Deep Learning Models: The integration of DA with a one-dimensional Convolutional Neural Network (CNN-1D) resulted in a predictive model that consistently and significantly outperformed Support Vector Regression (SVR), even an optimized SVR with an RBF kernel. The augmented CNN-1D model (optimized with three convolutional layers, each featuring 128 filters) achieved exceptional precision and robust generalization, exemplified by an RMSE of 0.045 and an Overall Index of Model Performance (OIMP) of ~0.97 during testing (Study #2 Conclusion). • Enhanced Capture of Complex Dynamics: The DA-enhanced CNN-1D model demonstrated a superior ability to capture complex, non-linear relationships, and spatial-temporal patterns inherent in the solar still operational data, resulting in more accurate Pstd predictions compared to both traditional non-linear methods and deep learning models trained without augmentation (Study #2 Conclusion). • Methodological Innovation in Output Interpretation: Beyond prediction, the DA study also introduced a pioneering threshold-based classification method for freshwater outputs. This technique provided enhanced interpretability and stability in categorizing system performance, mitigating the influence of outliers, and offering more practical insights than traditional quartile-based approaches (as noted in Study #2 elements). 6.2.3 Overarching Contributions • Provision of Data-Efficient Modeling Frameworks: Collectively, this PhD has delivered two validated, data-efficient frameworks for developing high-accuracy predictive models for conventional solar stills, reducing the reliance on extensive and costly experimental data collection campaigns. 200 • Enhanced Understanding of Solar Still Performance: The developed models and analytical techniques provide deeper insights into the key parameters that influence solar still productivity, paving the way for more informed design modifications and operational adjustments. • Addressing Limitations of Traditional and Simulation-Based Models: The research has provided robust ML-based alternatives that can potentially overcome the limitations of simpler linear models and specific physics-based simulations, particularly in handling wide ranges of input variables such as high solar radiation. 6.3 Overall Conclusion This doctoral thesis successfully demonstrates that the strategic application of Transfer Learning and Data Augmentation significantly advances the predictive modeling of freshwater productivity in conventional single-slope solar stills. The findings conclusively show that TL can effectively bootstrap model performance by leveraging knowledge from related, more complex systems, while DA can substantially enhance model robustness and accuracy by enriching limited datasets. Both approaches yield models superior to traditional regression techniques and standard machine learning models trained from scratch, particularly when data availability is a constraint. The research confirms that these advanced methodologies are not merely theoretical constructs but translate into practical tools capable of delivering accurate, reliable, and generalizable predictions. The ability to precisely forecast Pstd, coupled with innovative methods for interpreting these predictions, empowers stakeholders to optimize solar still design, improve operational efficiency, and enhance the economic feasibility of solar desalination, particularly in arid and remote regions. This work, therefore, contributes a valuable suite of tools and insights to 201 the field of sustainable water resource management, underscoring the transformative potential of intelligent data-driven approaches in addressing critical global challenges. 6.4 Recommendations Based on the findings and contributions of this research, the following recommendations are proposed: 6.4.1 For Practical Application and Industry 1. Adoption of Developed Models: Operators and designers of conventional single-slope solar stills are encouraged to adopt the developed TL-enhanced ANN and DA-enhanced CNN-1D models for Pstd forecasting to aid in performance monitoring, operational decision-making, and system optimization. 2. Integration into Design Tools: The predictive models should be considered for integration into software tools used for designing and evaluating solar desalination systems, allowing for more accurate upfront performance assessments. 3. Data Collection Standardization: While this research offers solutions for limited data, continued efforts towards standardized, high-quality data collection from diverse solar still installations would further benefit the development and validation of even more robust models. 6.4.2 For Future Research 1. Exploration of Broader TL Source Domains: Investigate the efficacy of transferring knowledge from a wider array of source domains for TL, including different types of solar energy systems or other thermodynamic processes, to further enhance model initialization for solar stills. 202 2. Benchmarking Against Advanced Data Augmentation Techniques: Conduct comparative studies benchmarking the tailored Gaussian noise-based DA method against other advanced DA techniques, such as Generative Adversarial Networks (GANs), particularly for time-series data, to determine if further improvements in synthetic data generation can be achieved for solar still modeling. 3. Hybrid Modeling Approaches: Explore hybrid models that combine the strengths of the TL-initialized networks with DA-enhanced training datasets to potentially achieve synergistic performance improvements. 6.5 Path Forward: Integrating Solar Stills with Emerging Sustainable Technologies The advancements made in accurately predicting and understanding solar still performance open exciting avenues for integrating these desalination units with other sustainable technologies, moving towards holistic and circular economy approaches. The following outlines a visionary path forward: 6.5.1 Physics-Informed Neural Networks (PINNs) for Enhanced Model Robustness and Interpretability • A significant future direction involves the development of Physics-Informed Neural Networks (PINNs) for solar still modeling. PINNs integrate the governing physical laws (e.g., heat and mass transfer equations relevant to solar still operation) directly into the loss function of the neural network during training. • This approach can lead to models that are not only data-driven but also consistent with fundamental physical principles. This can improve model generalization, especially when extrapolating to unseen conditions, reduce the reliance on large datasets, and enhance the interpretability of the models by ensuring their predictions adhere to known physics. 203 • The challenge lies in accurately formulating the relevant partial differential equations (PDEs) for solar stills and effectively incorporating them into the deep learning framework. 6.5.2 Integration of Solar Stills with Electrolyzers for Green Hydrogen Production • Freshwater produced by solar stills is a crucial input for water electrolyzers used in green hydrogen production. A promising research avenue is the design, simulation, and optimization of integrated solar still-electrolyzer systems. • This involves developing comprehensive models (using simulation tools like MATLAB/Simulink, analytical equations, or further ML techniques) that couple the solar still's freshwater output directly to an electrolyzer powered by a renewable source (potentially the same PV system assisting the still or a dedicated one). • The objective would be to predict and optimize the daily green hydrogen yield based on solar irradiance, ambient conditions, still design, and electrolyzer efficiency. This would contribute to decentralized, sustainable hydrogen production, particularly valuable in off-grid or remote locations. • Economic feasibility studies and lifecycle assessments of such integrated systems would also be critical. 6.5.3 Continued Exploration of Advanced Machine Learning Models Beyond GANs for data augmentation, other advanced ML architectures and paradigms should be explored for solar still modeling. This could include attention mechanisms, transformers (for time-series forecasting), and reinforcement learning for optimizing operational parameters in real-time. 204 • Investigating ensemble methods that combine predictions from diverse models (e.g., TL-based, DA-based, physics-based components) could also lead to more robust and accurate overall predictions. 6.6 Concluding Remarks The journey undertaken in this PhD has underscored the profound impact that advanced computational intelligence can have on optimizing established renewable energy technologies like solar stills. By pushing the boundaries of predictive modeling through Transfer Learning and Data Augmentation, this research not only provides immediate solutions for enhancing solar desalination but also lays a foundation for future integrated systems that promise even greater contributions to global water and energy sustainability. 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E., Abdelgaied, M., & Abdelaziz, “A comparative study of hemispherical solar stills with various modifications to obtain modified and inexpensive still models,” Environ. Sci. Pollut. Res., vol. 28(39), pp. 55667–55677, 2021. 225 Appendices Appendix A: Mathematical Symbols Definition Symbol Name Definition/ Meaning Υ𝑦 ⎯ Output variable identified as distillate water. 𝑤𝑦𝑗 ⎯ Weights between 2nd hidden and output layers. 𝑥𝑖 ⎯ Input variables. 𝑤𝑗𝑘 ⎯ Weights between the 1st and 2nd hidden layers. 𝑤𝑘𝑖 ⎯ Weights between the input and first hidden layers 𝑚 ⎯ Number of neurons in the 1st hidden layer. 𝑝 ⎯ Number of neurons in the 2nd hidden layer. 𝑛 ⎯ Number of neurons in the input layer 𝑏𝑘 ⎯ Bias values of the neurons in the 1st hidden layer. 𝑏𝑗 ⎯ Bias values of the neurons in the 2nd hidden layer. 𝑏𝑦 ⎯ Bias values of the neurons in the output layer. 𝐹 ⎯ Activation function. 𝐹𝑖 ⎯ Hidden units/ neurons in the hidden layers. 𝑤𝑖 ⎯ Weight values that are attached to each input. 𝑦 ⎯ Predicted parameter for the MLR model formula. 𝛽 ⎯ The intercept of the MLR model formula. 𝛽𝑖 ⎯ The coefficients of the predictors. 𝑥𝑖 ⎯ The predictors of the MLR model formula. 𝑋0 ⎯ Original values of input and output variables. 𝑋𝑛 ⎯ Normalized value. 𝑋𝑚𝑖𝑛 ⎯ Minimum of input and output variables. 𝒴𝑚𝑖𝑛 ⎯ Minimum of input and output variables. 𝒴𝑚𝑎𝑥 ⎯ Maximum of input and output variables. 𝒴𝑜,𝑖 ⎯ Observed input and output values. 𝒴𝑝,𝑖 ⎯ Predicted value by the machine learning models. ?̅?𝑜 ⎯ Averaged observed/ mathematically obtained values. ?̅?𝑝 ⎯ Predicted values/ theoretically estimated from averaging. 226 𝑛 ⎯ Number of observations or dataset size. 𝑋𝑑𝑎𝑡𝑎 ⎯ Original input feature matrix (365 × 5) 𝒴𝑑𝑎𝑡𝑎 ⎯ Original output column (365 × 1) 𝑋𝑡𝑠[𝑖] ⎯ Time-series input with look-back window = 7 𝒴𝑡𝑠[𝑖] ⎯ Output value corresponding to each time-window sample 𝑋𝑡𝑟𝑎𝑖𝑛 , 𝒴𝑡𝑟𝑎𝑖𝑛 ⎯ Training data split (70%) 𝑋𝑣𝑎𝑙 , 𝒴𝑣𝑎𝑙 ⎯ Validation data split (10%) 𝑋𝑡𝑒𝑠𝑡 , 𝒴𝑡𝑒𝑠𝑡 ⎯ Testing data split (20%) ?̃?𝑡𝑟𝑎𝑖𝑛[𝑖, 𝑗] ⎯ Augmented input sample using Gaussian noise ?̃?𝑡𝑟𝑎𝑖𝑛[𝑖, 𝑗] ⎯ Ground truth label (unchanged during augmentation) 𝒩(0, σ2) ⎯ Gaussian noise with mean 0 and variance σ² 𝑋𝑠𝑐𝑎𝑙𝑒𝑑 , 𝒴𝑠𝑐𝑎𝑙𝑒𝑑 ⎯ Normalized features and labels using Min-Max scaling 𝑁 ⎯ Total number of training instances 𝑍(𝑙)[𝑖, 𝑗] ⎯ Output of convolution before activation 𝐴(𝑙)[𝑖, 𝑗] ⎯ Activation output at time step [𝑖, 𝑗] from the current layer 𝐴(𝑙−1)[𝑖 + 𝑘] ⎯ Activation output at time step [𝑖, 𝑗] from the previous layer 𝐴(0) = 𝑥 ⎯ Original input time series to the first convolutional layer 𝑤(𝑙) [𝑘, 𝑗] ⎯ Weight of kernel position k for filter j 𝑏(𝑙)[𝑗] ⎯ Bias term for filter j 𝑃 ⎯ Padding size 𝐿𝑖𝑛 ⎯ Input sequence length 𝐿𝑜𝑢𝑡 ⎯ Output sequence length 𝑆 ⎯ Stride (1) 𝐾 ⎯ Kernel size (3) 𝑘 ⎯ Kernel index from 0 to 𝐾 − 1 (𝐾 = 3) 𝑖 ⎯ Time index (temporal position) 𝑗 ⎯ Filter index (1 to 128) 𝑙 ⎯ Layer index (𝑙 = 1,2,3) 𝑓 𝜖 ℝ𝑀 ⎯ Flattened feature vector, M = T × filters ℎ𝑚 ⎯ Output from the 𝑚-th neuron in the dense hidden layer max(0, . ) ⎯ ReLU activation function. 227 𝑊𝑚𝑛 ⎯ Weight connecting 𝑛-th feature to 𝑚 -th neuron in the dense hidden layer. 𝑏𝑚 ⎯ Bias term associated with the 𝑚-th neuron in the dense hidden layer. 𝑓𝑛 ⎯ 𝑛-th input value from the flattened layer 𝑓 𝜖 ℝ𝑀 𝑀 ⎯ Total number of neurons in the dense hidden layer (128). ?̂? ⎯ Predicted scalar output value from the network (water productivity). 𝑤𝑚(0) ⎯ Weight connecting 𝑚-th neuron in the dense hidden layer to output layer. 𝑏(0) ⎯ Bias term in the output layer. 𝜂 ⎯ Learning rate ∈ [10⁻⁴, 10⁻²] λ ⎯ Regularization strength ∈ [10⁻⁴, 10⁻²] 𝑀 ⎯ Total number of neurons in the dense hidden layer (128). ?̂? ⎯ Predicted scalar output value for a generic input sample 𝑥 𝑤𝑚(0) ⎯ Weight connecting m-th neuron in the dense hidden layer to output layer. 𝑏(0) ⎯ Bias term in the output layer. 𝜂 ⎯ Learning rate ∈ [10⁻⁴, 10⁻²] λ ⎯ Regularization strength ∈ [10⁻⁴, 10⁻²] 𝜃𝑡 ⎯ Learnable parameter (weights and biases) vector at iteration t 𝜃𝑡+1 ⎯ Updated set of parameters for the next iteration ∇𝜃ℒ ⎯ Gradient loss function ℒ with respect to the parameters 𝜃 at iteration 𝑡 𝑥i ⎯ Support vectors from training 𝑥 ⎯ Current input for which we are predicting ?̂? 𝛼𝑖 , 𝛼𝑖∗ ⎯ Dual Lagrange multipliers 𝐾(𝑥𝑖 , 𝑥) ⎯ RBF kernel function that measures similarity between input vectors 𝑏 ⎯ Model bias 𝑁 ⎯ Total number of training instances γ ⎯ Kernel coefficient ℒSVR ⎯ SVR loss function/ learning objective w ⎯ Weight vector in the induced feature space C ⎯ SVR Regularization parameter ε ⎯ Width of the margin (tube) around the regression function 𝒴i ⎯ Actual continuous output value ?̂?i ⎯ Predicted continuous output for the i-th training sample 𝑥i 𝒩(0, σ2) ⎯ Gaussian noise with mean 0 and variance σ² 228 Appendix B: Tables including 3-D Results and Figures Solar still integrated with photovoltaic SIMULINK/ theoretical results are tabulated herein under tables (B.1-12): B.1: Solar still area, Ast m2, Is: solar radiation MJ/m2.day, Pst: feed tank flow rate productivity kg/day. Table B.1: Solar still area, Ast m2, Is: solar radiation MJ/m2.day, Pst: Productivity kg/day. Is/Pst 1 2 3 4 5 Ast, m2 15 0.343780 0.687560 1.031340 1.375120 1.718899 Tamb= 25 oC 16 0.317175 0.634349 0.951524 1.268698 1.585873 17 0.294391 0.588783 0.883174 1.177566 1.471957 18 0.274662 0.549324 0.823986 1.098648 1.373310 20 0.242199 0.484398 0.726597 0.968796 1.210994 B.2: PV total system area, At m2, at ambient temperature 25 oC: Table B.2: PV total system area, At m2, at ambient temperature 25 oC Is/ Pst 1 2 3 4 5 At, m2 15 6.00780 12.01561 18.02341 24.03122 30.03902 Tamb= 25 oC 16 5.54286 11.08571 16.62857 22.17143 27.71428 17 5.14470 10.28941 15.43411 20.57882 25.72352 18 4.79992 9.59984 14.39976 19.19968 23.99960 20 4.23260 8.46520 12.69781 16.93041 21.16301 B.3: Solar still efficiency, Effst %, at ambient temperature 25 oC: Table B.3: Solar still efficiency, Effst %, at ambient temperature 25 oC Is/Pst 1 2 3 4 5 Effst, % 15 47.123176 47.123176 47.123176 47.123176 47.123176 Tamb= 25 oC 16 47.883727 47.883727 47.883727 47.883727 47.883727 17 48.554802 48.554802 48.554802 48.554802 48.554802 18 49.151313 49.151313 49.151313 49.151313 49.151313 20 50.165382 50.165382 50.165382 50.165382 50.165382 229 B.4: Solar still areas at different solar radiation energies (Is, MJ/m2.day): Table B.4: Solar still areas at different solar radiation energies (Is = MJ/m2.day) Tamb /Pst 1 2 3 4 5 Ast, m2 25 0.343780 0.687560 1.031340 1.375120 1.718899 Is=15 30 0.362078 0.724155 1.086233 1.448311 1.810389 35 0.382433 0.764866 1.147299 1.529731 1.912164 40 0.405213 0.810426 1.215639 1.620852 2.026065 45 0.430879 0.861758 1.292637 1.723515 2.154394 Tamb / Pst 1 2 3 4 5 Ast, m2 25 0.317175 0.634349 0.951524 1.268698 1.585873 Is=16 30 0.332686 0.665372 0.998058 1.330744 1.663430 35 0.349792 0.699585 1.049377 1.399170 1.748962 40 0.368754 0.737507 1.106261 1.475014 1.843768 45 0.389888 0.779776 1.169665 1.559553 1.949441 Tamb / Pst 1 2 3 4 5 Ast, m2 25 0.274662 0.549324 0.823986 1.098648 1.373310 Is=18 30 0.286218 0.572436 0.858655 1.144873 1.431091 35 0.298789 0.597579 0.896368 1.195158 1.493947 40 0.312516 0.625032 0.937547 1.250063 1.562579 45 0.327564 0.655128 0.982692 1.310256 1.637820 Tamb / Pst 1 2 3 4 5 Ast, m2 25 0.242199 0.484398 0.726597 0.968796 1.210994 Is=20 30 0.251140 0.502281 0.753421 1.004561 1.255702 35 0.260767 0.521534 0.782302 1.043069 1.303836 40 0.271162 0.542323 0.813485 1.084646 1.355808 45 0.282419 0.564838 0.847257 1.129676 1.412095 B.5: Solar still glass cover areas at solar radiation energies (Is = 15,20 MJ/m2.day), respectively: Table B.5: Solar still glass cover areas at solar radiation energies Tamb / Pst 1 2 3 4 5 Ag, m2 25 0.515670 1.031340 1.547009 2.062679 2.578349 Is=15 30 0.543117 1.086233 1.629350 2.172466 2.715583 35 0.573649 1.147299 1.720948 2.294597 2.868247 40 0.607819 1.215639 1.823458 2.431278 3.039097 45 0.607819 1.215639 1.823458 2.431278 3.039097 Tamb / Pst 1 2 3 4 5 Ag, m2 230 25 0.363298 0.726597 1.089895 1.453193 1.816492 Is=20 30 0.363298 0.726597 1.089895 1.453193 1.816492 35 0.391151 0.782302 1.173452 1.564603 1.955754 40 0.406742 0.813485 1.220227 1.626970 2.033712 45 0.423629 0.847257 1.270886 1.694514 2.118143 B.6: Solar still glass cover areas at solar radiation energies (Is = 15,20 MJ/m2.day), respectively: Table B.6: Solar still glass cover areas at different solar radiation energies and productions Is /Tamb 25 30 35 40 45 d, cm 15 6.371791 7.273657 8.224862 9.231117 10.299189 Is=15 16 4.970934 5.801309 6.673329 7.591392 8.560633 17 3.674551 4.443940 5.248948 6.093035 6.980188 18 2.468136 3.184884 3.932446 4.713591 5.531479 20 0.280621 0.911099 1.565296 2.245066 2.952492 Is /Tamb 25 30 35 40 45 Effst, % 15 47.123176 44.741776 42.360376 39.978976 37.597576 Is=20 16 47.883727 45.651165 43.418602 41.186040 38.953477 17 48.554802 46.453567 44.352331 42.251096 40.149861 18 49.151313 47.166813 45.182313 43.197813 41.213313 20 50.165382 48.379332 46.593282 44.807232 43.021182 Is /Tamb 25 30 35 40 45 Pstd, kg/m2.day 15 2.908838 2.761838 2.614838 2.467838 2.320838 16 3.152838 3.005838 2.858838 2.711838 2.564838 17 3.396838 3.249838 3.102838 2.955838 2.808838 18 3.640838 3.493838 3.346838 3.199838 3.052838 20 4.128838 3.981838 3.834838 3.687838 3.540838 Is /Tamb 25 30 35 40 45 Pdye, kg/m2.day 15 3.706376 3.510560 3.315231 3.120413 2.926137 16 4.032416 3.835843 3.639719 3.444066 3.248907 17 4.359637 4.162363 3.965505 3.769083 3.573116 18 4.687958 4.490030 4.292491 4.095357 3.898645 20 5.347629 5.148512 4.949739 4.751321 4.553272 Is /Tamb 25 30 35 40 45 Tg, oC 15 25.324532 28.649531 32.293758 36.220148 40.399246 16 26.442429 29.460169 32.884309 36.650444 40.711175 17 28.346013 30.773475 33.798813 37.289345 41.155974 231 18 31.985533 33.120847 35.343097 38.314024 41.835389 20 104.000656 52.774601 45.244476 43.985461 45.198440 Is /Tamb 25 30 35 40 45 Tw, oC 15 36.380204 35.589118 34.942737 34.403945 33.947236 16 38.723422 37.474787 36.498039 35.712200 35.065461 17 42.538613 40.367777 38.777716 37.561712 36.600650 18 49.765523 45.317353 42.405508 40.349645 38.819341 20 223.159234 89.493498 64.628885 54.143805 48.358881 B.7: Total photovoltaic cost, PVCt, $ at different ambient temperatures 25, 30, 35 oC, respectively: Table B.7: Total photovoltaic cost, PVCt $ at different ambient temperatures Is/ Pst 1 2 3 4 5 PVCt, $ 15 253.34583 506.69165 760.03748 1013.38330 1266.72913 Tamb=25 oC 16 249.32186 498.64372 747.96557 997.28743 1246.60929 17 245.87599 491.75197 737.62796 983.50394 1229.37993 18 242.89198 485.78396 728.67595 971.56793 1214.45991 20 237.98204 475.96408 713.94612 951.92816 1189.91019 Is/ Pst 1 2 3 4 5 PVCt, $ 15 266.8303 533.6605 800.4908 1067.3211 1334.1513 Tamb=30 oC 16 261.5149 523.0298 784.5447 1046.0596 1307.5745 17 256.9977 513.9954 770.9931 1027.9908 1284.9885 18 253.1114 506.2229 759.3343 1012.4457 1265.5572 20 246.7678 493.5355 740.3033 987.0711 1233.8389 Is/ Pst 1 2 3 4 5 PVCt, $ 15 281.8308 563.6617 845.4925 1127.3233 1409.1542 Tamb=35 oC 16 274.9619 549.9237 824.8856 1099.8475 1374.8093 17 269.1732 538.3464 807.5197 1076.6929 1345.8661 18 264.2286 528.4572 792.6858 1056.9144 1321.1431 20 256.2271 512.4541 768.6812 1024.9083 1281.1353 Is/Tamb 1 2 3 4 5 Pst, kg/day 15/25 253.3458 506.6917 760.0375 1013.3833 1266.7291 PVCt, $ 16/30 261.5149 523.0298 784.5447 1046.0596 1307.5745 4-D Plot 17/35 269.1732 538.3464 807.5197 1076.6929 1345.8661 18/40 276.3672 552.7345 829.1017 1105.4689 1381.8361 20/45 277.5019 555.0038 832.5057 1110.0076 1387.5095 232 B.8: Convective heat transfer coefficient, hc W/m2.oC at different ambient temperatures and the same feed tank flow rate productivities (i.e., 1-5 kg/day): Table B.8: Convective heat transfer coefficient, hc w/m2.oc at different ambient temperatures Is /Tamb 25 30 32 34 35 hc, W/m2.oC 15 22.074659 33.416511 43.288021 63.086631 82.934925 16 21.489443 31.432206 39.397596 53.765556 66.365625 17 19.958258 28.307247 34.407454 44.365196 52.162584 18 16.951520 23.821317 28.275592 34.857124 39.522937 20 2.277265 8.599214 11.314537 14.379399 16.124937 Is /Tamb 25 26 27 28 30 hc, W/m2.oC 15 22.074659 23.581894 25.365697 27.509258 33.416511 16 21.489443 22.866403 24.472176 26.369762 31.432206 17 19.958258 21.174811 22.565449 24.174268 28.307247 18 16.951520 18.033575 19.228282 20.564512 23.821317 20 2.277265 3.555492 4.808283 6.056231 8.599214 B.9: Heat transfer energies, Q’s kW, including evaporation, thermal load inside the still, energy between water and glass cover, energy between glass cover and ambient at different solar radiations, and feed tank flow rate productivities respectively: Table B.9: Heat transfer energies, Q’s kW at different solar radiation energies & water productions Is/Pst 1 2 3 4 5 Qload 15 0.1611468 0.3222936 0.4834405 0.6445873 0.8057341 Tamb= 25 oC 16 0.1585873 0.3171746 0.4757618 0.6343491 0.7929364 17 0.1563954 0.3127909 0.4691863 0.6255818 0.7819772 18 0.1544974 0.3089948 0.4634922 0.6179896 0.7724870 20 0.1513743 0.3027486 0.4541229 0.6054972 0.7568715 Is/Pst 1 2 3 4 5 Qload 15 0.1697239 0.3394479 0.5091718 0.6788957 0.8486197 Tamb= 30 oC 16 0.1663430 0.3326859 0.4990289 0.6653719 0.8317148 17 0.1634697 0.3269394 0.4904091 0.6538787 0.8173484 18 0.1609977 0.3219955 0.4829932 0.6439909 0.8049887 20 0.1569627 0.3139254 0.4708881 0.6278508 0.7848134 233 B.10: Cost analysis for the design model system at different solar radiation energy, feed tank flow rate productivities, and ambient temperature: Table B.10: Cost analysis for the design model system at different solar radiation energies Is/Pst 1 2 3 4 5 TCC, $ 15 85.98794 171.97589 257.96383 343.95178 429.93972 Tamb = 25 oC 16 79.33329 158.66657 237.99986 317.33315 396.66643 17 73.63466 147.26931 220.90397 294.53863 368.17328 18 68.69984 137.39969 206.09953 274.79937 343.49922 20 60.58000 121.16000 181.74000 242.31999 302.89999 Is/Pst 1 2 3 4 5 TCC, $ 15 90.56469 181.12938 271.69407 362.25876 452.82345 Tamb = 30 oC 16 83.21307 166.42613 249.63920 332.85227 416.06534 17 76.96537 153.93075 230.89612 307.86150 384.82687 18 71.59033 143.18065 214.77098 286.36130 357.95163 20 62.81647 125.63294 188.44940 251.26587 314.08234 B11: Area ratios for solar still standalone, PV standalone, and combined at different solar radiation energies, feed tank flow rate productivities, respectively: Table B.11: Area ratios for solar still standalone, PV standalone and combined at different solar radiations energy Is/Pst 1 2 3 4 5 Ast, m2 15 0.3437799 0.6875598 1.0313397 1.3751195 1.7188994 Tamb = 25 oC 16 0.3171746 0.6343491 0.9515237 1.2686982 1.5858728 17 0.2943914 0.5887829 0.8831743 1.1775657 1.4719572 18 0.2746620 0.5493241 0.8239861 1.0986482 1.3733102 20 0.2421989 0.4843978 0.7265967 0.9687956 1.2109945 Is/Pst 1 2 3 4 5 At, m2 15 6.007804 12.015608 18.023412 24.031215 30.039019 16 5.542856 11.085713 16.628569 22.171425 27.714282 17 5.144705 10.289409 15.434114 20.578818 25.723523 18 4.799919 9.599838 14.399758 19.199677 23.999596 20 4.232602 8.465204 12.697806 16.930408 21.163010 234 B12: Cost ratios for solar still stand alone, PV standalone, and combined at different solar radiation energies, feed tank flow rate productivities, respectively: Table B.12: Cost ratios for solar still stand alone, PV standalone and combined at different solar radiations energy Is/Pst 1 2 3 4 5 TCC, $ 15 85.98794 171.97589 257.96383 343.95178 429.93972 Tamb = 25 oC 16 79.33329 158.66657 237.99986 317.33315 396.66643 17 73.63466 147.26931 220.90397 294.53863 368.17328 18 68.69984 137.39969 206.09953 274.79937 343.49922 20 60.58000 121.16000 181.74000 242.31999 302.89999 Is/Pst 1 2 3 4 5 PVCt, $ 15 253.3458 506.6917 760.0375 1013.3833 1266.7291 Tamb = 25 oC 16 249.3219 498.6437 747.9656 997.2874 1246.6093 17 245.8760 491.7520 737.6280 983.5039 1229.3799 18 242.8920 485.7840 728.6759 971.5679 1214.4599 20 237.9820 475.9641 713.9461 951.9282 1189.9102 Is/Pst 1 2 3 4 5 SS+PV, $ 15 339.3338 678.6675 1018.0013 1357.3351 1696.6688 Tamb = 25 oC 16 328.6551 657.3103 985.9654 1314.6206 1643.2757 17 319.5106 639.0213 958.5319 1278.0426 1597.5532 18 311.5918 623.1837 934.7755 1246.3673 1557.9591 20 298.5620 597.1241 895.6861 1194.2481 1492.8102
Thesis/Dissertation
eng
Chemical and Biological Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Gopaluni, Bhushan
Data-efficient deep learning for predictive modelling of conventional single slope solar stills : leveraging transfer learning and tailored data augmentation strategies
Text