Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Atoom, Adam Izzeldeen
Master of Applied Science - MASc
University of British Columbia
Thermoacoustic oscillations in combustors need to be monitored and mitigated as they directly impact efficiency and safety of land-based power generation systems. Monitoring the thermoacoustic oscillations requires acquisition of high-resolution flame chemiluminescence images, which is not readily available in industrial settings due to the lack of optical access to the combustor. To mitigate thermoacoustics, this thesis proposes using few sensors to produce low-resolution flame chemiluminescence images, which are then upscaled using machine learning to high-resolution flame chemiluminescence images. A multi-path convolutional upscaling neural network (NN) is proposed and used in the present study to upscale the low-resolution flame chemiluminescence images to high-resolution flame chemiluminescence images. The effectiveness of the proposed NN is validated using image similarity metrics, and comparisons are made with existing image upscaling NNs in the literature. The performance of our NN is further assessed for predicting high-resolution spatial thermoacoustic source term. The proposed NN achieved more accurate upscaling and spatial thermoacoustic source term calculation compared to previous works in the literature. As a result, the present study demonstrates the feasibility of real-time detailed monitoring of thermoacoustic oscillations in industrial applications using few sensors.
Upscaling Very Low-ResolutionChemiluminescence Images forPrediction of Thermoacoustic SourceTerm Using Machine LearningbyAdam Izzeldeen AtoomB.Sc. Hons., The University of Jordan, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe College of Graduate Studies(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)November 2024© Adam Izzeldeen Atoom, 2024The following individuals certify that they have read, and recommend to the Collegeof Graduate Studies for acceptance, a thesis entitled:Upscaling Very Low-Resolution Chemiluminescence Images for Predic-tion of Thermoacoustic Source Term Using Machine Learningsubmitted by Adam Izzeldeen Atoom in partial fulfilment of the requirements of thedegree of Master of Applied ScienceDr. Anas Chaaban, School of EngineeringCo-supervisorDr. Sina Kheirkhah, School of EngineeringCo-supervisorDr. Ahmad Al-Dabbagh, School of EngineeringSupervisory Committee MemberDr. Zheng Liu, School of EngineeringSupervisory Committee MemberDr. Shahria Alam, School of EngineeringUniversity ExamineriiAbstractThermoacoustic oscillations in combustors need to be monitored and mitigated as theydirectly impact efficiency and safety of land-based power generation systems. Monitoringthe thermoacoustic oscillations requires acquisition of high-resolution flame chemilumines-cence images, which is not readily available in industrial settings due to the lack of opticalaccess to the combustor. To mitigate thermoacoustics, this thesis proposes using few sen-sors to produce low-resolution flame chemiluminescence images, which are then upscaledusing machine learning to high-resolution flame chemiluminescence images. A multi-pathconvolutional upscaling neural network (NN) is proposed and used in the present study toupscale the low-resolution flame chemiluminescence images to high-resolution flame chemi-luminescence images. The effectiveness of the proposed NN is validated using image similar-ity metrics, and comparisons are made with existing image upscaling NNs in the literature.The performance of our NN is further assessed for predicting high-resolution spatial ther-moacoustic source term. The proposed NN achieved more accurate upscaling and spatialthermoacoustic source term calculation compared to previous works in the literature. Asa result, the present study demonstrates the feasibility of real-time detailed monitoring ofthermoacoustic oscillations in industrial applications using few sensors.iiiLay SummaryThis research addresses the challenge of monitoring the interactions of heat and soundin combustion systems, which are critical for the efficiency and safety of power generationsystems. Since the high-resolution images needed for this task are difficult to obtain inindustrial settings, the study proposes using few sensors along with a new machine learningmethod to extract high-resolution images from the few sensors. This allows for monitoringthe combustion using a sensor setup that is viable in industrial settings. This methodoutperforms existing solutions, offering a valuable tool for better monitoring and managingpower systems in real-world applications.ivPrefaceThis thesis was carried out under the supervision of Dr. Anas Chaaban and Dr. SinaKheirkhah at the School of Engineering of the University of British Columbia. Both su-pervisors provided guidance and feedback throughout the research process. There was nouse of generative artificial intelligence in the research, the drafting of, and the preparationof the thesis. A journal article based on the main findings of this thesis is being preparedfor submission.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thermoacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Chemiluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Thermoacoustic oscillations . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Thermoacoustic source term . . . . . . . . . . . . . . . . . . . . . . . 31.3 Image upscaling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Interpolation-based upscaling methods . . . . . . . . . . . . . . . . . 41.3.2 Deep learning-based image upscaling methods . . . . . . . . . . . . . 71.4 Research gap and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Chapter 2: Data acquisition and preparation . . . . . . . . . . . . . . . . . . 132.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Dataset preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.1 Data split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15viTABLE OF CONTENTS2.2.2 Pre-processing of CL images . . . . . . . . . . . . . . . . . . . . . . . 162.2.3 Downscaling procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Chapter 3: Chemiluminescence image upscaling and thermoacoustic sourceterm calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1 Network architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Calculation of the thermoacoustic source term . . . . . . . . . . . . . . . . . 233.2.1 Amplitude and phase calculation . . . . . . . . . . . . . . . . . . . . 233.2.2 Thermoacoustic source term . . . . . . . . . . . . . . . . . . . . . . . 253.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Chapter 4: Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 284.1 Performance of the upscaling network . . . . . . . . . . . . . . . . . . . . . 284.2 Performance in predicting the thermoacoustic source . . . . . . . . . . . . . 304.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Limitations of the current approach . . . . . . . . . . . . . . . . . . . . . . 365.3 Implications for industrial applications . . . . . . . . . . . . . . . . . . . . . 365.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38viiList of FiguresFigure 1.1 Example of upscaling with nearest neighbor interpolation. (a) Orig-inal image. (b) Image upscaled using nearest neighbor interpolation. 5Figure 1.2 Example of upscaling with bilinear interpolation. (a) Original image.(b) Image upscaled using bilinear interpolation. . . . . . . . . . . . 5Figure 1.3 Example of upscaling with bicubic interpolation. (a) Original image.(b) Image upscaled using bicubic interpolation. . . . . . . . . . . . . 6Figure 1.4 GLEAN architecture reproduced from [1]. The layers denoted by“E”, “S”, and “D” correspond to the encoder, the generative latentbank, and the decoder layers, respectively. . . . . . . . . . . . . . . 8Figure 1.5 The SwinIR architecture reproduced from [2]. RSTB is the resid-ual swin transformer block, which consists of multiple stacked swintransformer layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 1.6 SpecGAN architecture reproduced from [3]. DFEB is the deep fea-ture extraction block. RFB is the registration and fusion block. . . 10Figure 1.7 PIESRGAN architecture reproduced from [4]. RDB is the residualdense block. BN is the batch normalization block. . . . . . . . . . . 12Figure 2.1 The experimental setup, which is similar to that in [5, 6]. . . . . . . 14Figure 2.2 Train test split for one repeat (10,000 images) of the experiments.The shaded part is not used for either training or testing. Thetraining set images are sampled randomly from the training part. . 16Figure 2.3 Pre-processing steps of CL images. (a) is the averaged backgroundnoise image. (b) is the white-field image. (c) is the original CLimage with a resolution of 1024 × 1024. (d) is the CL image aftersubtracting the background noise (a). (e) is (d) after normalizingby the white field image (b). (f) is the CL image with a resolutionof 128× 128 as a result of binning the original CL image (c) . . . . 17Figure 2.4 Diagram of the proposed approach. (a) Full optical access allowshigh-resolution imaging. (b) High-resolution flame image example.(c) Limited optical access with sensor placement. (d) Low-resolutionsensor output, showing Gaussian convolution effect. (e) Gaussiankernel weight distribution. . . . . . . . . . . . . . . . . . . . . . . . 18viiiLIST OF FIGURESFigure 3.1 The Multi Path Chemiluminescence and Pressure Network architec-ture. The network features two paths: one for low-resolution imageshighlighted in blue and another for pressure data that is highlightedin yellow. The thermoacoustic source term calculation process ishighlighted in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 3.2 Power spectral density (PSD) of the spatially averaged CL signalover multiple repeats. The dominant frequency is approximately 80Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.3 A sample of filtered pressure fluctuations as a function of time. . . . 25Figure 3.4 (a) is a segment of the filtered pressure with the amplitude shownusing a dashed red curve. (b) is a segment of filtered intensity val-ues of a random CL image pixel with the amplitude shown using adashed red curve. (c) is the thermoacoustic source term calculatedusing the instantaneous amplitude and phase of the pressure and CLpixel intensity fluctuations. . . . . . . . . . . . . . . . . . . . . . . . 26Figure 3.5 (a–d) are the CL images at different timestamps. (e–h) are CL inten-sity fluctuations amplitudes at the corresponding times that resultsin (a–d) were acquired. (i–l) are the phase of the flame chemilumi-nescence fluctuations. (m–p) are the thermoacoustic source term. . 27Figure 4.1 Samples showcasing the performance of the MPCP-net predictingthe upscaled CL images for several upscaling factors. . . . . . . . . 29Figure 4.2 A ground truth image (first row), a 4× upscaled image (second row)and a 32× upscaled image (third row). The insets are shown to theright side of the images. . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 4.3 The variation of PSNR for upscaling the CL images versus the up-scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 4.4 (a) Temporal variation of the pressure (solid red curve) and pressureamplitude (dashed blue curve). (b–e) are the ground truth thermoa-coustic source term at t = 575, 620, 641, and 700 ms, respectively(see the solid circular data points in (a)). (f–i) and (j–m) are thecalculated thermoacoustic source term using 16× and 32× upscaledCL images, respectively. The time instants in (f–i) and (j–m) matchthose in (b–e). The colorbar value MAX indicates the highest ther-moacoustic source term value calculated. . . . . . . . . . . . . . . . 32Figure 4.5 PSNR for spatial thermoacoustic source term prediction versus theupscaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33ixAcknowledgementsI would like to thank my supervisors, Dr. Anas Chaaban and Dr. Sina Kheirkhah,for their support and mentorship throughout my research. Their insightful advice andsupport not only guided me through this project but also helped me develop my researchskills. Their contribution to my growth as a researcher has been invaluable, and I am trulygrateful for the opportunity to work under their supervision. I would also like to extend mysincere thanks to Liam Krebbers, who performed the experiments and provided us with thedata. Additionally, I am grateful for the financial support from Mathematics of InformationTechnology and Complex Systems (MITACS) and Lantern Machinery Analytics Inc.I am also deeply appreciative of my parents, whose love and support have been a sourceof strength during this journey. My deepest gratitude goes to my mother, whose endlessencouragement, patience, and belief in me have been a constant source of motivation. Hersupport has made this achievement possible.xDedicationTo my mother, my greatest believer. She is the most important person in my life, andI dedicate every achievement I have ever accomplished and will ever achieve to her.xiChapter 1IntroductionThis thesis studies the feasibility of predicting the thermoacoustic oscillations by lever-aging a small number of optical sensors. Accurate monitoring of these oscillations is crucialfor maintaining the safety of gas turbine engines, furnaces, and other power generationsystems. This work evaluates the accuracy of the proposed approach and compares withexisting methods in the literature. The following sections outline the motivation for thisresearch, review relevant background, and highlight the research gaps in the literature.1.1 MotivationThermoacoustic (pressure and heat release rate) oscillations are detrimental to theoperation of several engineering equipment, including furnaces and gas turbine engines [7–11]. These oscillations arise from the interaction between unsteady heat release rate andacoustic waves [12]. In extreme cases, thermoacoustic oscillations can lead to catastrophicfailure, and as a result, these oscillations have been identified to be a safety concern [11].Thus, mitigating thermoacoustic oscillations is crucial for the safe operation of combustionsystems.One of the primary tools for monitoring the heat release rate (and eventually ther-moacoustics) is flame chemiluminescence (CL) imaging [10]. CL is the emission of lightproduced by chemical reactions, resulting in a species transitioning from an excited elec-tronic state to a lower energy state [13]. The CL image can be combined with pressuremeasurements to obtain the so-called thermoacoustic source term, which allows for themonitoring of thermoacoustic oscillations.The acquisition of pressure data is relatively straight forward, since it can be acquiredusing a pressure sensor. In laboratory settings, the CL images can be acquired using high-resolution imaging of combustion radicals that are electronically excited due to heat releasein the flame region. Indeed, to acquire these images, the imaging device must have opticalaccess to the inside of the combustor, which can be ensured in a lab setting. Thoughacquiring high-resolution CL images can be experimentally feasible in laboratory settings,such imaging in industrial settings is challenging due to the lack of or at best limited)optical access [14–16].To address this challenge, this thesis envisions a solution that involves the deploymentof a few CL sensors that require limited optical access in the combustor, so that spatialsamples of the CL can be acquired by these sensors. However, deploying a limited number11.2. THERMOACOUSTICSof sensors results in low-resolution CL images, which may not be adequate for accuratemonitoring of thermoacoustic oscillations. To address this challenge, machine learningtechniques can be utilized to upscale the low-resolution CL images to high-resolution ones.This thesis focuses on the second part, i.e., the upscaling of low-resolution CL images. Itexplores the application of machine learning models for upscaling very low-resolution CLimages to high-resolution ones, that in turn allow for monitoring flame chemiluminescenceand thermoacoustic oscillations for industrial applications.Understanding the feasibility of this upscaling is important in order to determine ifinvesting into the aforementioned sensor system is beneficial, which, if true, can be exploredin future research. In the following, the literature related to chemiluminescence imaging,thermoacoustics, and the production of high-resolution images from low-resolution imagesare discussed.1.2 ThermoacousticsCombustion entails several physical and chemical processes, out of which the two rele-vant processes for this thesis are introduced next.1.2.1 ChemiluminescenceChemiluminescence refers to the emission of light generated by chemical reactions,where a species transitions from an excited electronic state to a lower energy state [13].Chemiluminescence can be used to measure several properties of the combustion process.For instance, the Chemiluminescence from the excited states of radicals such as OH∗, CH∗and CO∗2, is often used in reacting flows to measure, for example, the fuel-air equivalenceratio [17–19], study flame propagation dynamics [20–22], calculate the laminar flame speed[14, 23, 24], or measure the approximate location of the heat release rate in the combustionchamber, especially in turbulent premixed flames [25, 26]. Of importance to this study isthe temporally resolved measurement of chemiluminescence to investigate the heat releaserate (q˙′) oscillations [27]. These along with pressure (p′) oscillations are referred to asthermoacoustics [7–9].1.2.2 Thermoacoustic oscillationsThermoacoustic oscillations refer to the process of acoustic waves perturbing the flame,causing variations in heat release rate, which in turn generates more acoustic waves, cre-ating a feedback loop. This feedback can lead to large pressure oscillations and can poten-tially cause mechanical damage to combustion systems. Ultimately, nonlinear dissipativeeffects limit the oscillation growth, resulting in a steady limit cycle [7, 28]. Understandingthese coupling mechanisms is critical in developing strategies to mitigate oscillations, par-ticularly in practical industrial applications. The key mechanisms for the development of21.2. THERMOACOUSTICSthermoacoustic oscillations are outlined below.− Acoustic-flame coupling occurs when perturbations in the reacting flow, induced byacoustic waves, lead to changes in the flame’s area or position, thereby modulating therate of heat release. This is often observed when acoustic waves wrinkle a premixedflame, causing flame surface variations and thus generating fluctuating heat release[7].− Unsteady strain rates are caused by flow instabilities that modify the flame area orreaction rates. These modifications fluctuate with the flow field and can act as asource of oscillatory energy when the proper conditions exist.− Vortices, shed from obstacles or generated by flow instabilities, interact with theflame, increasing its surface area and causing a sudden spike in heat release when theflame wraps around these vortices. Vortices can also ignite unburnt fuel, which leadsto rapid heat release, further stimulating the pressure waves [29].− When a flame is close to a wall, the flame can interact with the boundary, rapidlymodifying the flame surface and generating significant heat release fluctuations. Forexample, when a flame impinges on a wall, it experiences rapid changes in surfacearea, which can induce acoustic radiation [30].− Lastly, inhomogeneities in reactant composition can drive instabilities [31]. Fluctu-ations in the fuel-air equivalence ratio, caused by acoustic interactions with the fuelinjection system, can create inhomogeneities in the flame, leading to time-delayedheat release. The delay promotes the occurrence of the thermoacoustics.The Rayleigh criterion is key for studying the impact of coupling between pressure andheat release rate oscillations [12], with this criterion studied next.1.2.3 Thermoacoustic source termThe phase relation between q˙′ and p′ plays a role in whether the oscillations grow ordecay. This relation can be characterized by the thermoacoustic source term:ψs(x, y, z, t) =1T∫ T0p˜′(x, y, z, t) ˜˙q′(x, y, z, t) cos∆ϕ(x, y, z, t)dt (1.1)where (x, y, z, t) refers to the coordinate in the three-dimensional space and time, T is theperiod of the oscillations, ∆ϕ is the phase difference between q˙′ and p′, and p˜′(x, y, z, t) and˜˙q′(x, y, z, t) are the instantaneous amplitudes of pressure and heat release rate oscillations,which can be estimated from the absolute value of the Hilbert transform of q˙′ and p′ [27].There are no widely accepted methods for directly measuring the thermoacoustic source31.3. IMAGE UPSCALING METHODSterm ψs. Instead, it is typically inferred from indirect measurements of pressure and heatrelease rate. For |∆ϕ(x, y, z, t)| < π/2, the oscillations could grow (ψs > 0), and for|∆ϕ(x, y, z, t)| > π/2, they could decay (ψs < 0).Thermoacoustic instabilities represent a significant challenge for combustion systems,and mitigation techniques often rely on high-resolution experimental data to provide in-sights into the coupling mechanisms, which can be challenging under industrial conditionsdue to the limited optical access. This makes the development of techniques to infer high-resolution data from limited sensors essential for industrial applications.1.3 Image upscaling methodsTo facilitate monitoring the thermoacoustic oscillations, high-resolution CL images arerequired. Since acquiring high-resolution CL images using a camera can be challenging (ifeven possible) in an industrial setting, it is important to explore less invasive and potentiallymore feasible methods such as using a few sensors for producing a low-resolution CL image.To produce such high-resolution images from low-resolution images, the present studyproposes the use of upscaling methods. Such upscaling could be achieved via traditionalinterpolation-based upscaling methods and deep learning-based methods. In the followingsubsections, literature related to both methods is discussed.1.3.1 Interpolation-based upscaling methodsInterpolation-based methods estimate pixel values in the upscaled image by computingweighted average of nearby pixels in the original image. These methods differ in howthey calculate these weights, and the choice of method directly impacts the quality ofthe resulting upscaled image. The most commonly used interpolation methods includenearest neighbor interpolation, bilinear interpolation, and bicubic interpolation. A detaileddiscussion of these methods is provided below.Nearest neighbor interpolationNearest neighbor interpolation is one of the simplest techniques for image upscaling.It assigns the value of the closest pixel in the original image to the corresponding positionin the upscaled image [32]. Nearest neighbor interpolation is computationally efficientto implement, making it a practical choice for image upscaling in resource constrainedenvironments. However, such upscaling often produces blocky artifacts, as shown in Fig.1.1. This results in a pixelated appearance, especially when the scaling factor is large, asneighboring pixels in the upscaled image may have abrupt intensity changes.41.3. IMAGE UPSCALING METHODSNearest neighbor interpolation(a)(b)Figure 1.1: Example of upscaling with nearest neighbor interpolation. (a) Original image.(b) Image upscaled using nearest neighbor interpolation.Bilinear interpolation(a)(b)Figure 1.2: Example of upscaling with bilinear interpolation. (a) Original image. (b) Imageupscaled using bilinear interpolation.Bilinear interpolationFor a given pixel whose intensity is to-be-interpolated, the Bilinear interpolation methoduses the intensity of the four nearest pixels and calculates a weighted average of theirintensities [32]. This weighting is influenced by the distance of the to-be-used pixels’intensities for the interpolation, with the farther pixels featuring a smaller weight. Suchinterpolation allows for achieving smoother results, as shown in Fig. 1.2 [33]. Specifically,for upscaling an image using the bilinear interpolation method, the intensity at a givenpixel located at (x, y) is given byIupscaled(x, y) =1∑i=01∑j=0wij × I(x+ i, y + i), (1.2)with Iupscaled(x, y), I(x, y), and wij being the intensity of the pixels in the upscaled imageat coordinates (x, y), the intensity of the pixels in the original image at coordinates (x, y),and the distance-based weights, respectively.51.3. IMAGE UPSCALING METHODSBicubic interpolation(a)(b)Figure 1.3: Example of upscaling with bicubic interpolation. (a) Original image. (b) Imageupscaled using bicubic interpolation.Bicubic interpolationThe bilinear interpolation allows for producing smoother upscaled images compared tothose from the nearest neighbor interpolation. As a result, the former method introducessome degree of blurring, which is not desirable. To help address this, the bicubic interpo-lation [32] allows for addressing this issue via using the intensities of the 16 nearest pixelsand a third order polynomial. Such interpolation provides more accurate results comparedto both the nearest neighbor and bilinear interpolations, as shown in Fig. 1.3 [34].The bicubic interpolation takes into account a 4× 4 neighborhood around each targetpixel located at (x, y). The pixel intensities are calculated using cubic polynomials, whichresult in smoother approximations given byIupscaled(x, y) =2∑i=−12∑j=−1wij × I(x+ i, y + i). (1.3)The bicubic interpolation generally produces visually appealing results [32]. However,interpolation using this method is computationally more expensive than both the nearestneighbor and bilinear interpolations [34].Several studies [32] have compared the effectiveness of the above-reviewed interpola-tion methods. These studies suggest that the nearest neighbor interpolation is the leastexpensive yet least accurate method of interpolation; however, the bicubic method is themost expensive yet most accurate interpolation method. The bilinear interpolation methodoffers a balance between computational cost and the upscaled image quality [34].In several engineering applications, for example those relevant to the present study, pre-serving the high-frequency information is key to the interpolation. However, the traditionalinterpolation methods introduced above fail to preserve such high-frequency information inthe upscaled images. For such applications, the above methods tend to introduce artifactssuch as blurring and pixelation, especially for large upscaling factors [34]. These limitationshave motivated the development of more advanced methods, such as those based on deeplearning, which are discussed in the subsequent sections.61.3. IMAGE UPSCALING METHODS1.3.2 Deep learning-based image upscaling methodsDeep learning networks, such as the Super Resolution Convolutional Neural Network(SRCNN) [35], have demonstrated superior performance (closer prediction to the GroundTruth (GT)) to the traditional interpolation methods [36]. Improving the performanceof SRCNN, the Super Resolution Generative Adversarial Network (SRGAN) and the En-hanced Super Resolution Generative Adversarial Network (ESRGAN) used adversarialand perceptual losses and generated photo-realistic textures from very low-resolution im-ages [37, 38]. The performance of Generative Adversarial Networks was further improvedusing vision transformers, e.g., Image Restoration Using Swin Transformer (SwinIR) [2],the Hybrid Attention Transformer [39], and the Dual Residual Connection Transformer.The state-of-the-art image super-resolution networks are commonly developed for upto a ×4 upscaling factor [36]. It has been shown [40] that the ability to further increasethe upscaling factor is limited by the diversity present in the utilized datasets, such asthe DIV2K dataset, which contains diverse, high-resolution 2K images. To overcome thislimitation, methods such as the Generative Latent Bank for Large-Factor Image SuperResolution (GLEAN) [1] have used pre-trained latent banks. GLEAN has demonstratedsuccess in achieving large upscaling factors (up to ×64) for specific categories, such ashuman faces. However, methods such as GLEAN primarily focus on generating visuallypleasing images rather than accurately reconstructing the GT images. While the GLEANmethod may be used for non-engineering applications, it requires modifications for use inengineering-relevant applications, such as upscaling the CL images [34]. Specifically, forengineering applications, the modifications to the state-of-the-art image super-resolutionnetworks are required to ensure they produce upscaled images that are close to the GTimage.Despite the limitation of the state-of-the-art image super-resolution networks, those,specifically GLEAN and SwinIR, are the most relevant to the present study and are re-viewed here.GLEANGLEAN is a deep learning model designed for producing large-factor upscaled images.The GLEAN network uses Generative Adversarial Networks (GANs) along with a pre-trained latent bank to generate upscaled images from low-resolution ones [1]. The GLEANarchitecture is shown in Fig. 1.4, and consists of three primary components:1. Latent Feature Bank: A pre-trained generative model that encodes rich imagepriors, which are crucial for high-quality image reconstruction.2. Encoder-Decoder Network: Responsible for mapping the low-resolution inputinto the latent space of the pre-trained generative model.71.3. IMAGE UPSCALING METHODSE0 E1 E2 E3 E4 S0 S1 S2 S3 S4 S5 D0 D1 D2 D3Figure 1.4: GLEAN architecture reproduced from [1]. The layers denoted by “E”, “S”,and “D” correspond to the encoder, the generative latent bank, and the decoder layers,respectively.3. GAN Framework: A discriminator network that enforces the realism of the gener-ated high-resolution images.The GLEAN model is trained using a combination of perceptual loss, adversarial loss, andpixel-wise L1 loss, all of which facilitate GLEAN to maintain consistency across differentscales and to generate images with finer details and fewer artifacts [1]. Experimental resultsdemonstrated that GLEAN significantly outperforms previous methods for producing large-factor upscaled images, particularly upscaling factors larger than 8 [1].SwinIRSwinIR is a deep learning model that is designed to facilitate image restoration, in-cluding super-resolution, denoising, and compression artifact reduction [2]. The SwinIRarchitecture is shown in Fig. 1.5, and consists of three main modules:1. Shallow Feature Extraction: A convolutional layer that captures basic featuresfrom the input image.2. Deep Feature Extraction: A stack of Residual Swin Transformer Blocks (RSTBs)that capture both local and global features through a shifted window method.3. Image Reconstruction: A module that combines shallow and deep features toreconstruct the upscaled images.The above modules facilitate SwinIR to process the images in a hierarchical manner us-ing shifted windows. These allow SwinIR to capture interactions between distant pixels,reducing artifacts which are typically present in previous methods. SwinIR captures the81.3. IMAGE UPSCALING METHODSShallow FeatureExtraction RSTBRSTBRSTBRSTBRSTBRSTBConv+HQ ImageReconstructionFigure 1.5: The SwinIR architecture reproduced from [2]. RSTB is the residual swintransformer block, which consists of multiple stacked swin transformer layers.long-range spatial dependencies while maintaining closeness to GT and computational ef-ficiency.Domain-specific large-factor image upscalingWhile the aforementioned models such as GLEAN and SwinIR have brought significantadvancements in generating upscaled images with large upscaling factors, these models areprimarily designed for natural image datasets such as DIV2K. This limits the applica-tion of GLEAN and SwinIR in upscaling images while maintaining closeness to GT indomain-specific datasets such as the application in this thesis [3, 4]. To help address this,domain-specific characteristics can be used, with two examples reviewed here. Specifically,Ref. [3] introduced Spectra-Guided Generative Adversarial Networks (SpecGANs), whosearchitecture is presented in Fig. 1.6. As shown in the figure, a dual-branch network archi-tecture is used in SpecGANs to combine the spatially rich hyperspectral data with RGBinputs. This allowed producing upscaled images while maintaining high visual fidelity andaccurate semantic content.91.3. IMAGE UPSCALING METHODSRFBDFEBDFEBRFBDFEBDFEB++ConvE1E2E3S0S1S2S3S4S5D1D2D3D4D5DoutFigure 1.6: SpecGAN architecture reproduced from [3]. DFEB is the deep feature extraction block. RFB is the registration andfusion block.101.4. RESEARCH GAP AND OBJECTIVESFor combustion related applications, which are relevant to the present study, Bode et al.[4] improved the GAN-based image upscaling methods by introducing a physics-informedenhanced super-resolution GAN, referred to as PIESRGAN and schematically presented inFig. 1.7. This method incorporates physical constraints for predicting turbulent premixedflames data. They [4] used high-fidelity direct numerical simulation (DNS) data as theGT. Then, filtered subgrid information along with PIESRGAN was used to recover high-resolution flame structures on grids that were significantly coarser than that of the DNS.Ultimately, the works of [3, 4] highlight the flexibility of domain-specific super-resolutionmethods and loss functions in utilizing different types of auxiliary information either in theform of spectral data in the spatial domain, as that in [3], or flow-related information [4] toallow generate super-resolution results. Both approaches facilitated upscaling images withimproved closeness to the GT compared to those in the state-of-the-art image upscalingmodels.1.4 Research gap and objectivesIn industrial combustion systems, the ability to monitor and mitigate thermoacousticoscillations is crucial for maintaining operational efficiency and safety. Such monitoring andmitigation require high-resolution CL image acquisition, which is challenging at best forcombustion industrial applications. This is because the combustion chambers, at best, mayallow for limited optical access which often restricts the use of advanced imaging systems.As a result, only low-resolution CL images may be obtained. These low-resolution imagesare insufficient for capturing the fine flame details, which are important for detectingand analyzing thermoacoustic oscillations. Traditional interpolation methods for upscalingthese images fail to restore the lost high-frequency details because they were designedfor low upscaling factors. Current state-of-the-art upscaling methods are inaccurate inupscaling images for large upscaling factors. Such large upscaling is required for monitoringthe thermoacoustic oscillations as only a few sensors can be used for data acquisition.Therefore, there is need for advanced techniques that can accurately upscale very low-resolution CL images to high-resolution ones.The goal of this thesis is to assess the feasibility of using data from few sensorsalong with newly developed machine learning networks to accurately monitorthermoacoustic oscillations of industrial combustion systems in real time. Toachieve the goal of this thesis, the following tasks are followed.− A new neural network that allows upscaling very low-resolution CL images to high-resolution ones at lower computational cost compared to that of the state-of-the-art is developed. This task is completed via incorporating the acquired pressurefluctuations data into the network to enhance the closeness of the upscaled imagesto the ground truth.111.5. THESIS OUTLINEGeneratorInputConv3dLeakyReLURDBRDBRDBConv3d+Conv3dLeakyReLUConv3dLeakyReLUConv3doutputDiscriminatorInputConv3dLeakyReLUConv3dBNLeakyReLUDenseLeakyReLUDropoutDenseoutputFigure 1.7: PIESRGAN architecture reproduced from [4]. RDB is the residual dense block.BN is the batch normalization block.− The effectiveness of the developed neural network by benchmarking its performanceagainst state-of-the-art image super-resolution methods for upscaling the CL imagesis assessed.− The upscaled high-resolution images generated by the network are used to evaluatethe closeness of the predicted thermoacoustic source term to the its ground truth.1.5 Thesis OutlineTo achieve the thesis objective, the following chapters present the details of datasetpreparation, the proposed deep learning architecture, and its evaluation. In particular,Chapter 2 details the experimental setup, diagnostics, and methods followed to process theacquired experimental data. Chapter 3 focuses on the chemiluminescence image upscalingand the prediction of the thermoacoustic source term, outlining the development of theupscaling network as well as the calculation of the thermoacoustic source term. Chapter 4presents the results of the network’s performance in upscaling the CL images and comparesthis performance against that of the state-of-the-art methods, as well as comparing thepredicted thermoacoustic source term with its ground truth. Finally, the conclusions of thethesis, limitations of the current approach, and directions for future research are presentedin Chapter 5.12Chapter 2Data acquisition and preparationThe thesis focuses on a data-driven approach for image upscaling using deep learning.As such, dataset preparation is an important step to accomplish this. This chapter out-lines the data acquisition and the preparation of the acquired data for training the neuralnetwork.2.1 Experimental setupAn experimental setup in the Combustion for Propulsion and Power Laboratory at TheUniversity of British Columbia - Okanagan Campus was used to collect the data requiredfor this thesis. Details of the experimental setup and diagnostics are provided next.2.1.1 SetupThe experimental setup consists of a diffuser section, a settling chamber, and a gasturbine model combustor, see Fig. 2.1. The diffuser and settling chamber were identicalto those used in past investigations, see for example [5, 6, 41, 42]. The combustor wascomposed of a plenum and an optically accessible combustion chamber, which are identicalto those in [5, 6]. The optical accessibility is crucial here for collecting the CL images.Note that the goal of this work is to understand the potential of obtaining the required CLimages without this optical accessibility, which is relevant for industrial settings.The setup was fed with fuel, which was a mixture of 60% (by volume) methane and40% hydrogen, and air. The fuel–air equivalence ratio was fixed at 0.6 following past work[41, 42]. This fuel-air equivalence ratio was selected as the thermoacoustic oscillations wererelatively pronounced for this condition, providing more variability in the CL images, whichgenerally translates to more difficult upscaling. The methane/hydrogen mixture and airflowrates were measured using a Brooks SLA 5853 and an Alicat 5000 MCRH mass flowcontrollers, respectively.2.1.2 DiagnosticsThe diagnostics include a high-speed flame chemiluminescence imaging as well as pres-sure measurement hardware. This hardware allows for recording detailed temporal andline-of-sight-integrated spatial information about the combustion process.132.1. EXPERIMENTAL SETUPUV BandpassFilter (310 nm) IntensifierHigh-speed High-resolution CameraPressure TransducerFigure 2.1: The experimental setup, which is similar to that in [5, 6].CL Imaging hardwareThe system includes a high-speed camera, an image intensifier, a UV Nikon lens, anda bandpass filter. The high-speed camera (Photron Fastcam Nova S12) used in this studyis equipped with a high-speed image intensifier (Invisible Vision UVi 1850B). This setupallows for the capture of CL images at a frame rate of up to 10,000 frames per secondat full resolution (1024×1024 pixels2). The effective resolution of the captured images isapproximately 198 µm [5]. The intensifier enhances the camera’s sensitivity to the weaklight emitted during combustion, particularly in the ultraviolet range, which is crucialfor detecting the chemiluminescence. For the examined turbulent premixed flames, theacquired CL emissions are deemed to relate to the flame heat release rate, which is key forthermoacoustics analysis.A UV Nikon lens with a focal length of 105 mm and an aperture f-number of 1.4 wasused to focus the light emitted by the flame onto the camera sensor. The lens is optimizedfor UV light. The lens is equipped with a bandpass filter, with a center wavelength of 310142.2. DATASET PREPARATIONnm and a bandwidth of 20 nm. This notch includes the emission wavelength of the fromOH radical and other species excited in the heat release region [43].Pressure measurement hardwareTo measure the pressure fluctuations, a piezoelectric pressure transducer (Model 106B52from PCB Piezotronics) was flush-mounted on the wall of the combustor plenum, which ispositioned upstream of the combustion chamber. This transducer is capable of capturingthe pressure oscillations associated with thermoacoustics, providing real-time data on thepressure changes within the chamber.Dataset acquisitionBoth CL and pressure data were acquired with an acquisition frequency of 10 kHz. Theacquisition frequency was sufficient to capture the dynamics of thermoacoustic oscillationsas the dominant frequency of thermoacoustic oscillations was present at a frequency of∼80Hz.During each repeat, CL images and pressure data were recorded for one second. Theexperiments were repeated 7 times and in total, 70,000 CL images and pressure measure-ments were simultaneously acquired.2.2 Dataset preparationThe dataset was split into a training set and a testing set for use in training andtesting the proposed upscaling architecture. Moreover, the CL images were required tobe downscaled to emulate data collection using few sensors. The data splitting, CL imagepre-processing, and CL image downscaling are discussed next.2.2.1 Data splitFor each repeat of the experiments, the frames were split into training and testingsubsets along with a data gap between training and testing data, as schematically shownin Fig. 2.2. Specifically, the data acquired for each experiment was split to 4937 imagesfrom which a subset is selected as the training set, and 4937 images for testing. The gapof 126 images was implemented between the trained and tested images to ensure the CLimages used for training and testing are separated by at least one cycle of thermoacousticoscillations, which was about 80 Hz (corresponding to 10000/80 ≈ 126 CL images).After splitting the data in every repeat into training and testing sections, randomimages were sampled from the training section with a sampling probability of 50%, whichleft 4937×0.5 = 2478 images to be used for training compared to the original 4937 images.The random sampling was implemented to reduce overfitting and increase the diversity152.2. DATASET PREPARATIONTraining Testing4937 Images 4937 Images12610000 ImagesFigure 2.2: Train test split for one repeat (10,000 images) of the experiments. The shadedpart is not used for either training or testing. The training set images are sampled randomlyfrom the training part.of the flame structures by introducing temporal separation between the images used fortraining.2.2.2 Pre-processing of CL imagesThe acquired images required to be pre-processed following several steps. These stepsare shown in Fig. 2.3. First, there was background noise that needed to be removed.Background noise was quantified by capturing images with the UV lens capped, ensuringno light from the flame reached the camera sensor. These background images, as shown inFig. 2.3(a), were averaged and subtracted from the raw CL images, as seen in Fig. 2.3(d).This step is particularly important for enhancing the signal-to-noise ratio, allowing formore accurate detection of chemiluminescence emissions [26].After background subtraction, the images had varying overall intensities (brightness)due to non-uniform sensitivity caused by the image intensification process. To correct forthis, the CL images were normalized using a white-field image, as depicted in Fig. 2.3(b),resulting in the adjusted image seen in Fig. 2.3(e).The images were originally larger than needed for this work. To reduce their size, theimages (which initially had a resolution of 1024×1024 pixels2 as shown in Fig. 2.3(e)) werebinned into 8×8 pixel windows. The average intensity in each window was calculated,reducing the image resolution to 128×128 pixels, as shown in Fig. 2.3(f). This reducedresolution was necessary to decrease both the data processing time and the computationtime for training the upscaling network. The smaller 128×128 images were used as theground truth for network training [26].2.2.3 Downscaling procedureTo simulate the output of low-resolution CL sensors, the 128×128 CL images weredownscaled to various resolutions. For instance, to replicate the output of an 8 × 8 arrayof photo detectors, the resolution of the 128 × 128 CL images decreased to (128/8) ×(128/8). The reduction in the resolution was carried out by applying a convolution to the128× 128 CL images. The kernel of the convolution was a Gaussian function, representing162.2. DATASET PREPARATION(c) (d)(a)(e)(b)(f)Figure 2.3: Pre-processing steps of CL images. (a) is the averaged background noise image.(b) is the white-field image. (c) is the original CL image with a resolution of 1024× 1024.(d) is the CL image after subtracting the background noise (a). (e) is (d) after normalizingby the white field image (b). (f) is the CL image with a resolution of 128× 128 as a resultof binning the original CL image (c)the sensitivity pattern of a single photodetector [44], which is envisioned to replace theCL imaging camera. The highest sensitivity of this filter is at the center and graduallydecreases towards the edges. This downscaling provides the low-resolution input imagesthat are used for training of the upscaling network.This process involves positioning each kernel over predefined intervals on a regular8× 8 grid laid across the high-resolution image. Specifically, the filter is applied at evenlyspaced positions: each kernel is centered at intervals of 16 pixels (in both the horizontaland vertical directions) on the original high-resolution 128× 128 image. Thus, the outputof each sensor in the array represents the weighted sum of the pixel intensities within itscoverage area, with the weight being highest at the center of the filter and decreasing withdistance from the center, as described by the Gaussian function.A summary of the methodology is schematically shown in Fig. 2.4. Specifically, Figs. 2.4(a,b) present the combustor and a high-resolution CL image, respectively. The resolutionof this image is then reduced, producing a very low-resolution chemiluminescence image(see Fig. 2.4(d)) emulating the output of a small array of sensors that could hypotheti-cally feature limited access to the combustor (see Fig. 2.4(c)). The low-resolution image(Fig. 2.4(d)) is produced by applying a Gaussian convolution (marked in red in Fig. 2.4(d))to the high-resolution image (Fig. 2.4(b)), where the pixel intensity is a weighted sum of172.3. SUMMARY(a) (b) (c) (d) (e)Figure 2.4: Diagram of the proposed approach. (a) Full optical access allows high-resolutionimaging. (b) High-resolution flame image example. (c) Limited optical access with sensorplacement. (d) Low-resolution sensor output, showing Gaussian convolution effect. (e)Gaussian kernel weight distribution.pixel intensities of the high-resolution image with weights peaking at the center and de-creasing outwards as illustrated in Fig. 2.4(e). The low-resolution image (Fig. 2.4(d)) is tobe used to reconstruct the high-resolution image (Fig. 2.4(b)).2.3 SummaryIn this chapter, the experimental methodology and dataset preparation, which areneeded for the development of the neural network, were detailed. The setup for collectingCL images and pressure measurements along with the data splitting, pre-processing, anddownscaling the CL images to simulate low-resolution sensor data were discussed. Atthe end of the steps described in this chapter, the dataset that is required for trainingand testing the upscaling model was obtained. The next chapter will discuss the neuralnetwork architecture and training process used to upscale the low-resolution CL images.18Chapter 3Chemiluminescence imageupscaling and thermoacousticsource term calculationUpscaling a low-resolution CL image to a higher resolution one is necessary in order toestimate the thermoacoustic source term. Ideally, the low resolution CL image should beobtained using an small array of sensors. In this thesis, the low resolution image is emulatedby downscaling a high resolution image as explained in Chapter 2. In this chapter, a neuralnetwork for upscaling the CL images and training procedure are discussed.3.1 Network architectureWhile it is possible to upscale the low-resolution CL images using these images only, it isproposed to combine the low-resolution images with pressure data since this can improvethe upscaling due to the mutual information between the CL images and the pressuredata. To this end, a multi-path neural network, which is referred to as the Multi PathChemiluminescence and Pressure Network (MPCP-Net), was developed. The multi-patharchitecture was chosen to independently process the image data and pressure data beforecombining them for final predictions. This allows the model to extract features from bothsources individually, while merging their information at later stages. The architecture ofMPCP-Net is presented in Fig. 3.1. As shown in the figure, the developed NN includestwo main paths. The first path processes the low-resolution CL images using convolutionalblocks and pixel shuffle layers. The second path uses linear layers along with the pressurefluctuation data, which is closely related to the thermoacoustic oscillations. The details ofeach path are presented next.193.1. NETWORK ARCHITECTURELR CL Image LRCLInputConvBlockPixelShuffleConvBlockPixelShuffleConvBlockPixelShuffleConvBlockPixelShuffleMultiplyConcatConvBlockupscaled CL ImageConvReLUConvReLUConvReLUPressureLinearReLULinearReLUReshapeConv BlockCalculate SpatialRayleigh GainCLPhaseCLAmplitudePressurePhasePressureAmplitudeSpatial ThermoacousticSource TermFigure 3.1: The Multi Path Chemiluminescence and Pressure Network architecture. The network features two paths: one forlow-resolution images highlighted in blue and another for pressure data that is highlighted in yellow. The thermoacoustic sourceterm calculation process is highlighted in red.203.1. NETWORK ARCHITECTUREFirst path: convolutional blocks and pixel shuffle layersThe first path of the network processes the low-resolution CL images through a series ofconvolutional blocks. These blocks are designed to extract features from the input imagesthat are relevant for upscaling. Convolutional layers were chosen here to capture the localspatial dependencies in images, which is needed for image upscaling tasks [45]. Specifically,the first convolution layers help in extracting low-level features such as edges, while thelast convolution layers extract the high-level features such as the flame structures.Each convolutional block consists of convolutional layers followed by ReLU (RectifiedLinear Unit) activation functions. The convolutional layers extract the structural featuresin the image. The ReLU activation function introduces non-linearity into the model byapplying a function f(x) given byf(x) = max(0, x), (3.1)where x is the input of the ReLU activation function. The convolutional blocks also featuredense residual connections, as residual connections have been shown to improve the trainingof super-resolution models [34]; that is, the output of select layers is added back to theinput of subsequent layers, see Fig. 3.1.As part of the upscaling network, the pixel shuffle layers were implemented after eachconvolutional block, as introduced in [46]. The Pixel Shuffle layer, also known as the sub-pixel convolution layer, is used to upscale feature maps in convolutional neural networks.It rearranges elements in a tensor to increase its spatial resolution. For an input tensorX with the dimensions of (B,Cr2, H,W ), where B is the batch size, C is the number ofoutput channels, r is the upscaling factor, H is the image height, and W is the imagewidth, the Pixel Shuffle operation produces an output tensor Y with the dimensions of(B,C,Hr,Wr). In summary, the Pixel Shuffle layer increases the spatial resolution of theinput tensor by rearranging its channels into a larger spatial grid. These layers rearrangethe pixels in the feature maps, upscaling the images by redistributing the pixel valuesacross a larger grid.One alternative approach that could have been considered is the use of transformer-based architectures. Transformer models, which leverage self-attention to capture long-range dependencies. However, transformers tend to be more data-hungry and computation-ally expensive. Specifically, transformers require significantly larger datasets for training[47]. With limited data, transformers run the risk of overfitting, making them less suit-able for the case studied here. Additionally, convolutional networks benefit from inductivebiases like locality and translation equivariance, making them better suited for structureddata like the chemiluminescence images that were use here [47].Similarly, while Generative Adversarial Networks (GANs) [48] have been widely used inimage generation and super-resolution, especially for producing perceptually higher-qualityimages [1], they were not considered for this study. The focus of this work is on engineeringapplications where the accuracy of the upscaled image reconstruction is more important213.1. NETWORK ARCHITECTUREthan generating visually pleasing results. GANs tend to emphasize perceptual quality andmight introduce artifacts that distort the spatial information critical to our task. Thismakes our architecture a more suitable fit for our image upscaling task.Second path: integration of pressure data and linear layersThe second path of the network integrates pressure fluctuations into the upscalingprocess. The decision to incorporate pressure data arises from the physical correlationbetween pressure oscillations and variations in flame characteristics, which are capturedin the CL images. By integrating this secondary modality, the network can better predictchanges in the flame’s spatial patterns, which might not be fully evident in the imagesalone.This path consists of linear layers followed by ReLU activation functions, which processthe pressure data and extract features that are relevant for enhancing the upscaled CLimages. The output of the second path is multiplied by the output of the first pathwhich allows the network to amplify or attenuate the intensities of the pixels based onthe information in the pressure data. This multiplication enables the pressure featuresto modulate the upscaled intensity in the CL images directly. The outputs of the secondpath are also concatenated with the output of the first path, see Fig. 3.1. Concatenationafter multiplicative interaction ensures that the two feature vectors (from CL images andpressure input) are combined in such a way that adds both individual contributions of eachpath as well as their interaction.In traditional convolutional networks, these inputs would have to be synthesized earlyin the network, which may limit the ability to extract detailed or distinct features fromeach modality. By using separate paths, the NN can learn two sets of features: one thatonly focuses on the spatial information from the CL images, and another that focuses ontemporal pressure variations. This division of information processing allows the model tospecialize in the kind of features it must extract from each source, and only combine themvia concatenation at a later stage. This approach has been shown to be successful in workssuch as [3, 49].Training and optimizationThe network was trained for 100 epochs using the Adam optimizer with a learning rateof 1 × 10−3. The Adam optimizer was chosen for its ability to adapt the learning rateduring training, leading to faster convergence and improved performance [50]. Throughoutthe training process, the Mean Absolute Error (MAE) loss function, which is the averageabsolute difference between the pixel intensities in the predicted and ground truth images,was used to monitor accuracy. The MAE was defined asMAE =1nn∑i=1|Ipredicted,i − Iground truth,i|, (3.2)223.2. CALCULATION OF THE THERMOACOUSTIC SOURCE TERMwhere n denotes the total number of pixels, and Ipredicted,i and Iground truth,i represent thepixel intensities of the predicted and ground truth images at pixel i, respectively. Thisloss function has shown superior performance compared to other loss functions for theprediction of super-resolution images [51].The Peak Signal-to-Noise Ratio (PSNR) was used to monitor upscaling accuracy sincethe PSNR allows for prioritizing similarity to the original image over perceptual quality [34],which is more important for engineering applications such as combustion health monitoring.The PSNR was defined asPSNR = 10 log10(MAX2MSE), (3.3)where MSE is the Mean Squared Error between the pixel intensities in the ground truthand upscaled images, and MAX (the maximum intensity of the ground truth CL image) isunity in the present study.In addition to PSNR, other evaluation metrics such as the Structural Similarity Index(SSIM) [52] could also be considered to assess the perceptual quality of the upscaled images.However, given the specific focus of the present study, i.e. engineering application, that theaccuracy of the spatial information is paramount, PSNR was used as the primary metric.3.2 Calculation of the thermoacoustic source termIn this section, the methodology used to calculate the thermoacoustic source term usingtime-resolved pressure signal and CL images is discussed. The CL images provide time-resolved spatial information about the flame, and each pixel in the image represents a timeseries of the CL intensity data. The pressure signal, recorded simultaneously, captures theacoustic behavior of the system. To quantify the interaction between acoustic pressure andheat release rate, the thermoacoustic source term is calculated. Key to this calculation isthe instantaneous amplitudes of the pressure and CL data as well as the phase differencebetween the two signals, which are discussed next.3.2.1 Amplitude and phase calculationLet p′(t) denote the time-resolved pressure fluctuations, and I ′(x, y, t) represent theCL intensity time series for the pixel located at position (x, y) in the CL image. Bothp′(t) and I ′(x, y, t) were bandpass filtered around the dominant frequency of the pressureoscillations. As shown in Fig. 3.2, the power spectral density of the spatially averagedchemiluminescence signal over multiple repeats reveals that the dominant frequency of theoscillations is approximately 80 Hz.To compute the instantaneous amplitude and phase of the oscillations, the Hilberttransform was applied to both the pressure signal p′(t) and the flame chemiluminescencesignal I ′(x, y, t) at each pixel of the CL image. An example of the filtered pressure fluctu-ations, with an inset, is shown in Fig. 3.3.233.2. CALCULATION OF THE THERMOACOUSTIC SOURCE TERM00.51PSD00.51PSD101 102 10300.51Frequency (Hz)PSDFigure 3.2: Power spectral density (PSD) of the spatially averaged CL signal over multiplerepeats. The dominant frequency is approximately 80 Hz.The analytic signal for both the pressure (p′′(t)) and CL intensity at a pixel (I ′′(x, y, t))can be written asp′′(t) = p′(t) + iH(p′(t)), (3.4)I ′′(x, y, t) = I ′(x, y, t) + iH[I ′(x, y, t)], (3.5)where H{·} denotes the Hilbert transform. The instantaneous amplitudes and phases ofthe pressure and CL intensity are then given byp˜′(t) =√p′(t)2 +H[p′(t)]2, (3.6a)I˜ ′(x, y, t) =√I ′(x, y, t)2 +H[(I ′(x, y, t)]2, (3.6b)ϕp(t) = atan(p′′(t)), (3.6c)ϕI(x, y, t) = atan(I′′(x, y, t)), (3.6d)where p˜′(t), I˜ ′(x, y, t), ϕp(t), and ϕI(x, y, t) are the instantaneous amplitude of the pressure,amplitude of the CL intensity fluctuations at coordinates (x, y), phase of the pressure, andphase of the CL intensity fluctuations, respectively, as a function of time t.243.2. CALCULATION OF THE THERMOACOUSTIC SOURCE TERM0 200 400 600 800 1000−40−2002040Time (ms)Pressure(Pa)500 540 580 620 660 700−40−20020Time (ms)Pressure(Pa)Figure 3.3: A sample of filtered pressure fluctuations as a function of time.3.2.2 Thermoacoustic source termOnce the amplitudes and phases are computed for both the pressure and the CL inten-sity signals, the spatial thermoacoustic source term can be calculated using Eq. (1.1). Inthis calculation, it is assumed thatq˙′(x, y, z, t) ≈ I ′(x, y, t), (3.7a)p′(x, y, z, t) ≈ p′(t), (3.7b)∆ϕ(x, y, z, t) ≈ ϕp(t)− ϕI(x, y, t). (3.7c)Exemplary signals that present the steps for calculation of the thermoacoustic sourceterm at a pixel are shown in Fig. 3.4. The results in Fig. 3.4(a), (b), and (c) presentthe pressure fluctuations, flame chemiluminescence intensity fluctuations at a given pixel,as well as the corresponding computed thermoacoustic source term variation at the pixeland over time. The amplitudes of the pressure and flame chemiluminescence intensityfluctuations are shown by the red dashed curves in the figure.The process of calculating the thermoacoustic source term using the pixel intensity ofCL images and the corresponding pressure values and for all pixels is shown in Fig. 3.5.Specifically, the results in the first and second rows present I(x, y, t) as well as I˜ ′(x, y, t),respectively. The results in the third and fourth rows present ∆ϕ and ψs, respectively. The253.2. CALCULATION OF THE THERMOACOUSTIC SOURCE TERM500 540 580 620 660 700-20020Time (ms)Pressure(Pa)Pressure (Pa)Pressure Amplitude (Pa)500 540 580 620 660 700-0+Time (ms)I′ (x,y,t)I ′(x, y, t)I˜ ′(x, y, t)500 540 580 620 660 700-0+Time (ms)ψs(a)(b)(c)Figure 3.4: (a) is a segment of the filtered pressure with the amplitude shown using adashed red curve. (b) is a segment of filtered intensity values of a random CL image pixelwith the amplitude shown using a dashed red curve. (c) is the thermoacoustic sourceterm calculated using the instantaneous amplitude and phase of the pressure and CL pixelintensity fluctuations.results are presented for different time instants of t = 500, 525, 575, and 620 ms. It canbe seen that the thermoacoustic source term alternates between positive and negative asthe phases of the pressure and CL pixel intensity signals vary over time as the sign of thethermoacoustic source term is a function of the cosine of the difference between the phasesof pressure and CL pixel intensity signals.263.3. SUMMARY(a) (b) (c) (d)(e) (f) (g) (h)(i) (j) (k) (l)(m) (n) (o) (p)II˜ ′ϕIψst = 500 ms t = 525 ms t = 575 ms t = 620 ms-MAX0MAX−π0πFigure 3.5: (a–d) are the CL images at different timestamps. (e–h) are CL intensityfluctuations amplitudes at the corresponding times that results in (a–d) were acquired. (i–l) are the phase of the flame chemiluminescence fluctuations. (m–p) are the thermoacousticsource term.3.3 SummaryIn summary, the MPCP-Net, a multi-path neural network is designed and introducedfor upscaling low-resolution CL images using both image data and pressure fluctuations.The network’s architecture, including its two primary paths, and the training process werepresented and discussed. The chapter also outlined the methodology for calculating thethermoacoustic source term from the upscaled CL images.The following chapter will present the performance of MPCP-Net and compare thiswith the state-of-the-art models like GLEAN and SwinIR, assessing MPCP-net’s abilityto reconstruct high-resolution CL images, and evaluate the accuracy of predicting thethermoacoustic source term using the PSNR metric.27Chapter 4Results and discussionThis chapter assesses the performance of our upscaling network, MPCP-Net, in recon-structing high-resolution CL images from low-resolution CL images. MPCP-Net’s effective-ness is compared with that of the state-of-the-art networks, e.g., GLEAN and SwinIR usingPSNR metrics. Also, the accuracy of predicting thermoacoustic source term is evaluated.4.1 Performance of the upscaling networkIn this section, first, the performance of the network discussed above for generatinghigh-resolution CL images from low-resolution CL images is assessed and comparisons aremade with the performance of available upscaling NNs in the literature.In Fig. 4.1, random samples of the CL image upscaling predictions using the proposednetwork and the GT high-resolution CL images are plotted. The first column of Fig. 4.1presents an example of a ground truth flame CL image. The images in the first, second,and third rows of the second column in Fig. 4.1 present 32, 16, and 8 times downscaledimages of those in the first column, where downscaling is realized as described in Sec. 2.2.3.The results in the third column of the figure are the upscaled images using the very lowresolution images in the second column along with MPCP-Net described in Sec. 3.1. Ascan be seen, the general structure of the flame CL may be reproduced effectively, with morepronounced differences between the upscaled images and the ground truth appearing for 16and 32 times upscaling factors. For example, a ground truth image and the correspondingupscaled images for 4× and 32× upscaling factors are shown in Figs. 4.2(a), (b) and (c),respectively, with the insets enlarged and shown to the right-hand-side of the images. Ascan be seen, the structures that are present in the ground truth image are captured in theupscaling process for upscaling factors such as 4×, however, these structures may not becaptured for high upscaling factors as high as 32×.For all upscaling factors, the performance of MPCP-Net was evaluated using the PSNRand comparisons were made with the state-of-the-art networks (GLEAN and SwinIR) andthe bicubic interpolation method, with the results presented in Fig. 4.3. Additionally,Fig. 4.3 shows the PSNR values for the predictions of our model without including thepressure signal for upscaling the CL images. It is important to note that both MPCP-Netand the NNs used in the literature were not pre-trained, since the existing pre-trainedstate-of-the-art networks exhibited worse performance. This is because the datasets thatwere used for pre-training (such as the ImageNet dataset) of existing networks uses images284.1. PERFORMANCE OF THE UPSCALING NETWORKGT Image VLR Image Upscaled Image32×16×8×Figure 4.1: Samples showcasing the performance of the MPCP-net predicting the upscaledCL images for several upscaling factors.from a wide range of categories that are far from the CL images.The effectiveness of MPCP-Net was further tested across different upscaling factors,ranging from 4× to 32×. Bicubic interpolation, which is the best interpolation-basedupscaling method [32], achieved lower PSNR than all other methods across all upscalingfactors. As expected, the MPCP-Net’s performance (evaluated using the PSNR) improvedas the upscaling factor decreased, reflecting the inherent challenges of accurately recon-structing images with larger upscaling factors. It is also observed that MPCP-Net featureslarger PSNR compared to those of GLEAN and SwinIR, which primarily focus on naturalimages upscaling. GLEAN and SwinIR struggled to maintain the accuracy in the contextof CL imaging. These methods often prioritize perceptual quality over exact pixel accu-racy, which can lead to visually appealing results that may not accurately reflect the truephysical phenomena captured in the images which is a requirement in critical scenariossuch as combustion.For smaller upscaling factors, such as 4×, 8×, and 16×, MPCP-Net was able to recon-struct high-resolution images that closely matched the ground truth, with minimal loss ofdetails. However, as the upscaling factor increased to 16× and 32×, some fine details couldbe lost in the reconstruction process.In addition to the PSNR, the performance of the MPCP-Net and of GLEAN and SwinIRwere assessed using the time it took for upscaling the CL images. The calculation times294.2. PERFORMANCE IN PREDICTING THE THERMOACOUSTIC SOURCEGTImageUpscaledImage4×UpscaledImage32×Figure 4.2: A ground truth image (first row), a 4× upscaled image (second row) and a 32×upscaled image (third row). The insets are shown to the right side of the images.were not substantially influenced by the upscaling factor, but were significantly influencedby the utilized network. Specifically, on a single RTX3060TI GPU, MPCP-Net, GLEAN,and SwinIR took about 2, 90, and 36 ms to upscale the CL images. The smaller requiredtime for upscaling the CL images was due to MPCP-Net featuring a simpler architecturewhich is designed for upscaling the CL images compared to those of GLEAN and SwinIRwhich are designed for general purpose image upscaling. The time period of upscaling CLimages using MPCP-Net corresponds (2 ms) corresponds to 500 Hz, which is about six timeslarger than the frequency of thermoacoustic oscillations in the present study, suggestingMPCP-Net may also be suitable for control of thermoacoustic oscillations, where SwinIRand GLEAN can upscale images with a rate of 10 Hz which is 10 times smaller than thefrequency of thermoacoustic oscillations. However, control of these oscillations was not theobjective of the present study and is not examined here.4.2 Performance in predicting the thermoacoustic sourceThe high-resolution images (representing an area of a height of 70 mm and a width of72mm), the pressure data, along with Eq. (1.1) were used to calculate the thermoacousticsource term, following the procedure presented in Sec. 3.2. The accuracy and timelinessof these calculations are critical, as they directly impact the ability to monitor and controlthe oscillations in real-time.304.2. PERFORMANCE IN PREDICTING THE THERMOACOUSTIC SOURCE2×2(64×)4×4(32×)8×8(16×)16×16(8×)32×32(4×)1020304050Sensor Array Resolution(Upscaling Factor)PSNR(dB)MPCP-NetMPCP-Net (w/o pressure input)SwinIRGLEANBicubic interpolationFigure 4.3: The variation of PSNR for upscaling the CL images versus the upscaling factor.An example of the pressure oscillations along with the pressure amplitude is shown bythe solid red and dashed blue curves in Fig. 4.4(a), respectively. For time instants t = 500,525, 575, 620, 641, and 700 ms (see the solid black circular data points in Fig. 4.4(a)), thecorresponding measured thermoacoustic source term (obtained from the ground truth im-ages) is presented in Fig. 4.4(b–e), respectively. Examples of the computed thermoacousticsource term obtained from the 16× upscaled images are presented in Figs. 4.4(f–i), andthose obtained from the 32× upscaled images are presented in Figs. 4.4 (j–m). As can beseen, the computed thermoacoustic source term using the upscaled images is generally ingood agreement with the ground truth thermoacoustic source term. However, comparingthe results in Figs. 4.4(f–i) and Figs. 4.4(j–m) shows that relatively small size thermoa-coustic source term structures such as those shown by the black circles in Fig. 4.4(b, f, j)may not be accurately reconstructed for 32× upscaled images, see the corresponding regionshown by a black circle in Fig. 4.4(j).314.2. PERFORMANCE IN PREDICTING THE THERMOACOUSTIC SOURCE500 540 580 620 660 700−40−2002040Time (ms)Pressure(Pa)Pressure (Pa)Pressure Amplitude (Pa)(a)(b) (c) (d) (e)(f) (g) (h) (i)(j) (k) (l) (m)GT16×32×t = 575 ms t = 620 ms t = 641 ms t = 700 ms-Max0MAXψFigure 4.4: (a) Temporal variation of the pressure (solid red curve) and pressure amplitude(dashed blue curve). (b–e) are the ground truth thermoacoustic source term at t = 575,620, 641, and 700 ms, respectively (see the solid circular data points in (a)). (f–i) and (j–m)are the calculated thermoacoustic source term using 16× and 32× upscaled CL images,respectively. The time instants in (f–i) and (j–m) match those in (b–e). The colorbar valueMAX indicates the highest thermoacoustic source term value calculated.324.2. PERFORMANCE IN PREDICTING THE THERMOACOUSTIC SOURCE2×2(64×)4×4(32×)8×8(16×)16×16(8×)32×32(4×)2025303540455055Sensor Array Resolution(Upscaling Factor)PSNR(dB)MPCP-NetSwinIRGLEANFigure 4.5: PSNR for spatial thermoacoustic source term prediction versus the upscalingfactor.The performance in calculating the thermoacoustic source term using the upscaled CLimages produced by the MPCP-Net and the upscaled images produced by state-of-the-artones was evaluated using the PSNR, with the results presented in Fig. 4.5. The results showthat for 64× upscaling, the PSNR values are similar for all networks. This is anticipated tobe due to the very low-resolution of the 64× downscaled CL images, which makes upscalingchallenging for all networks. However, as can be seen in the figure, decreasing the upscalingfactor increases the PSNR, with MPCP-Net featuring superior performance compared toGLEAN and SwinIR.It’s important to note that the thermoacoustic source term PSNR differs from andexhibits somewhat of a different trend compared to the upscaled image PSNR. This dis-crepancy arises because the thermoacoustic source term, ψs(x, y, z, t), is calculated usinga sequence of upscaled images and pressure values over time, rather than directly fromthe upscaled images alone. The calculation involves the temporal integration, p˜′(x, y, z, t),and heat release rate, ˜˙q′(x, y, z, t), along with the phase difference ∆ϕ(x, y, z, t) betweenq˙′ and p′. This approach means that the thermoacoustic source term PSNR reflects theaccuracy of a dynamic process reconstructed from these images, which can lead to differentperformance metrics and trends compared to the quality of individual upscaled frames.334.3. SUMMARY4.3 SummaryThis chapter evaluated the performance of MPCP-Net against established networkslike GLEAN and SwinIR in upscaling CL images and predicting the thermoacoustic sourceterm. MPCP-Net demonstrated higher accuracy and outperformed the other methods interms of both PSNR and processing time, particularly at lower upscaling factors. Somechallenges were noted with larger upscaling factors, as fine details may be lost. The re-sults highlight MPCP-Net’s potential for real-time applications, especially in combustionmonitoring.The next chapter will summarize the key findings of this research and discuss its broaderimplications, while outlining opportunities for future improvements and industrial appli-cations.34Chapter 5ConclusionsThe main goal of this thesis was to study the feasibility of using machine learning andfew sensors to monitor thermoacoustic oscillations in a gas turbine model combustor. Amulti-path neural network was developed and proposed for upscaling chemiluminescence(CL) images of turbulent premixed flames. The network combines the low-resolution (LR)CL images and the corresponding pressure data to upscale the LR chemiluminescenceimages to high-resolution (upscaled) CL images. The performance of the proposed networkis evaluated using the Peak Signal to Noise Ratio (PSNR) as well as the time requiredfor upscaling. The results show that the proposed approach outperforms state-of-the-artmethods such as SwinIR and GLEAN for upscaling chemiluminescence images. Also, thetime required for upscaling on a given machine is at least one order of magnitude smallerusing the proposed network, compared to SwinIR and GLEAN. This improvement is due tothe proposed network’s architecture, which prioritizes similarity to the ground truth imagesover pleasing visuals, and the use of pressure data to enhance the upscaling process.The upscaled images are then used to calculate the spatial thermoacoustic source term.The results show that our approach is capable of accurately calculating the source term,with the accuracy in calculation of this parameter assessed using the PSNR. The resultsshowed that the PSNR was larger than that obtained from SwinIR and GLEAN for es-timating the thermoacoustic source term. The results demonstrated that our approachfacilitates retaining the spatio-temporal information during the upscaling process. Suchaccurate calculation of the thermoacoustic source term has implications for controlling thethermoacoustics using limited number of flame-related information.5.1 Summary of ContributionsThe key contributions of this work are as follows:− A multi-path convolutional neural network was developed and trained. This net-work is capable of accurately reconstructing high-resolution images from very low-resolution ones, leveraging both image data and pressure fluctuation data.− The integration of pressure data into the upscaling process allowed to improve thenetwork’s ability in preserving the spatial details in the upscaled images, which ledto more accurate monitoring of the thermoacoustic oscillations.355.2. LIMITATIONS OF THE CURRENT APPROACH− The feasibility of real-time monitoring of thermoacoustic oscillations in industrialcombustion systems using few sensors combined with machine learning techniqueswas demonstrated.5.2 Limitations of the current approachWhile the developed upscaling network was able to effectively upscale low-resolutionchemiluminescence images to high-resolution ones, the current approach is limited.First, for large upscaling factors, fine flame details may be lost, which can impact theaccuracy of the thermoacoustic source term prediction.Second, the network’s performance is highly dependent on the quality and diversity ofthe training data. The CL images used for training were specific to a particular type of com-bustion system and flame configuration (turbulent swirling methane/hydrogen/air flames),which may limit the generalizability of the network to other systems or configurations.Third, for the turbulent swirling premixed flames examined here, the fuel-air equiv-alence ratio (and as a result the generated power) was fixed. The performance of thedeveloped model is unknown for other fuel-air equivalence ratios, other test conditions,flame configurations, etc.5.3 Implications for industrial applicationsThe results of this study have significant implications for industrial applications, partic-ularly in the context of small scale power generation units, furnaces, and possibly gas tur-bine engines. The ability to accurately upscale low-resolution CL images to high-resolutionones in real-time provides a powerful tool for monitoring these oscillations, and potentiallymonitoring and predicting combustion health.5.4 Future workThe limitations identified in this study provide several avenues for future research anddevelopment. The following are some potential directions for extending and improvingupon the work presented in this thesis.Integration with control systemsIntegrating the upscaling network with active control systems for thermoacoustic os-cillations may be performed using real-time, high-resolution CL images and pressure data.The network could potentially inform control algorithms that adjust combustion parame-ters in response to detected oscillations, leading to mitigation of thermoacoustics.365.4. FUTURE WORKExperiment with Simultaneous Low and High-Resolution Data CollectionFuture research should include an experiment where both low-resolution and high-resolution CL images are captured at the same time. This would entail using a sensorarray for capturing low-resolution images alongside the high-resolution camera for high-resolution imaging. This could directly validate the feasibility of our upscaling methodby using actual low-resolution sensor data, ensuring our approach can accurately upscalereal-world low-resolution CL images to high-resolution ones.Application to other combustion systemsExpanding the application of the developed network to other types of combustion sys-tems, such as rocket engines and industrial furnaces, would help to generalize the findingsof this study. This would require collecting and training on datasets from these differ-ent systems, potentially involving a wider variety of flame types and operating conditions.Moreover, adapting the network to work with other forms of image-based data, such asparticle image velocimetry, could potentially further improve the predictions.Further refinement of the networkFuture work could focus on refining the network architecture to address the loss of finedetails at high upscaling factors. This could involve exploring more advanced network de-signs, such as multi-scale feature extraction or hybrid models that combine convolutionalnetworks with other types of neural networks, such as transformers, to enhance detailpreservation. Additionally, incorporating more sophisticated loss functions, such as per-ceptual loss or adversarial loss, could potentially help improve the quality of the upscaledimages, particularly in terms of capturing subtle features that are critical for accuratethermoacoustic monitoring.Extending to 3D imagingExpanding the upscaling network to handle 3D data could provide a more comprehen-sive understanding of thermoacoustic oscillations. Future work could involve developing3D convolutional networks and acquiring volumetric CL data to reconstruct full 3D flamestructures. This approach would better capture the complex, three-dimensional nature ofcombustion processes, leading to improved monitoring and control strategies in industrialapplications.37Bibliography[1] Kelvin C.K. Chan, Xintao Wang, Xiangyu Xu, Jinwei Gu, and Chen Change Loy.GLEAN: Generative latent bank for large-factor image super-resolution. 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Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Chaaban, Anas
Kheirkhah, Sina
Upscaling very low-resolution chemiluminescence images for prediction of thermoacoustic source term using machine learning
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