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Prediction of water distribution system pipes and isolation valves failure using Bayesian models with… Demissie, Gizachew Ababu 2017

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PREDICTION OF WATER DISTRIBUTION SYSTEM PIPESAND ISOLATION VALVES FAILURE USING BAYESIANMODELS WITH THE CONSIDERATION OF SOILCORROSION AND CLIMATE CHANGEbyGizachew Ababu DemissieM.Sc., UNESCO-IHE Institute for Water Education, The Netherlands, 2010B.Sc., Arbaminch University, Ethiopia, 2004A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)October 2017c© Gizachew Ababu Demissie, 2017The undersigned certify that they have read, and recommend to the College of Gradu-ate Studies for acceptance, a thesis entitled: PREDICTION OF WATER DISTRIBU-TION SYSTEM PIPES AND ISOLATION VALVES FAILURE USING BAYESIANMODELS WITH THE CONSIDERATION OF SOIL CORROSION AND CLIMATECHANGE submitted by GIZACHEW ABABU DEMISSIE in partial fulfillment of the require-ments of the degree of Doctor of PhilosophyDr. Solomon Tesfamariam, School of EngineeringSupervisor, ProfessorDr. Rehan Sadiq, School of EngineeringSupervisory Committee Member, ProfessorDr. Sumi Siddiqua, School of EngineeringSupervisory Committee Member, ProfessorDr. Cigdem Eskicioglu, School of EngineeringSupervisory Committee Member, ProfessorDr. Keekyoung Kim, School of EngineeringUniversity Examiner, ProfessorDr. Emilio Bastidas-Arteaga, University of NantesExternal Examiner, ProfessorOctober 26, 2017(Date Submitted to Grad Studies)iiAbstractAging water distribution system pipes and valves are at stake due to progressive deterio-ration. Deterioration of the pipes and valves might be as a result of static, operational anddynamic (time-dependent) factors. The impact of these factors are manifested in the form ofdeclined water quality, diminished hydraulic capacity, increased leakage rate and frequent pipebreaks. Reported literature shows that there are a limited number of comprehensive modelswhich integrate characteristics of these factors. As a result, municipalities have been facing achallenge in predicting pipe failure and practicing proactive decision making.The primary objective of this research was to develop a comprehensive Bayesian (BayesianBelief Network (BBN), Dynamic Bayesian Network (DBN) and Bayesian Model Averaging(BMA)) models to predict/forecast pipe and valve failures by considering driving factors withparticular attention to soil corrosion and climate change. Firstly, a comprehensive BBN-basedSoil Corrosivity Index (SCI) model was developed to account for interdependencies amongdifferent soil parameters. The developed BBN-SCI model combines in situ, experimental,and expert opinion data sources. This model is, then, extended to BBN-based RemainingService Life (RSL) model which predicts pit depth and quantifies the probability and time tofailure for cast iron pipes. The next part of this research evaluates the failure of valves usingBBN-based failure mode and effect analysis. The DBN model considers static, operationaland time-dependent factors to predict annual and monthly pipe failure rates. Finally, theBMA model integrates climate projection data for future pipe failure forecasting. Overall, thisresearch integrated physical, environmental, and operational factors speculated in contributingto failures of pipes and valves.The data analysis and methodology proposed in this study will help water utility managersand operators to make informed decision making for efficient design and construction of a newwater supply systems or planning renewal and rehabilitation programs for old water supplysystems. By implementing this methodology, water utilities can incorporate the most impactingiiiAbstractpipe and valve failure factors, specifically soil corrosion and climate change, in operational,tactic, and strategic level decision making.ivPrefaceI, Gizachew Ababu Demissie, prepared all the contents of this thesis including literaturereview; assessment and analysis of data; development and application of models; interpretationof results; and writing of the manuscripts under the supervision of Dr. Solomon Tesfamariam.The other co-authors of the articles include Drs. Rehan Sadiq, and Yonas Dibike. Drs. SolomonTesfamariam and Rehan Sadiq reviewed all the manuscripts and provided critical feedback onthe improvement of the papers and thesis while Dr. Yonas Dibike provided technical advice,critical comments and editing of the manuscript modified for chapter chapter 7 (Demissie et al.2017a). Most of the contents of this thesis are either published or submitted for publication injournals and conference proceedings as listed below: A version of chapter 3 has been partially published in the conference proceedings ofthe 12th International Conference on Applications of Statistics and Probability in CivilEngineering (ICASP) with a title “Prediction of soil corrosivity index: A Bayesian beliefnetwork approach”(Demissie et al. 2015). A version of chapter 4 has been published in the ASCE – Journal of Pipeline Systems En-gineering and Practice with a title “Considering soil parameters in prediction of remainingservice life of metallic pipes: Bayesian belief network model”(Demissie et al. 2016). A version of chapter 5 is under internal review for a possible publication in the peer-reviewed journal with a title of “Failure mode and effect analysis of valves using Bayesianbelief network”(Demissie et al. 2017b) A version of chapter 6 is published in the ASCE – Journal of Risk and Uncertainty inEngineering Systems, Part A: Civil Engineering with a title “Prediction of pipe failure byconsidering time-dependent factors: A dynamic Bayesian belief network model”(Demissieet al. 2017c).vPreface A version of chapter 7 is under internal review for a possible publication in the peer-reviewed journal with a title of “Forecasting pipe failure using climate model projections:A Bayesian model averaging approach”(Demissie et al. 2017a)viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxivChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Chapter 2: Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Effect of Soil Corrosion on Metallic Pipes and Valves . . . . . . . . . . . . . . . . 72.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Methods of Soil Corrosivity Index Prediction . . . . . . . . . . . . . . . . 72.2 Prediction of Remaining Service Life of Metallic Pipes Based on Soil Corrosivity 112.2.1 Corrosion Pit Characterization Methods . . . . . . . . . . . . . . . . . . . 112.2.2 Prediction Methods for Remaining Service Life of Metallic Pipes . . . . . 132.3 Climate Change and Water Supply System Pipes . . . . . . . . . . . . . . . . . . 17viiTABLE OF CONTENTS2.3.1 Emission Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Global Climate Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.3 Global Climate Projections Through CMIP5 . . . . . . . . . . . . . . . . 222.3.4 Downscaling of Global Climate Model outputs . . . . . . . . . . . . . . . 232.3.4.1 Regional Climate Models . . . . . . . . . . . . . . . . . . . . . . 242.3.4.2 Statistical Downscaling . . . . . . . . . . . . . . . . . . . . . . . 242.3.5 Downscaled Climate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Valves of Water Supply System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.2 Isolation Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4.3 Previous Studies on Valve Failure . . . . . . . . . . . . . . . . . . . . . . . 27Chapter 3: Prediction of Soil Corrosivity Index Using Bayesian Belief Network 283.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Soil Corrosivity Parameter Identifications . . . . . . . . . . . . . . . . . . 293.2.1.1 Soil Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.1.2 Soil Moisture Content . . . . . . . . . . . . . . . . . . . . . . . . 303.2.1.3 Soil pH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.1.4 Redox Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.1.5 Soil Sulfides Content . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.2 Bayesian Belief Network Model for Prediction of Soil Corrosivity Index . 333.2.2.1 Overview of Bayesian Belief Network . . . . . . . . . . . . . . . 333.2.2.2 Bayesian Belief Network – Soil Corrosivity Index Model Devel-opment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3 Water Supply System of the City of Calgary . . . . . . . . . . . . . . . . . . . . . 373.4 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.1 Bayesian Belief Network Sensitivity Analysis . . . . . . . . . . . . . . . . 393.4.2 Scenario Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4.3 BBN-SCI Model Validation Using Spatial Clustering method . . . . . . . 423.4.4 BBN-SCI versus AWWA 10-point method . . . . . . . . . . . . . . . . . . 443.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45viiiTABLE OF CONTENTSChapter 4: Prediction of Remaining Service Life of Metallic Pipes Using BayesianBelief Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3.2 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Chapter 5: Failure Mode and Effect Analysis of Valves . . . . . . . . . . . . . . 625.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.2.1 Failure Mode and Effect Analysis . . . . . . . . . . . . . . . . . . . . . . . 645.2.2 BBN - FMEA Model Development . . . . . . . . . . . . . . . . . . . . . . 665.2.3 Corrosion Failure Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.4 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.3.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.3.2 Influence Diagram Based Decision Making . . . . . . . . . . . . . . . . . . 755.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Chapter 6: Dynamic Bayesian Network Model for Prediction of Pipe Failure 806.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.2.1 Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.2.1.1 Pipe Attributes and Operational Factors . . . . . . . . . . . . . 816.2.1.2 Environmental Factors . . . . . . . . . . . . . . . . . . . . . . . 826.2.2 Dynamic Bayesian Network Model for Pipe Failure Prediction . . . . . . . 846.2.2.1 Dynamic Bayesian Network . . . . . . . . . . . . . . . . . . . . . 846.2.2.2 Inferring Methods for Dynamic Bayesian Network . . . . . . . . 866.2.2.3 Learning Techniques for Dynamic Bayesian Networks . . . . . . 876.2.2.4 Dynamic Bayesian Network Model Development . . . . . . . . . 886.2.3 Model Validation and Implementation: Case Study for the City of Calgary 916.3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97ixTABLE OF CONTENTS6.3.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.3.2 Dynamic Bayesian Network Model Results . . . . . . . . . . . . . . . . . 986.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Chapter 7: Forecasting Pipe Failure Using Climate Model Projections – BayesianModel Averaging Approach . . . . . . . . . . . . . . . . . . . . . . . 1047.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.2.1 Bayesian Model Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2.2 Climatic Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . 1077.2.3 Covariate Selection Methods . . . . . . . . . . . . . . . . . . . . . . . . . 1107.2.4 Bayesian Model Averaging Development, Training and Validation . . . . . 1117.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.3.1 Covariate Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.3.2 Bayesian Model Averaging Training Results . . . . . . . . . . . . . . . . . 1147.3.3 Bayesian Model Averaging Testing Results . . . . . . . . . . . . . . . . . 1167.3.4 Pipe Failure Rate Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . 1187.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Chapter 8: Conclusions and Recommendations . . . . . . . . . . . . . . . . . . . 1258.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.2 Originality and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1278.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.4 Recommendations for Future Research . . . . . . . . . . . . . . . . . . . . . . . . 129Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Appendix A: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150xList of TablesTable 1.1 Drinking water infrastructure’s physical condition grade for Canada andUSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Table 2.1 Soil corrosivity classification based on two scoring methods . . . . . . . . 8Table 2.2 AWWA 10-point method soil test evaluation . . . . . . . . . . . . . . . . . 9Table 2.3 Summary of reported studies adopted soil properties for prediction of soilcorrosivity potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Table 2.4 Summary of pit depth and pitting rate prediction models . . . . . . . . . 14Table 2.5 Corrosion parameters for two-phase corrosion pit model (Rajani andTesfamariam 2007): with permission from the copyright owner . . . . . . 16Table 2.6 Characteristics of RCPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Table 3.1 SCI-BBN model soil parameters state discretization . . . . . . . . . . . . 35Table 3.2 Node states for scenario analysis of BBN-SCI model . . . . . . . . . . . . 42Table 4.1 Definition of parameters and their states used in the proposed BBN model 51Table 4.2 Statistical summary of input parameters for Monte Carlo simulations. . . 55Table 5.1 Modes and causes of valve failure . . . . . . . . . . . . . . . . . . . . . . . 66Table 5.2 Possile effect of valve failure and recommended actions . . . . . . . . . . . 68Table 5.3 Definition of BBN-FMEA variables (nodes) and their state discretization . 70Table 5.4 Decision making based on influence diagram . . . . . . . . . . . . . . . . . 77Table 6.1 Pipe’s physical attributes and operational factors . . . . . . . . . . . . . . 82Table 6.2 Two time slices prior and transitional probability for the annual DBNmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Table 6.3 Description of random variables and node states discretization for annualand monthly DBN models . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Table 6.4 Total number of recorded breaks for different pipe material and diameter 93xiLIST OF TABLESTable 6.5 Comparison of predicted versus recorded annual pipe breaks from 1970-2015 99Table 6.6 Comparison of predicted versus recorded monthly pipe breaks from 2000-2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Table 7.1 Frequentist and BMA variable selection approaches . . . . . . . . . . . . . 113Table 7.2 Training performance for the considered models (CI pipes) . . . . . . . . . 115Table 7.3 The performance of the considered models for different prediction/forecastinghorizon (CI pipes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Table 7.4 Summary of the city of Calgary CI pipes data properties by 2014 . . . . . 119Table A.1 Summary of available NDT technologies and their applicability to differentwater distribution pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Table A.2 Available climate model output for different models and experiments . . . 152xiiList of FiguresFigure 1.1 Components of WSS (Walski et al. 2003) . . . . . . . . . . . . . . . . . . 1Figure 1.2 Condition of Canadian drinking water system based on replacement values 2Figure 1.3 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 2.1 CMIP5 multi-model simulated time series from 1950 - 2100 for a changein global annual mean surface temperature relative to 1986 - 2005 (Nauelset al. 2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.2 Effect of climate changes on WSS pipes . . . . . . . . . . . . . . . . . . . 19Figure 2.3 Annual FI and TI for the city of Calgary: computed from CanESM2(CMIP5) RCP 8.5 emission scenario . . . . . . . . . . . . . . . . . . . . . 19Figure 3.1 Proposed framework for BBN-SCI model . . . . . . . . . . . . . . . . . . 29Figure 3.2 Effect of soil temperature on soil resistivity . . . . . . . . . . . . . . . . . 31Figure 3.3 Effect of soil moisture content on soil resistivity . . . . . . . . . . . . . . 31Figure 3.4 Proposed framework for BBN-SCI model . . . . . . . . . . . . . . . . . . 35Figure 3.5 Percentage of recorded metallic pipe breaks based on pipe materials . . . 37Figure 3.6 Pipe material distribution for the city of Calgary . . . . . . . . . . . . . . 38Figure 3.7 The city of Calgary’s total number of pipe breaks with respect to yearof installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.8 Sensitivity of SCI node due to finding at the parent nodes . . . . . . . . 41Figure 3.9 Hot spot analysis (Getis and Ord G∗i method) of pipe breakage rate andcomparison with predicted SCI (expected value) . . . . . . . . . . . . . . 44Figure 3.10 BBN-SCI model versus AWWA 10-point method . . . . . . . . . . . . . . 45Figure 4.1 Overview of remaining service life prediction and proposed safety index . 48Figure 4.2 Proposed Remaining Service Life Bayesian belief network model . . . . . 49Figure 4.3 Node state probability distribution considered for coefficient ‘a’ . . . . . 50Figure 4.4 Node state probability distribution considered for coefficient ′b′ . . . . . . 50xiiiLIST OF FIGURESFigure 4.5 Flow chart for prediction of remaining service life of metallic pipes . . . . 52Figure 4.6 Sensitivity of pit depth node due to finding at the other nodes . . . . . . 54Figure 4.7 Statistical fitting types used for Monte Carlo simulations input parameters. 56Figure 4.8 Flow chart used to embed the Monte Carlo simulations to the pit depthBayesian belief network model . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 4.9 Sensitivity of pipe remaining service life and safety index to change ininput parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 4.10 Probability of corrosion initiation time and remaining service life . . . . . 59Figure 4.11 The variation of cumulative probability of pipe failure due to externalcorrosion in different soil corrosivity index . . . . . . . . . . . . . . . . . 60Figure 4.12 Pit depth for specific corrosion initiation time in different soil corrosivityindex classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 5.1 Proposed methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 5.2 BBN model for valve FMEA . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 5.3 Distribution of valve types for the city of Calgary . . . . . . . . . . . . . 72Figure 5.4 Age classification of valves for the city of Calgary (years) . . . . . . . . . 72Figure 5.5 The city of Calgary isolation valves probability distribution . . . . . . . . 73Figure 5.6 Comparison of ages between three valve types for the city of Calgary valves 73Figure 5.7 Sensitivity analysis result (Entropy reduction) at “corrosion failure” and“severity” nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 5.8 Influence diagram for optimized decisions (highlighted) . . . . . . . . . . 76Figure 5.9 Spatial representation of predicted probabilities of corrosion failure . . . 78Figure 5.10 Criticality matrix for corrosion failure scenario . . . . . . . . . . . . . . . 78Figure 6.1 Proposed methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 6.2 (a) A BBN/DBN with three nodes; and (b) A DBN unrolled for threetime (t) slices, where nodes B and C are a static nodes and node A is adynamic node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 6.3 Major types of inferencing techniques in DBN. The shaded region rep-resents the interval that contains evidence (t1 − t2). The vertical arrowsrepresent the time at which we compute belief states, t, is the currenttime, and T is the sequence length or the final time slice . . . . . . . . . 87Figure 6.4 Proposed DBN pipe failure prediction model (unrolled for two time slices) 91xivLIST OF FIGURESFigure 6.5 Temperature and precipitation chart for 1885 - 2012 climate normals atCALGARY INT’L A. meteorological station . . . . . . . . . . . . . . . . 92Figure 6.6 Failure records of CI and DI pipes from 1956 - 2014: City of Calgary . . 93Figure 6.7 Percentage of recorded pipe failures based on pipe material. . . . . . . . 94Figure 6.8 Comparison of cumulative human (operator) and corrosion induced breaks(1956 - 2015): city of Calgary metallic pipes . . . . . . . . . . . . . . . . 94Figure 6.9 Monthly pipe breaks in the City of Calgary from 2000 - 2015 . . . . . . . 95Figure 6.10 Annual TI, FI and RD at CALGARY INT’L A from 1956 - 2015 . . . . . 95Figure 6.11 Recorded and computed climatic factors (a) PPT and PET, (b) TI, (c)FI and (d) RD from 2000 - 2015 . . . . . . . . . . . . . . . . . . . . . . . 96Figure 6.12 Average TI, FI and PPT at CALGARY INT’L A from 2000 - 2015 . . . 97Figure 6.13 DBN sensitivity analysis result for four-time slices . . . . . . . . . . . . . 97Figure 6.14 Comparison of predicted (expected value) (* DBN model trained usingcombined data (CI, DI and ST pipes) and ** DBN model trained usingdata categorized based on pipe material) and recorded number annualpipe breaks (a) CI, (b) DI, (c) ST and (d) Overall (metallic) pipes . . . . 101Figure 6.15 Comparison of predicted (expected value) (* DBN model trained usingcombined data (CI, DI and ST pipes) and ** DBN model trained usingdata categorized based on pipe material) and recorded number monthlypipe breaks (a) CI, (b) DI, (c) ST and (d) Overall (metallic) pipes . . . . 102Figure 7.1 Proposed framework for pipe failure forecasting using BMA . . . . . . . . 105Figure 7.2 Spatial grid cells for statistical downscaling of climatic attributes for thecity of Calgary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Figure 7.3 PPT, TAVG, FI, TI, and RD for RCP 2.6 and RCP 8.5 at grid cell 44 . . 109Figure 7.4 Failure rate of the city of Calgary’s CI pipes by their ages . . . . . . . . 110Figure 7.5 Training and hold-out (test) datasets considered for models 1-5 . . . . . . 111Figure 7.6 Posterior inclusion probabilities of covariates for Model 1 to 5 . . . . . . 113Figure 7.7 Standardized coefficients and PIP of FI and TI for Model 1, Model 3,and Model 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure 7.8 Predicted versus recorded monthly CI pipe breaks for Model 5 . . . . . . 115Figure 7.9 Comparison between observed and predicted monthly number of CI pipebreaks for Model 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116xvLIST OF FIGURESFigure 7.10 Model 1: 5 and 20 years’ predictive cumulative probability distributionsfor CI pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Figure 7.11 5 years predictive performance of Models 1-4 (a - d) for CI pipes. . . . . 118Figure 7.12 Cumulative probability curve of expected pipe failure rates for (a) large,(b) medium, and (c) small diameters . . . . . . . . . . . . . . . . . . . . 120Figure 7.13 5 years pipe failure rate forecast for CI pipes with smaller diameters (ato c), and larger diameters (d to f) . . . . . . . . . . . . . . . . . . . . . . 122Figure 7.14 20 years pipe failure rate forecast CI pipes with smaller (a to c) andlarger diameters (c to f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123xviList of Abbreviations2TBN Two-slices Temporal Bayesian Network.AC Asbestos Cement.AGE Age of Pipe.AR5 Fifth Assessment Report.ASCE American Society of Civil Engineers.AWWA American Water Works Association.BBN Bayesian Belief Network.BCI Bayesian Credible Intervals.BCOGC British Columbia Oil and Gas Commission.BMA Bayesian Model Averaging.CALGARY INT’L A Calgary International Airport Meteorological Station.CanAM4 Fourth Generation Atmospheric Global Circulation Model.CanCM4 Fourth Generation Coupled Global Climate Model.CanESM2 Second Generation Earth System Model.CCCma Canadian Center for Climate Modelling and Analysis.CCOHS Canadian Center for Occupational Health and Safety.CGCM Canadian Global Climate Models.CI Cast Iron.CIRC Canadian Infrastructure Report Card.CMIP5 Coupled Model Inter-comparison Project Phase 5.CON Concrete.CP Cathodic Protection.CPD Conditional Probability Distribution.CPT Conditional Probability Tables.xviiList of AbbreviationsCRD Collaborative Research and Development.CSERVS Number of Commercial/Industrial Service Connections.CU Copper.DAG Direct Acyclic Graph.DBN Dynamic Bayesian Network.DI Ductile Iron.EM Expectation Maximization.ET Evapo-transpiration.FI Freezing Index.FMEA Failure Mode and Effect Analysis.FPVC Fusible Polyvinyl Chloride.GCMs Global Climate Models.GEVD Generalized Extreme Value Distribution.GHGs Greenhouse Gases.GIS Geographic Information Systems.IPCC Intergovernmental Panel on Climate Change.LAM Limited Area Model.MAPI Minimum Antecedent Precipitation Index.MCMC Markov Chain Monte Carlo.MCs Monte Carlo Simulations.ML Maximum Likelihood.NDT Non-Destructive Testing.NET Net Evapotransportation.NOPF Number of Previous Failures.NSERC Natural Science and Engineering Research Council of Canada.PBIAS Percent Bias.PCIC Pacific Climate Impacts Consortium.PDIA Pipe Diameter.PE Polyethylene.PET Potential Evapo-transpiration.PIP Bayesian Posterior Inclusion Probability.PLNG Pipe Length.PMAT Pipe Material.xviiiList of AbbreviationsPPT Precipitation.PVC Polyvinyl Chloride.RCMs Regional Climate Models.RCP Representative Concentration Pathway.RD Rain Deficit.RMSE Root Mean Squared Error.RPN Risk Priority Number.RSERVS Number of Residential Service Connections.RSL Remaining Service Life.SCI Soil Corrosivity Index.SI Safety Index.SRES Special Report on Emission Scenarios.ST Steel.TAVG Average Temperature.TI Thawing Index.TNBRKS Total Number of Pipe Breaks.UGF University Graduate Fellowship.UNBS United Nation Bureau of Standards.USA United States of America.VINT Vintage.WSS Water Supply System.xixList of Symbols◦C Degree Celsius.µ Population mean.ρ Soil resistivity.σ Population standard deviation.θ a BMA parameter or future observation.CH4 Methane.CO2 Carbon dioxide.D Data.Ecp Cell potential.E Evidence.p(E) Probability that an evidence takes place.FM Failure Modes.Gi Hypothesis based on proximity.G∗i Hypothesis based on clustering.H+ Hydrogen ion.H Hypothesis.I Heat index.kg Kilograms.mm Millimetre.mg Milligrams.mV Millivolts.n Number of spatial features.N2O Nitrous oxide.ohms− cm Ohms centimetre.xxList of SymbolsPmax Maximum pit depth.P Pit depth.Pr Pitting rate.p(H) Prior probability distribution of hypothesis.PARMS Event-based pipe failure model.p(E|H) Statistical model.p(H|E) Posterior probability distribution.R2 Coefficient of determination.S Sample standard deviation.t Time.to Corrosion initiation time.Tm Average daily temperature.Tmin,n Minimum daily temperature.Tmax,n Maximum daily temperature.V Volts.W/m2 Watt per square meter.xxiAcknowledgementsForemost, I would like to thank The God Almighty for granting me the strength, courage,knowledge, and opportunity to be part of his plan. “Through him all things were made; withouthim, nothing was made that has been made.”(John 1:3)This research could be impossible without the financial support from Natural Science andEngineering Research Council of Canada (NSERC) Collaborative Research and Development(CRD); Mitacs and Mitacs industry partners: the City of Calgary, Russell NDE SystemsInc, and British Columbia Oil and Gas Commission (BCOGC); and the University of BritishColumbia–University Graduate Fellowship (UGF).It is a heartfelt gratitude to express thanks to my supervisor and a mentor Dr. SolomonTesfamariam. His dedication, keen interest in the area of my specialization, and healthy atti-tude in helping his students are the key facts for the completion of this research. His timelyand scholarly advice supplemented with his experience in scientific approaches helped me tocomplete my task effectively and efficiently.I would like to express my sincere thanks to my committee members Dr. Rehan Sadiq andDr. Sumi Siddiqua for their valuable comments and constructive suggestions. I would alsolike to thank Dr. Yonas Dibike for his continuous critical comments and suggestions for theimprovement of this research.I acknowledge everyone who shared me their insights, opinions, and experiences. Specialthanks to my friend Dr. Getnet Betrie, my colleagues Dr. Husnain Haider, Dr. Golam Kabir,Dr. Alex Francisque, Hassan Iqbal, Yekenalem Abebe, Nurbaiah Mohammad Noh (Baie), andBalek Ngandu.Special thanks to my wife, Yetim, her encouragement, inspiration, true hope, and sacrificesare the reason for the successful completion of this research. Kennaa and Keetii, the littleangels who came to my life during this period, you made my life so perfect and extremelychallenging. Because of you, I realized how to deal with difficult circumstances. Maya, thankxxiiAcknowledgementsyou for understanding in these stressful years, you are my strong, smart, and beautiful daughter.In the end, I enthusiastically offer my regards and blessings to all of those who motivatedand encouraged me during this study.xxiiiDedication———————————————————***———————————————————To my family, who always supported, cared and understoodme throughout my academic endeavor,particularly this one.———————————————————***———————————————————xxivChapter 1: Introduction1.1 Background and MotivationA complex network of modern Water Supply System (WSS) is used to deliver safe andreliable water from the sources to the customer’s taps. This system consists of the physicalinfrastructures that include collection systems, treatment, storage, transmission pipes, distri-bution pipes and supporting appurtenances (Figure 1.1). Due to their spatial diversificationand accessibility, these components are susceptible to both natural and human-related influ-ences. The age and the complexity of the network, in addition to the prediction uncertaintiesof environmental condition and operational characteristics, posed a substantial impact on itsoverall integrity. Although the WSS existing today are under the burden, delivering a betterlevel of service is also expected as a result of increased public awareness and advancement inlifestyle. This condition, in turn, contributes to the complexity of its overall management.Figure 1.1: Components of WSS (Walski et al. 2003)Condition grading and assessment of overall infrastructure systems have been highlightedworldwide by both governments and local infrastructure utility managers. In the United States,11.1. Background and MotivationAmerican Society of Civil Engineers (ASCE)’s 2013 Report Card for America’s Infrastructure(Herrmann 2013) reported that the drinking water infrastructure system has been assessed andgiven a score of infrastructure condition grade D (poor: at risk). In Canada, the first CanadianInfrastructure Report Card (CIRC) in 2012 assessed the state of the country’s drinking waterinfrastructure (Fe´lio 2012). In this report, on an average about 15.4% of drinking water systemcondition grade rated between “fair” and “very poor” based on the replacement costs. The2016 CIRC report also shows that there is a decrease in drinking water infrastructure system’scondition (CIRC 2016). Figure 1.2 indicates the condition of drinking water infrastructure inCanada in 2016 based on their replacement values. The reported grades of drinking waterinfrastructure (Canada and the United States of America (USA)) for the years 2009,2012,2013,2016, and 2017 are summarized and presented in Table 1.1. This summary shows that there isno significant change in the condition of drinking water infrastructure grades in both countriesfor the series of infrastructure condition reports. The ASCE 2013 and 2017 reports also revealthat due to the aging and deterioration of water pipes, in the United States, there are anestimated 240,000 water main breaks happening per year.Figure 1.2: Condition of Canadian drinking water system based on replacement values21.1. Background and MotivationTable 1.1: Drinking water infrastructure’s physical condition grade for Canada and USAReport YearCountryUSA Canada2017 D NA2016 NA Good: adequate for now (29% Ranks fair or below)2013 D NA2012 NA Good: adequate for now (15.4% Ranks fair or below)2009 D− NA*A = Exceptional: fit for the feature, B = Good: adequate for now, C = Medicore:requires attention, D = Poor: at risk, F = Failing/Critical: unfit for purpose, NA =not applicableWSS pipes and valves deteriorate structurally and functionally due to the impact of environ-mental condition and as a result of adopted operational practices. The structural deteriorationof pipes and valves diminishes the resiliency of pipe in handling external and internal stresses;however, degradation of internal surface impacts the hydraulic capacity of the pipe and de-grades the quality of water to be transported (Kleiner and Rajani 2001). The evidence ofdeterioration of water supply system pipes and valves are most often manifested in the formof degraded water quality, diminished hydraulic capacity, high leakage rate, and frequent pipebreak (Boulaire et al. 2009; Francisque et al. 2014; Practices 2003). Various factors have beenknown to contribute to the deterioration and breakage of pipes and valves (Al-Barqawi andZayed 2006; Kleiner and Rajani 2001). These factors can be categorized as factors related tophysical characteristics, operational practices and environmental conditions in which the pipeis installed. Kleiner et al. (2003) and Kleiner and Rajani (2000) classify these factors as static,operational and dynamic (time-dependent) factors. Several studies have been done to inves-tigate the effect of the first and second factors on pipe breakage rates (Hu and Hubble 2007;Rogers and Grigg 2009); however, little work has been done on the effect of dynamic factors.Most of the developed pipe breakage rate prediction models have assumed the time-dependentpipe failure factors as static (no change with respect to time) (Al-Barqawi and Zayed 2006;Kabir et al. 2015a,b; Wang et al. 2009a). However, considering dynamic factors can help to un-derstand their impacts on breakage rate patterns of pipes (Kleiner et al. 2003). Understandingthe pipe’s breakage rate and pattern is an efficient and a cost-effective means of determining31.1. Background and Motivationthe condition grade of a WSS (Kleiner et al. 2003). Descriptions of these factors are presentedin subsection 6.2.1.Climate change related factors are expected to be an influential factor in understandingthe integrity of WSS (Boulaire et al. 2010; Wols and van Thienen 2014; Wols and Van Thienen2014). Due to their daily, monthly and annual variations, climatic factors such as Freezing Index(FI)(represent freezing temperature), Thawing Index (TI) (represent thawing temperature) andRain Deficit (RD) (manifestation of soil moisture content) are considered as dynamic factors(Claudio et al. 2014; Kleiner et al. 2003). Studies which consider climate change factors inprediction of pipe failures are recently reported (Boulaire et al. 2010; Claudio et al. 2014;Kleiner et al. 2003; Wols and van Thienen 2014; Wols and Van Thienen 2014). Claudio et al.(2014) adopted a stochastic model (Standard Linear Extended Yule Process) to model pipefailures by considering time-dependent factors such as the number of previous pipe failures,aging, and climate. These authors argue that considering the effect of climate can indicatethe seasonal and yearly variation in the number of pipe failures. Kleiner et al. (2003) used astatistical modeling technique to analyze the effect of time-dependent factors on breakage ratepatterns in water mains. The considered climatic time-dependent factors include FI and RD.However, the effect of thawing temperature is not considered in the study of (Kleiner et al. 2003).Boulaire et al. (2010) developed a pipe failure prediction model for different climate scenarios.Theses scenario include failure prediction without climate change factors, with climate changefactors but future climate change neglected and with climate data from climate change model.This study has shown the impact of climate change factors on pipe failure rates and pattern;however, it is only pertinent to the Australian climate.Physical characteristics of the environment with a perspective of soil corrosivity also con-tributes to the deterioration of pipe systems. In literature, the factors that accelerate corrosionof metallic pipes and valves are reported as stray electrical currents, soil properties such asmoisture contents, chemical and microbiological contents, electrical resistivity, aeration, redoxpotential, the degree of compaction and others (Demissie et al. 2015; Rajani et al. 2000; Sadiqet al. 2004a,b). Different corrosion protection methods can be used as a preventive managementmethod or mitigation option to prevent failure as result of corrosion (Wang et al. 2014). Theseprotections can be implemented as a direct protection by incorporating physical barriers suchas coating and/or by employing external sources such as cathodic protection. However, theexternal corrosion might suddenly be activated even under a protected condition as a resultof damaged protections initiated by operational practices or environmental impacts. Hence,41.2. Research Objectivesexternal corrosion, a treat to metallic pipes and valves, has to be addressed before imposingserious consequences due to unexpected failures.1.2 Research ObjectivesThe primary objective of this dissertation is to develop Bayesian models as an alternativeapproach for water supply distribution pipe and valve failure risk assessment. These modelscan be used by a decision-maker to evaluate, plan ahead, control and reduce the possibilityof pipe and valve failures effectively and efficiently. Specifically, the proposed Dynamic/StaticBayesian belief network and Bayesian Model Averaging (BMA) based framework are integratedto Geographic Information Systems (GIS) platforms. The primary objective of this study iscomposed of the following sub-objectives:1. Develop a robust Bayesian belief network based soil corrosivity index prediction model.2. Develop a Bayesian belief network based remaining service life prediction model.3. Develop a Bayesian belief network based Failure Mode and Effect Analysis (FMEA) modelfor prioritization of valve failures.4. Develop a Dynamic Bayesian Network (DBN) model for prediction of pipe failure ratesby considering time-dependent pipe failure parameters5. Develop a BMA pipe failure forecasting model using climate model projections.1.3 Thesis OrganizationFigure 1.3 presents the organization of this Ph.D. dissertation. The dissertation is writtenbased on the manuscripts submitted/published in either journal or presented/published in con-ference proceedings. Each publication contributes to the sub-objectives listed in section 1.2.The background, motivation, objectives and the structure of this thesis are introduced in chap-ter 1. Chapter 2 presents the literature review which assisted the achievements of the objectivesin this research. Chapters 3 to 5 are prepared, to answer the research limitations identified inchapter 2, from either published or submitted manuscripts. The final chapter, chapter 8, com-prises of summary, conclusions, originality, contributions, limitations and recommendations.51.3. Thesis OrganizationChapter 1Chapter 2Prediction of Soil Corrosivity Index Using BayesianBelief NetworkChapter 3 (Objective 1)Prediction of Remaining Service Life of MetallicPipes Using Bayesian Belief NetworkChapter 4 (Objective 2) Chapter 5 (Objective 3)Dynamic Bayesian Network Model for Prediction ofPipe FailureChapter 6 (Objective 4)Forecasting Pipe Failure Using Climate ModelProjections - Bayesian Model Averaging ApproachChapter 7 (Objective 5)Conclusions and RecommendationsChapter 8Literature ReviewIntroductionFailure Mode and Effect Analysis of ValvesFigure 1.3: Thesis organization6Chapter 2: Literature Review2.1 Effect of Soil Corrosion on Metallic Pipes andValves2.1.1 OverviewSoil and their inherent properties play a significant role in the corrosion process of buriedmetallic pipes and valves. This process is a naturally occurring process in which the surfaceof a metallic structure is oxidized or reduced by chemical or electrochemical reaction with theenvironment (Hubbell 2003). As pipes are buried underground, the predominant environmentalfactor which plays a role in aggravating the corrosion process is the corrosive nature of soil dueto its properties. It can be initiated as a result of low resistivity of soil, lower pH, the presenceof anaerobic bacteria, chlorides, sulfate and sulfides, the difference in the soil composition,differential aeration of soil around the metallic pipes and stray direct current from externalsources (AWWA 1999; Cunat 2001; EPA 2009; Sparks 2003). The process, with an increasingexposure time, results in a significant loss of thickness and subsequent reduction in structuralcapacity (Rajani and Tesfamariam 2007). Thus, it is of interest to municipalities managingpipes to determine the potential for corrosion and develop a proactive mitigation strategy.Detailed descriptions of considered soil properties are presented in subsection 3.2.12.1.2 Methods of Soil Corrosivity Index PredictionSeveral scoring methods have been proposed by researchers to rate the degree of soil cor-rosivity on buried metallic pipes. The most widely known of these methods is the 10-pointscoring method (Table 2.2) proposed by American Water Works Association (AWWA) and was72.1. Effect of Soil Corrosion on Metallic Pipes and Valvesdeveloped for ductile iron pipes (AWWA 1999; Barnard et al. 2005). The AWWA 10-pointmethod considered a weighted aggregation of five soil properties. The soil of scores less thanten points is regarded as non-aggressive soil whereas the soil of scores equal to or greater thanten points is distinguished as aggressive soil. Rim-Rukeh and Awatefe (2006) modified theAWWA (1999) method by considering soil temperature and amount of chloride in the soil toinvestigate the corrosivity of the soil to low carbon steel pipe. However, these methods are lim-ited in providing adequate information about the degree of soil corrosivity (Sadiq et al. 2004b).Spickelmire (2002) also proposed a 25-point method which modified the 10-point method byincorporating other soil corrosivity factors, additional pipe design/function factors, and oper-ational parameters. Due to its data-intensive nature, Spickelmire (2002) 25-point method ismore applicable on large sized water pipe than small sized water pipes. The classification ofSpickelmire’s 25-point and AWWA’s 10-point scoring methods of soil corrosivity quantificationare summarized and presented in Table 2.1.Table 2.1: Soil corrosivity classification based on two scoring methodsReferences Soil corrosivity (∑5i ri)AWWA (1999) Aggressive >10Non aggressive < 10Soil corrosivity (∑15i si)Spickelmire (2002) Mild 0- 14.5Appreciable 20 - 24.5Severe >2582.1. Effect of Soil Corrosion on Metallic Pipes and ValvesTable 2.2: AWWA 10-point method soil test evaluationSoil properties Characteristics value PointsSoil resistivity (Ohm-cm) < 1, 500 10≥ 1, 500− 1, 800 8> 1, 800− 2, 100 5> 2, 100− 2, 500 2> 2, 500− 3, 000 1> 3000 0Soil pH 0.0− 2.0 52.0− 4.0 34.0− 6.5 06.5− 7.5 07.5− 8.5 0> 8.5 3Redox potential mV > +100 0+50 to +100 3.50 to +50 4< 0 5Soil sulfides contents Positive 3.5Trace 2Negative 0Moisture contents Poor drainage, continually wet 2Fair drainage, generally moist 1Good drainage, generally dry 0*If sulfides are present and low or negative redox potential results areobtained, add three points for this range.Statistical and soft computing techniques have also been applied to assess the aggressivenessof the soil to metallic pipes based on different soil properties (Bhattarai 2013; Cunat 2001;Doyle et al. 2003; Liu et al. 2010; Najjaran et al. 2004, 2006; Sadiq et al. 2004b). Bhattarai(2013) characterized soil corrosivity rates based on soil properties collected at 23 representative92.1. Effect of Soil Corrosion on Metallic Pipes and Valveslocations. Liu et al. (2010) applied a predictive data mining approach to explore the relationshipbetween soil properties and pipe corrosion pit growth rate. Sadiq et al. (2004b) and Najjaranet al. (2006) used fuzzy based approaches that consider soil parameter of AWWA (1999) 10-point scoring method. Doyle et al. (2003) studied the correlation between external corrosionas a result of soil properties and pitting rates using the data collected for the city of Torontoarea over a period of two years using statistical techniques.Cunat (2001) examined the degree ofcorrosion to stainless steel buried in soil considering different soil properties, microbial activities,and stray current from external sources. Different authors also approached the classificationof soil corrosivity potential. Sadiq et al. (2004b) classified the soil corrosivity potential intonon-corrosive, moderately corrosive and corrosive; however, Najjaran et al. (2004) classified ascorrosive and non-corrosive only. Table 2.3 presents the summary of previous studies whichused soil properties to predict soil corrosivity potential. However, the reported studies have alimitation in considering the complex nature of soil environment, inter-dependencies betweensoil parameters and their contribution to metallic pipe corrosions. Most utilities have limitedinformation about their soil parameters and also expensive to collect the data needed to adoptthe existing approaches.Table 2.3: Summary of reported studies adopted soil properties for prediction of soil corrosivitypotentialMethods Soil property CorrosivitypotentialReferences10-point scor-ing methodSoil resistivity, pH, redox potential, sul-fide and soil moisture contentCorrosive andnon-corrosiveAWWA(1999)12-Factor eval-uationSoil resistivity, pH, redox potential, sul-fide and soil type, water content, buffer-ing capacity, chloride and sulfate concen-trations, ground water level, horizontaland vertical soil homogeneities and elec-trochemical potentialHighly corro-sive, virtuallynot corrosive,slightly corro-sive and corro-siveMetalogic(1998)Continued on next page102.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil CorrosivityTable 2.3 – continued from previous pageMethods Soil property CorrosivitypotentialReferences25-point scor-ing methodSoil resistivity, pH, redox potential, sul-fide and soil type, sulfate content, mois-ture, pipe size, pipe maximum designsurge pressure factor, pipe minimum de-sign life factor, pipe location and leakrepair difficult factor, potential inferencesources and pipe zone back fill materialMild, moder-ate, apprecia-ble and severeSpickelmire(2002)Fuzzy-basedmethodThe same as 10-point scoring method Non-corrosive,moderatelycorrosive andcorrosiveSadiq et al.(2004a)Fuzzy expertsystemThe same as 10-point scoring method Non-corrosive(0) and mostcorrosive (1)Najjaranet al. (2006)Data miningtechniqueSoil resistivity, soil pH, Redox potential,soil sulfides content and percentage of clayfinesMaximumcorrosion pitgrowth rateLiu et al.(2010)StatisticalanalysisSoil resistivity, redox potential, pH,sodium, chlorides and percentage of clayfinesMaximum pitdepth, pit areaand pit volumeKleiner et al.(2011)2.2 Prediction of Remaining Service Life of MetallicPipes Based on Soil Corrosivity2.2.1 Corrosion Pit Characterization MethodsDue to corrosion, metallic pipes “leached out” and leaves black graphite flakes which retainsthe original shape of the pipe masking the area of the corroded part of pipes but has virtuallyno structural strength (Doyle et al. 2003). This process frequently threatens the wall thickness112.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil Corrosivityof metallic pipes. The loss of metallic pipe wall thickness due to the effect of corrosion canbe prevalent in a uniform or localized forms (Rajani and Tesfamariam 2007). An estimate ofpipe wall thickness loss (i.e pit depth) most often can be made in terms of pitting rate, pitdepth, pit area (i.e. pit width and pit length) or through holes. According to the Helical ScrewFoundation system design manual for new construction (Hubbell 2003), types of corrosion areclassified as follows:− Uniform or near uniform - corrosion takes place in all areas of the metal at the same orsimilar rate.− Localized - some areas of the metal corrode at different rates than other areas due toheterogeneities in the metal or environment.− Pitting - very highly localized attack at specific areas, which result in small pits that maypenetrate to perforation.Corrosion pit measurement can be characterized by a direct and indirect approaches (Ra-jani et al. 2000). The direct approach uses measurements taken by Non-Destructive Testing(NDT) technology on operating pipes. NDT is a technique for inspecting, testing, or evaluatingmaterials, components or assemblies for discontinuities, or differences in characteristics of anengineering structure without destroying the serviceability of the system or even single parts(ASNDT 2014). The main objective of NDT is to provide the inspector with quantitative aswell as qualitative information which can be achieved by detecting, locating and sizing any de-tected flaws (Gros 1996). These flaws could be in the form of cracks, voids, corrosion, inclusions,delamination, impact damage and holes. The summary of available NDT technologies and theirapplicability to water supply pipes are presented in Table A.1 (Costello et al. 2007; Liu et al.2012a,b). The indirect approach (i.e. destructive testing) is where the measurements are takenon the exhumed pipe samples (Rajani et al. 2000). This approach requires the removal of pipesample from pipe wall to check for remaining pipe wall thickness, pit depths or any damagesand residual strength (Liu et al. 2012b). Compared to the direct approach, this approach isdestructive in nature and mostly performed on a limited number of samples.122.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil Corrosivity2.2.2 Prediction Methods for Remaining Service Life of Metal-lic PipesDeterioration of aging metallic water mains is an increasing concern for all consumers andowners (i.e. water utilities) as it reduces the ability of water mains to deliver safe and reliablepotable water without interruptions (Rajani and Tesfamariam 2007). Factors, such as castingand manufacturing defects; operational conditions; the size of pipes; and environmental effects(i.e. extreme events like flood and drought, earthquake and corrosive soil environment), have adirect and an indirect contribution to the structural resilience of metallic pipes (Rajani et al.2000). The structural failures of metallic pipes due to corrosion occur, not only in old pipes butalso reported to play a prevalent role in the premature failures of new pipes (Li and Mahmoodian2013; Mohebbi et al. 2000; Spickelmire 2002). As a result, considerable studies have beenundertaken in the past few years on the corrosion of metallic pipes and their service lives (Liand Mahmoodian 2013; Mohebbi et al. 2000; Rajani et al. 2000; Rajani and Tesfamariam 2007;Randall-Smith et al. 1992; Sadiq et al. 2004b; Vela´zquez et al. 2009).For instance, Rajani et al. (2000) proposed a corrosion prediction model to estimate theRemaining Service Life (RSL) of grey cast iron mains that consider the corrosion pits to bethe main factor that reduces the structural capacity of the pipes. Sadiq et al. (2004b) alsodeveloped a probabilistic risk analysis method to predict the RSL of cast iron pipes based onthe Monte Carlo simulations. Rajani and Tesfamariam (2007), on the other hand, developeda probabilistic time to failure model by integrating exponential corrosion model (Rajani et al.2000) and a model based on Winkler-type pipe-soil interaction to estimate time to failure(Rajani and Tesfamariam 2004; Tesfamariam et al. 2006). Li and Mahmoodian (2013) alsoproposed a methodology that quantitatively assesses the risk of pipe failure to predict its RSLusing a time-dependent reliability theory, in which mathematical regression was used to derivean empirical model for maximum pit growth of corrosion based on readily available data.These studies considered several modeling approaches to estimate the corrosion pit depthor pitting rates for service life prediction. The proposed corrosion prediction models varybetween linear, power and exponential functions (Rajani and Tesfamariam 2007). The reviewof corrosion prediction models by Cole and Marney (2012) also categorizes these corrosionprediction models as stochastic or empirically derived models from field experiments, parameter-based methods, data-driven methods, and partially multi-scale type models. Romanoff (1957)proposed the first corrosion model as a power law relationship between maximum pit depth132.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil Corrosivity(Pmax) and time-based on the wide-ranging of data collected by the United Nation Bureauof Standards (UNBS). Rossum (1969) also developed a corrosion pit depth estimation model,the first model to consider soil parameter, considering the aeration level of the soil as differentscenarios. This author further proposed the corrosion pit depth model by considering the role ofcell potential (Ecp), soil pH and soil resistivity (ρ) as a parameter to model pit growth. Most ofthe corrosion pit models proposed after 1969 are based on the equations of Romanoff (1957) andRossum (1969). For example, Ahammed and Melchers (1994) developed a probabilistic powerfunction model similar to the Romanoff (1957) pit depth model for estimating the corrosionfailure in steel pipes. Table 2.4 shows the summary of the available corrosion prediction models.Table 2.4: Summary of pit depth and pitting rate prediction modelsReferences Application Equation DescriptionsRomanoff(1957)Maximumpit depthPmax = Ktm Pmax is maximum pit depth. K andm are constants. K is used to cor-rect the dimensional relationships ofthe equations and m varies between0 and 1 and is dependent on the pipematerial and the effect of externalenvironment on the pipeRossum(1969)Pit depth P = KntnP = Kn(Ecpρ)ntnEcp = 10− pHP = Kn[(10−pH)tρ ]nP is pit depth; t is time in years; n issoil aeration constants (ranges from0.17 for soils of good aeration to 0.67for soils of very poor aeration); Knis a constantRajani et al.(2000)Pit depthand pittingrateP = at+b(1−exp(−ct))Pr = a+ bc(exp(−ct))P is a pit depth; Pr is pittingrate; a is a minimum corrosion rate(mm/yr.); t is corrosion initiationtime and b and c are constantsContinued on next page142.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil CorrosivityTable 2.4 – continued from previous pageReferences Application Equation DescriptionsVela´zquezet al. (2009)Maximumpit depthPmax = K(t− to)v Pmax is the maximum pit depth; t isthe exposure time; to is the pit ini-tiation time; K and v are constantsderived from regression analysis ofsoil and pipe parametersThe above corrosion models (Ahammed and Melchers 1994; Romanoff 1957; Rossum 1969)have a limitation in accounting for the varying nature of corrosion rate. The corrosion rateis high at the beginning, never infinite but it reaches the steady state later (Rajani et al.2000; Rajani and Tesfamariam 2007). Using the models explained above can theoreticallylead to infinite corrosion rates at the earlier time intervals and negligible corrosion rates atthe largest time intervals. Rajani et al. (2000) argues that the use of power functions is notappropriate for the estimation of RSL as it leads to underestimations and proposed a two-phasemodel to address this limitation. In this model, the first phase (linear type model) is used toaccommodate the slow linear corrosion pit growth and the second phase (exponential model)is used to accommodate the rapid corrosion pit growth. The equations of the model proposedby Rajani et al. (2000) to predict the pit depth and pitting rate, which include the constantsa, b and c, is presented in Table 2.4. The constant a corresponds to a minimum corrosionrate, while the combination of the constants (a + bc) represents the maximum corrosion rate.The values of these constants depend on the metallic property of the pipe (e.g. nature ofpipe material or alloy, pipe surface condition/roughness, moisture absorptivity etc.) and thecorrosivity of the soil environment (Rajani and Tesfamariam 2007). The value of the constantc also depends on time and is assumed to be 0.0058/year (Rajani et al. 2000). Rajani andTesfamariam (2007) attempted to estimate the values of these constants for Cast Iron (CI) pipe(values presented in Table 2.5)based on the observations of full penetration age of corrosionpits. For example, considering Rajani et al.’s equation, the full penetration age of a 150 mmdiameter CI water main with a wall thickness of 9.652 mm is approximately 15 years in a soilof very high corrosivity, 40 years in a soil of low soil corrosivity, but never happens in soil ofvery low corrosivity.152.2. Prediction of Remaining Service Life of Metallic Pipes Based on Soil CorrosivityTable 2.5: Corrosion parameters for two-phase corrosion pit model (Rajani and Tesfamariam2007): with permission from the copyright ownerSoil corrosivity Minimum corrosion b (mm) c (per annum) Maximum corrosionrate, a (mm/year) rate, (a+bc) (mm/year)(1) (2) (3) (4) (5)VHC 0.0336 15.60 0.058 0.9384HC 0.0294 13.65 0.058 0.8211MC 0.0252 11.70 0.058 0.7038LC 0.0210 9.75 0.058 0.5865VLC 0.0042 1.95 0.058 0.1173VHC = very high corrosivity, HC = high corrosivity, MC = medium corrosivity, LC= low corrosivity, VLC = very low corrosivityVela´zquez et al. (2009) developed a statistical model from an analysis of 259 discrete samplesof cathodically protected steel pipes that had been buried in various soil types for approximately23 years. The analysis was made based on the Rossum (1969) model. A multivariate non-linearregression analysis was conducted with the maximum pit depth (Pmax) as a dependent variableand soil and pipe characteristics as the independent variables. The corrosion pit initiation time(to) was considered as a parameter estimated from the regression analysis. Moreover, Caleyoet al. (2009a) employed the Markov chain method to predict the pit depth. The transitionprobabilities between the pit states were derived as a function of environmental factors fromthe original pit growth model of Vela´zquez et al. (2009). Caleyo et al. (2009b) also adoptedthe above-modified formulation of Rossum (1969) to predict the maximum corrosion pit depthusing the probability distributions and the Monte Carlo simulations. A random vector of soiland pipe parameters were generated and used as an input for the Monte Carlo simulations for5000 trials. Then, the simulated pit depth was fitted to Generalized Extreme Value Distribution(GEVD) to identify the value of the constants.The previously reported studies have a limitation in addressing the complex nature of soilenvironment and its effect on metallic corrosion. Most of the reported techniques use a data-intensive approach but the available collected information by the water utilities is nearly negli-gible. The models explained above incorporated the soil and the pipe parameters informationto estimate pit depths or pitting rates. Yet, this information is either not readily available ordifficult and costly to obtain within appropriate time and resources.162.3. Climate Change and Water Supply System Pipes2.3 Climate Change and Water Supply System PipesDesign and construction of water infrastructure are normally based on historical climatedata. However, observations show that there have been changes in climatic pattern and statistics(Solomon 2007) that will most probably continue to the future. These changes in climate evolveas a result of the Earth’s internal dynamics (i.e., variations in the Earth’s orbit, sunspot cycles,changes in solar output) and changes in the external forcing’s (Lemmen and Warren 2004). Theexternal forcings result from a combination of natural phenomena such as volcanic eruptions andsolar variations; as well as human-induced changes which cause the variations in atmosphericcompositions (e.g., fluctuations in Greenhouse Gases (GHGs) and aerosols) (Le Treut et al.2007a). The topmost common GHGs directly emitted by humans are carbon dioxide (CO2),methane (CH4), and nitrous oxide (N2O) (Karl and Trenberth 2003). Increasing evidence ofanthropogenic influence on climate change has been noticed as a result of the advancement ofclimate and Earth Sciences (Matson et al. 2010). For example, Figure 2.1 shows the historicaland projected global average surface temperature changes simulated by multiple models basedon two Representative Concentration Pathway (RCP)s (i.e., 32 models for RCP 2.6, 39 modelsfor RCP 8.5). Summary for Policymakers19Figure SPM.7 |  CMIP5 multi-model simulated time series from 1950 to 2100 for (a) change in global annual mean surface temperature relative to 1986–2005, (b) Northern Hemisphere September sea ice extent (5-year running mean), and (c) global mean ocean surface pH. Time series of projections and a measure of uncertainty (shading) are shown for scenarios RCP2.6 (blue) and RCP8.5 (red). Black (grey shading) is the modelled historical evolution using historical reconstructed forcings. The mean and associated uncertainties averaged over 2081−2100 are given for all RCP scenarios as colored verti-cal bars. The numbers of CMIP5 models used to calculate the multi-model mean is indicated. For sea ice extent (b), the projected mean and uncertainty (minimum-maximum range) of the subset of models that most closely reproduce the climatological mean state and 1979 to 2012 trend of the Arctic sea ice is given (number of models given in brackets). For completeness, the CMIP5 multi-model mean is also indicated with dotted lines. The dashed line represents nearly ice-free conditions (i.e., when sea ice extent is less than 106 km2 for at least five consecutive years). For further technical details see the Technical Summary Supplementary Material {Figures 6.28, 12.5, and 12.28–12.31; Figures TS.15, TS.17, and TS.20}6.04.02.0−2.00.0(oC)423239historicalRCP2.6RCP8.5Global average surface temperature change(a)RCP2.6 RCP4.5 RCP6.0 RCP8.5 Mean over2081–21001950 2000 2050 2100Northern Hemisphere September sea ice extent(b)RCP2.6 RCP4.5 RCP6.0 RCP8.5 1950 2000 2050 210010.08.06.04.02.00.0(106  km2 )29 (3)37 (5)39 (5)1950 2000 2050 21008.28.07.87.6(pH unit)12910Global ocean surface pH(c)RCP2.6 RCP4.5 RCP6.0 RCP8.5 YearSPMFigure 2.1: CMIP5 multi-model simulated time series from 1950 - 2100 for a change in globalannual mean surface temperature relative to 1986 - 2005 (Nauels et al. 2013)The safety and reliability of water supply system have been threatened as a result of theaging and deterioration of WSS components (Wols and van Thienen 2016). In addition tothe aging and deterioration of WSS components, climate change presented the most challengesto water utilities (Laucelli et al. 2014). As a linear component of WSS, a water pipe failure(break/burst//leak) happens when aging and deterioration compromise its structural integrity(Rajani and Tesfamariam 2004). Deterioration of a pipe happens as a result of physical, me-172.3. Climate Change and Water Supply System Pipeschanical or chemical factors induced by external or internal causes (Rajani and Kleiner 2001).Physical deterioration can be caused by external and internal corrosions; soil moisture content(Kleiner and Rajani 2000); and cycles of freezing and thawing seasons (Demissie et al. 2017c);while impact, erosion, and stresses as a result of earth and traffic loads can cause mechanicaldeterioration (Rajani and Tesfamariam 2004). On the other hand, chemical deterioration canoccur due to the ingress of chemicals from the external environment and aggressiveness of waterconstituent (Lane and Neff 1969). Other factors, such as the status of cathodic protection, thenumber of residential and industrial service connections, break history, and water quality arealso considered as potential factors contributing to pipe failures.A change in climate is one of the factors anticipated to have an impact on the integrityof water pipes by intensifying the process of aging and deterioration. Figure 2.2 describes thegeneral climatic pathways which threaten the integrity of WSS pipes Wols and Van Thienen(2014). The most widely reported climate covariates believed to have an effect on pipe failure arederived from the amount of temperature and precipitation. RD is one of the climate covariateswhich manifests itself as available moisture in the soil. Wols and Van Thienen (2014) argue thatthe variation in soil moisture content as a result of climate change can result in partial settlingof soil which leads to pipe failure. Seasonal changes and trends of temperature have beenindicated to have a strong correlation with the number of pipe failures (Demissie et al. 2017c;Habibian 1994; Kleiner et al. 2003). For instance, (Laucelli et al. 2014) indicated that the colderclimate (i.e., represented by FI) noticed to have a significant effect on pipe failure comparedto the warmer climate (i.e., represented by TI). Most of the reported studies investigated thesignificance of freezing temperature on pipe failure; however, the effect of a warmer climate isnot considered in most pipe failure prediction models (Instanes 2003). Figure 2.3 shows theaverage freezing and thawing index for the city of Calgary computed from downscaled climatemodel output. For the period considered (1950-2100), both the FI and TI shows an increasingtrend; however, the increment rate for the TI is higher compared to that of the FI.182.3. Climate Change and Water Supply System PipesSoil  moistureFloodingGround water level risePrecipitationWater consumption  (internal pressure)Freezing effectThawing effectTemperatureSalinationCorrosionSea level riseUprooting of treesWind Increased frequency of  pipe breaksFigure 2.2: Effect of climate changes on WSS pipes1950 1975 2000 2025 2050 2075 2100Time (year)-2000-1000010002000300040005000FI/TI (degree-days)FITIFigure 2.3: Annual FI and TI for the city of Calgary: computed from CanESM2 (CMIP5) RCP8.5 emission scenarioA physically and/or statistically based pipe failure prediction models have been developed192.3. Climate Change and Water Supply System Pipesto enhance the capacity of water utilities in order to make informed decision making in reha-bilitation and renewal programmes (Kleiner and Rajani 2001). Application of physically basedpipe failure models to asses the structural resiliency of pipes are unrealistic due to the scarcityand cost of accurate data (Kleiner and Rajani 2000). The efficiency of purely statistical models,on the hand, depends on the availability of historical data. In previous studies, most of theproposed models mainly utilized the mentioned pipe failure factors related data. These modelshave shown to be dependent on the availability of historical data/information which is mostoften not readily available for use with water utilities (Al-Barqawi and Zayed 2006; Kabir et al.2015a,b; Wang et al. 2009a) In additions, some of the methods presented are highly localizedto hotter climate and reluctant to predict pipe failure rates by considering time-dependent fac-tors. Few of these studies are elaborated in the next paragraphs. Gould and Kodikara (2008)applied an exploratory statistical analysis of historic failure information and the impact of theAustralian local climate to investigate the effect on pipe failure rates. This study reveals thatseasonality in annual climate cycles significantly affects pipe failure rates. Between the monthsof December and May, a higher variation of failure rates was observed than in other months.In addition, higher failure rates have been found for the pipes located in reactive soils duringthe summer season. A correlation of pipe failure and weather parameters shows that only twoof the thirteen weather parameters considered in the study were strongly correlated to pipefailure rates (i.e. net evaporation and minimum antecedent precipitation index). According tothis author, these parameters indicate that there is a clear evidence that weather affects thesoil type directly and pipe failure rates indirectly.Kleiner and Rajani (2000) also indicated that predicting or forecasting the “true”deteriorationrate of pipe is a key direction towards the estimation of an accurate remaining service life ofpipes. The accurate remaining service life, in turn, contributes to an effective planning andimplementation of rehabilitation and renewal programmes.Boulaire et al. (2009), on the other hand, presented how to improve an event-based failuremodel (i.e. PARMS) by incorporating the effect of seasonal and/or annual climatic variations.This study incorporated the Minimum Antecedent Precipitation Index (MAPI) and Net Evap-otransportation (NET) weather parameters in PARMS failure model. Similarly, Kleiner et al.(2003) used a multivariate time-exponential model proposed by Kleiner and Rajani (2000) toexamine the effect of climatic, aging and operational factors on pipe failure for a short andlong-term level of infrastructure planning. According to Kleiner et al. (2003), considering theeffect of time-dependent factors such as aging, FI, RD, the cumulative length of replaced mains202.3. Climate Change and Water Supply System Pipesand cumulative length of cathodic protection are crucial in characterizing the failure frequencyof pipes.2.3.1 Emission ScenariosEmission and socio-economic scenarios are most widely used to describe the climatic featuresusing different factors such as GHGs, pollutants of air, changes in socio-economy, a change oftechnology, energy and land use (Van Vuuren et al. 2011). These factors have been usedas a variable input to run climate models and considered as a foundation of climate impactassessments, mitigation options needs to be considered, and their attributed costs. Differentscenarios have been considered for these purposes, for instance, IS92 scenarios (Leggett et al.1992) and Special Report on Emission Scenarios (SRES) (Nakicenovic and Swart 2000). TheRCPs, the latest development, is a scenario which considers GHGs emission, air pollution,land use trajectories, and mitigation policies (Moss et al. 2010). RCPs consist of four sets ofpathways covering the period of 1850-2100 with different radiative forcing or climatic forcinglevels (i.e. 8.5, 6, 4.5 and 2.6 W/m2), namely, RCP 8.5, RCP 6/RCP 4.5 and RCP 2.6. TheRCPs are considered to be a mitigation scenarios leading to low forcing level (RCP 2.6), mediumstabilization scenarios (RCP 4.5/RCP 6) and very high baseline emission scenarios (RCP 8.5).The characteristics of the RCPs are described in Table 2.6. Van Vuuren et al. (2011) suggeststhat RCP scenarios can be used as an input for climate change modeling, mitigation analysis,impact assessment and forming an analytical thread in climate research.Table 2.6: Characteristics of RCPsScenario RCP 2.6 RCP 4.5 RCP 6 RCP 8.5Greenhouse gasemissionsVery low Medium-lowmitigationVery low miti-gation mediumbaselineHigh miti-gation highbaselineAgricultural area Medium (cropland and pas-ture)Very low forboth croplandand pastureMedium (cropland) very low(pasture) Low(total)Medium (crop-land and pas-ture)Air pollution Medium tolowMedium Medium Medium tohigh212.3. Climate Change and Water Supply System Pipes2.3.2 Global Climate ModelsGlobal Climate Models (GCMs) are models based on the principles of fluid and thermody-namics (Stute et al. 2001). GCMs are mathematical representations of Earth’s climate systemprocesses based on physical principles such as conservation of mass, energy, and momentum,considering a wealth of observations (Smith et al. 1998). These models can be considered as alaboratory in which numerical experiments of climate change in the past, present, and future isprovided (Solomon 2007). Changes in different meteorological variables in GCMs are estimatedfor grid boxes that have a coarser resolution of between 100 and 300 km, 10 to 20 vertical layersin the atmosphere, and involves about 30 layers in the oceans (Knight 2016). GCMs havebeen employed to simulate observed features of recent climate and past climatic variances andable to reproduce extreme warm and cold air outbreaks and frost days reasonably well (IPCC2016). These models have shown a considerable confidence in providing credible quantitativeestimates of future climate change, particularly for coarse resolutions (i.e. at a continentaland above scales) (Le Treut et al. 2007a). However, a confidence in model estimates variesdepending on the considered climate variables. For instance, high confidence has been seen inthe estimation of temperature while low confidences in precipitation (Le Treut et al. 2007b).Generally, GCMs has been known to provide a clear picture of a warming climate in responseto increasing greenhouse gases emission in the last decades of development.2.3.3 Global Climate Projections Through CMIP5Coupled Model Inter-comparison Project Phase 5 (CMIP5) is the most recent and newset of coordinated climate model experiments which was first initiated in the September 2008meeting that involved 20 climate modeling groups from different countries (Taylor et al. 2007).The primary goal of this project was to contribute a framework for coordinated climate changeexperiments by incorporating simulations for evaluation in the Intergovernmental Panel on Cli-mate Change (IPCC) – Fifth Assessment Report (AR5) (Stocker 2014). The CMIP5 projectionsare created by employing an assemblage of new global climate models (Knutti and Sedla´cˇek2013) that reflect varying degrees of recent progress in climate change study and modeling.CMIP5 climate projections are also generated using a new set of climate forcing scenarios (i.e.,RCPs) that consider new progress in integrated assessment modeling to distinguish the futuredevelopments in overall global GHGs emission. However, despite the progress, the horizontalresolution of most GCMs (Canadian Global Climate Models (CGCM)) making CMIP5 centen-222.3. Climate Change and Water Supply System Pipesnial projections are of order 1-2◦, mainly as a result of computational constraints (Guilyardiet al. 2011). These limitations affect the ability of these models to represent important localforcing features (e.g., land surface heterogeneity, coastlines, and territorial water bodies), whichcan alter the global climate on regional to local scales (Vera et al. 2013). The coarse resolutionalso prevents CGCM from granting an actual description of severe weather events which areof primary interest in estimating the societal influence of changes in climate variability (Giorgiand Mearns 1999). It also means that the spatial scale gap between the regional climate datadirectly available from CMIP5 and the data required for impact assessment and decision makingis still an unavoidable fact.2.3.4 Downscaling of Global Climate Model outputsA different downscaling approach can be used as a means of relating the large-scale atmo-spheric predictor variables to local or station scale meteorological series such as temperature andprecipitation (Dibike and Coulibaly 2005). The downscaling of regional climate information tolocal scale is a basic requirement which gives confidence in the informed decision making regard-ing climate change impacts. This information is needed for the impact assessment of climatechange on human and natural systems (Solomon 2007). It can also be used in the developmentof the suitable climatic variability adaptation and risk analysis and management strategies atlocal to regional levels. In previous years, several downscaling methods have been proposed tosolve the scale gap between GCMs and Regional Climate Models (RCMs) (Trzaska and Schnarr2014). The two most commonly practiced downscaling methods are dynamical downscaling andstatistical downscaling. In dynamical downscaling, the RCMs are applied (run) over a limitedgeographical area at a better resolution using GCMs simulation results as a boundary condi-tion for a lateral and surface boundaries (Dibike and Coulibaly 2005; Giorgi and Mearns 1999).In statistical downscaling, a technique which uses statistical relationships between large-scaleclimate predictors and regional to local scale predictands is developed for prediction (Hewitsonand Crane 1996). The developed relationship is then applied to GCMs output to downscale thesimulated global scale climate data of the GCMs to the local scale. The following subsequentsections discuss the descriptions of the dynamical and statistical downscaling.232.3. Climate Change and Water Supply System Pipes2.3.4.1 Regional Climate ModelsRCMs are an alternative approach to statistical downscaling of climatic variations, whichmakes use of a high-resolution regional climate models (Smith et al. 1998). It is also called aLimited Area Model (LAM). The RCMs have higher resolution (i.e. 25-100 km) than GCMs thatmakes these models simulate the important climate processes very well. However, since RCMsuse boundary conditions from GCMs, some measured data might be necessary for validation(i.e. 30 years of observed or recorded data) (Smith et al. 1998). The output of RCMs have agreat value for diagnostic studies of the climate and hydrological processes (Rodenhuis et al.2007), which can be used as an in input data for Modelling of WSS pipe failures.2.3.4.2 Statistical DownscalingThe statistical downscaling technique can be employed using several methods such asweather classification, regression analysis, and weather generator methods (Hewitson and Crane1996; Wilby and Wigley 1997). In the past, most of these methods have been applied in the pastfor downscaling of climate parameters; for instance, Wilby et al. (2002) developed a statisticaldownscaling model which uses a hybrid of stochastic weather generator and regression-basedmethods. Stochastic weather generator downscaling technique generates a synthetic time seriesof weather data based on the statistical characteristics of observed weather for a specific location(Katz 1996; Semenov and Barrow 1997). In regression-based downscaling, a regression functionis used to represent a direct quantitative relationship between the predictands and predictors(Karl et al. 1990; Wigley et al. 1990). The regression-based downscaling method most often de-pends on the choice of the mathematical transfer function, predictor variables, and proceduresused in statistical fittings (Dibike and Coulibaly 2005). A temporal neural network has alsobeen used as downscaling techniques to capture the complex relationship between large-scalepredictors and locally observed meteorological variables such as precipitations and temperature(Dibike and Coulibaly 2005).2.3.5 Downscaled Climate DataA downscaled climate model output covering the case study area of interest is extremelyimportant in the modeling of the impacts of climate change on built infrastructures. In thisregard, the availability of freely downscaled climate data creates an opportunity towards theimplementation of cost-effective and proactive decisions with a considered impacts of future242.4. Valves of Water Supply Systemclimate scenarios. The trend shows that the climate change modeling institutions are alreadyon the path of this initiative. For instance, the climate model output data which are basedon CMIP5 project, explained in 2.3.3, are freely available for different regions of the worldfor different spatial and temporal resolution. Canadian Center for Climate Modelling andAnalysis (CCCma) is one of these institutions which participate in this project. The modelsdeveloped by CCCma under the CMIP5 project include the Fourth Generation AtmosphericGlobal Circulation Model (CanAM4), the Fourth Generation Coupled Global Climate Model(CanCM4) and the Second Generation Earth System Model (CanESM2) (CMIP5 2015). Theseclimate models have been developed by CCCma to study climate change, climate variabilityand understand the climate system’s governing processes (CCCma 2014). CCCma providesseveral climate models output freely for time scales ranging from seasons to decades. Table A.2summarizes the available climate model output data from CCCma under different experimentalsetup. On the other hand, the climate data statistically downscaled by Pacific Climate ImpactsConsortium (PCIC) and freely available from the PCIC’s web repository provides a better(roughly 10km resolution) for all provinces of Canada (PCIC 2014). The PCIC’s climate datais available for the climate variables such as minimum temperature, maximum temperature,and precipitation through an interactive map user interface for different RCP scenarios, modelcombination and time periods.2.4 Valves of Water Supply System2.4.1 BackgroundModern WSS consists of intake structures, water mains (transmission and distribution net-work of pipes), pumps, treatment plants, fire hydrants and valves to transport water fromsources to customers; tanks and reservoirs that store water to accommodate fluctuations indemand as a result of varying rates of usage or fire protection needs and other supporting in-frastructures (Wang et al. 2010). These components as an asset can be categorized into twogroups: water mains and appurtenance assets. Appurtenances are assets associated with thedistribution and transmission network that have a supplementary function to the pipe assets(i.e. pipe bodies, joints, tees) (Marlow and Beale 2012). The amendment by Canadian Cen-ter for Occupational Health and Safety (CCOHS) in 2012 under a regulation of drinking watersystem on Ontario Regulation 420/12 states that “appurtenances” include valves, a valve cham-252.4. Valves of Water Supply Systember, hydrant, hydrant lead, flow meter, curb stop, maintenance access point, personnel accessopening or other minor accessory parts of water mains (CCOHS 2012).Valves are a mechanical device by which the flow of fluid may be started, stopped, orregulated by a movable part that opens or obstructs passage of flow (Ozger and Mays 2004).Based on their functions, valves can be grouped into four categories (Ysusi 2000): (1) isolationvalve (2) control valve (3) blow-offs, and (4) air-release and vacuum-release valve. The Europeanstandard EN 736-1:1995 explains that isolation valve is intended for use only in the closed orfully open position; control valve is a power-operated device which changes the fluid flow rateand pressure in a process of control system; and regulating valve is a valve intended for use inany position between closed and fully open situations.2.4.2 Isolation ValvesIsolation valve plays a critical role in a water supply system for subsystem isolation. Thisvalve is significantly important in effective isolation of parts of a network during the incidenceof pipe bursts/breaks, pipe inspection and maintenances and other emergency situations (Junet al. 2007; Trietsch et al. 2006). Subsystem isolation is mostly required to repair or rehabilitatea broken component, to allow removal of equipment and shut down of a system and can be doneby closing adjacent isolation valves (Jun et al. 2007). Due to its long period of non-functionalityin operational period, this valve is susceptible to internal built up of deposits, deterioration ofseals, failures of connecting seals and their main parts due to corrosion impacts (Marlow et al.2012). The failure of pipes can be managed using isolation valve but the failure of isolationvalve itself can have a tremendous consequence on the system’s disruption and subjected toloss of property and associated costs. Hence it is vital to assess the condition of these valvesand differentiate the ones most vulnerable and at risk of failure.Failure of valves in general as an asset is asset and context specific, being influenced byfactors such as the type of valve, difference in manufacturers, difference in management ap-proaches, quality of the installation, the external and internal environment the valve is exposedto (Marlow and Beale 2012; Marlow et al. 2012). Most often as the parts of the isolation valveare metallic, its condition deteriorates and leads to failure as a result of fatigue, corrosion (due tothe aggressiveness of external and internal environment) and occurrence of wear-out (Jun et al.2007). The failure of this appurtenance can impose system’s cost on hydraulic performance,pipe damage, inability to carry out flushing. This could be manifested in the form of pipe262.4. Valves of Water Supply Systembursts, decrease in the ability to carry out main flushing, a decrease in hydraulic performances,etc.2.4.3 Previous Studies on Valve FailurePrevious studies have given a considerable attention to the failure of water mains (Jowittand Xu 1993; Kabir et al. 2015a,b; Kimutai et al. 2015; Kleiner et al. 2003; Lin et al. 2015);however, a limited number of studies have been reported on the risk of appurtenance (e.g.valves and hydrants) failures (Marlow and Beale 2012; Marlow et al. 2012). For instance,in order to understand the condition of appurtenances, a condition assessment survey wasperformed on the water mains appurtenances by Marlow and Beale (2012), where twenty-fiverespondents of water utilities from Australia, New Zealand, United States, Canada and theUnited Kingdom participated. The result of the survey revealed that most of the respondent ofthe survey assures that isolation valves and fire hydrants were the most problematic group ofwater main appurtenances. Marlow et al. (2012) developed a pragmatic risk indexing schemeto prioritize the isolation valves for inspection based on the risk concepts. To estimate theoverall potential for deterioration, the hierarchical factors related to age, external and internalenvironment, the effect of service disruption and response time after failure event are considered.In order to calculate the overall risk index from the lower level indices, Marlow et al. (2012),was used an analytic hierarchy process. In addition to the above studies, there have beenfew studies reported on condition assessment of valves and water systems utility assets ingeneral (Christofferson et al. 2002; Clair and Sinha 2012; Marlow et al. 2007; Marlow and Beale2012). However, from the existing studies, there is less evidence that indicates the detailedidentification, modeling, and analysis of valve failure.27Chapter 3: Prediction of Soil Corrosivity In-dex Using Bayesian Belief Network 13.1 BackgroundSoil corrosivity is one of the environmental hazards that affect metallic pipes as a result oftheir direct contact with the surrounding soil. It is a random and complex process which involvesdifferent factors. Many studies have been reported to predict the soil corrosivity potential usingsurrounding properties of soil such as resistivity, pH, redox potential, etc. However, the reportedstudies have a limitation in considering the inter-dependency among soil properties in theprediction of soil corrosivity potential. Besides, Most utilities often have little information abouttheir soil parameters, as it is expensive to collect the data needed to adopt the existing methods.In general, the reported studies are either based on highly intensive data or considered limitedsoil parameters and their inter-dependencies in predicting soil corrosivity potential. In thischapter, a Bayesian Belief Network (BBN)-Soil Corrosivity Index (SCI) model is developed tosolve the limitation of available data and inter-dependencies among considered soil parameters.The proposed method uses a combination of empirical evidence, experimental data, and expertopinion to predict the SCI.3.2 MethodologyFigure 3.1 describes the proposed methodology for the SCI prediction model. Potentialsoil corrosivity index parameters and their inter-dependencies are identified. Based on theidentified parameters, a casual relationship among parameters and with the SCI is formulated.The conditional dependencies are formulated based on the processed soil data collected by the1A version of this chapter is partially presented and published in the conference proceedings of The 12thInternational Conference on Applications of Statistics and Probability in Civil Engineering (ICASP12) with atitle of “Prediction of soil corrosivity index: A Bayesian belief network approach”(Demissie et al. 2015)283.2. Methodologycity of Calgary and expert elicitation. In the end, the developed BBN-SCI model is validatedby the pipe failure rates using a spatial clustering technique.Data/Information(points, lines and areas)Create databaseBaysein Belief Network - SoilCorrosivity Index (BBN-SCI)modelAttribute table and maps of soilinformationPopulate soilinformation tothe pipesPre-processing of information using GISPost-processing of information using GIS(SCI mapping for each metallic pipe in the system)Microsoft ExcelValidation using recorded pipefailure data.Spatial clusteringSoil Corrosivity Parameter IdentificationBBN - SCI Model DevelopmentBBN - SCI Model ValidationFigure 3.1: Proposed framework for BBN-SCI model3.2.1 Soil Corrosivity Parameter IdentificationsThe nature of soil plays a significant role in the corrosion of metallic pipes. The responsiblesoil properties can be divided into five major categories. These are soil resistivity, moisturecontent, pH, redox potential, and es content. The interdependencies among the major soilproperties and minor soil properties such as; soil porous medium aeration; oxygen content; the293.2. Methodologypresence of acids, sulfides, and bacteria; and soil temperature will be discussed in the followingsubsections.3.2.1.1 Soil ResistivitySoil resistivity is the soil property which is affected by soil solution containing a differentconcentration of ions produced due to the action of subsurface water on the chemical constituentof soil. It is a measure of how strongly the soil resists the flow of electricity. Higher resistivityof the soil indicates less ability of the soil to pass the electric current (Ellwood et al. 1993).The electrical resistivity of soil is affected by the soil moisture content, the soil temperature,the degree of soil compaction, and the concentration of different salts and their movement(AEMC 2002; Doyle 2000; Doyle et al. 2003; Fukue et al. 1999; Romanoff 1957; Sadiq et al.2004a). As shown in Figure 3.2 and 3.3, at a lower temperature and moisture content of thesoil, the electrical resistivity of the soil is found to be significantly high and vice versa. Besides,availability of high concentration of soluble salts in the soil and the compaction of soil createthe higher electrical resistivity of the soil (Romanoff 1957). Higher probability of corrosion isexpected at the lower soil resistivity (< 1,500 ohm-cm), while the lower probability of corrosionis expected at the higher soil resistivity (> 3,000 ohm-cm) (Sadiq et al. 2004a). Hence, thesoil resistivity in conjunction with other affecting soil properties are the stressors (factors) indetermining the corrosivity of the soil.3.2.1.2 Soil Moisture ContentPrevailing soil moisture content is one of the important soil parameters which affect the soilcorrosion (AWWA 1999). As depicted in Figure 3.3, at a low percent of soil moisture contents,the electrical resistivity of soil is very high. A technical manual on soil resistivity by (AEMC2002) also illustrates that when the percent of soil moisture content is less than 20%, theresistivity of soil changes quite rapidly. For soil moisture content above 20%, the resistivity ofsoil is constant and fall under the category of very low soil resistivity. In fact, low soil resistivityindicates high soil corrosivity. Subsequently, the moisture content of the soil is affected by thevariability of groundwater. If the water table is near the top of the soil, it indicates that thesoil has a regularly high percent of moisture content. On the other hand, higher soil moisturecontent indicates that aeration of soil porous media is very low and vice versa. In literature,the soil moisture content is reported as “Poor drainage” when the soil condition is continuallywet, “Fair drainage” when the soil condition is generally moist, and “Good drainage” when the303.2. Methodologysoil condition is continually dry (AWWA 1999).0125250375500-20 -10 0 10 20S oi l  r es i st i vi t y ( Oh m-c m) x 103Soil temperature (oC)Romanoff (1957)AEMC (2002)Figure 3.2: Effect of soil temperature on soil resistivity01002003000 10 20 30 40S oi l  r es i st i vi t y ( Oh m-c m) x 103Soil moisture content (%)Romanoff (1957)Top soil (AEMC 2002)Sandy loam soil (AEMC 2002)Clay soil (Fukue 1999)Figure 3.3: Effect of soil moisture content on soil resistivity313.2. Methodology3.2.1.3 Soil pHThe pH is a measure of a soil’s acidity or alkalinity, and it is the measure of hydrogen ion(H+) and other ions that carry currents in the soil. Carbonic acid, various minerals (and/ortheir leaching), organic and inorganic acids are used to determine the pH value of soil (AWWA1999). The high and low amount of current carrying ion corresponds to, respectively, a lowand high pH value. For the current to flow, there must be a potential difference between twopoints that are electrically connected and immersed in an electrolyte (Hubbell 2003). Hence,corrosion occurs through the loss of metal ions at anode points or areas.3.2.1.4 Redox PotentialRedox potential is a measure of the attraction of a substance for electrons (i.e. its electro-negativity) and measured in Volts (V ). Oxygen concentration and soil moisture content de-termine the redox potential of the soil. The higher oxygen content of soil indicates the higherredox potential (AWWA 1999). The lower redox potential means less aeration in a soil porousmedia and this gives a favorable environment for the action of aerobic bacteria. Rapid changesin moisture content also strongly affect soil aeration status. When the soil pores are filled withwater, the diffusion of oxygen will be restricted and the consumption of oxygen will rapidlybe facilitated (Sparks 2003). Better access for air in the soil porous media and with availableeasily decomposable organics results in the depletion of oxygen and production of redox-activeorganic compounds. The fluctuating water table causes the buried iron/metallic structures toalternate between oxidized and reduced forms over a period of seasons (Fiedler et al. 2007).This variability in oxidation and reduction is a natural process of redox potential, which clearlyshows the corrosion potential developing around buried metallic structures.3.2.1.5 Soil Sulfides ContentThe presence of sulfates and sulfate-reducing bacteria in soil might be a risk for buriedmetallic structures. In a microbial process, sulfates can be converted to highly corrosive sulfidesby anaerobic sulfate-reducing bacteria (Cunat 2001). Hence, testing and detailed analysis of soilsamples for microbial activities for the presence of sulfides content can indicate the corrosivenessof soil due to sulfides content (Sadiq et al. 2004b). In literature, the test results of sulfides arereported as “positive”, “trace”, and “negative” (AWWA 1999).323.2. Methodology3.2.2 Bayesian Belief Network Model for Prediction of Soil Cor-rosivity Index3.2.2.1 Overview of Bayesian Belief NetworkBBN is a popular analytical framework in causal studies where the causal relations areencoded by the topology of the network (Ellis and Wong 2008). BBN captures our uncertain orimprecise belief about the relation between a set of variables that are relevant to some problems.According to Pearl (1988), BBN is a graphical model that permits probabilistic relationshipsamong the set of variables. It is represented by a Direct Acyclic Graph (DAG), in which thenodes represent stochastic variables of interest and the links identify direct causal influencesbetween the linked variables (Krieg 2001).BBN uses the Bayesian calculus, which distinguishes BBN from other causal belief networks,to determine the state probabilities of each node or variable from the predetermined conditionaland prior probabilities (Krieg 2001). As a result, in BBN, the following procedures are followed(SAS 2007): The first procedure is formulating prior probability distribution of hypothesis,p(H), which shows beliefs (i.e. mean, skewness, etc.) of the parameters. Secondly, the statisticalmodel, p(E|H), will be used to describe the distribution of a given data or evidence, E, fora given hypothesis, (H). Finally, the beliefs about the hypothesis, H, will be updated bycombining prior probability and the data through the estimation of the posterior probabilitydistribution, p(H|E), using Bayesian theorem.p(H|E) = p(E|H)p(H)p(E)=p(E|H)p(H)∫p(E|H)p(H)dH (3.1)where, p(H) = a prior probability distribution of hypothesis H; E = the observed data orevidence; p(E) = the probability that the evidence, (E), takes place; p(E|H) = the statisticalmodel used to describe the distribution of the data or evidence, (E), given the hypothesis, (H).With n possible outcomes, (H1, ...,Hn), Equation 3.1 can be expressed as,p(Hi|E) = p(E|Hi)p(Hi)p(E)=p(E|Hi)p(Hi)∑ni=1 p(E|Hi)p(Hi)(3.2)In BBN, each node can be forced to update the posterior probabilities for each of its hy-potheses on the receipt of data messages from its immediate neighbors (Krieg 2001). BBNalso supports the computation of the probabilities of any subset of variables given evidenceabout any other subset (Tesfamariam and Mart´ın-Pe´rez 2008). These dependencies are quan-333.2. Methodologytified through a set of Conditional Probability Tables (CPT) in which each variable is assigneda CPT of the variable given its parents. Efficient algorithms have also been developed andapplied to perform inference and learning in Bayesian belief networks.In failure analysis, probabilistic relationships can be represented between failure and thecauses of failure using BBN. Given the causes of failure, the BBN can be used to compute theprobabilities of the occurrence of various failure scenarios. Based on the computed probabilityof failure, the severity of any failure scenarios can also be easily identified. BBN models canbe an asset when multiple information sources needed to be combined and modeling an inter-dependency between causes of failures and failure modes is of a priority (Demissie et al. 2015).3.2.2.2 Bayesian Belief Network – Soil Corrosivity Index Model Develop-mentThe BBN-SCI is developed based on the identified soil parameters as depicted in Fig-ure 3.4. Considered nodes and their state’s discretization are also presented in Table 3.1.Inter-dependency among the selected soil parameters and their effect on the SCI are carefullyidentified. Fifteen soil parameters are considered to determine the SCI point values based on(AWWA 1999) 10-point method. The measured soil parameters, used to set-up and train theBBN-SCI model, were collected at different locations by the city of Calgary. The soil electricalresistivity measurement was taken at points in which all the points are distributed around thelaid metallic pipes. Tests of redox potential, soil pH, soil moisture content, soil temperatureand soil sulfides content were observed at a typical test point in the city of Calgary.A polygon was constructed considering the mentioned points using geographic informationsystem tool (Arc GIS) to extrapolate/interpolate the information (i.e., Thiessen polygons anal-ysis). Expert knowledge is combined with the available data for the other soil parameters suchas sulfates; salts; the degree of compaction; the presence of sulfate-reducing bacteria; the pres-ence of organic, inorganic, and carbonic acids; groundwater variability; the oxygen content ofthe soil; and aeration of soil porous medium. Based on these data, the Expectation Maximiza-tion (EM) algorithm implemented in BBN software (Netica) is used to optimize the conditionalprobability of the considered nodes (Norsys 2014).The developed model was integrated with Microsoft Excel using a visual basic programminglanguage to read and write data from/to Microsoft Excel. The pre- and post-processing ofcollected input soil parameter values, mapping of clustered attributes and final soil corrosivityindexes, respectively, are undertaken in a GIS platform. The GIS helps to visualize a spatial343.2. Methodologyrepresentation of the soil parameters, clustered attributes, and final indexes of each pipe in thestudy area. The BBN model output was discretized into five linguistic indexes, very low, low,medium, high and very high. The linguistic presentations of the result help decision makersunderstand their system’s corrosion vulnerability apparently.Aeration of soil porous mediaPresence of saltsSoil resistivityTemperatureDegree of compaction Organic/Inorganic acidsAvailability of sulfates in SoilSoil Corrosivity Index Soil  sulfides contentPresence of sulfate reducing bacteriaRedox potentialGround water variabilitySoil pH Carbonic acidSoil moisture contentOxygen contentFigure 3.4: Proposed framework for BBN-SCI modelTable 3.1: SCI-BBN model soil parameters state discretizationNodes References* Node state discretization Source**Soil resistivity 1 Very high (≥3000), High (2500 -3000), Medium (2100 - 2500), Mod-erately low (1800 - 2100), Low (1500- 1800), and Very low (< 1,500)√Redox potential 1; 2 Very high (> +100), High (+50 -+100), Low (0 - +50), and Very low(< 0)√Soil sulfides content 1 Positive (>3mg/kg), Trace (2-3mg/kg), and Negative (<2mg/kg)√Soil pH 1 Very high (≥ 8.5), High (7.5 − 8.5),Moderately high (6.5 – 7.5), Medium(4.0 – 6.5), Low (2.0 -4.0), and Verylow (< 2.0)√Continued on next page353.2. MethodologyTable 3.1 – continued from previous pageNodes References* Node state discretization Source**Presence of sulfate-reducing bacteriaPresent (High) and Not present(low)+Availability of sulfatein soil3 Available (High) and not available(low)+Soil moisture content 1; 4 Good drainage (High), Fair drainage(Medium), and Poor drainage (low)√Oxygen content of soil 3 Excess oxygen in the soil (High) andlow oxygen in the soil (low)+Temperature of soil 5; 4 Soil temperature > 0oC(High) andsoil temperature ≤ 0oC (low)√Presence of salts in thesoil5; 4 High salt concentrations (High) andlow salt concentration (low)+Presence of carbonicacid3 Excess carbonic acid (High) and lowcarbonic acid (Low)+Ground water variabil-ity2 Consistent (High) and variable(Low)+Degree of compactionof soil3 Highly compacted (High) and lesscompacted (Low)+Presence ofOrganic/Inorganicacids3 Excess org/inorganic acid (High)and low organic/inorganic acid(Low)+Aeration of soil porousmedia3 Excess aeration (High) and less aer-ation (High)+Soil corrosivity index(SCI)1 Very high (>13), High (10-13),Medium (7-10), Low (3.5-7), andVery low (0-3.5)*1 = AWWA (1999), 2 = Fiedler et al. (2007), 3 = Sadiq et al. (2004b), 4 = AEMC (2002),and 5 = Romanoff (1957); and **√= measured data, and + = engineering judgment363.3. Water Supply System of the City of Calgary3.3 Water Supply System of the City of CalgaryThe city of Calgary is located at the confluence of the Bow and Elbow Rivers in the provinceof Alberta, Canada. According to Statistics Canada (2011), a population of 1,096,833 resides inthe City of Calgary, which makes the city the largest city in the province and the third-largestmunicipality in the nation. A record from Environment Canada at Calgary international airportmeteorological station (Environment Canada 2015), average daytime maximum and minimumtemperatures in Calgary range from 22.9 ◦C and 9.5 ◦C in mid-July to 3.1 ◦C and -15.4 ◦C inmid-January, respectively. Extreme temperature of the city ranges from -45 ◦C (recorded in1893) to 36.1 ◦C (recorded in 1919).The city’s WSS provides quality drinking water to homes, business or institutions through-out the city of Calgary for more than one million residing populations. This system consists ofover 4650 km of water mains of which above 2035 km are metallic pipes (Brander 2004; Cityof Calgary 2014). The city of Calgary WSS includes a group of pipe materials such as Duc-tile Iron (DI), CI, Steel (ST), Copper (CU) and Non-Metallic (i.e. Polyvinyl Chloride (PVC)and Concrete Pipe). Figure 3.6 depicts the spatial distribution and the comparison of overallCalgarys WSS pipe. Metallic pipes (i.e. CI, DI, and ST) experienced the most breaks in thissystem. Also, metallic pipes are the most vulnerable pipes to external corrosion. As a result,these pipes are considered for further analysis and demonstration of the developed BBN model.From the summary of metallic pipes depicted in Figure 3.5, pipes of material DI, CI, and SThave experienced around 53%, 40%, and 7% pipe breaks, respectively. Similarly, Figure 3.7shows the trend of the city’s metallic pipes based on the total number of recorded pipe breakseach year with respect to the year of installation.CI, 40%DI, 53%ST, 7%Figure 3.5: Percentage of recorded metallic pipe breaks based on pipe materials373.3. Water Supply System of the City of CalgaryPipe materialsCI pipesDI pipesNon-metallic pipesST pipesUnknown0 9.54.75 Kilometers±Figure 3.6: Pipe material distribution for the city of Calgary383.4. Result and DiscussionCI DI ST Grand Total558 55845 4556 561 14 42 20 09 90 04 43 33 33 323 2323 2354 6 6019 0 194 421 211 16 63 311 1118 1838 3821 2102004006008001 91 01 92 51 93 71 94 71 95 71 96 71 97 71 98 71 99 7T ot al  numb er  of  br ea ksYear of InstallationCIDISTFigure 3.7: The city of Calgary’s total number of pipe breaks with respect to year of installation3.4 Result and Discussion3.4.1 Bayesian Belief Network Sensitivity AnalysisThe conditional probability of BBN models can be estimated based on either expert elici-tation or collected information (data). The results of the estimation might lead to inaccuracyas a result of available incomplete information and expert’s partial knowledge of the domain(Coupe and Van Der Gaag 1998). Hence, by performing sensitivity analysis, the significanceof input parameters on the final outcomes of the BBN model can be identified (Demissie et al.2015; Pearl 1988). In literature, different methods have been reported for performing sensitivityanalysis of BBN models (Bednarski et al. 2004; Coupe´ and van der Gaag 2002). For instance,Mutual information (entropy reduction), variance reduction and variance of beliefs estimationsmethods are the most widely used methods of sensitivity assessment in BBN models (Norsys2014; Pearl 1988).The variance of a node Q or a node Q having a real number state value, V (Q = f) giventhe evidence F , can be computed as (Norsys Software Corp 2014),V (Q|f) =∑q(q|f)[Xq − E(Q|F )]2 (3.3)E(Q) =∑qp(q)Xq (3.4)393.4. Result and Discussionwhere q is the state of the node Q; f is the state of the varying node; Xq is the numericreal value corresponding to state q;∑q() means the sum of overall states q of Q; E(Q) is theexpected real value of Q before any new findings and E(Q|f) is the expected real value of Qafter a new finding f for node F .The mutual information, I(Q,F ), of two discrete random variables Q (i.e. the query vari-able) and F (i.e. the varying variable) can be defined as (Norsys Software Corp 2014),I(Q,F ) =∑f∈F∑q∈Qp(q, f)log(p(q, f)p(q)p(f)) (3.5)where q is a state of the query variable, f is a state of the varying variable, p(q, f) is the jointprobability distribution function of Q and F , and p(q) and p(f) are the marginal probabilitydistribution functions of Q and F , respectively.A variance reduction BBN sensitivity analysis method is performed at the outcome node(i.e., SCI). Previously reported studies also adopted this method to perform the sensitivity anal-ysis of outcome nodes with similar state characteristics (Stelzenmu¨ller et al. 2010; Tesfamariamand Mart´ın-Pe´rez 2008). This analysis was performed to determine the absolute degree andthe rank order of influence of parent nodes (e.g. soil resistivity) on the child node (i.e., soil cor-rosivity index). As shown in Figure 3.8, the result of the computed variance reduction for soilresistivity, soil temperature, and redox potential nodes are the highest top three contributorsto the variance of reduction, respectively. However, the presence of acids and soil moisture con-tent are the least contributor to variance reduction. According to Pearl (1988), the parameterswhich have shown the maximum value of variance reduction most often have a major effect onthe outcome nodes. As a result, analysis entails that the resistivity of the soil, soil temperature,and redox potential has the greatest influence on the degree of soil corrosivity. On the contrary,the presence of acids and soil moisture content of soil are found to be least changing parameterson the soil corrosivity.403.4. Result and Discussion1.312 8.56 3.268984 Temperature of soil1.078 7.03 2.685948 Redox potential1.032 6.73 2.571335 Soil pH0.881 5.75 2.195352 Presence of salts in the soil0.809 5.27 2.01471 Soil sulfides contents0.457 2.98 1.137666 Ground water variability0.213 1.39 0.530462 Oxygen content of soil0.128 0.83 0.318427 Aeration of soil porous media0.128 0.83 0.318427 Degree of compaction of soil40.13 100 Presence of bacteriaSoil moisture contentAvailability of sulfate in soil38.20 \\ Presence Organic/Inorganic acids19.57 \\ Presence of carbonic acid9.64 \\ Pipe wall thickness6.81 \\ Coefficient 'c'5.58 \\5.17 \\3.27 \\2.69 \\2.57 \\2.20 \\2.01 \\1.14 \\0.53 \\0.32 \\0.32 \\0 12.5 25 37.5 50Soil resistivityTemperature of soilRedox potentialSoil pHPresence of salts in the soilSoil sulfude contentGround water variabilityOxygen content of soilAeration of soil porous mediaDegree of compaction of soilPresence of bacteriaAvailability of sulfate in soilSoil moisture contentPresence Organic/Inorganic acidsPresence of carbonic acidNormalized % of variance reductionPresence of salts in the soilAeration of soil porous mediaDegree of compaction of soilAvailability of sulfate in soilPresence Organic/Inorganic acidsFigure 3.8: Sensitivity of SCI node due to finding at the parent nodes3.4.2 Scenario AnalysisThe proposed model is applied to two scenarios to understand behavior and response ofSCI as a result of the change in soil corrosivity parameters. These two scenarios are definedas scenario one (bad soil condition) and scenario two (good soil conditions) based on theircontribution to soil corrosivity. The considered soil parameter and their states for each scenarioand the result (i.e., SCI) in this analysis are summarized and presented in Table 3.2. Thescenario results indicate that the probability distribution of SCI node reasonably explains theresponse of SCI nodes to the nature of soil properties.413.4. Result and DiscussionTable 3.2: Node states for scenario analysis of BBN-SCI modelNodes Scenario one Scenario twoSoil resistivity Very low Very highRedox potential Very low Very highSoil sulfides Contents Positive NegativeSoil pH Very low Very highPresence of sulfate-reducing bacteria Present Not presentAvailability of sulfate in soil High LowSoil moisture content Poor drainage Good drainageOxygen content of soil Low HighTemperature of soil High LowPresence of salts in the soil High LowPresence of carbonic acid High LowGround water variability Low HighDegree of compaction of soil High LowPresence Organic/Inorganic acids High LowAeration of soil porous media Less aeration Excess aerationVery high = 98.00% Very high = 0.64%High = 0.47% High = 0.66%Soil corrosivity index Medium = 0.51 Medium = 0.62%,Low = 0.46% Low = 0.62%Very low = 0.52% Very low = 97.50%3.4.3 BBN-SCI Model Validation Using Spatial Clustering methodSpatial clustering is an unsupervised data mining technique in which a “cluster”is consid-ered as a geographically limited group of occurrences of sufficient size and concentration to beunlikely to have occurred by chance (Elliot 1989). Spatial clustering can be categorized intotwo (Aldstadt 2010): (i) Global clustering - a method used to determine if clustering is presentor not in the study area by providing a single statistic summary of the spatial pattern of theregion. This approach can be applied to polygon and point data types. (ii) Local clustering - a423.4. Result and Discussionmethod that examines specific sub-regions or neighborhoods within the study area to determineif the area represents a cluster of high values (a hot spot) or low values (a cold spot). Similarly,local clustering methods can also be applied to point and polygon data types. Local Moran’s(cluster and outlier analysis) (Anselin 1995) and Getis-Ord (hot spot analysis) (Getis and Ord1992; Ord and Getis 1995) are the local geostatistical clustering analysis tool implemented inArc GIS (ESRI 2011).In this study, the linguistic classes of BBN-SCI result was validated with a locally clusteredpipe breakage rate (no of breaks/km/year) using Getis-Ord hot spot analysis (Equations 3.6- 3.9). Figure 3.9 shows the comparison of pipe breakage rate hot spot analysis with the soilcorrosivity indexes for the city of Calgary metallic pipes. As it can be observed, the modelwas able to indicate the hot spot and cold spot spatial locations. Very high to very low soilcorrosivity indexes indicated the hot spot (high pipe breakage rate) and cold spot (low pipebreakage rate) areas, respectively.Gi =∑nj=1Wijxj∑nj=1 xj(3.6)G∗i =∑nj=1Wijxj − x∑nj=1WijS√n∑nj=1W2ij−(∑nj=1Wij)2n−1(3.7)x =∑nj=1 xjn(3.8)S =√∑nj=1 xjn− (x)2 (3.9)whereGi is the hypotheses based on proximity; G∗i (z-score) is the hypothesis based on clusteringfor j values in the vicinity of i; Wij is a spatial weights vector between feature i and j; x andS are the mean and standard deviation; n is the number of features in the study area; xj is anattribute value for the feature j; and a positive value of G∗i indicates clustering of high valuesand a negative value indicates a cluster of low values.433.4. Result and DiscussionSCIVery lowLowMediumHighVery highPipe breakage ratesGetis-Ord Gi*-(Z Score)(-8.00) - (-2.60)(-2.60) - (-1.20)(-1.20) - (0.38)  (0.38) - (2.75) (2.75) - (8.36)Ü0 4 82 KilometersFigure 3.9: Hot spot analysis (Getis and Ord G∗i method) of pipe breakage rate and comparisonwith predicted SCI (expected value)3.4.4 BBN-SCI versus AWWA 10-point methodFigure 3.10(a) describes the result of BBN-SCI model (i.e., probability distribution of SCI)and AWWA 10-point method for a selected sample of soil parameters indicated as X, and Yin Figure 3.10. The result indicates that the AWWA 10-point method provides only pointestimates of soil corrosivity index. However, the BBN-SCI model provides the full probabilitydistribution of the SCI states for the given input soil parameters. Whereas, both methodscan provide comparatively similar expected values of SCI. The AWWA 10-point method isapplicable only when the values of the five major soil parameters described in Table 2.2 areknown. Conversely, the proposed BBN-SCI can elicit the information from indirect causal soilparameters when the information about direct causal factors are limited. Figure 3.10 (b) showsthe plot of expected values of SCI from BBN-SCI model and computed SCI value from AWWA10-point.443.5. Summary0.1 0.4 2.37.789.50.2 0.984.013.01.90.025.050.075.0100.0VL L M H VHProbability (%)SCIBBN-SCI(Point X)BBN-SCI(Point Y)0.05.010.015.020.00.0 3.5 7.0 10.5 14.0 17.5 21.0AWWA 10 piontBBN-SCI (Expected value)AWWA: non-aggressiveM H VHXYAWWA: aggressiveVL L(a)(b)Figure 3.10: BBN-SCI model versus AWWA 10-point method3.5 SummaryThe main objective of this chapter was to identify the soil parameters which contribute tosoil corrosivity and use this information to predict the SCI. A combination of collected dataand empirical data; expert opinion and different literature were used to set up the model nodestates and train the CPT of the model. A review had been made to identify and define the453.5. Summaryrepresentative node of the BBN-SCI model and their casual relationships and inter-dependenciesamong the nodes. A BBN sensitivity analysis was performed at the SCI node to determine theabsolute degree and the rank order of influence of parent nodes (soil properties) on the childnode (soil corrosivity index). Also, scenarios have been tested to evaluate the capability of themodel in handling the extreme cases of soil conditions on the soil corrosivity index. Finally,the model result was demonstrated on the water distribution system of the city of Calgary andvalidated with recorded pipe breakage rate using the spatial clustering method. The validationof the model reveals that the model was reasonably identified the spatial coverage of the hotspot and cold spot soil corrosivity areas of the city of Calgary.46Chapter 4: Prediction of Remaining ServiceLife of Metallic Pipes Using Bayesian BeliefNetwork 24.1 BackgroundRemaining Service Life (RSL) is a core part of the asset management “what?”questions tobe considered in the implementation of repair and renewal programs (Vanier 2001). Okoh et al.(2014) defined the RSL as the time remaining for an asset to perform its functional capabilitiesbefore failure. However, the service life of an asset is not explicitly dependent on the failureof an asset; repair can extend the asset life if it is repairable. In a water supply system, thepipe’s service life most often can be extended by adopting repair and maintenance programmes.Vanier (2001) and Si et al. (2011) defined RSL as the actual period during which the asset or anyof its components performs without unforeseen costs of disruption for maintenance and repair.Similarly, Marlow et al. (2009) defined the RSL of an asset as the time left before a significantcapital intervention is required. A significant capital investment (e.g. replacement option) ofan asset can be an option, if the components of an asset are either no longer functional or itreaches its economic life period (Vanier 2001). The overall keyword can be assumed as the“unforeseen” which is dependent on the individual explanation. Si et al. (2011) also contendsthat the definition of RSL is dependent on the context and the operational characteristics ofpipes. In this chapter, we assume that the RSL is a period of the present time and the first failuredue to corrosion. For instance, Figure 4.1 shows a typical representation of RSL, safety index,corrosion initiation time and time to failure of a 150 mm diameter CI pipe with a standard wallthickness of 9.652 mm exposed to low soil corrosivity. In this illustrative figure, metallic pipe2A version of this chapter is published in the Journal of Pipeline Systems Engineering and Practice with atitle of “Considering soil parameters in prediction of remaining service life of metallic pipes: A Bayesian beliefnetwork model”(Demissie et al. 2016).474.2. Methodologycorrosion is first initiated fifteen years after the year of pipe installation. Corrosion initiationtime is the time at which corrosion is first initiated on a metallic pipe due to the corrosive soilenvironment.Although an increasing number of studies have been reported in the last decades to estimateRSL of metallic pipes, most of them are either data intensive or consider limited soil and pipeparameters. In this chapter, a BBN model is proposed to handle the problem of different datascarcity and the dependency between parameters. The proposed approach uses a combinationof empirical data, experimental data, expert opinion and a mathematical model to predict thesoil corrosivity and pit depth. Then, a simple programming logic was used to predict the RSLof metallic pipes. Finally, the performance of the model was evaluated using a BBN sensitivityanalysis. Monte Carlo Simulations (MCs) were also performed using randomly generated inputfrom measured statistical parameters (e.g., mean and standard deviation) to indicate the effectof input parameters on RSL and safety index of metallic pipe. 0.00.20.40.60.81.00.02.44.87.29.60.0 10.0 20.0 30.0 40.0 50.0 60.0S af et y I nd ex ( SI )P it  de pt h or  P ip e wa ll  th ic kne ss( mm)Age of pipe in (years)Pit depthStandard pipe wall thicknessSITime to failureRemaining service lifeCorrosion initiation timeStarting point of corrosion Present age of pipeFigure 4.1: Overview of remaining service life prediction and proposed safety index4.2 MethodologyFigure 4.2 shows the proposed pit depth BBN model. The model was developed by inte-grating the BBN-SCI model and a mathematical model (i.e., Rajani et al. (2000) two-phasedmathematical corrosion model). In the development of pit depth BBN model, a software devel-484.2. Methodologyoped by Norsys Software Corporation’s (Norsys 2014), Netica, was used. Netica was preferreddue to its simplicity for dynamic linking with the Microsoft Excel. The developed model wasintegrated with Microsoft Excel using a visual basic programming language to read and writefrom/to excel and employ iterative type programming logic, respectively and embed MonteCarlo simulations.The nodes in this model represent the variables influencing the corrosion pit depth. TheCPT table for the pit depth node state was estimated based on the explained mathematicalmodel. The constants a, and b are defined as a real, continuous and normally distributed nodes.Figures 4.3 and 4.4 represent the normal distribution of these constants while Table 2.5 presentstheir mean values. The standard deviations of 0.0015 and 0.31 are considered to define the nodestate values of a and b, respectively. However, coefficient c was considered as a constant nodeof state value equals to 0.058 per annum, as this parameter is a constant value (Rajani et al.2000; Rajani and Tesfamariam 2007). Table 4.1 summarizes the suggested nodes, node statesand their parameter values.Soil Corrosivity IndexRedox potentialOxygen contentGround water variabilitySoil moisture contentAeration of soil porous mediaba cPit depth Safety IndexTime of corrosion intiationPipe wall thicknessSoil  sulfides contentPresence of sulfate reducing bacteriaAvailability of sulfates in SoilSoil pH Carbonic acidPresence of saltsSoil resistivityTemperatureDegree of compaction Organic/Inorganic acidsFigure 4.2: Proposed Remaining Service Life Bayesian belief network model494.2. Methodology0.00 0.01 0.02 0.03 0.040.00.20.40.60.81.0Value of coefficient 'a'Cumulative probability  VLLMHVHFigure 4.3: Node state probability distribution considered for coefficient ‘a’0 5 10 150.00.20.40.60.81.0Value of coefficient 'b'Cumulative probability  VLLMHVHFigure 4.4: Node state probability distribution considered for coefficient ′b′504.2. MethodologyTable 4.1: Definition of parameters and their states used in the proposed BBN modelNodes References Node states discretization Types of data and methodsusedSCI√VH (> 13); H (10 − 13); M(7− 10); L (3.5− 7); VL (0−3.5);BBN-SCI model discussedin chapter 3Coefficient a † and ‡ VL (µ = 0.0042 σ = 0.0015);L (µ = 0.0210 σ = 0.0015); M(µ = 0.0252 σ = 0.0015); H (µ= 0.0294 σ = 0.0015); VH (µ= 0.0336 σ = 0.0015)Normal probability distri-bution for each states (Fig-ure 4.3)Coefficient b † and ‡ VL (µ = 1.95 σ = 0.31); L(µ = 9.75 σ = 0.31); M (µ =11.75 σ = 0.31); H (µ = 13.50σ = 0.31); VH (µ = 15.6 σ =0.31)Normal probability distri-bution for each states (Fig-ure 4.4)Coefficient c † and ‡ A constant node of value =0.058 per annumCorrosion initia-tion time (year)250 - 300; 200 - 250; 150 - 200;100 - 150; 50 - 100; 0 - 50Pit depth (mm) 21 - 18; 15 - 18; 12 - 15; 9 -12; 6 - 9; 3 - 6; 0 - 3‡ and NDT measured dataPipe wall thick-ness (mm)6 - 8; 8 - 10; 10 - 12; 12 - 14;14 - 16;Pipe wall thickness stan-dards and literatureSafety index H (0.00 - 0.30); M (0.30 -0.75); L (0.75 - 1.00)Proposed√= Demissie et al. (2015), † = Rajani and Tesfamariam (2007), ‡ = Rajani et al. (2000),VH = very high, H = high, M = medium, L = low, VL = very low, µ = mean, σ = standarddeviation514.2. MethodologyThe corrosion initiation time was estimated based on the measured pit depth with a simpleiterative type programming logic as described in the flowchart (Figure 4.5). First, the BBN-SCImodel predicts the pit depth by changing the corrosion initiation time beginning from the earlyinitiation period. Next, it compares the predicted pit depth with the measured pit depth. Ifthe predicted pit depth is less than the measured pit depth, the model continues predicting thepit depth by changing corrosion initiation time. Hence, the moment at which the predictedpit depth is equaled to the measured pit depth is the pipe’s corrosion initiation time. In thedevelopment of BBN model, a software developed by Norsys Software Corporation’s (Norsys2014), Netica, was used. Netica was preferred due to its simplicity for dynamic linking with theMicrosoft Excel. The developed model was integrated with Microsoft Excel using a visual basicprogramming language to read and write from/to excel and employ iterative type programminglogic, respectively and embed Monte Carlo simulations.StartDetermine soil corrosivity index  (SCI)Predict pit depth by changing corrosion initiation time Is the predicted pit depth equals to the measured pit depth?Is the predicted pit depth greater or equals  to pipe  wall thickness ?Report time to failureEstimate coefficients "a", "b" and "c"Report corrosion initiation timeNoYesNoYesCalculate safety index (SI)Calculate the remaining service life of pipeRead soil parameters to BBNRead pit depth to BBNRead pipe wall thickness to BBNFigure 4.5: Flow chart for prediction of remaining service life of metallic pipesA pipe wall thickness node was introduced to predict the pipe’s time to failure. The same524.3. Result and Discussionprocedure used in the estimation of corrosion initiation time was used; however, in the predictionof time to failure, the predicted pit depth was compared with the pipe wall thickness. In fact,pipe failure happens when the pipe wall thickness is threatened by an excessive growth of pitdepth. Therefore, the RSL of a pipe is the difference between the time to failure and thecorrosion initiation time. In order for the decision makers to understand the pipe condition, aSafety Index (SI) node was introduced. SI is the ratio of pit depth (predicted or measured) andpipe wall thickness, which varies between 0 and 1. A value of zero indicates no corrosion anda value of one indicates the pipe failure as a result of excessive corrosion.4.3 Result and Discussion4.3.1 Sensitivity AnalysisThe pit depth node of the model developed in this study is a continuous node with nodestates values assigned as a real number. For this reason, the variance reduction method wasused in this study to determine the variation of pit depth nodes because of a variation inconsidered nodes. Hence, a variance reduction method of BBN sensitivity assessment methodwas performed to determine the absolute degree and the rank order of influence of parent nodeson the child node.Result of the sensitivity analysis for the model described in Figure 4.2 is summarised inFigure 4.6. For pit depth node, the computed variance reduction for safety index, time ofcorrosion initiation, coefficient a and b and SCI nodes are the highest top five contributors ofvariance reduction. However, pipe wall thickness and coefficient c are found to be the leastcontributors for variance reduction. The result of this analysis shows that the sensitivity of thechild node significantly dependent on the variability of parent nodes. Therefore, safety index,coefficient a and b, SCI and time of corrosion initiation are nodes, which have the greaterinfluence on pit depth node. On the other hand, pipe wall thickness and coefficient c are foundto be non-influencing nodes for pit depth node.534.3. Result and Discussion0 10 20 30Safety indexTime of corrosion initiationCoefficient 'b'Soil corrosivity indexCoefficient 'a'Soil resistivityTemperature of soilRedox potentialSoil pHPresence of salts in the soilSoil sulfides contentsGround water variabilityOxygen content of soilAeration of soil porous mediaDegree of compaction of soilPresence of bacteriaSoil moisture contentAvailability of sulfate in soilPresence Organic/Inorganic acidsPresence of carbonic acidPipe wall thicknessCoefficient 'c'Normalized variance reductionNormalized variance reductionFigure 4.6: Sensitivity of pit depth node due to finding at the other nodes4.3.2 Monte Carlo SimulationsMCs is an alternative to analytical mathematics for understanding statistical sampling dis-tributions and evaluating its behavior in random samples using random samples taken froma known population of simulated data (Mooney 1997). This simulation provides a technicalbasis for understanding empirical and experimental data (Landau and Binder 2009). In or-der to address the random corrosion initiation time, a MCs was used to understand the effectof the input parameters on the output (i.e. RSL and safety index) of the BBN model. Thebest-fit statistical type of distribution with the mean and standard deviations from measuredparameters was used as inputs to the MCs. A normal distribution was the best-fit type for soilpH, pipe wall thickness, soil resistivity, and pit depth. On the other hand, soil sulfides con-544.3. Result and Discussiontent, soil temperature, and soil moisture content were found to be the best fit to a log-normaldistribution. However, redox potential was best fit to Weibull distributions. This assessmentwas based on the measured values for all input parameters collected by the city of Calgary in1998 inventory on cast iron pipes. Figure 4.7 and Table 4.2 show, the curve fitting types usedand the statistical summary of input parameters, respectively. For a random input of variables,generated using the best-fit statistical parameters, RSL of metallic pipes and safety index wereevaluated using the BBN model 3000 times. The MCs was embedded in pit depth BBN modelto generate input parameters. The implementation processes and activity flows considered toembed the MCs in pit depth BBN model is described by a flowchart shown in Figure 4.8.Table 4.2: Statistical summary of input parameters for Monte Carlo simulations.Measured inputs Weibull Normal Log-normalln(β) 1α R2 µ σ R2 ln(xo) σ R2Soil pH 2.11 0.01 0.86 8.15 0.16 0.91 2.10 0.02 0.91Soil sulfide (mg/kg) 0.72 0.36 0.83 1.90 0.97 0.79 0.52 0.48 0.92Pipe wall thickness (mm) 2.38 0.05 0.97 10.58 0.67 0.99 2.36 0.06 0.99Redox potential (mV ) 5.54 0.07 0.95 246.95 19.52 0.93 5.51 0.08 0.91Soil resistivity (ohms−cm) 7.79 0.30 0.93 2194.06 791.00 0.95 7.63 0.38 0.95Soil moisture content (%) 3.67 0.08 0.86 37.61 4.06 0.93 3.62 0.11 0.96Soil temperature (◦C) 2.64 0.17 0.70 13.20 3.25 0.80 2.55 0.23 0.84Pit depth (mm) 1.61 0.36 0.97 4.47 1.79 0.98 1.41 0.45 0.95554.3. Result and Discussion   Measured Lognormal distribution Weibull distribution Normal distribution0.00.20.40.60.81.07.5 7.7 7.9 8.1 8.3 8.5 8.7P(pHi<)Soil pH 0.00.20.40.60.81.00.0 1.0 2.0 3.0 4.0 5.0P(S i<)Soil sulfides content (mg/kg)0.00.20.40.60.81.08.6 9.6 10.6 11.6P(pwt i<)Pipe wall thickness (mm)0.00.20.40.60.81.0180 230 280P(Gi<)Redox potential (mV)0.00.20.40.60.81.0500 1500 2500 3500 4500P(ρi<)Soil resitivty (Ohm-cm)0.00.20.40.60.81.027 32 37 42 47P(MC i<)Soil moisture content (%)0.00.20.40.60.81.06.0 10.0 14.0 18.0 22.0P(T i<)Temperature (oC) 0.00.20.40.60.81.00.0 5.0 10.0P(d i<)Pit depth (mm)Figure 4.7: Statistical fitting types used for Monte Carlo simulations input parameters.564.3. Result and DiscussionStartDetermine soil  corrosivity index  (SCI)Predict pit depth by changing corrosion initiation time Is the predicted pit depth equals to thegenerated pit depth?Is the predicted pitdepth greater or equals to generated pipe wall thickness ?Report time to failureGet expected value of  coefficients "a", "b" and  "c" from BBN modelReport corrosion initiation timeNoYesNoYesCalculate safety index (SI)Calculate remaining  service life of pipeRandomly generate  soil  parameter valuesRead  gnerated soil  parameter values in to  BBN modelCan soil paramter be generated?Get expected value  of soil parameters  from BBN modelYesNoRandomly generate pit depthRead generated  pit depth to BBN modelRandomly generate  pipe wall thickness  Read generated  pipe wall thickness  to BBN modelFigure 4.8: Flow chart used to embed the Monte Carlo simulations to the pit depth Bayesianbelief network modelAs shown in Figure 4.9, the sensitivity analysis result of MCs shows that soil pH, soiltemperature, soil moisture content and redox potential have less significance on the output ofthe model. Pit depth is a significant contributor to a decrease in RSL of metallic pipe, whilepipe wall thickness and soil sulfide contents have a significant influence on its increment. Pipewall thickness and soil resistivity are instead significant contributors to a decrease in safetyindex, while pit depth and soil sulfides contents mostly contribute to its increment.574.3. Result and Discussion-100% -50% 0% 50% 100%Soil sulfides contentSoil resistivitySoil pHSoil temperatureSoil moisture contentRedox potentialPit depthPipe wall thicknessContribution of input to output (%)RSLSIFigure 4.9: Sensitivity of pipe remaining service life and safety index to change in input pa-rametersThe MCs result, Figures 4.10(a) and 4.10(b), show the probability of RSL and time ofcorrosion initiation for different classification of SCI, respectively. As it can be seen, the prob-ability of corrosion initiation time is very high when the soil is highly corrosive and very lowprobability when the soil is non-corrosive. For this reason, in a highly corrosive soil, there isa high probability that the RSL of the pipe is very low. Otherwise, in low corrosivity soils,the probability of having a high RSL of the pipe is very high. Based on the result shown inFigure 4.11, in very high, high, medium and low soil corrosivity environment, the probabilityof pipe failure due to external corrosion is very high if the age of the pipe is between 15 and 22,25 and 35, 45 and 55, and greater than 120 years, respectively. The figure also shows that, invery low soil corrosivity, the probability of pipe failure due to external corrosion is either veryinsignificant or failure never happens. In Figure 4.12, the pit depth model outputs (i.e. pitdepths) characteristics for a specific time of corrosion initiation installed in different behaviorof soil, corrosivity are presented.584.3. Result and Discussion0.00.20.40.60.81.00 20 40 60 80 100P rob ab il i tyRemaining service life (years)Very high SCIHigh SCIMedium SCILow SCIVery low SCI(a) Remaining service life0.00.20.40.60.81.00 20 40 60 80 100P rob ab il i ty  of  cor ros i on i ni t iat i on Time of exposure (years)Very high SCIHigh SCIMedium SCILow SCIVery low SCI(b) Time of corrosion initiationsFigure 4.10: Probability of corrosion initiation time and remaining service life594.4. Summary0.00.20.40.60.81.00 20 40 60 80 100 120P rob ab il i ty  of  pi pe  b re akTime to failure (years)Very high SCIHigh SCIMedium SCILow SCIVery low SCIFigure 4.11: The variation of cumulative probability of pipe failure due to external corrosionin different soil corrosivity index0.03.06.09.012.00 10 20 30 40 50 60 70 80 90 100Ext er nal  cor ros i on p it  de pt h ( mm)Age of pipe (years)Very high SCIHigh SCIMedium SCILow SCIVery low SCIFigure 4.12: Pit depth for specific corrosion initiation time in different soil corrosivity indexclasses4.4 SummaryThe main objective of this chapter was to predict the RSL of metallic pipes. The soilparameters, which are representing corrosivity of soil environment was identified and used forprediction of corrosion pit depth, time of corrosion initiation and time to failure with themain objective of predicting RSL of metallic pipes. A technique of combining expert opinion,604.4. Summaryempirical data, mathematical model and programming logic was used to employ the model.A detailed review had been made to identify and define the representative node of the BBNmodel and their casual relationships and interdependencies among the nodes. A BBN sensitivityanalysis was performed at pit depth node to determine the absolute degree and the rank orderof influence of parent nodes on the child node. The best-fit distribution statistical parameters(i.e. mean and standard deviation) of measured input parameters were used to embed the MCsin the BBN model to identify the sensitivities of model output (i.e. RSL and safety index) fora change in the input variables.61Chapter 5: Failure Mode and Effect Analysisof Valves 35.1 BackgroundThis chapter presents a framework for conducting a failure mode and effect analysis ofvalves in a WSS. The proposed framework identifies available failure modes attributed to thevalves and evaluates the impact of failure on the WSS. All the failure modes, causes, effectsand recommended actions are identified to develop a robust BBN model for each failure sce-narios. Later, corrosion failure scenario was considered for further analysis using the collecteddata/information from the city of Calgary. A probability of failure due to external corrosionwas determined using the BBN-SCI model developed in chapter 3, the condition of externalprotection and age of valves. Finally, the failure severities were estimated based on the degreeof corrosion failure. Sensitivity analysis of the corrosion failure scenario was also performed tounderstand the influence of variation in input parameters on output parameters. The developedcorrosion failure scenario was converted to influence diagram in order make optimized decisionmaking. Finally, the utility of the proposed model was demonstrated on the city of CalgaryWSS isolation valves.5.2 MethodologyThe proposed methodology in this study is shown in Figure 5.1. The first step in thisstudy is identifying applicable valve failure modes, effects and recommended actions during anevent. Based on the identified failure modes, a general BBN based Failure Mode and EffectAnalysis (FMEA) model which include all the identified failure modes was developed. In the3A version of this chapter is under internal review for a possible publication in the peer-reviewed journal witha title of “Failure Mode and Effect Analysis of Valves Using Bayesian Belief Network”(Demissie et al. 2017b).625.2. Methodologysecond step, a detailed corrosion failure scenario of isolation valve BBN model was consideredfor further analysis. This step includes corrosion failure scenario BBN model development,data processing, and model sensitivity analysis. Finally, in the third step, the corrosion failurescenario was extended to influence diagram based decision-making method and demonstratedon the city of Calgary WSS isolation valves. In the end, the developed decision network modelresult was integrated to GIS. The following subsections briefly discuss the topics considered inthis methodology.Figure 5.1: Proposed methodology635.2. Methodology5.2.1 Failure Mode and Effect AnalysisFMEA is a systematic and proactive method for evaluating a process or a system to identifywhere and how it might fail and to assess the relative impact of different failures, in orderto identify the parts of the process or system that are the most in need of maintenance orreplacement (IHI 2004). Chang and Cheng (2010) described FMEA, a systematic way to identifyand evaluate the effects of different component failure modes of a system to determine whatcould eliminate or reduce the chance of failure and to document the system in consideration.A system may usually have multiple modes of failure or multiple causes and effects. FMEAuses Risk Priority Number (RPN) to determine the risk priorities of each failure modes (Wanget al. 2009b). RPN is the product of the likelihood of occurrence of failure (O), the likelihoodof detection of failure (D) and the severity of the failure (S).RPN = O × S ×D (5.1)These risk factors can be estimated using numbers ranging from 1 to 10. A number assignedto the severity of failure indicates the level of seriousness of failure, the number given to theoccurrence of failure represents how often the failure occurs and the detection numbers designatethe level of detectability of the failure (Povolotskaya and Mach 2012). Conventional FMEA isefficient in the analysis of failure; however, it has the following limitations:− Lacks sufficient/critical knowledge and structure to represent causal relationship betweencauses and effects (Lee 2002)− Conditional probabilities are not considered.− Lacks in considering multiple information sources and inter-dependency between failureevents and causes.As a result, in this chapter, a BBN based FMEA has been developed. The developed BBN-FMEA considers multiple scenarios of failure modes and prioritize the risk of valve failure basedon the identified failure modes. BBN have a capability and better structure to represent thecausal relationship between causes and effects. In addition,BBN is an alternative risk assessmentmethod in regards of combining multiple information sources and their interactions (Bartramand Mahadevan 2014; Hunink et al. 2014; Kabir et al. 2015a).In order to better represent and use the capability of BBN in failure mode and effect analysis,Lee (2002) suggested a simplistic way to convert conventional FMEA to the Bayesian network645.2. Methodologybased FMEA model. In the development process of BBN based FMEA model for isolationvalve, in this study, the following sequence of steps suggested by Lee (2002) are employed:1. Build failure scenarios: In this step, individual scenarios are constructed for identifiedisolation valve failure modes.2. Severity annotation: A severity nodes are incorporated, in this step, for each of theidentified failure scenarios.3. Compile the BBN: In this step, each failure scenarios associated with the severity nodesare compiled.4. Extract and plot: Extract the probability of failure and severity distribution for eachfailure scenarios.5. Update: Revise the failure scenario model to reflect an improvement made as a result ofthe BBN-FMEA analysis.The conventional FMEA presents the severity as a point distribution, however, the BBN-FMEA represents in the form of probability distribution. Also, the BBN-FMEA represent theseverity of the event in terms of conditional probability. Conditional severity variable/node canbe represented as follows (Lee 2002):SD = p(S|FE, Vi) (5.2)where SD is severity distribution, S is severity, FE is failure event and VS is other influ-encing variables. In the case of multiple failure scenarios which occurs at a time, such that{FE1, FE2, ...FEn} represent n failure scenarios with associated severities {S1, S2, ...Sn}, thetotal severity of the system realized STotal can be calculated by Equation 5.3. However, theglobal impact of total severity of the system realized (i.e. absolute severity) can be calculatedby Equation 5.4.STotal = Max(S1, S2, ...Sn) (5.3)STotal = Sum(S1, S2, ...Sn) (5.4)655.2. Methodology5.2.2 BBN - FMEA Model DevelopmentThree steps can be followed to develop a BBN model (Ge et al. 2014): The first step involvesthe development of the graphical structure indicating the relevant cause and effect variables.This step emphasizes the causal relationship between considered variables. The second stepinvolves the quantification of conditional relationships among the considered variables. In thisstep, conditional relationships among variables can be maintained either through learning orexpert elicitation. The final step is model inferencing that uses the BBN model to visualize thequantitative relationships given causes or effects.Literature has been reviewed to determine the probability of valve failure and identifythe modes of failure, causes of the failures and the possible effects of the failures and actionthat has to be taken to reduce or avoid the occurrences of the failures of valves (Marlowand Beale 2012; Marlow et al. 2012; Nesbitt 2011; Trowbridge et al. 1988). These failuremodes, causes, and effects of valves are briefly presented in Tables 5.1 and 5.2. A BBN-FMEAmodel is developed based on the identified failure modes. Firstly, a general BBN model whichpredicts the probability of valve failure was developed (Figure 5.2). Secondly, a single failurescenario (corrosion failure) was selected to further analyze the model and implement the BBNbased failure mode and effect analysis. Considered node states and their discretization for thedeveloped general BBN-FMEA are presented in Table 5.3. The detailed model developmentprocess, considered parameters and implementation of the corrosion failure scenario will bediscussed in the following section.Table 5.1: Modes and causes of valve failureModes CausesLeak at seal or gasket (FM1) Manufacturing defects, faulty installation, damage(punctures or fracture), deterioration as a result ofwear-out or agingSplit/cracked body (FM2) Due to fatigue, high internal or external pressure anddue to faulty installation.Bolt/Nut failure (FM3) External impacts, corrosion, deterioration due to age,wear-out and fatigue.Spindle failure (FM4) High stress, valve exercising by inexperienced operatorContinued on next page665.2. MethodologyTable 5.1 – continued from previous pageModes CausesSeized ball/mushroom (FM5) Manufacturing defect and the environment in whichthe valve is operating.Jumper valve failure (FM6) Water hammer (Sudden change in pressure), corrosionof its parts.Corrosion failure (FM7)(a) Internal corrosion Water quality parameters: Turbidity, bio-film growth(water age and free residual chlorine), water velocity,water pH and color of water.(b) External corrosion Includes: low resistivity of soil; lower pH; presence ofsulfate-reducing bacteria, chlorides, sulphate and sul-phides; difference in soil composition; differential aer-ation of soil around the appurtenances; variation ofgroundwater level; stray direct current from externalforces; and higher soil moisture content (discussed inchapter 3).(c) Failure of coating/protection Improper surface preparation, improper coating se-lection, improper application of coating, failure dueto curing time, lack of protection against water andaqueous systems (i.e. corrosive environment such aschlorides), mechanical damage of coating during trans-portation and installation, operation and maintenance.Internal mechanical damage (FM8) Entrance of debris in a pipe or appurtenances.Degradation of material excludingcorrosion and coating failure (FM9)Involves degradation and/or attack of plastic, elas-tomeric or other non-metallic components.Failure to operate (FM10) Failure to operate may be the result of one or moreof the above failure mechanisms and may lead to pipefailure.675.2. MethodologyTable 5.2: Possile effect of valve failure and recommended actionsModes Possible effects of failure Recommended actionsFM1 Hydraulic performance of the system leadsvalve or pipe failure due to leaked waterFix or change the seal/gasketFM2 Leakage, create a room for corrosion If possible maintain the cracks,either replace the valveFM3 Valve and pipe failure or system failure in gen-eralChange bolt/nutFM4 Breaks spindle, bending of spindle Change the spindleFM5 Effect on hydraulic performances, difficulty inoperation, maintenance and management of thewhole system, pipe system structural failureMaintain or replaceFM6 Leakage, water loss, extra load on water systems Replace the jumperFM7(a) Water quality, increased aggressiveness of wateron corrosion inhibitorMaintain good water quality inthe systemFM7(b) Deterioration of valves and failure of bolts andnuts which leads to failureUse protection in areas where soilcorrosivity index is very highFM7(c) Increase in external corrosion Use the right and correct methodof coating/cathodic protectionFM8 Entrance of debris in a pipe or appurtenancesDifficulty in valve operation, system failureInspect and remove the debrisFM9 Leakage, corrosion of parts etc. Inspect and maintain or replacethe degraded parts of the valvesFM10 Difficulty in operation and maintenances, failureto deliver the intended hydraulic performance,pipe system structural failureReplace the valve685.2. MethodologySeverity(FM10)TotalSeverityDamage(punctures orfracture)Manufacturing defectsLeak at sealor gasketSeverity(FM6)Severity(FM9)Severity(FM7)Severity(FM1)Severity(FM8)Severity(F4)Severity(FM3)Severity(FM2)Severity(FM5)StressSpindlefailureValveexercisingExternalimpactsDeterioration of partsBolt/nutfailureSplit/cracked bodyFatigueInternal orexternalpressureDeterioration of gasketFaultyinstallationFailure ofprotection/coatingExternalcorrosionCorrosionfailureProblemin designInternalcorrosionOperatingenvironmentSeizedball/mushroomFailure tooperateDegradation ofnon metalliccomponentElastometricNon metallicdegradationEntrance of debrisin pipe or valveInternalmechanicaldamageCorrosionof its partsWaterhammerJumpervalve failureCorrosion failureFigure 5.2: BBN model for valve FMEA695.2. MethodologyTable 5.3: Definition of BBN-FMEA variables (nodes) and their state discretizationVariable (node) Node states (discretization)External corrosion (represented by soil corrosivity index) {Very high (>13), High(10-13), Medium (7-10), Low (3.5-7.0), Very low (0-3.5)}Age of valves (years) { 0-15, 15-30, 30-45, >45 }Severity nodes from FM1 to FM10 and Total Severity {Catastrophic, Critical,Marginal, Minor}Corrosion failure, Deterioration of gasket, External impacts, Fa-tigue, Internal corrosion, Internal or external pressure and Stress{High, Medium, Low}Water hammer {Strong, Medium, Weak}Spindle failure {Fail, No fail}Operating environment {Good, Bad}Valve exercising {Proper, Improper}Seized ball/mushroom {Seized, Not seized}Bolt/nut failure, Corrosion of its parts, Damage (punctures orfracture), Degradation of non-metallic component, Deteriorationof parts, Elastomeric, Failure of protection/coating, Failure to op-erate, Faulty installation, Entrance of debris in pipe or valve, In-ternal mechanical damage, Jumper valve failure, Leak at seal orgasket, Manufacturing defects, Non-metallic degradation, Problemin design and Split/cracked body{Yes, No}5.2.3 Corrosion Failure ScenarioA predominant deterioration mechanism on the exterior of metallic pipes and valves iselectro-chemical corrosion with the damage occurring in the form of corrosion pits (Kleinerand Rajani 2001; Makar et al. 2001). A metal loss through the time due to this corrosion willeventually lead to a metallic pipe or appurtenance failure. It is prominent that the physicalenvironment of pipes and appurtenances have a significant impact on the deterioration and fail-ure rates. Similarly, internal corrosion as a result of the quality of the water to be transported705.2. Methodologymight also impact pipe and appurtenance structural deterioration. Impact of internal corrosion,given a well-managed water quality in the system, is less significant compared to the externalcorrosion of pipes and valves. As a result, in this chapter, due to the insignificance of the effectof internal corrosion on the structural failure of valves only external corrosion is considered.The following subsections present the modeling techniques and the considered influential ex-ternal corrosion failure parameters. In this chapter, the BBN-SCI model proposed in chapter 3(Demissie et al. 2015) was used to predict the degree of external corrosion (Figure 5.8). In thismodel, limitation of data has been taken into consideration by combining in situ measureddata, experimental data, available literature and expert elicitation.5.2.4 Data ProcessingThe city of Calgary’s WSS consists of over 70,500 valves (City of Calgary, 2014). It iscomposed of 12 types of valves: namely; Air valve control, Bypass valve, Flushing assemblyvalve, Pressure reducing valve, Anti-surge valve, Check valve, Hydrant valve, Service valve,Automatic air valve, Main valve (isolation valve) and Wash out valves. Main valve, Hydrantvalve and Service valve covers 60.9%, 22.4% and 12.1%, respectively (Figure 5.3). The othernine types of valves only take 4.6% of the total valves in the system. The analysis made on theage of the valves in the system also shows that 10% of the valves are aged more than 45 years(Figures 5.4 and 5.5). However, in this study, only main valves (isolation valves) are consideredfor further analysis, as these valves represent more than half of the valves in the water supplysystems and their vulnerability to failure due to their operational behavior. Although the cityof Calgary started keeping the record of pipe breaks since 1950’s, the records of failures relatedvalves are not reported as a concern.715.2. Methodology272 4 801 429 205 29 49115806429702198532800075001500022500300003750045000Air Valve Control Anti Surge Automatic Air ValveBy Pass Valve Check Valve Flanged Outlet ValveFlushing Assembly Valve Hydrant Valve Main ValvePressure Reducing Valve Service Valve Wash OutFigure 5.3: Distribution of valve types for the city of Calgary15 or less36%15-3031%30-4523%> 45 10%Figure 5.4: Age classification of valves for the city of Calgary (years)725.2. Methodology0.00.20.40.60.81.00 9 18 27 36 45 54 63 72 81 90 99Cumul at i ve  p rob ab il i tyAge of isolation valves (years)Figure 5.5: The city of Calgary isolation valves probability distribution050010001500200025000 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 81 86 92 101106T ot al  count  of  val ve sAge of valvesHydrant valvesIsolation valvesService ValveFigure 5.6: Comparison of ages between three valve types for the city of Calgary valvesSpatial location of valves and their ages are extracted from the GIS-database of the city ofCalgary WSS. The base year was fixed to 2015. Assume a valve having a year of installation2005, its age will be 10 years. Available soil information has also been processed using GISanalysis. The SCI-BBN model (Demissie et al. 2015) node states were trained using 109, 971point measurement of soil electrical resistivity and other soil parameters collected at 343 testsites. This data was collected by the city of Calgary to investigate the increased risk of pipe735.3. Result and Discussionfailure rates. Expert elicitation was considered in order to estimate the conditional probabilityfor the states of nodes “Severity”, “corrosion failure”and “satisfaction”. The severity nodesconsidered in each failure scenarios were assumed to have a uniform level of node state dis-cretization (i.e. {Catastrophic, Critical, Marginal and Minor}). The uniform discretization isaimed to facilitate the uniformity for the computation of absolute and global severity of valvefailure during multiple failure events.5.3 Result and Discussion5.3.1 Sensitivity AnalysisA BBN sensitivity analysis based on the mutual dependencies have been performed at“corrosion failure” and “severity” nodes with respect to other parameters to understand theeffect of variation in the input variable on these nodes. As shown in Figure 5.7, major soilparameters, soil corrosivity index and the status of external protection are the most influencingparameters on the probability of corrosion failure and its severity. This analysis also shows thatthe age of the isolation valve is found to be a less influential parameter for corrosion failurecompared to major soil parameters and the corrosivity of soil.745.3. Result and Discussion0 50Corrosion failureSeverityFailure of protectionSoil corrosivitySoil resistivitySoil temperatureSoil pHRedox potentialAgePresence of saltsSoil sulfidesOxygen contentAeration of soilDegree of compaction of soilPresence of sulfate reducing bacteriaAvailability sulfatesAciditySoil moistureGround water variabilityNormalized mutual information Sensitivity measure at node "corrosion failure"Sensitivity measure at node "severity"Figure 5.7: Sensitivity analysis result (Entropy reduction) at “corrosion failure” and “severity”nodes.5.3.2 Influence Diagram Based Decision MakingFollowing the development, determination of CPT and sensitivity analysis of the BBNmodel, the BBN corrosion failure scenario model is converted to influence diagram (decisionnetwork) in order to assist in optimized decision making. In decision network, incoming arcsto a decision, chance, and utility nodes represent available information at the time of thedecision, probabilistic dependence and what the utility depends on, respectively. A utility nodenamed “satisfaction” and a decision node named “decision” have been defined. An elementarydecision alternatives such as “Do nothing”, “Repair” and “Replace” are selected. The influencediagram optimizes the decision based on the level of satisfaction defined in the “satisfaction”755.3. Result and Discussionnode and the probability of corrosion failure. The level of satisfaction varies between 0 and 10,where 0 means dissatisfied by the optimized decision and 10 means satisfied by the optimizeddecision. A level of satisfaction based on the combination of the probability of corrosion failureand the decision alternatives to be optimized are presented in Table 5.4. For example, if thestate probabilities of corrosion failure is { High = 94.5 %, Medium = 3.5 % and Low = 2.0% } the optimized decision to choose the intervention alternatives based on the defined levelof satisfaction (Table 5.4) are 0.68/10, 2.2/10 and 8.75/10 for “Do nothing” “Repair” and“Replace”, respectively.Aeration of soil porous mediaPresence of saltsSoil resistivityTemperatureDegree of compaction Organic/Inorganic acidsSoil pHSoil moisture contentGround water variabilityRedox potential Soil Corrosivity IndexOxygen contentCorrosion failure SeverityDecisionFailure of protection / coatingSatisfactionAgeAvailability of sulfates in Soil  Carbonic acidPresence of sulfate reducing bacteriaSoil  sulfides contentFigure 5.8: Influence diagram for optimized decisions (highlighted)765.3. Result and DiscussionTable 5.4: Decision making based on influence diagramProbability of corrosion failure Decision alternatives Level of satisfactionHigh Do Nothing 0.5High Repair 2.0High Replace 9.0Medium Do Nothing 1.0Medium Repair 6.0Medium Replace 7.0Low Do Nothing 9.0Low Repair 5.0Low Replace 0.5The developed model was demonstrated on the city of city of Calgary water supply systemisolation valves. The final model result (probability of corrosion failure) of Calgary WSS iso-lation valve are integrated to GIS. Figure 5.9 shows the spatial representation of the predictedprobability of corrosion failure for individual isolation valves. This prediction was performedbased on the assumption that there is a failure of external protection. For the given predictedprobability of corrosion failure, a criticality matrix can be extracted and plotted as shown inFigure 5.10.775.4. SummaryDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDD DDDDDDD DDDDD DD DDDDDDDDDDDDDDDDDD DD DD DDDD DDDDDDDDDDDDDD DDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD D DDDDDDDDDDD DDDDDDDDDDD DDDDDDDDDDDDDDDDDDDD DDDD DDDDDDDDDD DDDDDDDDDDDDDDDDD DDDDDDD DDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDD DDDDDDDDDD DDDDD DDDDDDDDDDDDDDDD DDDDDDDDDDDDDDD DDDDD DDDDDDDDDDDDDD DDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDD DDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDD DDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD 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")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")") ")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")") ")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")") ") ")")")")")")")")")")")") ")")")")")")")")")")")")")")")")")")")")")")")") ")")")")")")")")")")")")")") ")")")")")")")")")")")")")")")")") ")")")")")")") ")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")")") ")")")")")")")")")")")")")")") Probability (Corrosion failure = High)") Probability (Corrosion failure = Medium)") Probability (Corrosion failure = Low)D Isolation valvesWater pipesFigure 5.9: Spatial representation of predicted probabilities of corrosion failureHighMediumLow0.0000.2000.4000.6000.8001.000CatastrophicCritical Marginal MinorHigh 0.860 0.080 0.050 0.010Medium 0.450 0.300 0.200 0.050Low 0.050 0.100 0.350 0.500P rob ab il i ty  of  Oc cur enc eSeverity of failureFigure 5.10: Criticality matrix for corrosion failure scenario5.4 SummaryThis chapter focused on the development of a Bayesian belief network model for the failuremode and effect analysis of isolation valves. The main objective of the study was to provide an785.4. Summaryefficient BBN based failure mode and effect analysis model for valves to prioritize failures. TheBBN-FMEA model is proposed to prioritize the failure of valves in water supply system, due toits ability to combine multiple information from different sources and combine them consideringtheir interdependencies as a result of cause-effect relationships. BBN is a flexible methodto incorporate more variables and qualitative or quantitative information whenever available(Kabir et al. 2015a). In addition, the nature of knowledge encapsulation and its structure torepresent the causal relationship between parameters makes BBN the most preferable directedgraphical probabilistic network model. The BBN network identified for each failure modesbased on causes of valve failures are either expert-driven or based on the reviewed literature.For each identified modes of failures, a failure scenario was proposed to model valve failure.Theses failure scenarios are finally combined to develop a comprehensive valve failure BBN-FMEA model. In the end, a single failure scenario (i.e. the corrosion failure) was selected todemonstrate the model using the data collected by the city of Calgary.79Chapter 6: Dynamic Bayesian Network Modelfor Prediction of Pipe Failure 46.1 BackgroundWSS is a lifeline of the modern city. Transmission and distribution pipes, spatially dis-tributed components of the WSS, are most often vulnerable to failure (leakage/breakage/burst).Many factors contribute to pipe failure. These factors can be categorized as pipe’s physicalattributes, operational practices, and environmental factors (e.g., climatic factors and soil cor-rosivity). The impact of failure factors can be static or dynamic (time-dependent) in nature.This chapter quantifies the impact of time-dependent factors on the annual and monthly trendof pipe failures. It considers a DBN as an alternative model for prediction of pipe failures.The developed DBN model was trained using annual and monthly data categorized based oncombined (metallic pipes) and specific pipe material. The annual model was considered to pre-dict the annual pipe failure trends while the monthly model was used to evaluate the seasonalvariations and trends of pipe failure.6.2 MethodologyFigure 6.1 depicts the proposed methodological framework adopted for this chapter. Ini-tially, pipe attribute data (e.g., pipe material), operational data (e.g., cathodic protection), soilinformation and pipe breakage data were gathered from the city of Calgary’s GIS database. Thecollected soil information was used to predict the SCI using the model proposed in chapter 3.To compute the input climate parameters, the weather data obtained from Environment andClimate Change Canada (EC 2015) was utilized. In the next stage, a DBN model was developed4A version of this chapter is published in the ASCE–ASME Journal of Risk and Uncertainty in EngineeringSystems, Part A : Civil Engineering with a title of “Prediction of Pipe Failure by Considering Time-dependentFactors: A Dynamic Bayesian Belief Network Model”(Demissie et al. 2017c).806.2. Methodologyusing pipe attribute, environmental factors, and operational data. In the end, the developedmodel was validated and demonstrated using the case study WSS (the city of Calgary) pipedata.Parameter Identification(Input Processing)EnvironmentalfactorsOperationaldataPipe attributesDynamic Bayseisan Network(Model Development)Model Validation andImplementationFigure 6.1: Proposed methodology6.2.1 Parameter IdentificationKey factors which contribute to pipe failures can be categorized as pipe’s physical attributes,operational factors, and environmental factors. The following subsequent sections present thedescriptions and available computing techniques of different pipe failure factors.6.2.1.1 Pipe Attributes and Operational FactorsPipe attributes and operational factors include Pipe Material (PMAT), Pipe Diameter(PDIA) (mm), year of installation (year), Pipe Length (PLNG) (mm), Number of Previous Fail-ures (NOPF), Vintage (VINT), type of service connections (i.e., Number of Residential ServiceConnections (RSERVS), Number of Commercial/Industrial Service Connections (CSERVS))and status of Cathodic Protection (CP). Description of these factors and their effects on thepipe failure are presented in Table 6.1.816.2. MethodologyTable 6.1: Pipe’s physical attributes and operational factorsStatic factors DescriptionPipe material Pipes made from different materials have different failure modes. Pipe materialincludes metallic pipes, concrete pipes and plastic pipes.Pipe wall thickness The thinner the wall of the pipe the faster penetration through as a result ofcorrosion (metallic pipes).Pipe vintage Vintage is a reference to the manufacturing period of the pipe which can be usedas an indicator for pipe degradation. Different pipe manufacturing periods areassociated with different pipe failure probabilities. For example, a period of man-ufacturing of thin and thick wall CI have different impact in case of corrosion.Pipe diameter Smaller diameter are more likely to break than a larger diameter (Rajani andTesfamariam 2004; Rajani et al. 1996). Specifically, in CI pipes, as the diame-ter increases the wall thickness increases. As a result, the smaller diameter CIpipe susceptible to corrosion failure. Smaller pipes with thinner walls also havea reduced ability to resist external loading and bending stresses (Mackey et al.2014).Cathodic protection Cathodic protection is a technique used to control corrosion in buried and wa-terfront structures by minimizing the difference in potential between anode andcathode (Corrosionist 2016).Year of installation Year of installation is the way to keep track of how long the pipe has been buriedunderground.Service connections Service connections can either be a residential service connection or a commer-cial/industrial service connections. The number and the type of connection fromthe water mains may contribute to pipe breaks.6.2.1.2 Environmental FactorsSome of the time-dependent environmental factors contributing to pipe failure are attributedto the nature of climate (Kleiner et al. 2003). Climatic factors can be as a result of climaticchange/variability factors (e.g., temperature, precipitation) (Instanes 2003; Kleiner et al. 2003).The climatic factor, the change in temperature, can be represented as a FI for a cooler seasonand as a TI for the warmer season. The effect of precipitation received by the earth surfaceon the pipe breaks, on the other hand, can be quantified in the form of RD. In addition toclimatic factors, external soil corrosion also significantly contributes to pipe failures (Demissieet al. 2015, 2016; Doyle et al. 2003). The detailed discussion of the effect of soil corrosion on826.2. Methodologypipe failure is presented in chapter 3. The climatic factors and their quantification methodswill be presented as follows:FI is a parameter used to account for the severity of a freezing period and is expressed inthe unit of degree-days (◦Cd) (Friedl et al. 2012). This parameter is calculated by summingthe average daily temperature in all days in a given freezing period, in which the average dailytemperature (Tm) is below freezing point (0◦C).FI =n∑i=1Tm,n ∗ d (6.1)Tm,n =Tmin,n + Tmax,n2(6.2)where Tmin,n and Tmax,n is minimum and maximum daily temperature in◦C measured for nmonths or years, respectively.TI is an environmental load parameter used to determine the magnitude of the thawingseason (Instanes 2003). TI is extremely important parameter in regions where the effect ofhigh temperature is prominently affecting the pipe failure. It is an integral of the sinusoidal airtemperature variation during one year for Tm > 0◦C and is estimated as:TI =n∑i=1Tm,n ∗ d (6.3)where Tm,n is calculated by Equation 6.2.RD is the difference between the amount of Precipitation (PPT) received and the amount ofwater lost due to Potential Evapo-transpiration (PET). Higher RD implies that PPT receivedby the environment is lower than the PET from the environment and vice-versa. RD is themanifestation of moisture content level of soil (Farewell et al. 2012). The moisture level of thesoil, as a result of the RD significantly affects the pipe breakage rate (Farewell et al. 2012;Kleiner et al. 2003). Lower soil moisture level (i.e. high RD) contributes to the shrinkage of soilporous medium and higher soil moisture level (i.e low RD) in turn contributes to an increasedswelling of soil, which in turn facilitates frost penetration.Since 1940’s several techniques have been proposed to estimate the amount water lost dueto PET (Hargreaves et al. 1985; Monteith and Others 1965; Penman 1948; Thornthwaite 1948).Thornthwaite equation (Thornthwaite 1948), Penman equation (Penman 1948) and Penman-Monteith equation (Monteith and Others 1965) are few of many. Recent studies also show836.2. Methodologythat remote sensing techniques have been employed to successfully estimate potential evapo-transpiration (Cristiano et al. 2015; French et al. 2015; Huo et al. 2011; Kustas and Norman1996). However, in this chapter, the Thornthwaite equation expressed below is used to estimatethe PET. This method quantifies monthly PET based on average monthly temperature andlocation (i.e latitude).PET = 1.6(10TmI)α (6.4)α = (6.75× 10−7)I3 − (7.71× 10−5)I2 + (1.792× 10−2)I + 0.49239 (6.5)I =12∑i=1(Tm,i5)1.514 (6.6)where I is heat index which depends on the 12 monthly mean temperatures Tm,i. Then, theRD can be estimated based on PPT and PET as (Kleiner et al. 2003)RD = PET − PPT (6.7)where PPT is amount of precipitation in mm and PET is the amount of evaporation andtranspiration that will happen if a sufficient water source is available.6.2.2 Dynamic Bayesian Network Model for Pipe Failure Pre-diction6.2.2.1 Dynamic Bayesian NetworkDynamic extension of DBN model refers to the modeling of dynamic systems (Figure 6.2).The DBN model provides a visceral graphical representation of the system and employs sta-tistical inference and learning techniques of BBN to model dynamic systems (Pavlovic et al.1999). This approach combines graphical theory and probabilistic theory to model temporal(time-dependent) systems as a result of its nature of capturing the forward flow of time (Mur-phy 2002; Wu et al. 2015). Similar to BBN, DBN is a directed graphical model both within andbetween time slices (Murphy 2002). Conditional Probability Distribution (CPD) of each nodecan also be estimated independently. Each state at a time, t, is assumed to be only dependenton the immediately preceding state (i.e., it is assumed to be a first-order Markov system model)(Wu et al. 2015). Most often, DBN model the temporal evolutions of the system by consideringtwo-time slices. DBN can be represented as a pair of (N1, N→), where N1 is a Bayes’ net which846.2. Methodologydefines a prior probability (initial model) p(X) and N→ is a Two-slices Temporal BayesianNetwork (2TBN) which defines P (Xt|Xt−1). This relationship can be formulated as follows:p(Xt|Xt−1) =N∏i=1p(Xit |Pa(Xit)) (6.8)where Xit is the ith node at time t(i = 1, 2, ..., N) and Pa(Xit) = parents of Xit in the directedgraphical formulation.ABCA[t-1]B[t-1]A[t]B[t]A[t+1]B[t+1]C(a) (b)Figure 6.2: (a) A BBN/DBN with three nodes; and (b) A DBN unrolled for three time (t)slices, where nodes B and C are a static nodes and node A is a dynamic nodeIn the first slice of the 2TBN, the nodes do not have any parameters associated with them,however in the second slice of the 2TBN, each node has an associated CPD, which definesp(Xit |Pa(Xit)) for every t(i = 1, 2, ..., N) (Hu et al. 2011; Murphy 2002). The parents of eachnode i, (Pa(Xti )), can either be in the ith time slice or in the (i−1)th time slice (Hu et al. 2011;Murphy 2002). The arcs between slices are used to reflect the causal flow of time (Hu et al.2011; Murphy 2002; Wu et al. 2015). A node is always called persistent if there is an arc fromXit−1 to Xit . The arcs within a slice can be put arbitrarily in any ways one wants (i.e. theirrelationships are unconstrained), as long as the intra-slice-model is acyclic (Murphy 2002; Wuet al. 2015). The overall semantics of DBN can be defined by “unrolling” each 2TBN until the856.2. Methodologylast T time-slice. Accordingly, the joint probability distribution can be computed by:p(X1:T ) =T∏t=1N∏i=1p(Xit |Pa(Xit)) (6.9)Three sets of parameters have to be defined to completely specify the DBN (Mihajlovic andPetkovic 2001) given a sequence of T observable variables (e.g., FI), O = {o1...oT }: (a) statetransition CPD (p(TNBRKSt|TNBRKSt−1)) to specify time dependencies between the states;(b) observation CPD (p(Ot|TNBRKSt)) to specify the dependencies of observation nodes withthe pipe break nodes at time slice t; and (c) initial state distribution, p(TNBRKS1), to definethe initial probability distribution of a node at the beginning of the process.6.2.2.2 Inferring Methods for Dynamic Bayesian NetworkThe state space of hidden (i.e., Total Number of Pipe Breaks (TNBRKS)) and observablevariables (nodes) determines the nature of DBN as discrete, continuous or combination of thetwo. Given the observable and hidden nodes, DBN can be used to infer unknown states ofa node (i.e. hidden nodes) and learn parameters of a DBN such that they best fit to theobserved data and make the best model for problems to be tackled. The CPD of unknownstates of a node in BBN/DBN can be inferred given the known observations and their initialprobability distributions (Mihajlovic and Petkovic 2001). The most common inferences in DBNare used to compute p(TNBRKSi,t|O:,t1:t2), where TNBRKSi,t represents the ith total numberof pipe breaks at time t and O:,t1:t2 represents all the evidence between between times t1 and t2.Different inferring techniques that can be used in DBN (Gao et al. 2014; Hulst 2006; Murphy2002) are discussed below and described in Figure 6.3.− Filtering: is an on-line recursive analysis used to estimate the belief states using Bayes’rule. The recursive estimation of belief states consists of two steps: predict (i.e., comput-ing p(TNBRKSt|O1:t−1)) and update (i.e., computing p(TNBRKSt|O1:t)).− Prediction: is the estimation of future state (i.e., computing p(TNBRKSt+dt|O1:t) wheredt > 0 is how far we need to predict), given all the evidences up to the current time t.− Smoothing: is the way of computing the state of the past given all the evidence up tocurrent time (Murphy 2002). There are two kinds of smoothing: fixed-lag smoothing,computes p(TNBRKSt−dt|O1:t), used to identify what happened at t−dt time steps given866.2. Methodologyall the past evidence up to the present, where dt > 0 and fixed interval smoothing (off-line), computes p(TNBRKSt|O1:T ) for all 1 ≤ t ≤ T , most commonly used as a subroutinefor off-line training.Figure 6.3: Major types of inferencing techniques in DBN. The shaded region represents theinterval that contains evidence (t1 − t2). The vertical arrows represent the time at which wecompute belief states, t, is the current time, and T is the sequence length or the final time slice6.2.2.3 Learning Techniques for Dynamic Bayesian NetworksMost often it is not easy to assign a CPT in a complex network of real problems. Hence,employing adequate learning algorithms is essential. Similar to the BBN, a very useful propertyof DBN is their ability to learn from observed data. Learning in DBN can be divided into twotypes (Larran˜aga et al. 2012): structure learning and parameter learning. Structure learningis used to determine the structure of DBN (topology of the network) from the observed data.However, parameter learning is used to estimate the statistical parameters (conditional proba-bilities) when the structure of the unrolled DBN is known. Most commonly reported learningalgorithms in literature employed for learning DBN parameters are Maximum Likelihood (ML)and EM (Do and Batzoglou 2008; Mihajlovic and Petkovic 2001; Murphy 2002).ML learning is used to adjust the parameters to achieve the best fit to a set of observedtraining data (Mihajlovic and Petkovic 2001; Pavlovic et al. 1999). As this method is aniterative algorithm, there is no guarantee that we reach to a global minimum solution (Pavlovicet al. 1999). Besides, if our DBN consists of hidden nodes (states that cannot be observed)and a set of training data with a missing values, ML learning algorithms cannot be used. Inthis situations, EM learning algorithms can be used to handle the problem of missing values intraining datasets.EM algorithm is a natural generalization of EM which enables parameter estimation inprobabilistic models with incomplete datasets (Do and Batzoglou 2008). This algorithm is876.2. Methodologyan iterative hill-climbing mathematical optimization algorithm that consists of an expectationstep (E-step) and a maximization step (M-step) (Hulst 2006). The E-step is the step at whichthe missing values of the observed data are estimated, and the M-step is the step at which theparameters are re-computed including the missing and estimated values as if they were observedvalues.6.2.2.4 Dynamic Bayesian Network Model DevelopmentThe DBN model structure, shown in Figure 6.4, is determined based on expert knowledge.The description of the nodes and state discretizations are presented in Table 6.3. FI, TI, RD,Age of Pipe (AGE), PMAT, PDIA, CSERVS, VINT, RSERVS, SCI, and CP are consideredas observable nodes (O = {o1...oT }) over a period of t = 1 to t = T . The dynamic nodesare FI, TI, RD, AGE and TNBRKS. FI, TI, RD and AGE nodes depend on their past andcurrent states; however, the variable TNBRKS depends on its previous state and the currentstate of all the observable pipe failure factors. The DBN model is unrolled to T time slices andtrained using the pipe failure history and corresponding pipe failure factors data. An increasein the number of parents and attributed states create an exponential growth in the complexityof the DBN network and child’s CPT, respectively (Bensi et al. 2014). In this study, the arrowdirection considered for the TNBRKS node is inverted to reduce the computational complexity(Figure 6.4). Franchin et al. (2016) argued that the original model (without reversing thearrow) and adopted model (with inverted arrow) are not equivalent; however, the later needsfewer data for training. To further reduce the computational complexity of the developed DBNmodel, two models: 1970-1990 and 1991-2015 are developed and combined to represent a singleDBN annual pipe failure prediction model (1970-2015).Following the same procedure, a complete model is developed for seasonal DBN pipe failureprediction model. The seasonal DBN pipe failure model is prepared on a monthly basis for 46months during the years 2000-2003. This model is used to demonstrate the monthly pipe failureprediction capability of the proposed DBN model. In both cases, the pipe breakage history;data related to pipe physical and operational characteristics; and climate factors are used tocompute the prior, conditional and transitional probability values.The prediction capability of these DBN models is tested by training the models using thedata based on combined (metallic) pipes and specific pipe material. The training of the DBNmodels is performed using the EM algorithm implemented in Netica (Netica 2010). The ef-fect of previous pipe breaks or past time-dependent parameters on the current parameter is886.2. Methodologyrepresented using a time-dependent transitional probabilities. For example, prior and the rep-resentative two-time slices transition probability values of the TNBRKS node are described inTable 6.2. The table also shows that when there is no data for training the states, the algorithmautomatically assigns equal conditional probabilities for the states.Table 6.2: Two time slices prior and transitional probability for the annual DBN model.NoofpipebreaksPrior probability (%) Transition probability (%) (1970 −→ 1971) Transition probability (%) (1978 −→ 1979)(1970) 0 1 2 3 4 to 13 0 1 2 3 4 5 to 130 98.42 98.23 1.62 0.14 0.02 0.00 95.69 3.85 0.40 0.04 0.02 0.001 1.43 93.58 6.42 0.00 0.00 0.00 92.81 6.47 0.72 0.00 0.00 0.002 0.11 87.50 12.50 0.00 0.00 0.00 100.00 0.00 0.00 0.00 0.00 0.003 0.03 99.99 0.00 0.00 0.00 0.00 99.99 0.00 0.00 0.00 0.00 0.004 to 13 7.14 7.14 7.14 7.14 7.14 7.14 7.14 7.14 7.14 7.14 7.14 7.14Table 6.3: Description of random variables and node states discretization for annual andmonthly DBN modelsName Node states (annual model)∗∗ Node states (monthly model)TNBRKS∗ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,130, 1, 2, 3, 4, 5PMAT CI, DI, ST CI, DI, STPDIA 100, 150, 200, 250, 300, 350, 400, 450,500, 600, 750, 900, 1050, 1200, 1350,1650, 1950)100, 150, 200, 250, 300, 350, 400, 450,500, 600, 750, 900, 1050, 1200, 1350,1650, 1950PLNG 0 - 35; 35 - 55; 55 - 80; 80 - 91; 91 -101; 101 - 118; 118 - 140; 140 - 169;169 - 200; 200 - 240; 240 - 310; 310 -1190;0 - 35; 35 - 55; 55 - 80; 80 - 91; 91 -101; 101 - 118; 118 - 140; 140 - 169;169 - 200; 200 - 240; 240 - 310; 310 -1190;VINT 0, 1 0, 1AGE* 0 - 9; 9 - 18; 18 - 26; 26 - 35; 35 - 44;44 - 53; 53 - 61; 61 - 70; 70 - 79; 79 -88; 88 - 96; 96 - 105;0 - 9; 9 - 18; 18 - 26; 26 - 35; 35 - 44;44 - 53; 53 - 61; 61 - 70; 70 - 79; 79 -88; 88 - 96; 96 - 105;Continued on next page896.2. MethodologyTable 6.3 – continued from previous pageName Node states (annual model)∗∗ Node states (monthly model)SCI very low (0 - 3.5); low (3.5 - 7);medium (7 - 10); high (10 - 13); veryhigh (>13);very low (0 - 3.5); low (3.5 - 7);medium (7 - 10); high (10 - 13); veryhigh (>13)FI* -1744 to -1631; -1631 to -1519; -1519to -1407; -1407 to -1294; -1294 to -1182; -1182 to -1070; -1070 to -958;-958 to -845; -845 to -733; -733 to -621; -621 to -508; -508 to -396;-341 to -273; -273 to -205; -205 to -136; -136 to -68;TI* 2043 - 2117; 2117 - 2190; 2190 -2264;2264 - 2338; 2338 - 2412; 2412 - 2486;2448 - 2560; 2560 - 2634; 2634 - 2708;2708 - 2782; 2782 - 2856; 2856 - 2930;0 - 120; 120 - 240; 240 - 360; 360 - 480;480 - 601;RD* -77 to -47; -47 to -17; -17 to 12; 12 to41; 41 to 71; 71 to 101; 101 to 130; 130to 160; 160 to 190; 190 to 220; 220 to249; 249 to 279;113 to 81; 81 to 49; 49 to 16; 16 to-16; -16 to -48CP Yes, No Yes, NoCSERVS 0 - 4; 4 - 8; 8 - 12; 12 - 16; 16 - 20; 20- 24; 24 - 28; 28 - 32; 32 - 36; 36 - 40;0 - 4; 4 - 8; 8 - 12; 12 - 16; 16 - 20; 20- 24; 24 - 28; 28 - 32; 32 - 36; 36 - 40;RSERVS 0 - 7; 7 - 14; 14 - 21; 21 - 28; 28 - 35;35 - 42; 42 - 49; 49 - 56; 56 - 63; 63 -70;0 - 7; 7 - 14; 14 - 21; 21 - 28; 28 - 35;35 - 42; 42 - 49; 49 - 56; 56 - 63; 63 -70;∗ Time dependent (dynamic) nodes, ∗∗ CI = Cast Iron, DI = Ductile Iron, and ST = Steel906.2. MethodologyCPPDIAtime (t-1) time (t)VINTRDRSERSCSERSSCIPMATTNBRKSTIFIAGECPPDIAVINTRDCSERSSCIPMATTNBRKSTIFIAGERSERSFigure 6.4: Proposed DBN pipe failure prediction model (unrolled for two time slices)6.2.3 Model Validation and Implementation: Case Study forthe City of CalgaryThe proposed DBN model is demonstrated on the city of Calgary WSS pipes. The cityof Calgary is located in the province of Alberta, Canada at 51.05◦N, 114.06◦W and elevatedapproximately 1045m above mean sea level. According to Ko¨ppen-Geiger climate classifica-tion (Peel et al. 2007), the city of Calgary has a humid continental climate mainly known assevere winters, no dry season, warm summers and strong seasonality. Figure 6.5 shows themean maximum temperature, mean minimum temperature, mean temperature, and an averageprecipitation of the city of Calgary computed from the data recorded at Calgary InternationalAirport Meteorological Station (CALGARY INT’L A) from 1885 - 2012. Climate data recordedat this meteorological station, obtained from Environment Canada web-repository (EC 2015),is used for the annual and monthly climate analysis presented in this chapter.916.2. Methodology020406080100-20-100102030401 2 3 4 5 6 7 8 9 10 11 12P re ci pi t at i on  ( mm)T emp er at ur e (o C)  Months (January - December)Average precipitation Mean maximum temperatureMean temperature Mean minimum temperatureFigure 6.5: Temperature and precipitation chart for 1885 - 2012 climate normals at CALGARYINT’L A. meteorological stationThe city of Calgary WSS is composed of 21.2% DI, 15.2% CI, 3.7% Asbestos Cement (AC)and Concrete (CON), 2.9% ST, 0.8% CU and 56.3% plastic pipes (PVC, Polyethylene (PE)and Fusible Polyvinyl Chloride (FPVC)). The city’s GIS database (1956-2015) shows that thecity started recording the pipe break data from the year 1956. Table 6.4 summarizes the to-tal number of breaks recorded from 1956-2015 for each pipe material for their respective pipediameters. The record shows that metallic pipes experienced around 95% of the total breakswhereas 5% of the breaks are attributed to AC, CON, CU and plastic pipes (Figure 6.7). Refer-ring to Figure 6.6, an increasing trend of pipe failure records have been seen from 1956 - 1980.However, due to the implementation of a proactive approach in replacement and protection ofaging and deteriorating water mains by the city of Calgary, starting from 1980’s a decline inthe trend of pipe failures have been observed (City of Calgary 2014). The reduced trend inpipe failure record has happened as a result of corroded metallic pipes replacement with DIand PVC pipes, implementation of retrofit programs that added cathodic protection to existingwater mains, and other rehabilitation and renewal interventions. In this study, due to the highpercentage of breaks, susceptibility to corrosion and effect of seasonal climate variability, onlymetallic (CI, DI, and ST) pipes are considered for further analysis.The GIS database shows that excluding pipe diameters less than 100 mm, 3413 CI pipesexperienced 8113 breaks and 2191 DI pipes experienced 5341 breaks during the years 1956-2015.The failure data summarized in Figure 6.8 shows that from early 1980’s the city of Calgaryhave been able to reduce the pipe breaks caused by the human (operator) error. However, thepipe failure induced by corrosion still plays a significant role in contributing to pipe breaks(Figure 6.8). Analysis of the data showed that 58.70%, 1.35% and 39.95% of the failures were926.2. Methodologycaused by corrosion, human (operator) error, and unknown reason, respectively. The recordedtotal number of monthly CI and DI pipes failure from 2000 to 2015, presented in Figure 6.9,also indicate that climatic seasonality plays a major role in pipe failures.Table 6.4: Total number of recorded breaks for different pipe material and diameterPipe materialPipe diameter (mm)100 125 150 200 250 300 350 400 450 500 600-1950 Grand totalAC 0 0 114 65 44 44 3 72 18 0 0 360CI 267 5038 976 830 649 36 167 45 50 55 8113CON 0 0 0 0 0 0 0 12 2 4 29 47DI 114 2317 1290 879 614 125 0 2 0 5341PLASTIC 0 3 100 63 22 20 0 8 0 0 1 217ST 0 0 7 1 3 4 0 9 2 21 54 101Grand Total 381 3 7576 2395 1778 1331 39 393 67 77 139 14179001002003004001954 1969 1984 1999 2014T ot al  numb er  of  br ea ksTime (year)CI DIFigure 6.6: Failure records of CI and DI pipes from 1956 - 2014: City of Calgary936.2. MethodologyAC(2.54%)CI(57.16%)CON(0.33%)CU(0.10%)DI(37.63%)PLASTIC1%ST(0.71%)Figure 6.7: Percentage of recorded pipe failures based on pipe material.0.00.51.01.52.02.53.003060901201501955 1975 1995 2015100's of workmanship caused brekas1 00 ' s of  pi pe  b re ak s Time (year)Breaks caused by external corrosion (C )Breaks caused by unknown (UNK)Total breaks (C, W and UNK)Breaks caused by workmanship (W)Figure 6.8: Comparison of cumulative human (operator) and corrosion induced breaks (1956 -2015): city of Calgary metallic pipes946.2. Methodology0102030401-Jan-00 1-Jul-02 1-Jan-05 1-Jul-07 1-Jan-10 1-Jul-12 1-Jan-15Numb er  of  pi pe  b re ak sMonthsCI DIFigure 6.9: Monthly pipe breaks in the City of Calgary from 2000 - 2015The FI and TI are computed from the maximum and the minimum temperature recordedat CCALGARY INT’L A meteorological station. Figures 6.10 and 6.12 show the annual andaverage seasonal weather related factors computed over a period of 1956-2015 and 2000-2015,respectively. The seasonal comparison of recorded PPT; and computed monthly FI, TI, Evapo-transpiration (ET), and RD for the period of 2000 - 2015 at CALGARY INT’L A meteorologicalstation are presented in Figure 6.11. Comparing annual and monthly weather factors considered,the monthly computed climate factors reasonably indicate the seasonal variation of each factorfor the case study area.-1000100200300-3000-10001000300050001955 1965 1975 1985 1995 2005 2015RD ( mm)F I a nd  T I ( De gr ee -d ay s)YearTI FI RDFigure 6.10: Annual TI, FI and RD at CALGARY INT’L A from 1956 - 2015956.2. Methodology0501001502002501-Jan-00 12-Sep-03 24-May-07 2-Feb-11 14-Oct-14PPT and PET (mm)MonthPETPPT(a)(e)01002003004005006001-Jan-00 12-Sep-03 24-May-07 2-Feb-11 14-Oct-14TI (Degree-days)-400-300-200-10001-Jan-00 12-Sep-03 24-May-07 2-Feb-11 14-Oct-14FI (Degree-days) (c)(b)-200-10001001-Jan-00 12-Sep-03 24-May-07 2-Feb-11 14-Oct-14RD (mm)Months(d)Figure 6.11: Recorded and computed climatic factors (a) PPT and PET, (b) TI, (c) FI and (d)RD from 2000 - 2015966.3. Result and Discussion0255075100-400-20002004006001 2 3 4 5 6 7 8 9 10 11 12P PT  ( mm)T I a nd  F I (o Cd )   Months (January-Decemebr)FI. TI. PPT.Figure 6.12: Average TI, FI and PPT at CALGARY INT’L A from 2000 - 20156.3 Result and Discussion6.3.1 Sensitivity AnalysisSensitivity analysis helps to understand how the variations in the input to a model affectthe model’s output (Sturlaugson and Sheppard 2015). The most commonly reported methodsof sensitivity analysis in DBN and BBN type models are entropy reduction (mutual informa-tion), variance reduction and variance of beliefs estimations (Bednarski et al. 2004; Coupe´ andvan der Gaag 2002; Norsys 2014; Pearl 1988). In this chapter, a variance reduction sensitivityanalysis method, implemented in Netica, is used to compute the normalized variance reductionof each pipe failure factors (Norsys 2014; Pearl 1988). The mathematical formulation of thevariance reduction method is presented in subsection 4.3.1. The analysis was performed on theTNBRKS node at a representative four-time slices. Figure 6.13 shows the normalized variancereduction of pipe failure factors for each time slices.Operational factorsAge and NOPF Environmental factorsPipe physical attribute010203040AGE NOPF CP CSERVS RSERVS PDIA PLNG PMAT VINT FI TI RD SCINor ma li ze d VRPipe failure factors1971198019902000Figure 6.13: DBN sensitivity analysis result for four-time slices976.3. Result and DiscussionThe figure indicates that there is an increasing and decreasing trend in variance reductionfor CP and SCI, respectively. The introduction of CP might be the reason for the drop ofvariance reduction for SCI. A slightly increasing trend is also seen for NOPF, RSERVS, andTI while there is a decreasing effect for the FI. An increase in the previous number failures,the number of residential connections and the thawing effect through the considered years canbe taken as an explanation for the increasing trends of NOPF, RSERVS, and TI. A slightlydecrease in variance reduction of FI can also be attributed to the decline in the freezing periodof the region. As indicated in this Figure, the higher variance reduction attributed to pipeage and NOPF combined are higher compared to the variance reduction of environmental,pipe physical, and operational factors. Pipe age, NOPF, and pipe physical factors are notthe impacting factors of pipe failures, but, influenced indirectly by the other factors such asoperational and environmental factors. For example, the higher the age of the pipe does notmean that it has been experienced frequent failures. The frequency of pipe failures might beas a result of direct and/or indirect impact of operational and environmental factors.6.3.2 Dynamic Bayesian Network Model ResultsAssessing the model performance helps to understand and quantitatively estimate the matchbetween the model predicted results and the recorded data. There are several performanceevaluation methods; however, in this study, the most frequently used methods are consideredto evaluate the predictive accuracy of the proposed DBN model. These are the Root MeanSquared Error (RMSE), the Coefficient of Determination (R2), and the Percent Bias (PBIAS).The equations of the considered evaluation criteria are given in Equations 6.10 – 6.12.RMSE =√√√√ 1nn∑i=1(Ri − Pi)2 (6.10)R2 = 1−∑ni=1(Ri − Pi)2∑ni=1(Ri − R¯i)2(6.11)PBIAS =∑ni=1Ri −∑ni=1 Pi∑ni=1Ri∗ 100 (6.12)where Ri is the number of the recorded pipe failures; R¯i is the mean of the recorded pipefailures; Pi is the predicted amount; n is a sample size; and k is the number of explanatoryvariables.The value of R2 is a measure of how well the model output represents the recorded data. R2986.3. Result and Discussion= 1 implies a perfect fit between measured and modeled data, whereas R2 = 0 means that thereis no match between observed and modeled output. The optimal value of PBIAS is zero, inwhich lower values indicate accurate model prediction. Positive and negative values of PBIASindicate model underestimation and overestimation bias, respectively (Gupta et al. 1999).The result (expected values) of the annual DBN pipe failure prediction model was comparedwith the recorded data from 1970 - 2015 for CI, DI, ST and the overall metallic pipes as presentedin Figure 6.14. The predicted number of pipe breaks for each pipe material are close to therecorded pipe breaks. The result of the DBN model trained using the data categorized based onpipe material reasonably predicted the total number of pipe breaks compared to the DBN modeltrained using combined metallic data. The DBN model trained using a combined metallic pipesdata over-predicted the total number of pipe breaks. Table 6.5 summarizes RMSE, PBIAS, andR2 of predicted versus recorded pipe breaks for the annual and monthly DBN models.Table 6.5: Comparison of predicted versus recorded annual pipe breaks from 1970-2015Evaluation methodDBN model trained using data based oncombined (metallic) pipesDBN models trained using data based onspecific pipe materialCI DI STOverallCI DI STOverall(metallic pipes) (metallic pipes)RMSE 57.8 99.7 2.2 94.6 9.8 25.6 0.4 32.1PBIAS -13.8 -42.0 -34.2 -25.9 -5.0 -13.9 -0.3 -8.7R2 0.4 0.9 0.7 0.8 0.99 0.96 0.92 0.98Observations (year) 46As indicated in Figure 6.14, monthly DBN model was developed to assess the seasonalvariations of pipe breaks in the years 2000-2003. Figure 6.15 shows the comparison between thepredicted and recorded monthly total number of breaks for two models: trained with combined(metallic) data and trained using data related to specific pipe material. The result shows thatthe DBN models trained using specific pipe material related data performed well compared tothe DBN model trained using combined metallic pipes data. The monthly DBN model trainedusing a combined pipes data, the same as the annual DBN model result, over-predicted thetotal number of pipe breaks. Table 6.6 shows the predictive performance comparisons of theconsidered pipe failure prediction models.996.3. Result and DiscussionTable 6.6: Comparison of predicted versus recorded monthly pipe breaks from 2000-2003Evaluation methodDBN model trained using data based oncombined (metallic) pipesDBN models trained using data based onspecific pipe materialCI DI STOverallCI DI STOverall(metallic pipes) (metallic pipes)RMSE 6.5 14.3 0.1 14.4 2.12 4.28 0.11 5.25PBIAS -17.0 -66.3 -21.4 -42.9 -11.24 -18.24 -17.88 -14.95R2 0.82 0.67 0.97 0.71 0.94 0.91 0.94 0.94Observations (month) 461006.3. Result and Discussion01002003004001970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014YearRecordedPredicted (*)Predicted (**)a)025050075010001970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014Total number of breaksYearb)04812161970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014Yearc)025050075010001970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014Yeard)Figure 6.14: Comparison of predicted (expected value) (* DBN model trained using combineddata (CI, DI and ST pipes) and ** DBN model trained using data categorized based on pipematerial) and recorded number annual pipe breaks (a) CI, (b) DI, (c) ST and (d) Overall(metallic) pipes1016.4. Summary20.45 4.87 12.71 8.73 5.90 14.89 3.95 7.06 16.68 15.179.39 11.96 16.13 15.13 6.94 15.85 6.67 15.55 13.02 7.760.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0029.84 16.83 28.84 23.86 12.85 30.73 10.62 22.61 29.69 22.93020406080Jan-00 Oct-00 Jul-01 Apr-02 Jan-03 Oct-03MonthsRecordedPredicted (*)Predicted (**)(a)0204060Jan-00 Oct-00 Jul-01 Apr-02 Jan-03 Oct-03Number of breaksMonths(b)0123Jan-00 Oct-00 Jul-01 Apr-02 Jan-03 Oct-03Months(c)020406080Jan-00 Oct-00 Jul-01 Apr-02 Jan-03 Oct-03Months(d)Figure 6.15: Comparison of predicted (expected value) (* DBN model trained using combineddata (CI, DI and ST pipes) and ** DBN model trained using data categorized based on pipematerial) and recorded number monthly pipe breaks (a) CI, (b) DI, (c) ST and (d) Overall(metallic) pipes6.4 SummaryThis chapter introduces a new approach, DBN pipe failure prediction model, which con-siders different static, dynamic and operational pipe failure factors for pipe failure prediction.This new approach is demonstrated on the city of Calgary WSS’s metallic pipes. The pipephysical and operational characteristics data obtained from the city of Calgary; and climatedata recorded at CALGARY INT’L A meteorological station and obtained from EnvironmentCanada web page repository was utilized to train the CPT of the proposed DBN model. Annual1026.4. Summaryand monthly predictive models were presented; the annual model showed the prediction of thetotal number of pipe breaks annually and the monthly model showed the monthly total numberof breaks and the seasonal pattern of pipe breaks. The CPTs of each model were trained basedon two data sets: data of metallic pipes combined and data categorized based on specific pipematerials. The predicted number of pipe breaks for each model were close to the recorded pipebreaks, especially the result from the model trained by data categorized based on pipe material.The predictive performance of the proposed DBN pipe failure prediction models were assessedusing the RMSE, R2, and the PBIAS. The computational results have shown that the modelswere able to predict the annual and monthly pipe breaks and their seasonal break patterns.103Chapter 7: Forecasting Pipe Failure UsingClimate Model Projections – Bayesian ModelAveraging Approach 57.1 BackgroundRapidly changing climate combined with the aging and deterioration of WSS pipes presentsa significant challenge to most water utility managers and operators. Water transmission anddistribution pipes are most often susceptible to the risk of failure (breakage/burst/leakage)as a result of their spatial inaccessibility. Under the circumstances, limited information isavailable to understand their deterioration process. This chapter provides a modeling approach,Bayesian Model Averaging, for using climate attributes to forecast CI pipe failure rates. Thedata from the city of Calgary is used for the demonstration of the developed BMA approachwith statistically downscaled climate data from the CMIP5 integrated to operational factors,pipe physical attributes, and external soil corrosion. The significance of identified pipe failurecovariates to pipe failure rates is evaluated. Impact of climate change on the failure rate ofsmaller-sized pipe diameters (100, 150, and 200 mm) is also compared to the medium (250, 300,and 350) and larger-sized pipe diameters (400, 450, 500, and 600 mm).7.2 MethodologyThe proposed framework for developing BMA pipe failure forecasting model is describedin Figure 7.1. The input data for the BMA pipe failure forecasting models was processed.These data include downscaled climate scenarios (i.e., RCP 2.6, RCP 6, and RCP 8.5); data5A version of this chapter is under internal review for a possible publication in the peer-reviewed journalwith a title of “Forecasting Pipe Failure Using Climate Model Projections: A Bayesian Model Averaging Ap-proach”(Demissie et al. 2017a).1047.2. Methodologyrelated to operational factors and pipe physical attributes collected from the city of CalgaryGIS database; and predicted soil corrosivity index discussed in chapter 3. After evaluating thesignificance of the covariates, successive BMA pipe failure forecasting models were developed.The performances of the developed BMA pipe failure forecasting models was evaluated usingthe RMSE, PBIAS, and R2. In the end, the final model (Model 5) was applied to short-termto long-term pipe failure rate forecasting of small to large diameter pipe groups.Climate attributes from  climate models (FI, TI, and RD)Operational data(CP, VINT, RSERVS,  and CSERVS) Soil corrosivity index(SCI)Pipe attributes(diameter, material,  length )Short-term and long-termpipe failure forecasting: basd on  different climate scenarios(Model 5)Ba ye si an Mode l Ave ra gi ng( BMA)( at tr ibut e se le ct ions )Pipe failure prediction: for  training and hold-out datasetsModel performance evaluations  for training and hold-out data setsBMA: Pipe failure  prediction/forecasting model(Calibration and Validation)(Model 1-5)Figure 7.1: Proposed framework for pipe failure forecasting using BMA7.2.1 Bayesian Model AveragingApplication of model averaging approach to minimize model uncertainty came into exis-tence in early 1960’s. For example, Roberts (1965) proposed a distribution which combines twodifferent expert knowledge based on a weighted averaged of their posterior distributions. Basedon this distribution, Lemer (1998) presented the principles of BMA and its advantage, for thefirst time, in accounting for the uncertainty involved in selecting the best models. BMA is anaverage of the posterior distributions of the selected best models weighted by their respectiveposterior model probabilities (Lemer 1998; Penny et al. 2006; Wasserman 2000). BMA reducesthe potential overconfidence of predictions and incorporates the model and parameter uncer-tainty by averaging over a class of different competing models (Bhat et al. 2011; Eklund andKarlsson 2007). Hoeting et al. (1999) consider, BMA as an intuitively attractive solution to1057.2. Methodologythe problem of accounting for model uncertainty.Statistical models (e.g., linear models) most often ignore model uncertainty and considera single best model from a class of several possible alternative models (Bhat et al. 2011),although the selected model may not always be the best. However, BMA can be used tocombine uncertainties as a result of many competing models (Jo et al. 2012). BMA is anaverage of the posterior distributions of the selected best models weighted by their respectiveposterior model probabilities (Wasserman 2000). BMA reduces the potential overconfidence ofpredictions and incorporates the model and parameter uncertainty by averaging over a class ofdifferent competing models (Eklund and Karlsson 2007).If θ represents the quantity of interest (e.g., a parameter or a future observation), the modelaveraged posterior distribution of θ for a given data D can be expressed as,p (θ | D) =k∑k=1p (θ |Mk, D) p(Mk|D) (7.1)where M1, . . . ,Mk denotes the considered models; p (θ|Mk, D) is the posterior distribution of θunder model Mk; and p(Mk|D) is the posterior probability of model Mk (Hoeting et al. 1999;Wasserman 2000). The posterior probability for model Mk can be computed as (Hoeting et al.1999),p (Mk | D) = p (D |Mk) p (Mk)∑Kl=1 p (D |Ml) p (Ml)(7.2)where,p (D |Mk) =∫p (D | θk) p(θk|Mk)dθk (7.3)p (D |Mk), is the marginal likelihood of the model Mk; θk is the parameter of Mk (i.e., vector);pr(θk|Mk) is the prior distribution of θk; and p (Mk) is the prior probability of Mk. Theposterior mean and standard deviation of θ can be estimated as (Amini and Parmeter 2011),E [θ | D] =K∑k=1θˆkp (Mk | D) (7.4)V ar [θ | D] =K∑k=1(V ar [θ | D,Mk] +θˆ2k)p (Mk | D)−E [θ | D]2 (7.5)where,θˆk = E[θ|D,Mk] (7.6)1067.2. MethodologyThe effectiveness of the BMA is based on the specifications of the prior distributions,pr(θk|MK) and the model space prior p (M1) , . . . , p (Mk) (Chipman et al. 2001). The practicalapproach to prior specification, when the prior information is not known, is to construct anon-informative and semi-automatic formulation of priors that allow the posterior to accumu-late probability at or near the actual model that generated the data (Chipman et al. 2001).The most common non-informative model space prior p (M1) , . . . , p (Mk) is a uniform priorexpressed as,p (Mk) =1K(7.7)However, in practical cases, the integral in Equation 3 can be evaluated using the Markov ChainMonte Carlo (MCMC) simulation to approximate the posterior distributions of the model,particularly when more than fourteen covariates are considered (Amini and Parmeter 2011).7.2.2 Climatic Parameter IdentificationDetailed parameter identification for pipe failure model is already explained subsection 6.2.1.This section discusses only the pipe failure parameters attributed to climate. Statisticallydownscaled climate data (i.e., temperature and precipitation) from CMIP5 experiments is usedto compute the climatic indexes (i.e., FI, TI, and RD). The PCIC provides forecasted climatedata from CMIP5 project through their web repository. These data include CMIP5 historicalruns for 1950 – 2100 corresponding to RCP 2.6, RCP 4.5, and RCP 8.5 emission scenarios(PCIC 2014). In this study, pipe failure comparison was made based on the PCIC climate datacorresponding to climate emission scenarios, RCP 2.6 and RCP 8.5, respectively. The climatedata was downscaled from the GCMs spatial resolution (grid cells) of 2.79◦ x 2.81◦ to roughly10km local spatial resolution. As shown in Figure 7.2, each spatial unit of the study area isgiven a unique code (e.g., 44) for which time series of climate attributes such as temperature andprecipitation are assigned. Then, time series of FI, TI and RD are computed for each spatialunit. The methods used to compute the FI, TI, and RD are presented in subsubsection 6.2.1.2.In the end, the computed climatic values are populated to the pipes physically located in thegrid cells using an Arc GIS spatial join tool (ESRI 2011). Figure 7.3 shows a typical example ofthe downscaled time series of Average Temperature (TAVG) and PPT; and computed FI, TI,and RD for grid cell 44 corresponding to the scenarios RCP 2.6, and RCP 8.5. Pipe attributesand operation factors are extracted from the city of Calgary GIS database which ranges from1956 - 2014. The database also consists of pipe failure history pipe failure rates by the age of1077.2. Methodologythe pipe presented in Figure 7.4), and several records of soil information such as, soil resistivity,soil moisture content, soil pH, etc. The descriptions of these parameters are summarized inTable 6.111 313534333216 26 46 56 66 7621 41 51 61 7115 25 453665 7514 24 44 54 64 7413 23 43 53 63 7312 22 42 52 62 7255Figure 7.2: Spatial grid cells for statistical downscaling of climatic attributes for the city ofCalgary.1087.2. Methodology0100200300Monthly PPT (mm)PPT RCP 2.6 PPT RCP 8.5-35-1501535Monthly TAVG (oc)TAVG RCP 2.6 TAVG RCP 8.5-750-550-350-1500Monthly FI(degree-days)FI RCP 2.6 FI RCP 8.50300600900Monthly TI(degree-days) TI RCP 2.6 TI RCP 8.51960 1980 2000 2020 2040 2060 2080 2100-1001020Monthly RD(mm)RD RCP 2.6 RD RCP 8.5Figure 7.3: PPT, TAVG, FI, TI, and RD for RCP 2.6 and RCP 8.5 at grid cell 441097.2. Methodology0 20 40 60 80 100Age (year)0246810Pipe failure rate (no/km/year)Figure 7.4: Failure rate of the city of Calgary’s CI pipes by their ages7.2.3 Covariate Selection MethodsDecision of choosing variables to be included in the final model are most often challengingand misleading, especially when a large number of covariates are used to model the responsevariable (Walli 2010). In pipe failure modeling, researchers considered different covariates.However, the type and nature of considered covariates so far vary as a result of different en-vironmental condition in which the pipes are operating (e.g., climatic condition and externalsoil corrosion); pipe physical attributes (e.g., length, diameter, material of pipes); operationalpractices; and the quality of water transported. A frequentist approach is a typical way ofdetermining the significance of a covariate in representing a given response variable (Johnson1999). This approach is based on the computed p-values1 of the covariates. A covariate with ap-value greater than α (e.g., α = 0.05 or 95% confidence interval) is considered be a covariatewith an insignificant effect on the response variable (i.e., the changes in a covariate with highp-value is unlikely to affect the response variable). Similarly, BMA approach is the most widely1p-vale is a probability which evaluates evaluates how well the sample data support the argument that thenull hypothesis is true (StatsDirect 2017). Higher p-value means the data is likely with a true null, where aslower p-value means the data is unlikely with a true null.1107.2. Methodologyapplied method to identify the importance of covariates. In this approach, the importance ofthe covariates are determined based on the Bayesian Posterior Inclusion Probability (PIP) (i.e.,the probability that the covariates should be included in the finally selected model (Viallefontet al. 2001). model 1(training dataset: 1956-1994)model 2(training dataset: 1956-1999)5,10,15,and 20 years prediction5,10, and 15 years predictionmodel 3(training dataset: 1956-2004) 5 and 10 years predictionmodel 4(training dataset: 1956-2009)model 5(training dataset: 1956-2014)5 years predictionT=1956 T=2014forecast horizonFigure 7.5: Training and hold-out (test) datasets considered for models 1-57.2.4 Bayesian Model Averaging Development, Training andValidationMost of the methods reported in the literature use a randomized process to divide the datainto training and hold-out datasets (Efron and Tibshirani 1997). However, in this study, thedata is assumed to be dependent on successive time space (i.e., failure in the previous monthmight have an effect on the failure of the current month). In order to understand the predictivelikelihood of BMA models 1-5, the data is successively split into training and hold-out samplesas presented in Figure 7.5. The purpose of considering successive training and hold-out samplesis to understand the parameter change in posterior distribution through time and the predictivecapability of the developed model, respectively. As the information is unknown at the beginningof the data (1956), a non-informative prior (i.e., uniform prior) is considered. Based on thedataset presented in Figure 7.5, the BMA pipe failure models are developed using a Bayesianmodel selection. The models are trained using the selected set of pipes from the City of Calgarywater supply system GIS database that have experienced at least one breaks in the period of1956-2014. The trained models are then tested and applied to predict the pipe failures for1117.3. Results and Discussiondifferent Bayesian Credible Intervals (BCI).7.3 Results and DiscussionTo forecast the future pipe failure rates for the city of Calgary, the BMA model is developedconsidering different factors. The developed model considers pipe physical attributes, failure his-tory, operational parameters, external soil corrosion, and downscaled climatic attribute. In thefollowing subsections, the BMA model training, testing, evaluation, and prediction/forecastingresults will be discussed.7.3.1 Covariate SelectionTable 7.1 presents the covariate selection result of the frequentist and BMA approaches.The presented result shows that covariates with the PIP less than 50% are mostly consideredto be non-significant covariates in the frequentist approach. Figure 7.6 describes the PIP foreach covariates of Model 1-5 and Figure 7.7 compares the PIP of climate covariates for Model1, Model 3, and Model 5. As described in Figure 7.6, a decrease in a PIP value of SCI overtime is observed. This might be as a result of introduced cathodic protection starting from late1980’s. Figures 7.6 and 7.7 also show that there is an increase in PIP values for RD, TI andCSERVS. The increase in values of these covariates indicates there is a time sensitive impact ofthe warming climate, the introduction of additional commercial/industrial service connections,and the introduction of cathodic protections on the rate of pipe failures. In this study, as therecould be a variation in the effect of covariates on the pipe failure over time, all the identifiedcovariates are considered and included in the finally chosen model for further analysis.1127.3. Results and DiscussionTable 7.1: Frequentist and BMA variable selection approachesCovariates Frequentist Approach (Model 5) BMA (Model 5)β SE p-value E(β|D) SD(β |D) pr(βi 6= 0|D)AGE -0.0280 0.00036 < 0.0001 -0.028033 0.000360 100%CP -0.1817 0.01434 < 0.0001 -0.182428 0.014693 100%CSERVS -0.0075 0.00193 0.0001 -0.007834 0.002100 99%FI -0.0001 0.00006 0.3576 -0.000001 0.000013 4%NOPF -0.0096 0.00310 0.0020 -0.007020 0.005061 73%PDIA -0.0002 0.00010 0.0868 -0.000016 0.000058 9%PLNG -0.0052 0.00005 <0.0001 -0.005222 0.000054 100%RD 0.0031 0.00337 0.3560 0.002559 0.003340 62%RSERVS -0.0064 0.00056 < 0.0001 -0.006415 0.000559 100%SCI 0.0037 0.00147 0.0119 0.001069 0.001819 30%TI 0.0001 0.00007 0.1403 0.000051 0.000060 47%VINT 0.0000 0.00001 <0.0001 0.000037 0.000007 100%Figure 7.6: Posterior inclusion probabilities of covariates for Model 1 to 51137.3. Results and DiscussionFigure 7.7: Standardized coefficients and PIP of FI and TI for Model 1, Model 3, and Model 57.3.2 Bayesian Model Averaging Training ResultsModel prediction performance assessment helps to understand and quantitatively estimatehow the model predicted results match the recorded data. The most frequently used modelperformance evaluation methods are the RMSE, the R2, and the PBIAS, which can computedbased on the Equations 6.10 – 6.12Table 7.2 shows the predictive performance evaluations of the considered BMA models 1 to5. The result showed a decrease in RMSE; and an increase in glspbias (i.e., enhanced predictiveperformance). The result of the performance evaluation indicated the influence of the successive1147.3. Results and Discussioninclusion of data to the BMA models based on the forward time. Figures 7.8 and 7.9 depicts thecomparison between the predicted and the recorded monthly number of pipe breaks for Model5. According to these figures, the model has shown an over prediction which agrees with theresult of PBIAS presented in Table 7.2. Moreover, Figure 7.9 indicates that the BMA modelpredicted the monthly pipe failures very well, particularly the peak pipe break periods.Table 7.2: Training performance for the considered models (CI pipes)Models R2 RMSE PBIAS1 0.91 2.633 -10.572 0.91 2.539 -10.143 0.91 2.493 -9.634 0.92 2.492 -9.315 0.93 2.482 -9.150 15 30 45 60 75 90Recorded monthly pipe breaks0153045607590Predicted monthly pipe breaksFigure 7.8: Predicted versus recorded monthly CI pipe breaks for Model 51157.3. Results and Discussion1960 1970 1980 1990 2000 2010Time (months)0306090Number of breaksRecordedPredictedFigure 7.9: Comparison between observed and predicted monthly number of CI pipe breaks forModel 57.3.3 Bayesian Model Averaging Testing ResultsThe BMA models (Model 1 to 4) demonstrated in Figure 7.5, are used to predict/forecast5-20 years to the future to examine the credibility of the model that we have to use for thepipe failure forecasting. Due to the range of available data, only Model 1-4 are used to pre-dict/forecast for a maximum of 20, 15, 10, and 5 years respectively. As described in Table 7.3and Figure 7.11, the performance of each model has changed significantly over the consideredsuccessive time period. Figure 7.10 also describes the comparison of 5 and 20 years’ predic-tion/forecasts for test datasets, 5%, 50%, and 95% BCI using Model 1. The figure pinpointsthat the probability of getting a particular failure rate in 20 years prediction is higher comparedto the 5 years prediction. The recorded CI data, which agrees with this result, also shows thatthere is less and controlled number of pipe breaks in the prediction period of 20 years (1995 -2014) compared to the training period of Model 1 (1956 - 1994).1167.3. Results and DiscussionTable 7.3: The performance of the considered models for different prediction/forecasting horizon(CI pipes)Model Prediction/forecasting horizon R2 RMSE PBIASModel 1 5 years 0.90 1.84 -12.4610 years 0.93 1.73 -9.5415 years 0.95 1.60 -5.5020 years 0.95 1.62 -1.33Model 2 5 years 0.95 1.30 -1.3310 years 0.95 1.63 -1.3315 years 0.96 1.47 2.67Model 3 5 years 0.96 1.15 1.5410 years 0.96 1.44 5.39Model 4 5 years 0.98 1.14 4.620 0.4 0.8 1.2 1.6 2Pipe failure rate (no/km/year)00.20.40.60.81Cumulative probability 5 years test dataset  5% BCI (5 years)95% BCI (5 years)20 years test dataset  5% BCI (20 years)95% BCI (20 years)Figure 7.10: Model 1: 5 and 20 years’ predictive cumulative probability distributions for CIpipes1177.3. Results and Discussion0 15 30 45 60Time (Months: 1995-1999)010203040Number of breaks (a) Recorded Predicted0 15 30 45 60Time (Months: 2000-2004)010203040Number of breaks (b) Recorded Predicted0 15 30 45 60Time (Months: 2005-2009)010203040Number of breaks (c) Recorded Predicted0 15 30 45 60Time (Months: 2010-2014)010203040Number of breaks (d) Recorded PredictedFigure 7.11: 5 years predictive performance of Models 1-4 (a - d) for CI pipes.7.3.4 Pipe Failure Rate ForecastingThe considered CI pipes are categorized as smaller diameters (100, 150, and 200 mm),medium diameters (250, 300, and 350), and large diameters (400, 450, 500, and 600 mm),summarized in Table 7.4, in order to forecast the future group pipe failure rates. Based onthese categories, the Final BMA model (Model 5) is applied to forecast short-term (5 years)1187.3. Results and Discussionto long-term (20 years) pipe failure rates. The BMA model considered the climate covariatesderived from RCP 8.5, RCP 6, and RCP 2.6 in addition to the other pipe failure parameters.However, this study is unable to identify a clear difference in pipe failure rates between theemission scenarios in the forecast horizon of 20 years. Therefore, the analysis presented in thischapter is only based on the BMA model which considered the climate covariates derived fromRCP 6 emission scenario.Table 7.4: Summary of the city of Calgary CI pipes data properties by 2014PipecategoryDiameters(mm)Numberof pipesNumber ofbreaksLength (kilo-meters)Minimumage by 2014(years)Maximumage by 2014(years)Small 100 99 267 33.85 48 104150 2098 5038 967.41 47 104200 439 976 173.05 47 104Medium 250 413 830 132.62 46 104300 301 649 101.54 46 104350 8 36 6.63 61 63Large 400 47 167 25.66 51 104450 19 45 7.71 50 104500 15 50 11.44 47 104600 14 55 11.63 60 63Figure 7.12 describes the cumulative probability of pipe failure rates for the explainedcategory of pipes. The result indicates that for all the categories of pipes, the probability ofgetting highest pipe failure is expected to be lower in long-term forecast compared to the shortterm forecast. Therefore, the result indicated a decrease in pipe failure rates in a 20 years timehorizon. The decreased pipe failure rates, might be for the fact that the climate covariates areless sensitive (i.e., identified in covariate selection section), the implementation of preventiveaction such as cathodic protections by the city of Calgary from late 1980’s (City of Calgary2014). The application of cathodic protection has a significant effect especially in reducing thepipe failures as result of external soil corrosion (Shipilov and Le May 2006). Over all, slightlythe highest pipe breakage rates are attributed to the smaller-sized diameter pipes compared tothe medium and larger-sized diameter pipes.1197.3. Results and Discussion0 0.1 0.2 0.3 0.4 0.5 0.600.250.50.751Cumulative probability(a)  5 years10 years15 years20 years0 0.1 0.2 0.3 0.4 0.5 0.600.250.50.751Cumulative probability(b)  5 years10 years15 years20 years0 0.1 0.2 0.3 0.4 0.5 0.6Pipe failure rates (no/km/year)00.250.50.751Cumulative probability(c)  5 years10 years15 years20 yearsFigure 7.12: Cumulative probability curve of expected pipe failure rates for (a) large, (b)medium, and (c) small diametersFigures 7.13 and 7.14 depict the scatter plot of 5 and 20 years forecast, respectively, forsmaller-sized and larger-sized pipes failure rate for 5%, 50%, and 95% BCI. The figures explicitlyindicate that the pipe failure rates show a decreasing trend with an increasing pipe age. Thedecreased trend could be as a result of the decrease in the significance of the climate covariatesor the introduction of intervention actions. Thcmais result agrees with the pipe failure rate1207.3. Results and Discussiontraining data presented in Figure 7.4. The scattered pipe failure rates noticed in Figure 7.13(a to f) shows the age group of pipes during the five year pipe failure forecast period (2015- 2019). The highest pipe failure rate was expected as presented in both figures for the 95%BCI(i.e., BCI is the credibility interval (e.g., 5%, 50%, and 95%) that the Bayesian parameter θcovers the parameter’s 5%, 50%, and 95% distribution, respectively) compared to the 5% BCI.In addition, the number of pipes and pipe failure record considered also reflected the differencesin the groups of smaller and larger pipe failure rates. As a result of the training data for theage group of 45 to 104 years (Table 7.4 and Figure 7.4), similar pattern and band of pipe failurerates are noticed for the 5 and 20 years forecast.1217.3. Results and Discussion45 65 85 10500.30.60.91.2 (d)5% BCI45 65 85 10500.30.60.91.2 (e)50% BCI45 65 85 105Age (year)00.30.60.91.2 (f)95% BCI45 65 85 10500.30.60.91.2Pipe failure rate (no/km/year) (a)5% BCI45 65 85 10500.30.60.91.2Pipe failure rate (no/km/year) (b)50% BCI45 65 85 105Age (year)00.30.60.91.2Pipe failure rate (no/km/year) (c)95% BCIFigure 7.13: 5 years pipe failure rate forecast for CI pipes with smaller diameters (a to c), andlarger diameters (d to f)1227.3. Results and Discussion45 65 85 105 12500.30.60.91.2Pipe failure rate (no/km/year) (a)5% BCI45 65 85 105 12500.30.60.91.2 (d)5% BCI45 65 85 105 12500.30.60.91.2Pipe failure rate (no/km/year) (b)50% BCI45 65 85 105 12500.30.60.91.2 (e)50% BCI45 65 85 105 125Age (year)00.30.60.91.2Pipe failure rate (no/km/year) (c)95% BCI45 65 85 105 125Age (year)00.30.60.91.2 (f)95% BCIFigure 7.14: 20 years pipe failure rate forecast CI pipes with smaller (a to c) and larger diameters(c to f)1237.4. Summary7.4 SummaryIn this chapter, a Bayesian model averaging was developed to forecast future pipe failurerates. The developed model was trained and tested using the data collected by the city ofCalgary and climate covariates derived from different RCPs emission scenarios. A successivetraining and test datasets division based on the year/month of pipe failure was consideredto understand the credibility of the developed model for future pipe failure forecasting. Thepredictive credibility of the proposed BMA model was evaluated using the RMSE, PBIAS andR2. The computed indicated that the developed BMA model was able to predict the monthlypipe breaks reasonably well. The final model (Model 5) was considered to forecast the futurepipe failure rates. The forecasted pipe failure rates showed that there is a decrease in pipe failurerates in the next 20 years as a result of considered interventions such as cathodic protectionsand projected changes in the climate covariates. While climate covariates derived from thedifferent RCP emission scenarios were used to develop BMA models, no significant differenceswere noticed in the pipe failure rates between the different RCPs in the forecast horizon of 20years.124Chapter 8: Conclusions and Recommenda-tions8.1 Summary and ConclusionsThe primary objective of this research was to develop a Bayesian model for the predictionWSS pipe and valve failure, with a special consideration of the effect soil corrosivity and climatechange. The effect of the characteristics of the surrounding soil and variable nature of climateare the most important factors in determining the frequency of pipe failure compared to the pipeattributes and operational factors. These factors are most often dynamic (time-dependent) innature. Considering this nature in designing a new WSS system or planning and implementinga renewal and rehabilitation programs for an existing WSS is a benefit for water utilities.In order to predict the degree corrosivity of the surrounding environment, a BBN-SCImodel was developed. The developed model was used to combine multiple information sources(i.e., expert opinion, measured data) and model the inter-dependency among contributing soilproperties and with SCI. The validation result of the study showed that the model was able toindicate the most corrosion-prone regions of the case study area. This result can help decisionmaker to opt out appropriate renewal and rehabilitation programs for the existing WSS and tochoose corrosion resistant pipe material in designing the new WSS.The developed BBN-SCI was extended to RSL perdition model by integrating with a math-ematical model (i.e., Rajani et al. (2000). The input parameters for the mathematical modelwas estimated using on the BBN-SCI model. The condition assessment data (i.e., pit depth)utilized in this study was measured/determined using either glsndt or destructive testing duringregular operational and condition assessment period by the city of Calgary. In the end, a BBNsensitivity analysis and MCs was applied to understand the effect of input parameters and onthe remaining service life of metallic pipes and the proposed SI. The developed RSL model1258.1. Summary and Conclusionsis one of the contributions for pipe operators and decision makers in planning short-term andlong-term proactive renewal and rehabilitation programs.The failure of appurtenances such as valves might have a tremendous impact on the in-tegrity of water distribution pipes. In the developed BBN-FMEA model, various scenarios ofvalve failure modes have been identified. Similar to the metallic pipe, valves are also susceptibleto the impact of external corrosion. Hence, from the identified failure scenarios, valve failuredue to external corrosion (i.e., corrosion failure scenario) was selected for demonstration. Sev-eral types of valves are involved in the operation of water systems; however, isolation valvesare chosen, in this study, due to susceptibility to failure as a result of their operational char-acteristics. Finally, the corrosion failure scenario was extended into influence diagram baseddecision making, where the operator/decision maker confirms the degree of satisfaction of themodel result using condition assessment data or expert knowledge.The DBN model introduces a new approach to model a time-dependent system. Pipe failurefactors such as pipe attributes, operational characteristics, soil properties and climate parame-ters are considered. The model was applied to annual and monthly and monthly pipe failures.The analysis of the model result shows that the model was able to identify the significant impactof the considered parameters through time. For instance, in this study, a decreased impact ofFI and SCI; and an increased influence of CP, RD, and TI was observed. The trend in thesignificance of pipe failure factors shows that there is a considerable change in pipe failure dueto the effects of warming climate and operational practices such as CP and pipe replacementinterventions. Hence, this model/methodology can be an asset for utilities to evaluate theimportance of time-dependent factors on their water distribution systems.The BMA model was aimed to assess the impact of climate factors on pipe failure rates byintegrating with climate projections. BMA was used to forecast the future pipe failure ratesfor CI pipes. The BMA covariate selection method adopted also indicated similar parametersignificance result obtained using the DBN model. Even though there was no difference noticedin the pipe failure rates as a result of various climate scenarios, the model was able to assess theeffects of climate change on the different category of pipe diameters and long-term to short-termpipe failure rates. The model result also shows that there is a decreasing trend of pipe failurerates in the future. The climate parameters are found to be less sensitive; however, the possiblereasons for the decreased rates of CI pipes might be due to the implementations of renewal andrehabilitation programs by the city of Calgary from early 1980’s.1268.2. Originality and Contributions8.2 Originality and ContributionsThe proposed research is one of the few studies that investigated the effect of dynamic (time-dependent), static and operational factors on pipe failure. Besides, it is one of the few methodsconsidered the prioritization of water supply system valves using Bayesian belief network basedfailure mode and effect analysis. Lack and insufficiency of collected data/information andlimited resources are an inevitable phenomenon for water utilities. Water utilities have alsobeen lacking a comprehensive and general model for investigating factors which contribute topipe failure.The proposed framework, in general, will aid water utility managers and operators to makean efficient, effective and informed decision making for designing of new systems or planningand implementing either pipes and valves condition assessment or proactive rehabilitation andreplacement programs. Specifically, the most outstanding contributions of this research aresummarized as follows: The developed BBN-SCI model can consider the scarcity of data and missing data prob-lem by combining Engineering skills and empirical evidence. The model is also able toinvestigate the inter-dependency between soil parameters and their effects on soil corrosiv-ity index. This model can be used to identify the hot spot and cold spot soil corrosivityareas. It can also help water utilities in planning and implementation of renewal andrehabilitation programs for metallic pipe assets. Besides, the model can also be used asinput for indicating the most corrosion-prone areas to pipe in the design of water supplysystem, specifically, in the selection of system’s pipe material. The topology of the devel-oped BBN-SCI model can be further adapted to other cities by training the CPT usingan appropriate expert and empirical evidence. The developed RSL model will be insensitive to the scarcity of data and missing dataproblem as it was considered to combine different data/information sources. It is alsoflexible in permitting further development of the model which can be used for real-timemonitoring of metallic pipe assets. In general, the developed model was able to integratethe external aggressiveness of soil environment to other data/information sources in theprediction of RSL of the metallic pipes. The developed model will be a fundamentalcontribution to implementing a proactive asset management strategies for metallic pipeassets in any water utilities.1278.3. Limitations The proposed BBN-FMEA model can be utilized to provide a decision maker for strategic,tactic or operational level planning and decision making. For strategic and tactic leveldecision making, the model can be able to identify the most vulnerable and at risk valvesin the water supply system (i.e. isolation valves). On the other hand, for the day today operational level decision making, the model can identify the high priority valves forscheduling repair, maintenance or replacement actions. Therefore, the proposed modelaimed to help the decision makers to act proactively and avoid the consequences of valvefailure which might be undesirable. The proposed DBN pipe failure models are robust and valid to help utility managers andengineers to predict the total annually, and monthly pipe breaks either for a single pipeor overall pipe systems. The result of the developed model can be further integrated withmore general WSS failure risk assessment tools and used for long-term or short-term pipesystem rehabilitation and renewal planning and implementations. The proposed modeland the presented pipe break analysis can also be useful for academicians, engineers, andpractitioners in the field. The proposed BMA approach demonstrates that the model can be implemented for in-formed decision making by water utility managers and operators for short to long-termplanning, and implementation of rehabilitation and renewal programs by incorporatingthe effect of climate change on pipe failure. This model can be extended to other waterutilities with similar problems. More importantly, the study identified the pipe failurerates on a monthly basis for different groups of pipes.8.3 Limitations In the BBN-SCI model, due to limited time-dependent soil data, the study assumedsoil corrosivity index as a static variable and only applied static Bayesian belief networkapproach. For the developed DBN pipe failure model, as a result of increased time slices which leadsto rapid growth of the DBN network and computational complexity, the inter-dependencyamong the considered pipe failure factors are not taken into account. The proposed pipe failure models (DBN and BMA) are both developed based on the pipe1288.4. Recommendations for Future Researchfailure data, in which the considered pipes experienced at least one pipe breaks in theirentire lifetime. In order to verify the identified failure scenarios in the developed BBN-FMEA model, inaddition to expert knowledge, operational, failure event, and condition assessment dataare extremely important.8.4 Recommendations for Future Research The developed BBN-SCI model, given the time and spatial resolution of data, can beextended to time-dependent soil corrosivity index model using dynamic Bayesian network. Given the limitation of DBN pipe failure models, the future work is to improve themodel by examining the cause and effect relationship between the failure factors. Be-sides, DBN model can be further enhanced, by integrating with the hydraulic models, topredict/forecast better annual and/or the monthly number of pipe failures. The DBN and BMA pipe failure models need further studies in the future to accommodatethe pipe categories which experienced no failures in order to gain more confidence ininformed decision making. 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(2000). “System design: An overview.” Water distribution systems handbook, 1–3.→ pages 26149Appendix150Appendix A: TablesTable A.1: Summary of available NDT technologies and their applicability to different waterdistribution pipesTechnology: available methodsMetallic Concrete PolyCI DI WS CPP/PCCPAC GRP PVC/uPVCPEDirect pit depth measurement: pointed mi-crometer or needle-point depth gauge, gridwith ultrasonic spot measurement, auto-mated ultrasonic scanner, and laser rangemeasurementX − −Visual inspection: operator entry inspec-tion, CCTV inspection, video endoscope,3D optical scanning, laser profiling andhandy scan 3DX X ?Electromagnetic inspection: magnetic fluxleakage, remote field eddy current, broadband electromagnetic, pulsed eddy current,ultra-wide band pulsed radar and groundpenetrating radarX X −Acoustic inspection: sonar profile, impactecho, acoustic emission and leak detectionX X XContinued on next page151Appendix A. TablesTable A.1 – continued from previous pageTechnology: available methodsMetallic Concrete PolyCI DI WS CPP/PCCPAC GRP PVC/uPVCPEUltrasonic testing: continuous measure,discrete measure, phased array, combinedultrasonic testing inspection and seismicpulse echoX(a) − ?Pipeline current mapper: X − −Radiographic testing: X − −Thermographic testing: X − −Pipe condition assessment from soil prop-erties: linear polarization resistances, soilproperties, soil resistivity, soil corrosivityand pipe to soil potential surveyX ? ?Sensor technologies: corrosion rate sensor,acoustic emission sensor, magnetostrictivesensors, conformable and flexible eddy cur-rent array, flexible ultrasonic transducer,guided wave sensor, damage sensor, mi-crowave back-scattering sensor and fibre-optic sensor and wireless sensor networksfor pipesX X ?(a) Due to larger grain structure ultrasonic thickness testing method is less accurate forpit cast iron, CI = cast iron, DI = ductile iron, WS = welded steel, CPP/PCCP =concrete pressure/pre-stressed concrete cylinder pipe, AC = Asbestos cement, GRP =glass-fibre reinforced polyester, PV C/uPV C = polyvinyl chloride/un-plasticized PVC, PE= polyethylene, X: available, ?: may/may not work, and −: not available.152Appendix A. TablesTable A.2: Available climate model output for different models and experimentsModels Experiment Experiment ID (Experiment name)CanESM2 CMIP5 1pctCO2 (1 percent per year CO2), abrupt4xCO2 (abrupt 4XCO2),esmControl (ESM pre-industrial control), esmFdbk1 (ESM feedback1), esmFdbk2 (ESM feedback 2), esmFixClim1 (ESM fixed climate1), esmFixClim2 (ESM fixed climate 2), esmHistorical (ESM his-torical), esmrcp85 (ESM RCP8.5), historical (historical), histori-calExt (historical extension), historicalGHG (GHG-only), histori-calMisc (other historical forcing), historicalNat (natural-only), pi-Control (pre-industrial control), rcp26 (RCP2.6), rcp45 (RCP4.5),rcp85 (RCP8.5), sstClim (control SST climatology), sstClim4xCO2(CO2 forcing), sstClimAerosol (all aerosol forcing), sstClimSulfate(sulfate aerosol forcing)LUCID L1B26 (RCP 2.6 scenario driven with CO2 emissions and all otherforcings but without land use change), L1B85 (RCP 8.5 scenariodriven with CO2 emissions and all other forcings but without landuse change), L1C26 (RCP 2.6 scenario driven with CO2 emissionsand all other forcings including land use change) L2A26 (RCP 2.6scenario driven with CO2 concentrations and all other forcings butwithout land use change) L2A85 (RCP 8.5 scenario driven with CO2concentrations and all other forcings but without land use change)GeoMIP G1 (quadruple preindustrial CO2 and balance with solar constant re-duction), G1oceanAlbedo (quadruple preindustrial CO2 balanced byincreased ocean albedo), G2 (1%per year CO2 increase from preindus-trial and balance with solar constant reduction), G4 (RCP4.5 2020-2069 and 5 Tg SO2 injection per year) G4cdnc (RCP4.5 with 50%increase of liquid cloud droplet concentration for oceanic low cloudsduring the period 2020-2069) sstClimG1oceanAlbedo (forcing due toquadruple preindustrial CO2 balanced by increased ocean albedo)CanAM4 CMIP5 amip (AMIP), amip4K (AMIP plus 4K anomaly), amip4xCO2(4xCO2 AMIP), amipFuture (AMIP plus patterned anomaly)Continued on next page153Appendix A. TablesTable A.2 – continued from previous pageModels Experiment Experiment ID (Experiment name)CanCM4 CMIP5 Runs for decades (10 and 30 years) initialised from 1960 to 2014,historical, rcp45 (RCP4.5)154

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