Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Balekelayi, Ngandu
Doctor of Philosophy - PhD
University of British Columbia
Developing an accurate deterioration model for sewer pipes is the basic step to a successful wastewater infrastructure management. However, it is difficult to predict exactly the change in the condition of sewer pipes since they are buried, and several factors influence their condition changes. These factors are collected through inspection and the deterioration models are built to understand the way they affect the condition of sewer pipes. However, only few pipes are inspected and not all the needed factors are collected. Thus, models are made from uncertain and incomplete data resulting in simplified approaches for quick and easy interpretation of the results. In this research, two semi-parametric models are developed to predict the deterioration of sewer pipes. The first model predicts the expected mean deterioration score of sewer pipes and the second gives the complete distribution of the output response through the analysis of its quantiles. In both models, variables are grouped into categorical where an ordinary least square estimation of parameters is applied and continuous variables where nonlinear smooth functions P-splines are applied. To account for unobserved covariates, models are enhanced through the inclusion of geospatial location of pipes as surrogate covariate that is estimated through a Gaussian Markov Random Field approach. The application of these models to the sewer inspection data of the city of Calgary shows a good agreement between the predictions and the observations. The estimation of the risk of pipes failure passes through the identification of critical areas in the network and their rankings, a metric resulting from the aggregation of multiple graph theoretic centrality measures is calculated. Two frameworks are proposed including the Bayesian approach when the hydraulic data are available to estimate the baseline metric and the Ordered Weighting Averaging that considers the decision maker’s attitude. Finally, the value of the information provided by the deterioration models is used to orient future inspections in the network. From the deterioration models’ information and errors, the value of information is calculated for each pipe in the network. The obtained values are projected on a GIS map for different horizons to help decision makers orient their priorities.
Advanced deterioration models forwastewater inspection prioritizationbyNgandu BalekelayiM.Sc.,UNESCO-IHE Institute for Water Education,Delft,The Netherlands, 2010B.Sc.A.,University of Mbujimayi, The Democratic Republic of Congo, 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)June 2019© Ngandu Balekelayi, 2019The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a thesis/dissertation en-titled:Advanced deterioration models for wastewater inspection prioritizationsubmitted byNgandu Balekelayi in partial fulfilment of the requirementsof the degree of Doctor of PhilosophySolomon Tesfamariam, School of EngineeringSupervisorZheng Liu, School of EngineeringSupervisory Committee MemberSumi Siddiqua, School of EngineeringSupervisory Committee MemberParamjit Gill, Statistics FacultyUniversity ExaminerRoyce Francis, School of Engineering and Applied Science,George Washington UniversityExternal ExamineriiAbstractDeveloping an accurate deterioration model for sewer pipes is the ba-sic step to a successful wastewater infrastructure management. However,it is difficult to predict exactly the change in the condition of sewer pipessince they are buried, and several factors influence their condition changes.These factors are collected through inspection and the deterioration modelsare built to understand the way they affect the condition of sewer pipes.However, only few pipes are inspected and not all the needed factors arecollected. Thus, models are made from uncertain and incomplete data re-sulting in simplified approaches for quick and easy interpretation of theresults. In this research, two semi-parametric models are developed to pre-dict the deterioration of sewer pipes. The first model predicts the expectedmean deterioration score of sewer pipes and the second gives the completedistribution of the output response through the analysis of its quantiles. Inboth models, variables are grouped into categorical where an ordinary leastsquare estimation of parameters is applied and continuous variables wherenonlinear smooth functions P-splines are applied. To account for unobservedcovariates, models are enhanced through the inclusion of geospatial locationof pipes as surrogate covariate that is estimated through a Gaussian MarkovRandom Field approach. The application of these models to the sewer in-spection data of the city of Calgary shows a good agreement between thepredictions and the observations. The estimation of the risk of pipes failurepasses through the identification of critical areas in the network and theirrankings, a metric resulting from the aggregation of multiple graph theoreticcentrality measures is calculated. Two frameworks are proposed includingthe Bayesian approach when the hydraulic data are available to estimatethe baseline metric and the Ordered Weighting Averaging that considers thedecision maker’s attitude. Finally, the value of the information provided bythe deterioration models is used to orient future inspections in the network.From the deterioration models’ information and errors, the value of infor-mation is calculated for each pipe in the network. The obtained values areprojected on a GIS map for different horizons to help decision makers orienttheir priorities.iiiLay SummaryIn this thesis, the author developed advanced deterioration models forwastewater pipes including nonlinear and linear relationships between co-variates and the deterioration score. The inclusion of surrogate variablewhich is the geospatial location of pipes to account for the unobservedand unknown variables enhances the predictive capabilities of the models.Critical areas in the network are identified using graph theoretical metrics.Operational risk is calculated and projected on GIS maps for visualizationand prioritization of inspections. Further support to the decision making isprovided through the analysis of the evolution of the value of informationprovided by the deterioration models over the planning horizon.ivPrefaceI, Ngandu Balekelayi, prepared all the contents of this thesis includingliterature review, accessing data, model development and analysis, interpre-tation of results and writing of the manuscripts under the supervision ofProfessor Solomon Tesfamariam. Dr. Solomon Tesfamariam reviewed allthe manuscripts and provided critical feedback in the improvement of themanuscripts and thesis. Most of the contents of this thesis are published, ac-cepted or submitted for publication in the following journals and conferenceproceedings.− A version of Chapter 3 has been published in ASCE-Journal of In-frastructure Systems with a title “Statistical inference of sewer pipesdeterioration using Bayesian geoadditive regression model” (Balekelayiand Tesfamariam, 2019b).− A version of Chapter 4 has been submitted in International Jour-nal of Approximate Reasoning: Uncertainty in Intelligent Systemswith a title “Geoadditive quantile regression model for Sewer pipesdeterioration using boosting optimization algorithm” (Balekelayi andTesfamariam, under review).− A version of Chapter 5 has been published in ASCE-Journal of WaterResources Planning and Management, with the title “Graph theoreticsurrogate measure to analyze reliability of water distribution systemusing Bayesian belief network-based data fusion technique” (Balekelayiand Tesfamariam, 2019a).− A version of Chapter 6 will be published in Sustainable and ResilientInfrastructure journal. The manuscript is under internal review.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . 11.1 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . 5Chapter 2: Literature review . . . . . . . . . . . . . . . . . . . . 72.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Sewer deterioration models . . . . . . . . . . . . . . . . . . . 82.3 Critical components identification . . . . . . . . . . . . . . . . 132.4 Prioritization of maintenance rehabilitation and replacement 172.5 Value of Information . . . . . . . . . . . . . . . . . . . . . . . 19Chapter 3: Statistical inference of sewer pipes deteriorationusing Bayesian geoadditive regression model . . . 223.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22viTABLE OF CONTENTS3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.1 Physical characteristics of pipes . . . . . . . . . . . . . 233.2.2 Maintenance data . . . . . . . . . . . . . . . . . . . . 233.2.3 Geospatial location . . . . . . . . . . . . . . . . . . . . 253.2.4 Bayesian geoadditive deterioration model . . . . . . . 253.3 Mathematical formulation of geoadditive models . . . . . . . 263.3.1 Linear model for the categorical variables . . . . . . . 263.3.2 Non-parametric model of the continuous variables . . 273.3.3 Bayesian Structured additive model . . . . . . . . . . 283.3.4 Geoadditive model . . . . . . . . . . . . . . . . . . . . 293.3.5 Variable selection and model development . . . . . . . 303.4 Wastewater system of the city of Calgary . . . . . . . . . . . 323.5 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 343.5.1 Physical covariates . . . . . . . . . . . . . . . . . . . . 343.5.2 Maintenance covariates . . . . . . . . . . . . . . . . . 403.5.3 Covariate interactions . . . . . . . . . . . . . . . . . . 413.5.4 Geospatial effects . . . . . . . . . . . . . . . . . . . . . 443.5.5 Future condition predictions . . . . . . . . . . . . . . 453.5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 463.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Chapter 4: Geoadditive quantile regression model for sewerpipes deterioration using boosting optimizationalgorithm . . . . . . . . . . . . . . . . . . . . . . . . 504.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.1 Structured additive quantile regression . . . . . . . . . 514.2.2 Boosting algorithm . . . . . . . . . . . . . . . . . . . . 544.2.3 Model development . . . . . . . . . . . . . . . . . . . . 564.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 574.3.1 Model Selected covariates . . . . . . . . . . . . . . . . 574.3.2 Covariates effects on the response variable . . . . . . . 654.3.3 Spatial effects . . . . . . . . . . . . . . . . . . . . . . . 704.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 714.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Chapter 5: Critical components identification using graph the-ory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 75viiTABLE OF CONTENTS5.2.1 Hydraulic modeling of pressurized pipes . . . . . . . . 755.2.2 Graph theoretical metrics . . . . . . . . . . . . . . . . 785.2.3 Betweenness . . . . . . . . . . . . . . . . . . . . . . . . 805.2.4 Topological Information Centrality . . . . . . . . . . . 805.2.5 Eigenvector centrality . . . . . . . . . . . . . . . . . . 815.2.6 Principal components centrality . . . . . . . . . . . . . 815.2.7 Bayesian belief network (BBN) based data fusion . . . 825.3 Application to water supply in the city of Richmond . . . . . 845.4 Results and Discussions . . . . . . . . . . . . . . . . . . . . . 855.4.1 Hydraulic reliability . . . . . . . . . . . . . . . . . . . 875.4.2 Topological reliability . . . . . . . . . . . . . . . . . . 875.4.3 Data fusion . . . . . . . . . . . . . . . . . . . . . . . . 935.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Chapter 6: Risk and value of Information-based inspectionprioritization for large wastewater system . . . . . 976.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.2 Risk based approach methodology . . . . . . . . . . . . . . . 1006.2.1 Ordered Weighted Averaging (OWA) . . . . . . . . . . 1006.2.2 Risk evaluation for sewer pipes . . . . . . . . . . . . . 1026.3 Methodology for the value of information . . . . . . . . . . . 1046.3.1 Decision tree . . . . . . . . . . . . . . . . . . . . . . . 1046.3.2 Decision-based on expected values . . . . . . . . . . . 1056.4 Application to wastewater network . . . . . . . . . . . . . . . 1086.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 1086.5.1 Critical areas delineation . . . . . . . . . . . . . . . . 1086.5.2 Risk of pipes failure . . . . . . . . . . . . . . . . . . . 1196.5.3 Example application of the risk approach in the pri-oritization of maintenance . . . . . . . . . . . . . . . . 1236.5.4 Probability of failure . . . . . . . . . . . . . . . . . . . 1276.5.5 Value of Information . . . . . . . . . . . . . . . . . . . 1286.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Chapter 7: Conclusions and recommendations . . . . . . . . . 1337.1 Summary and conclusions . . . . . . . . . . . . . . . . . . . . 1337.2 Originality and contributions . . . . . . . . . . . . . . . . . . 1347.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.4 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . 136Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137viiiTABLE OF CONTENTSAppendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Appendix A: Table: Example of data used to build deteriorationmodels . . . . . . . . . . . . . . . . . . . . . . . . . . 153Appendix B: Example code for statistical deterioration model . . . 155ixList of TablesTable 2.1 Pipes internal condition grade (ICG) description. . . 9Table 2.2 Regression models for sewers pipes deterioration (san-itary and storm) pipes. . . . . . . . . . . . . . . . . . 10Table 2.3 Summary of critical components assessment in pipesinfrastructure. . . . . . . . . . . . . . . . . . . . . . . 14Table 3.1 Covariates description. . . . . . . . . . . . . . . . . . 36Table 3.2 Characteristics of new pipes installed at Marlboroughand Woodbine. . . . . . . . . . . . . . . . . . . . . . . 48Table 4.1 The gradient descent algorithm. . . . . . . . . . . . . 55Table 4.2 Influential covariates for each selected percentile. . . . 59Table 5.1 Manning’s coefficient n for closed conduits flowing patlyfull (Chow, 1959). . . . . . . . . . . . . . . . . . . . . 79Table 5.2 Example of Nodes’coordinates, base water demand andelevation in the city of Richmond. . . . . . . . . . . . 86Table 5.3 Example of links connectivity and characteristics. . . 88Table 5.4 Example of hourly demand variation and characteris-tics in the city of Richmond. . . . . . . . . . . . . . . 89Table 5.5 Spearman correlation coefficients and spatial autocor-relation of the metrics. . . . . . . . . . . . . . . . . . 90Table 5.6 Twenty most critical nodes rankings using the WSRas baseline. . . . . . . . . . . . . . . . . . . . . . . . . 94Table 6.1 Transformation of Linguistic Degree of Optimism toOrness Values (Tesfamariam et al., 2010). . . . . . . . 103Table 6.2 Confusion matrix of the statistical deterioration model.129Table A.1 Example of data used to build deterioration models. . 154xList of FiguresFigure 1.1 Thesis organization. . . . . . . . . . . . . . . . . . . . 6Figure 3.1 Proposed framework for Bayesian geoadditive sewerdeterioration model. . . . . . . . . . . . . . . . . . . . 24Figure 3.2 Wastewater system in the city of Calgary. . . . . . . . 33Figure 3.3 Characteristics of inspected pipes classified in 4 mate-rial groups: the cementitious, clay, metallic and plas-tic pipes (City of Calgary). . . . . . . . . . . . . . . . 35Figure 3.4 Nonlinear partial effect of physical characteristics ofsewer pipes to the score metric. . . . . . . . . . . . . 38Figure 3.5 Maintenance data partial effects to pipes deterioration. 39Figure 3.6 Impact on the response of the interactions betweenthe covariates. . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.7 Impact of covariates’ interactions. . . . . . . . . . . . 42Figure 3.8 Geospatial effect of the unobserved covariates on theexpected mean score of pipes. . . . . . . . . . . . . . 43Figure 3.9 Future conditions predictions. . . . . . . . . . . . . . 46Figure 3.10 Model validation. . . . . . . . . . . . . . . . . . . . . 47Figure 4.1 Optimal number of function evaluation to avoid over-fitting in the lower quantile. . . . . . . . . . . . . . . 58Figure 4.2 Age covariate impacts in different quantiles. . . . . . 60Figure 4.3 Residential connection impacts in different quantiles. 61Figure 4.4 Length and material impacts in different quantiles. . 62Figure 4.5 Cleaning and backups impacts in different quantiles. . 63Figure 4.6 Root cuts and degrease impacts in different quantiles. 64Figure 4.7 Slope and depth impacts in different quantiles. . . . . 66Figure 4.8 Combined impacts in different quantiles. . . . . . . . 67Figure 4.9 Score prediction using pipe’s attributes. . . . . . . . . 68Figure 4.10 Score prediction using maintenance and environmen-tal factors. . . . . . . . . . . . . . . . . . . . . . . . . 69xiLIST OF FIGURESFigure 4.11 Spatial effects for (a) lower quantile model, (b) 50thpercentile and (c) upper quantile. . . . . . . . . . . . 70Figure 5.1 Proposed framework for critical component identifi-cation. . . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 5.2 Bayesian nelief network based data fusion . . . . . . . 83Figure 5.3 Richmond Water Supply Network. . . . . . . . . . . . 84Figure 5.4 Critical areas in the Richmond wdn. . . . . . . . . . . 91Figure 5.5 Phase angle variation between the PCC and the EVC. 92Figure 6.1 Proposed framework for risk and value of informationassessment . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 6.2 Description of a simple decision tree . . . . . . . . . . 104Figure 6.3 Critical areas in the the city of Calgary estimatedusing the betweenness centrality . . . . . . . . . . . . 109Figure 6.4 Critical areas in the the city of Calgary estimatedusing EVC metric . . . . . . . . . . . . . . . . . . . . 110Figure 6.5 Critical areas in the the city of Calgary estimatedusing PCC metric . . . . . . . . . . . . . . . . . . . . 111Figure 6.6 Critical areas in the the city of Calgary estimatedusing conservative OWA based data fusion . . . . . . 112Figure 6.7 Critical areas in the the city of Calgary estimatedusing normative OWA based data fusion . . . . . . . 113Figure 6.8 Critical areas in the the city of Calgary estimatedusing optimistic OWA based data fusion . . . . . . . 114Figure 6.9 Phase angle between the PCC and the principal eigen-vector (EVC) . . . . . . . . . . . . . . . . . . . . . . . 117Figure 6.10 Risk map of sewer pipes in the city of Calgary follow-ing the conservative approach . . . . . . . . . . . . . 120Figure 6.11 Risk map of sewer pipes in the city of Calgary follow-ing the normative approach . . . . . . . . . . . . . . . 121Figure 6.12 Risk map of sewer pipes in the city of Calgary follow-ing the optimistic approach . . . . . . . . . . . . . . . 122Figure 6.13 Changes in the normative risk map after 10% replace-ment of high risk pipes . . . . . . . . . . . . . . . . . 124Figure 6.14 Changes in the normative risk map after 20% replace-ment of high risk pipes . . . . . . . . . . . . . . . . . 125Figure 6.15 Changes in the normative risk map after 30% replace-ment of high risk pipes . . . . . . . . . . . . . . . . . 126Figure 6.16 Description of a simple decision tree . . . . . . . . . . 128xiiLIST OF FIGURESFigure 6.17 The value of information in the city of Calgary fromnow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 6.18 The value of information in the city of Calgary after25 years . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 6.19 The value of information in the city of Calgary after50 years . . . . . . . . . . . . . . . . . . . . . . . . . . 131xiiiList of AbbreviationsAC Asbestos cementANN Artificial Neural NetworkBBN Bayesian belief networkBETW BetweennessBR BrickCCTV Closed circuit television videoCI Cast IronCMP Corrugated Metal PipesCON ConcreteCservs Number of commercial service connectionsDMA District Metering AreaEVC Eigenvector CentralityGIS Geographical Information SystemGMRF Gaussian Markov Random FieldICG Internal Condition GradingLCMC Life-Cycle Maintenance CostMatcode Material codeMCMC Markov chain Monte CarloOWA Ordered Weighted AveragingP-spline Polynomial splinePACP Pipeline Assessment Certification ProgramPCC Principal Components CentralityPE PolyethylenePVC Polyvinyl chlorideRservs Number of residential service connectionsST SteelSVM Support Vector MachineTIC Topological Information CentralityVCT Vitrified clayVoI Value of InformationWDS Water Distribution SystemWRc Water Research CentrexivAcknowledgementsFirst, I thank the Almighty GOD, for granting me the opportunity tomaterialize this research in the present form.My deepest gratitude goes to my academic supervisor Professor SolomonTesfamariam, who had always been there to help me as a mentor. I reallyappreciate all his contributions of dedicated time, and great ideas to makemy PhD experience dynamic and exciting. I would like to thank him for hisencouragement that allowed me to grow as a researcher.I would like to also express my heartfelt thanks to my committee mem-ber Dr. Zheng Liu and Dr Sumi Siddiqua for their valuable comments andconstructive suggestions. I am grateful to my colleagues: Dr. Golam Kabir,Dr. Gizachew Demissie and Yekenalem Abebe, Kostas Skandalos and Sela-mawit Dires. It was a great pleasure to work with such a wonderful researchgroup. This research would not have been possible without the wonderfulresearch environment we created together.This research could not be possible without the financial support fromthe Natural Sciences and Engineering Research Council under the DiscoveryGrant programs, Mitacs-Accelerate and partial financial support from theUniversity of British Columbia as the University Graduate Fellowship.Special thanks to my wife Detty Bilonda for her indefectible support,encouragements and sacrifices. You made me dream, when I simply saw.You made me execute, when I simply thought. You made me listen, whenI simply heard. You made me live every moment, when I simply existed.Thank you DearGermain and Germaine, you are my champions.xvDedicationTo my familyxviChapter 1IntroductionWastewater systems are among the most expensive urban water infras-tructure that convey used water from household and industries to treatmentplants facilities (Hahn et al., 2002). Many existing sewer systems are un-der considerable stress due to deterioration of aging infrastructure (somepipes date back nearly 100 years), rapid urbanization and climate change.Renewed interest in urban development and gradual land use changes haveresulted in a drastic increase in loads and pressure on sewer networks thatcan lead to structural condition deterioration which can directly impact sen-sitive catchments, and ultimately population’s health and safety (Salmanand Salem, 2011; Halfawy et al., 2008; Davies et al., 2001a). For instance,in Canada, 27% of sewer pipes are in fair to poor condition representing aglobal replacement value of $24 billion (Infrastructure, 2016).The general degradation of existing sewer systems and changes into reg-ulations and demands for more transparency in decision-making led to thesearch of decision support tools for the definition of cost-effective manage-ment strategies (Ana et al., 2009). The gap between available funds tomaintain or improve the overall performance of sewer systems led munici-palities to prioritize inspection, maintenance, rehabilitation and replacement(Kabir et al., 2018b). Decision makers use defined indicators (e.g. the assetperformance, the risk of failure, the life cycle cost) to assess the return on in-vestment in complex large infrastructure networks (Alegre and Coelho, 2012;Halfawy et al., 2008). Risk based approaches have been extensively used inurban water infrastructure management (Mancuso et al., 2016; Kabir et al.,2015b; Baah et al., 2015; Salman and Salem, 2011; Fuchs-Hanusch et al.,2012). Utility managers focus on pipes or areas in the network where therisk of pipes failure is high, i.e. where the failure of pipes will lead to exten-sive service disruption and health or environmental damage (Sterling et al.,2009). On the other side, Elms and Brown (2013) evokes the incomplete-ness of risk, as applied in engineering (likelihood and consequence), andsuggested building more accurate failure (deterioration) models to reduceuncertainties. Syachrani et al. (2011) stressed the importance of developingaccurate deterioration models and reliable risk assessment for a successful1Chapter 1. Introductionurban water asset management. The risk perception depends on the qualityof the information provided by deterioration models.Three main approaches for sewer deterioration modeling are presented inthe literature: deterministic, statistical and artificial intelligence (Duchesneet al., 2013; Ana and Bauwens, 2010). These models are further categorizedinto two main groups: pipe group and pipe level models (Van Riel et al.,2014). Deterioration models at both levels are limited in their predictions ofthe structural performance of sewer pipes. They cannot reproduce the inher-ent complexity of physical deterioration of sewer pipes. The quality of thegroup pipe model prediction depend on the availability of large amounts ofinspection data. Besides, the amount of inspection data, individual modelsrequire a proper definition of the way the factors affect the output conditionof sewer pipes.Statistical models fit well with the stochastic nature of the deteriorationmodels and the type of data available (pipes condition states) (Duchesneet al., 2013). The majority of existing individual statistical deteriorationmodels assumes linear relationships between the expected relevant factorsand the structural condition or breakage rate of pipes (Ana et al., 2009; Tranet al., 2009a; Baik et al., 2006; Micevski et al., 2002; Ariaratnam et al., 2001).The reason behind the linearization of complex physical processes was thelack of data to build complex models since only a reduced number of datapoints of inspection were available. Moreover, linear models are simple todevelop, and their results easy to interpret. However, the conclusions drawnfrom these models never addressed the problems occurring when dealingwith entire network data (Syachrani et al., 2011). The representation ofa complex natural process into a linear model added to uncertainty in theinput parameter values will inevitably lead to inappropriate decisions thatmay impact the finance of the organization. Few studies introduced the non-linearity of the deterioration process and predict the condition of sewer pipesusing artificial neural networks (ANN) (Sousa et al., 2014; Tran et al., 2009b)and Support Vector Machine (SVM) (Mashford et al., 2010). However, theseapproaches need a substantial upfront work to define the internal architec-ture of the model that is critical to its predictive performance. Moreoverthe causal relationship between the independent factors and the responsecondition is not explicitly known. Since the adoption of proactive man-agement approach of sewer infrastructure, municipalities made significantefforts to collect more and accurate data from their system. The availabilityof large amounts of data and recent development of more accurate statisticalmodels allow the development of deterioration models that can replicate thecomplexity of individual pipe condition degradation over time.2Chapter 1. IntroductionAlthough intense data collection through municipalities, the majority offactors listed in Davies et al. (2001a) are not systematically collected. More-over, group pipe models show discrepencies for pipes installed at differentlocations in the same sewer system. Davies et al. (2001b) suggested a com-bination of multiple sources of data such as CCTV, map soil, traffic, groundwater information and geospatial location of pipes into a single deteriorationmodel. In the search of alternative sources of data, Dirksen et al. (2013)analyzed the settlement of sewer invert levels to predict the location and oc-currence of water stagnation in a wastewater system. Their approach allowsfor determining future sediment accumulation in the system from the invertlevel and soil type characteristics. Their study demonstrated the spatialdependency of the expected influencing factors in the deterioration of sewerpipes. The geospatial location of sewer pipes is a source of information thatcan enhance sewer pipes deterioration models. In contrast to the commonexpected mean regression, in which the conditional mean of the dependentvariable is the statistic of interest, getting information on the entire condi-tional distribution of the outcome structural condition of sewer pipes given aset of covariates is important in risk-based decision making. Observation ofextreme values in deterioration patterns of sewer pipes (e.g. newly installedpipes found in bad conditions or old pipes in good conditions) triggered thesearch of information about the relationships between the covariates andthe tails of the outcome distribution, not only the expected mean response.Quantile analysis of the dependent condition states of pipes will elucidatethe changing effects of the covariates on the outcome across the quantiles ofthe distribution and allow appropriate decision-making process.On the other side, the existing structural deterioration data do not al-low the evaluation of the sewer system level performance (Dirksen et al.,2013). Two types of sewer system level performance are considered in urbaninfrastructure systems analysis: the structural, i.e. related to mechanicalfailure and the operational, i.e. related to hydraulic failure (Deuerlein et al.,2009). Operational network level performance is mostly evaluated based onhydraulic simulation of urban water networks (Shuang et al., 2017; Torreset al., 2016; Perelman and Ostfeld, 2011; Ostfeld, 2005). Hydraulic mod-els are limited and difficult to update when the pipe’s friction factors arechanging due to the dynamics occurring in the system (e.g. settlement,breakage, sediment accumulation, inflow-infiltration, structural defects ap-pearance). Moreover, data related to these changes are not available. Thestructural performance evaluates the probability of the infrastructure net-work to remain connected after a disruptive event (e.g. the failure of oneor several pipes). Graph theory techniques allow to assess the connectivity31.1. Research objectivespattern of networked infrastructure (Agathokleous et al., 2017). From eachperformance type perspective, critical components are identified for main-tenance and inspection prioritization. The lack of operational data led tothe search of alternative techniques that could identify both types of criticalcomponents. Graph theoretic centrality metrics quantify the importanceof components relative to their position in the networked system. For in-stance, the failure of most connected nodes will have higher impact on theperformance than the failure of a terminal node connecting a private houseto the system. This approach is also limited because most of the existinggraph metrics (e.g. betweenness, topological information centrality) do notcapture both types of critical components (operational and structural) thatmay affect the network performances. Furthermore, the physical topologicalpattern of the network is not always identical to the operational topologybecause, the flow directions changes in the pipes due to the head distribu-tion at the nodes, the discharge in the pipes and the network redundancy(Agathokleous et al., 2017). In aging infrastructure, where pipe failure mayoccur, there is a need to determine a general approach that can define, fromthe topology of the network, a single metric that simultaneously capture thesystem connectivity and the operational performance. The use of such met-ric will reduce significantly the number of extensive hydraulic simulationsneeded to identify critical areas in large infrastructure systems.1.1 Research objectivesThe overall objective of this study is to develop an efficient inspectionand maintenance prioritization program for large sewer pipe systems. Thisresearch aims at developing advanced deterioration models through the in-clusion of nonlinearity characterized by smooth P-splines in regression baseddeterioration models. These models built from structured additive regres-sion technique will eventually include the spatial information of the locationof sewer pipes as a surrogate of missing factors that have not been observedbut have effect on the deterioration of sewer pipes. Next, graph theory anddata fusion techniques will be applied to networked infrastructure in or-der to identify critical components and define a network level performanceindicator for future planning decision making. The predicted condition ofsewer pipes and the assessed criticality are used for prioritization of sewerinspection, maintenance, repair or rehabilitation. Specifically, this studyaims to:1. Develop an enhanced nonlinear individual sewer pipes regression model41.2. Thesis organizationthat includes geospatial information as a surrogate covariate represent-ing the unknown and unobserved covariates.2. Develop quantile-based deterioration model to identify pipe’s attributesand environmental factors that are responsible of the occurrence forextreme conditions in the deterioration process.3. Develop a graph theoretic based model to predict the topological per-formance of large infrastructure systems and identify the componentsthat are critical in a scarce operational data environment.4. Develop a Bayesian belief network to conduct a risk-based prioritiza-tion of sewer pipes based on their criticality, the likelihood of failureand the rate of deterioration5. Develop a sewer network level performance metric evaluation modelto allow decision making at strategic and tactical levels.1.2 Thesis organizationThis thesis dissertation is written based on manuscripts submitted/pub-lished in either journal or presented/ published in conferences proceedings.51.2. Thesis organizationChapter 1IntroductionChapter 2Literature reviewChapter 3 (Objective 1)Statistical inference of sewer pipes deterioration using Bayesian geoadditive regression modelChapter 4 (Objective 1)Geoadditive quantile deterioration model for sewer pipes Chapter 5 (Objective 2 )Critical components identification using graph theoryChapter 6 (Objectives 3 and 4)Risk-value of information-based inspection prioritization for large wastewaterChapter 7Conclusion and RecommendationsFigure 1.1: Thesis Organization6Chapter 2Literature review2.1 OverviewSewer replacement and rehabilitation are capital intensive issues in urbanwater infrastructure management (Kapelan et al., 2011; Younis and Knight,2010). Renewal decision making in wastewater systems is multifaceted andfaces different challenges among which the available data, on which deci-sion are made, do not allow the prediction of system performance (Dirksenet al., 2013). Since the adoption of proactive approach in the managementof wastewater infrastructure systems, municipalities have made significantefforts to collect extensive and accurate condition data of their assets (Ster-ling et al., 2009). Due to financial limitation, only part of infrastructurenetworks are inspected. Collected data are used to assess the actual condi-tion of inspected pipes and build predictive models to evaluate uninspectedpipes conditions and future condition of the entire system. The selection ofpipes to be inspected is based on expert knowledge of the system and on theage of pipes. Thus, the constructed database are limited and not representa-tive of all possible factors that might affect the condition of sewer pipes. Thelimitation of predictive models to analyze complex deterioration process andthe lack of data both in quantity (only part of the network is inspected) andquality (e.g. the operator ability to interpret CCTV images have effect onthe information used in the model) introduce a significant source of uncer-tainty in the decision making (Dirksen et al., 2013). Improved deteriorationprediction models coupled to reliable assessment of critical components willenhance optimal decision making on the prioritization of maintenance andinspection.Many mathematical models have been developed to relate the deterio-ration level of individual sewer pipes to various explanatory variables (e.g.length, diameter) (Davies et al., 2001b; Ana and Bauwens, 2010). Thesemodels are either physically based (physical deterioration models mimic thephysical mechanism underlying the structural deterioration pipes) (Rajaniand Tesfamariam, 2004), artificial intelligence-based (e.g. Sousa et al., 2014;Tran et al., 2009a; Kleiner et al., 2006) and statistical (e.g. Caradot et al.,72.2. Sewer deterioration models2018; Sousa et al., 2014; Kley and Caradot, 2013; Kleiner, 2001). The lattertechnique copes well with the nature of the data describing the deteriorationof sewer pipes conditions (i.e., pipe condition rating) and are consequentlythe most often applied (Duchesne et al., 2013).In risk-based decision making, utility managers focus on individual levelrisk assessment and make decision without evaluating the impact of theirdecision on the network performance. Two different approaches (hydraulicand mechanical) are used to evaluate the network level performance in waterinfrastructure. Critical components are the components whose failure leadto the failure of the entire network system. A network system fails when itcannot perform the tasks it is designed for (e.g. back water flow in base-ment after the failure of a sewer pipe). Under a designated hazard (e.g. pipesdeterioration), hydraulic model simulations are run to identify critical com-ponents in urban infrastructure system (Ostfeld, 2012; Tolson et al., 2001).These models are useful as long as pipes are new and their internal frictionfactors are known. However, in aging infrastructure, individual pipe frictionfactors change due to age and the appearance of structural defects on thepipe’s body. 1. In addition, data from all the pipes in the network should becollected to calibrate and validate hydrodynamic models. Network level hy-draulic performance assessment needs more data that are not easy to collect.A surrogate measure of mechanical performance is the network connectivity.Graph theory allows an abstract representation of urban water networks asvertices that are interconnected through edges. If there exist at least onepath from each node to treatment facilities, then the network is connectedand reliable. Several graph theoretical metrics allow the identification ofcritical components based on their position in networks. However,each met-ric gives its own ranking making difficult the selection of metrics to evaluatethe connectivity. Bayesian belief network inference-based data fusion of anumber of graph theoretic metrics allows the aggregation of different sourcesof information while capturing the uncertainty related to each classification.2.2 Sewer deterioration modelsAfter an inspection, the observed defects on a pipe segment(cracks, frac-ture, broken, deformed, hole, collapse, joint, surface damage, lining failure,weld failure, lining repair, point repair) are assigned scores that representtheir severity, position and orientation. A condition grade based on the ag-gregation (statistical measure), the comparison to a threshold or a resultof a calculation is given to the pipe segment (Khazraeializadeh et al., 2014;82.2. Sewer deterioration modelsChughtai and Zayed, 2008). Most protocols (e.g. WRc, PACP) assign con-dition grade to sewers on a scale of 1 to 5 (Gedam et al., 2016). Table2.1 gives an example of condition grading following WRc scoring method asreported by Khazraeializadeh et al. (2014).Table 2.1: Pipes internal condition grade (ICG) description.Score S ICG Condition Description< 10 1 Excellent No defect, newly installed pipes10< S< 39 2 Good Defects start to appear40< S< 79 3 Fair Moderate defects undergoing deteriorating80< S< 164 4 Poor Severe defects that will reach to worst sit-uation in an expected period of timeS>165 5 Bad Care should be taken to the segment im-mediatelyPrediction models consider establishing a relationship between observedcondition of sewer pipes and a group of factors that are assumed to have aninfluence on the deterioration of the pipe condition(Ana and Bauwens, 2010).Statistical approach fits well with the nature of the process and is the mostused for deterioration of urban water infrastructure (Kabir et al., 2018b;Salman and Salem, 2011; Baik et al., 2006; Davies et al., 2001b). Severalmodels have been presented in the literature and none of them capturedthe exact relationships between the expected influencing factors (physical,environmental, operational, construction) and the deterioration of buriedpipe condition. Mostly, authors consider a linear relationship integrated inregression models because of their simplicity and the easy interpretationof the model output. A summary of these studies is presented in Table2.2. Stochastic model’s responses fit well the observed data and allows theprediction of future pipe’s conditions with acceptable levels of confidence(Tran et al., 2009a; Micevski et al., 2002).92.2. Sewer deterioration modelsTable2.2:Regressionmodelsforsewerspipesdeterioration(sanitaryandstorm)pipes.AuthorsFactorsMethodsAbrahamandWirahadikusumah(1999)Material,Soiltype,Groundwatertable,DepthcoverMarkovChainYang(1999)Material,Age,Diameter,Wastetype,DepthLogisticregressionAriaratnametal.(2001)Age,Diameter,sewertype,Depth,MaterialBinaryLogisticRegressionMicevskietal.(2002)Diameter,Material,soiltype,exposure(Dis-tancefromthecoastline)BayesianApproachBaiketal.(2006)Length,Size,Age,Material,SlopeOrderedProbitModelTran(2007)Size,hydrauliccondition,location(structuraldeterioration)MarkovChainTranetal.(2009a)Size,structuralcondition,location,Age,Slope(hydraulicdeterioration)ArtificialNeuralNetworksAnaetal.(2009)Age,Material,LengthBayesianLogisticRegressionSalman(2010)Age,Diameter,Length,Slope,Depth,DummyvariablesrepresentingMaterial,andRoadclassBayesianLogisticRegression,MultinomialRe-gression,OrdinalRegressionYounisandKnight(2010)Age,MaterialOrdinalRegressionMashfordetal.(2010)Diameter,Timelaid,Road,Grade,Startinvert,Endinvert,Material,∆Grade,∆Angle,Soilcor-rosivity,Sulfatesoil,GroundwaterSupportVectorMachineHarveyandMcBean(2014)Material,Age,Type(trunkorbrunch),Diam-eter,Length,Slope,Downstreaminverteleva-tion,Depth,Roadcoverage,watermainbreakswithin3mSupportVectorMachine-DecisionTreePredic-tiveModelSousaetal.(2014)Material,Diameter,Length,Depth,Slope,Age,VelocityLogisticRegression,Artifi-cialNeuralNetworks,SupportVectorMachineGedametal.(2016)Age,Diameter,DepthLinearRegression102.2. Sewer deterioration modelsTwo deterioration levels are considered in sewer pipes management: thecohort level (where pipes sharing certain characteristics such as length, di-ameter, material are assumed to have a homogeneous deterioration pattern)and the individual level. At the cohort level, the following techniques havebeen suggested in the literature: survival models (Baur and Herz, 2002) andMarkov models (Tran et al., 2009b; Micevski et al., 2002; Kleiner, 2001).Two approaches are used in the Markov models: the semi Markov, wherethe sojourn time in a given state is also modeled as a random variablefollowing a given distribution (Kleiner, 2001) and the homogeneous Markovmodel where transition probabilities are estimated at fixed times (Tran et al.,2009a; Micevski et al., 2002). At the component level, regression models arethe most used techniques (Ana et al., 2009). Suggested regression techniquesfor sewer pipes deterioration (logistic regression (e.g. Salman, 2010; Ari-aratnam et al., 2001), multiple regression (e.g. Chughtai and Zayed, 2008),multinomial logistic regression (e.g. Salman and Salem, 2011)) assume linearrelationship between the expected influencing factors and the deteriorationof pipes. Linear regression model’ s results are easy to interpret but themodel does not integrate the complexity of the physical phenomenon thatunderlies the deterioration of sewer pipes. Moreover, in parametric regres-sion models, the best model-based inference approach conditionally ignoresthe uncertainty related to the independent factors selection and the modelitself (Kabir et al., 2015d). In addition, the estimation of factors’ parame-ters is based on ordinary least squared error minimization (Fahrmeir et al.,2013).The uncertainty in the condition assessment extremely affect the reha-bilitation cost (Wright et al., 2006). Wright et al. (2006) used least costclassification methods to overcome the under prediction of linear regressionin the Vallejo Sanitary sewer systems in California US. The linear regres-sion gave 0.77% of deficiency(deterioration) rate while the CCTV data hasa deficiency rate of 7.3%. They finally used metaheuristic optimization toreduce the cost of misclassification. In the same trend, Kabir et al. (2018b)proposed the application of the Bayesian Modeling Averaging for factors’selection that is coupled to a Bayesian logistic regression. Although theirmodel reduces uncertainty in the prediction of sewer pipes, it still repre-sents linear relationships between the covariates and the dependent variableand its response is binary. Salman (2010) compared the results of multino-mial logistic regression, binary logistic regression on the same case study inCincinatti and he found that binary outperforms the multinomial logistic re-gression. The binary logistic regression model predicted 79.8% of non-failureand 50.1% of failure correctly representing an overall correct prediction of112.2. Sewer deterioration models65.8% outperforming the multinomial logistic regression that gave an overallcorrect prediction of 52.8% . He considered the following covariates: Age,diameter, length, slope, depth, dummy variables representing material, androad class.The logistic regression model’s output is binary (good or bad condition)and two probability distribution functions are the most appropriate to de-scribe such data: the binomial and Bernoulli distribution (Ariaratnam et al.,2001). However, the pipe conditions are expressed in multiple states (Ta-ble 2.1) that lead to a wide decision-making domain. The logistic functionlimitation restricts the decision area for maintenance and repairs selection.Therefore, in the presence of advanced methods of calculations, the logis-tic regression should not be preferred. On the other hand, the group levelmodels often have a problem of data coming from different areas and differ-ent pipes lumped in the same model. In fact, the deterioration rate is notthe same at any location in the system although pipes with the same char-acteristics lay underneath. Thus, considering Markov chain deteriorationmodel for cohort of pipes buried in different location will lead to differenttransition probabilities for the same cohorts because the deterioration ofpipes is a geolocalized process (Syachrani et al., 2011). To solve the abovelimitations of sewer deterioration predictive models, researchers considerednonlinear relationships in their models, Mashford et al. (2010) applied theSVM to predict the condition of wastewater collection in the city of Ade-laide in Australia. They considered four models each with increasing numberof covariates. They concluded that the increasing number of covariates donot increase the classification accuracy obtained using only the intrinsic at-tributes of sewers (diameter, time laid, road, grade, start invert, end invert,material). The additional factors, determined using spatial analysis in GIS,(slope change, angle change, soil corrosivity, sulfate soil, groundwater) werenot significant. Sousa et al. (2014) developed three models (logistic regres-sion, ANN, SVM) to assess the deterioration of trunk sewers of the SANESTinfrastructure system in Spain. They selected the material, diameter, length,depth, slope, age, and the velocity computed at half full pipes, as factorsinfluencing the deterioration process. The logistic regression revealed thatonly the material, length, depth and age are significant covariates. However,the depth and the material are the factors that increase the most the oddsof pipe failure. In their study, the failure of a pipe is equal to a pipe in con-dition 4 or 5 (Table 2.1). While the two data driven models outperforms thelogistic regression, it was difficult to conclude which of the two models wasrecommendable. They suggested two attitudes: the conservative attitude(lower performance, less variability) for the SVM and the less conservative122.3. Critical components identificationattitude (higher performance and more variability) for the ANN.Considering the deterioration of sewer pipes as complex physical, chemi-cal and biochemical process as stated by Kapelan et al. (2011), its represen-tation by linear parametric equations is simplistic and could be the sourceof uncertainties. It is important to introduce nonlinearity in the modeling.However, the artificial machine learning based approach is cumbersome andwill need tuning of parameters.2.3 Critical components identificationUrban water utilities managers aim at operating reliable networks thatprovide good quality, required quantity and pressure of water and safelyconvey the wastewater to treatment facilities. The reliability of the networkis defined as its ability to fulfill its designated tasks (Mohammed et al., 2015;Deuerlein et al., 2009; Korving et al., 2009; Ostfeld, 2004). Two types of re-liability are defined at both levels (individual and network): hydraulic andmechanical reliability.At the individual level, hydraulic reliability quantifiesthe capacity of the sewer pipe to convey the designated flow correspondingto its diameter size and the mechanical reliability measures the structuralcondition of the pipe. At the network level, hydraulic reliability refers to theability of the entire system to convey all produced wastewater from house-hold and industries to wastewater treatment plants(Marlow et al., 2010).The system level mechanical reliability is not well defined and the connec-tivity between pairs of pipes is used as a surrogate measure (Van Riel et al.,2014). Maintenance, replacement and repair decisions should be based onthe network level performance rather than the individual performance. Thehydraulic performance is easy to be monitored rather than the structuralperformance. When a pipe fails, the redundancy and the size of modernurban water infrastructure do not allow a rapid identification of the areawhere possible failure of a pipe may induce the observed decline in the net-work performance. Moreover, operational data are not always accessible toallow hydraulic calculations as suggested in previous studies (Tolson et al.,2001). On the other side, the localization of critical areas is important inlarge interconnected networks where the redundancy may hide the failure ofsome components and increase the consequences of such failure. Finally, thereduced access to financial resources makes the search of critical componentsin large infrastructure an important step in decision making.132.3. Critical components identificationTable2.3:Summaryofcriticalcomponentsassessmentinpipesinfrastructure.AuthorsMethodsReliabilitytypeNetworksizeQuimpoandShamsi(1991)minimalpath/minimalcutsetHydraulicHypotheticalandcityofNorwichYangetal.(1996)minimumcutsetMechanicalMetropolitanWaterDistrictofSouthernCaliforniaTanyimbohandTempleman(1993)TailoredmaximumentropyforsingleflowEntropyHypotheticalXuandGoulter(1998)MeanvaluefirstordersecondmomentmethodMechanicalHypotheticalcasestudyOstfeldetal.(2002)Lumpedsupply-LumpeddemandanalysisandMonteCarloHydraulicRegionalwatersupplyofNazarethTolsonetal.(2001)FirstorderreliabilitymethodHydraulicHypotheticalOstfeldetal.(2002)MonteCarlosimulationHydraulicHypotheticalcasestudyShinstineetal.(2002)MinimumcutsetHydraulic/MechanicalTucsonWaterDistributionSystemOstfeld(2012)DecompositionHydraulicHypotheticalYazdaniandJeffrey(2012)DemandAdjustedentropydegreeMechanicalRichmondandColoradoDunnandWilkinson(2012)Combinedoriginalflow,BetweennessanddegreecentralityHydraulic/MechanicalHypotheticalcasestudyAgathokleousetal.(2017)BetweennessHydraulic/MechanicalDMAfromtheWDSofthecityofNicosiadiNardoetal.(2018)EigenvectorcentralityMechanicalHypotheticalcasestudy142.3. Critical components identificationThe mechanical reliability expresses the structural condition of sewerpipes and the ability to convey the designated flow is captured by the hy-draulic reliability. Such metric is used at both levels: the individual andnetwork level. The individual level is function of the internal condition ofthe considered pipe. However, the network level is function of all the pipes’condition and their connectivity pattern. Thus, a decision of rehabilita-tion should ensure that the network level reliability is kept. This metricis then used to select the pipes that should be prioritized for inspectionand rehabilitation. Although, the following review is mostly based on waterdistributions, the application to sewer pipes is straightforward.Several approaches have been presented in the assessment of the topolog-ical reliability of water distribution networks (wdns). A summary of differ-ent approaches in the reliability analysis found in the literature is presentedin Table 2.3. From this Table, it can be observed that early applicationfor wdns was related to hydraulic reliability (Ostfeld, 2001; Quimpo andShamsi, 1991). Later, the existence of at least one reliable path connectingsource nodes to consumption nodes was considered as a measure of reliability(Ostfeld, 2004).The connectivity was assessed using graph theoretic approach based onthe minimum cut sets defined as a set of components that should fail simul-taneously to disconnect the source and the demanding nodes. This approachand many other existing techniques (e.g. Tung, 1985) are computationallyexpensive for large real networks. In addition, the quantification of individ-ual component contribution to the system level performance is not explicitlydefined. For example, in the minimum cut set approach, all the componentsin the cut set have the same criticality level. Under financial constraints,further analysis will be required to prioritize the components for inspectionand maintenance. In addition, a single pipe failure in wdns might influencethe pressure at several nodes and significantly affect the system capacity todeliver water to customers.On the other side, the lack of relevant data, especially in the case offailure events occurring in the network system and demand fluctuations, ledto the use of surrogate models based on graph theory to assess wdn’s per-formance (e.g. Torres et al., 2016; Herrera et al., 2015; Yazdani and Jeffrey,2011). These models provide a necessary first estimation of wdns’ perfor-mances (e.g.; resilience, reliability, vulnerability) before an in-depth analysis(i.e. inspection in the identified area coupled with the hydraulic analysis ofpressure records, customers complaints). Graph theory is an efficient mathe-matical tool to characterize and model the structural properties of complexnetworks (Boccaletti et al., 2006). Yazdani and Jeffrey (2012) compared152.3. Critical components identificationthe nodes degree centrality and the demanded adjusted entropy metric thatdepends on the nodes position, its entropy and water demand. This met-ric performed better than the degree metric than consider the number ofadjacent nodes as a measure of importance. Dunn and Wilkinson (2012)combined the original flow, i.e., the flow through the node calculated beforeany node failure/removal, the Betweenness centrality and the degree central-ity to predict the changes in flow when a node is removed. The combinedmetric is used as an importance measure to identify critical components inwdns. However, they considered the same characteristics (length, diameter,roughness coefficient) for all the pipes in the network and water demandat consumption nodes is assumed constant during the hydraulic simula-tions, i.e. the fluctuations in the water demand is not captured. Agathok-leous et al. (2017) reported a correlation between the network operation andthe topological performance. The determination of the backup digraphs asstated by Ostfeld (2005) was limited to their judgement of possible patternflow based on the pressure at nodes. The number of possible digraphs growsexponentially with the size of the network making this task very uncertain.The topological reliability may be influenced by the hydraulic reliability,i.e., the physical process occurring in the system. Thus, this metric can beused to inform the decision makers on the operational changes occurring inthe network, i.e., the reliability of the wdns. However, there is a limitationwhen using graph theoretical metrics to quantify the network componentimportance because each existing graph metric is defined to characterize aparticular aspect of the interactions occurring in a graph. A single graphtheoretical metric will not capture the hydraulic reliability that is a functionof the layout, the operations and the water quality in wdns.The combination of several metrics will ensure capturing more aspectsof urban water networks’ reliability such as the flow pattern changes due todemand fluctuation, pipes’ failure and energy losses. Zhou (2018) appliedTOPSIS to refine a criticality metric based on the structural condition of thepipe and its hydraulic importance. The combination process should increasethe probability of classification and identification (of critical components inurban water networks) and allow obtaining new information that is an en-hanced form of the input data (Castanedo, 2013; Dong et al., 2009). TheBayesian belief networks (BBN) are well suited for the data fusion becauseof their flexibility and they can be applied in several problems with multi-ple criteria where expert knowledge or preference may not be incorporated(Kabir et al., 2015a). In watewater systems, the conveyance of pipes isconsidered as a measure of importance. The failure of pipes with high con-veyance will lead to higher consequences than the failure of low conveyance162.4. Prioritization of maintenance rehabilitation and replacementpipes. However, when the hydraulic data are not available, it is not possibleto build a comparison baseline metric. Thus, the decision maker’s attitudecan be added to the metric’s ranks to build a Ordered Weighted Averaging(OWA) nonlinear combined metric that will capture all the uncertaintiesand support the decision making process (Tesfamariam et al., 2010).Ordered Weighted Averaging (OWA) is a simple, less computationallyexpensive technique that allows an adjustment of “anding” and “oring” be-haviour to represent the optimism of a multiple objective decision maker(O’Hagan, 1988). The concept was first proposed by Yager (1988). He de-fined a multicriteria problem where not all the criteria have to be satisfied.He quantified the proportion of satisfaction and defined OWA aggregationfunctions. The intrinsic properties of the OWA operator allow the oper-ator to lay between the “and” where all the criteria are satisfied and the“or” when only some of them are satisfied. This property is useful in com-plex networks assessed using graph centrality metrics because the multiplemetrics are bounded between different ranges and gives different rankingof the components. OWA is therefore an effective decision support tool toaggregate these multiples operators into a single and holistic metric (Sadiqand Tesfamariam, 2007). OWA aggregation technique has been used in theassessment of water main failure (Kabir et al., 2015c), seismic risk manage-ment (Tesfamariam et al., 2010) , aggregation of the water quality index(Sadiq and Tesfamariam, 2007) and in various other disciplines such as stu-dent selection for scholarships (Carlsson et al., 1997). In graph theory, theOWA operator has been used in the aggregation of multiple metrics in orderto identify critical components in complex networks where cascading failureis possible (Hernández-Perdomo et al., 2016).OWA is proposed and applied for the sewer pipes application .2.4 Prioritization of maintenance rehabilitationand replacementMaking decisions for renewal of sewer pipes is complex because of limitedknowledge on the actual condition of pipes and the impact, the proposedreplacement will have to the network level performance (Van Riel et al.,2014). In addition, the interaction of multiple actors does not make thedecision making an easy task. Three main indicators are used in the litera-ture,including asset performance, risk of failure and life cycle cost, to assessthe return of investment in complex large infrastructure networks (Halfawyet al., 2008). Halfawy et al. (2009) developed a multiobjective genetic algo-172.4. Prioritization of maintenance rehabilitation and replacementrithm optimization to select the most suitable set of pipes for renewal eachyear along with the performance improvement and risk reduction. Salmanand Salem (2011) applied a weighted scoring method to assess the conse-quence of sewer pipe failure. They applied a binary logistic regression tocompute the likelihood of failure. Then, they coupled the likelihood andthe consequence of failure to obtain the risk that is used to prioritize theinspection of pipes. Their approach is classic and decisions are made atthe individual pipe’s level. They do not evaluate the effect, the replacedpipes, will have to the overall performance of the network. Marzouk andOmar (2013) developed a life-cycle maintenance planning model of deterio-rating sewer network posed as a multi-objective optimization problem thatconsider the sewer network condition, service life and life-cycle maintenancecost (LCMC) as separate objective functions. They applied Markov chainmodel to predict future condition of sewer pipes in the network. A multi-objective genetic algorithm is used to automatically locate an appropriatemaintenance scenario that exhibits an optimized trade-off among conflictingobjectives. Monte Carlo simulation is used to account for LCMC uncer-tainties. Diao et al. (2014) developed a method that divides a wdn intoclusters where components in the cluster have stronger internal connectionsthan external one. Their method allows the identification of groups of crit-ical components and provides criticality prioritization based on the rank ofthe groups. Baah et al. (2015) applied a risk matrix and a weighted summulti-criteria decision-matrix to assess the consequence and risk of sewerpipe failure for a mid-sized city, using ArcGIS. The likelihood of failure isdetermined using a binary logistic regression. Compare et al. (2015) sug-gested a novel risk-based methodology to select the riskiest components ofthe network, based on qualitative expert statements about risk-related at-tributes and weights which characterize the relative importance of theserisks. Del Giudice et al. (2016) used a small sample of failure data and astatistical approach for the prioritization of preventive maintenance strate-gies of a sewer system. The method develops correlations between the mostimportant factors affecting the vulnerability of the network and this is usedto develop a vulnerability map of the network.The presented approaches use either the hydraulic simulation as a per-formance parameter to identify the set of pipes to be replaced or simply usean averaged condition state of the pipes in system as the level of service.Life cycle costing uses subjective discount rates and does not consider theeffect of the replacement on the network level performance. A pipe whosetotal life is at the maximum is the best candidate for replacement. However,in the context of prioritization, the considered pipe should be assessed in182.5. Value of Informationrespect of the network performance. An operational risk-based approachis preferred because it does not aggregate individual performance and theconsequence is defined in terms of criticality (the effect the failed pipe willhave to the system level performance). Furthermore, a BBN is proposed toreduce the uncertainty in the critical components identification.2.5 Value of InformationInformation collected through inspection is useful in the M/R/R plan-ning, the reduction of the uncertainty in the assessment of the components’actual condition states and the prediction of their future evolution (Li andPozzi, 2019; Malings, 2017). Unless limited by different types of constraints,every component in wastewater should be inspected. However, this is notthe case in practice because municipalities have limited funding that doesnot allow them to acquire, analyze and define strategies to react to newdata. The VoI metric is a mean for supporting the optimal collection of in-formation in the context of a decision-making problem The quantification ofthe uncertainty surrounding engineering processes has been widely investi-gated with the aim of reducing their impact on the decision-making process.Howard (1966) highlighted the impact of uncertain information on the eco-nomic decisions made in organizations. Water infrastructure managers relyon utility (loss) function that should be maximized (minimized) to provideoptimal sets of parameters supporting decision-making process. In waterinfrastructure, the optimization of the utility (loss) function passes throughgathering more information on system component conditions. A trade-offbetween the needed information and its acquisition cost should be foundbefore the installation of the monitoring system or launching inspection’scampaigns (Straub, 2014). Deterioration models play a role of supplyingthe missing information from uninspected pipes and forecast the future con-dition of pipes in the entire system. The value of new information providedthrough inspection campaigns and updated deterioration models and theiracquisition cost are essential tools supporting future decision making. Therelationships between the quality (precision) of the obtained information,the decision maker actions and the utility(loss) function should also be as-sessed. The benefit of an additional information on any system prior to itsacquisition can be quantified by the concept of Value of Information (VoI).This concept emerged from the decision theory under uncertainty (Peter-son, 2017). VoI enables the reduction of uncertainty in specific decision-making context through the collection of additional information. (Yokota192.5. Value of Informationand Thompson, 2004). Howard (1966) analyzed probabilistic and economicfactors affecting the decision making. He assigned numerical values for theelimination or reduction of any types of uncertainties in the decision pro-cess. His results show that the joint elimination of uncertainty even inindependent factors has a value that differ from the sum of the values ofeliminating uncertainties in each factor separately. Sheridan (1970) appliedthe VoI concept to the supervision of continuous processes. Miller (1975)investigated the dependence between the available information through theassessment of sequential information. The VoI has been applied in differentareas such as finance (Kadan and Manela, 2018), environment and health(Laxminarayan and Macauley, 2012) engineering automobile (Keisler andBrodfuehrer, 2009), in structure and infrastructure reliability engineering(Leon et al., 2015; Straub, 2014).In infrastructure management, the VoI is mostly used to assess the valueof acquisition and installation of monitoring systems. In large networks,Structural health monitoring requires the definition of an optimal sensorplacement on the components in the network. Among existing techniques(e.g. optimization that are time consuming), the VoI approach allows toassess the locations where sensors should be installed in order to collect use-ful information supporting the network decision making process. (Malings,2017). Malings and Pozzi (2018) calculated the optimal sensor placement tocollect information in a spatially distributed dynamic infrastructure systemwhose parameters vary in time. Quirk et al. (2018) used VoI to quantita-tively estimate a visual inspection campaign in a bridge network prior to itsimplementation. They used a Bayesian pre-post processing analysis. Theyalso included the human imperfection in the assessment of the condition rat-ings. Li and Pozzi (2017) model the relationships between VoI and differentfeatures of sensors system, deterioration models and the decision-makingprocess including the precision, the sensor availability, the degradation rate,the damage predictability, the reaction time, the repairs cost and economicfeatures. Pozzi and Der Kiureghian (2012) used the VoI to compare two al-ternatives bridges health monitoring systems to mitigate seismic risk. In thefirst alternative, the decision maker relies on intensity measures only whilein the second, he or she can have access to the monitoring system recordsto better tune the decision.In these works, the decision maker’s is unaware of the real condition ofthe infrastructure components However, his actions have a direct influenceof the condition states. For example, in sewer pipe decision making, ifthe manager is unaware of the real condition of a sixty(60) years old pipe,his decision to replace this pipe leads to the installation of a new pipe for202.5. Value of Informationwhich the ICG is 1 as per Table 2.1). In addition, the probability of theCCTV to detect defects on the body of a buried pipe is independent of theagent. Operation and Maintenance under uncertainty are mostly modeledfollowing the partially observed Markov decision process (Memarzadeh andPozzi, 2016) and dynamic Bayesian belief network (Luque and Straub, 2019).that consider the process as a Markov decision process where, only part ofinformation is available. Decision on the policy is a stochastic process thatis considered in the decision making. The VoI approach can be appliedto deterioration models with their classification errors to assess in order toguide future inspection programs.21Chapter 3Statistical inference of sewerpipes deterioration usingBayesian geoadditiveregression model3.1 BackgroundSewer pipes deterioration is complex and affected by several factors (e.g.the soil environment, surface and underground human activities). The lackof proper understanding of the physical deterioration process and limitedavailability of required data in physical models led to wide development ofstatistical models among which regression models play a key role. Regres-sion models are built from historical data to predict the actual and futurecondition of sewer pipes. While the stochastic nature of the sewer deteri-oration process is not easily captured by these modeling approaches, thereduced number of collected factors that can explain the deterioration pro-cess accentuated the problem. Most of the developed regression models aresimplistic because they assume a linear dependency between regressors andthe dependent variable to mimic a complex process such as sewer pipes de-terioration. In this chapter, a geoadditive semi parametric regression modelbased on smooth P-splines is used to represent the relationship betweensewer attributes and score obtained after rating observed defects followingWRc protocol. Moreover, unobserved covariates are accounted for throughthe inclusion of geospatial information of the pipes’ location as a surrogatecovariate in the model.3.2 MethodologyDavies et al. (2001a) listed 33 factors that are assumed to have an ef-fect on sewer deterioration. They grouped them into three main groups:223.2. Methodologyconstruction features (e.g. diameter, length), local external features (e.g.groundwater level, above ground traffic) and others (e.g. sewerage charac-teristics). A better representation of the causal relationship between thepipes scores and these factors will inevitably reduce uncertainties in modelpredictions. Figure 3.1 describes the proposed methodology for the devel-opment of advanced deterioration models. Based on available factors in thecity of Calgary sewer system database, a semi parametric regression model isdeveloped to predict the pipes score from its physical characteristics, main-tenance and the environment where it is buried. Validation and testing ofthe model is done over 25 % of randomly sampled data. The developedmodel is then used to predicted future condition of pipes buried at differentlocations in the network system.3.2.1 Physical characteristics of pipesPipes’ intrinsic characteristics are assumed to play a role in their dete-rioration. Several studies highlighted the importance of their impact to theactual condition state of sewer pipes (Younis and Knight, 2010; Ana et al.,2009). These characteristics are known from the construction and do notchange over the life of the pipe. They include: the length, diameter, materialand thickness. In this group category, some other extrinsic characteristicscan be added such as the pipe’s slope, the depth at which it is buried andthe soil characteristics around the pipe. These latter are responsible for theload transmission and the corrosivity for metallic pipes. However, in nor-mal inspection campaigns, these data are not systematically collected. Inaddition, the way, they affect the pipes’ condition are not well elucidated.3.2.2 Maintenance dataSewer pipes deterioration is complex and cannot be explained with theonly physical characteristics of pipes. Operational data (e.g. number oftimes a pipe has been cleaned,blocked or surcharged) carry information onthe the deterioration pattern of pipes that could be used to enhance predic-tion capabilities of sewer pipes’ deterioration models. Syachrani et al. (2013)proposed the use of "real age" as attribute to estimate the deterioration ofsewer pipes in the replacement of calendar age. The "real age" attributeinclude not only the calendar age but also the operational and location at-tribute of pipes that can increase the "real age" or lower the calendar age.The lack of required data to develop physical deterioration models thatappear to be more accurate can be compensated with the introduction in233.2. MethodologyNetwork Data (Inspection data and Geographical information on the pipes location)Geospatial location e.g. (x,y,z), disctrictCovariates classification categorical, continuous Bayesian Geoadditive model developmentParametric part (categorical covariates) Ordinary least square approachNon parametric part (continuous covariates) Penalized splines smooth functionsGeospatial information (location) Gaussian Markov Random FieldCCTV Inspection data  Defects coding following WRc Segment scores following WRcPhysical characteristics of pipes e.g. Length, Diameter, MaterialMaintenance data e.g. Previous flushes, repairsPipe score (dependent variable)Bayesian Inference (MCMC)  Model parameter estimation Pipe score predictionTranformation of pipe scores into internal condition grading Figure 3.1: Proposed framework for Bayesian geoadditive sewer deteriora-tion model.243.2. Methodologymodels of several maintenance data. The number of times roots have beencut from inside a pipe is an indicator of the state condition of the pipe bodyand should be included in the prediction of the state condition of the pipe.This is the same for the number of reported backups, degreases, cleaningand flushes that give information on the working behavior of the pipe.3.2.3 Geospatial locationAs stated for physical and maintenance data, the required data to de-velop accurate deterioration models (here an accurate model is a modelthat is built based on mathematical representation of the deterioration ofthe state conditions of sewer pipes) are not usually available and the un-derstanding of the deterioration itself is limited. In addition, for statisticalmodels, drawing a representative sample of asset stock is not easy. Sampledinspection data is not representative of all the possible attributes presentin the network. However, the pipe geographical location is known and em-bed information about loads, soil physical characteristics, groundwater levelfluctuations, pH and soil salinity.Conclusions drawn from non representative samples cannot be general-ized to pipes whose characteristics are not in the sample. For example, ifconcrete pipes have not been included in the model, prediction done withthe model cannot be applied to concrete pipes (Ahmadi et al., 2016). Thisis the same for the geospatial location of sewer pipes. Pipes buried at placeswhere the water table is above the depth of pipes will not have the samedeterioration level as pipes buried in dry areas even if they have the samephysical characteristics and maintenance records.3.2.4 Bayesian geoadditive deterioration modelNon-parametric and nonlinear models can potentially model the failureof technical systems accurately (Kabir et al., 2018). In order to predict thedeterioration of sewer pipes, a semi parametric model that combines a linearpart (only containing the categorical variables) and a nonlinear part (formedby the continuous covariates) is implemented in this study. Geospatial infor-mation is added to the model as a surrogate representing the unknown andunobserved covariates that may have impact on the deterioration. Quan-titative data (e.g. length, diameter) are modeled as continuous covariateswhile qualitative data (e.g. material, soil type) are represented in discreteform. The continuous output response is discretized to reduce computa-tional complexity in maintenance, rehabilitation and replacement decision253.3. Mathematical formulation of geoadditive modelsmaking. A summary of the proposed framework is given in Figure 3.1. Themathematical formulation of geoadditive models is discussed in the followingsection.3.3 Mathematical formulation of geoadditivemodels3.3.1 Linear model for the categorical variablesAssume the observations (yi,xi,zi ), i=1,. . . ,n are elements of the in-spection database where Yi (continuous variables) represents the pipe seg-ment score, xi = (xi1,. . . ,xiq) and zi=(zi1,. . . ,zip ) are vectors of categorical(e.g. material) and continuous covariates (e.g. age), respectively. In thestandard linear model, the errors are assumed (independent and identicallydistributed) i.i.d. normally distributed and the relationship between theresponse variable and the covariates is represented as:E(yi|xi, zi) = β0 +p+q∑j=0βjXj (3.1)where β0 is the intercept and βj are regression coefficients of both (cate-gorical and continuous) covariates Xj. Linear regression models have beenused to predict actual and future conditions of sewer pipes (e.g. Gedamet al., 2016). However, regression models are also required when a categori-cal response variable (e.g., in sewer pipes deterioration, the condition stateof pipes is represented by categorical levels going from newly installed pipe:condition 1 to the likely to fail pipes: condition 5), the effect of covariates isnonlinear, or if spatial or cluster specific heterogeneity must be considered.Generalized Linear Model (GLM) framework characterizes regression wherethe response is categorical. In GLM, the conditional expected mean of theresponse is given by:E(yi|xi, zi) = h(ηlineari ) (3.2)where ηlineari = linear predictor defined as ηlineari = x′iβ + z′iγ, h (·) isa response function that links the conditional mean of yi with ηlineari , thedistribution of yi belongs to an exponential family with the mean µi =E(yi|xi, zi) linked to ηlineari by µi = h(ηlineari ). For binary response, yi ∈0, 1, the expected mean E(yi|xi, zi) in Equation 3.2, is represented in termsof probability of yi to be in a given state, e.g., (pi = P (y = 1)). GLMsapplications for sewer pipes deterioration are: the logistic regression (Sousa263.3. Mathematical formulation of geoadditive modelset al., 2014; Salman, 2010; Ana et al., 2009; Ariaratnam et al., 2001; Davieset al., 2001b), ordinal regression with cumulative logit (Younis and Knight,2010) and multinomial regression (Salman, 2010). The main drawback ofthis approach is the linear dependency assumption between the categoricalresponse and the covariates. In the proposed framework, only categoricalcovariates are allowed to have parametric effects to the sewer pipes scoreand thus constitute the linear part of the proposed deterioration model.3.3.2 Non-parametric model of the continuous variablesFor nonlinear dependency on the covariates, the GLM are extended toGeneralized Additive Models where the linear predictors of continuous vari-ables are replaced by nonlinear smooth functions. The new defined semiparametric predictor ηi is represented as:ηi = x′iβ + f1(zi1) + ...+ fp(zip) (3.3)where f1, . . . , fp = nonlinear smooth functions of the continuous covariatesand x′iβ is the parametric part. In the frequentist approach, the smoothfunctions fj of a continuous covariate zip are approximated by a polynomialspline of degree lj . Each spline fj represents a linear combination of mj =hj + lj − 1 B-Spline basis function Bj,k evaluated at specified knots zj,min =ξj,1 < ξj,2 < ... < ξj,hj = zj,max.fj(zi,j) =mj∑k=1γj,kBj,k(zi,j) , i = 1 · · ·n , j = 1 · · · p (3.4)where γj,k = amplitude that accordingly scale the B-Splines Bj,k to fit theobserved data. The good fit of data is obtained by allowing a high number ofequidistant knots and imposing a roughness penalty 4j∑mjk=d+1(4dγj,k) onadjacent B-Splines coefficients γj,k that smoothen the function fj . Generally,20 to 40 equidistant knots are recommended to ensure enough flexibility(März et al., 2016). Moreover, the penalty term λj considers the tradeoffbetween the good fit to the data and the amount of smoothness of thefunction fj . The d-th (4d) order operator represents the difference betweentwo amplitudes of consecutives B-splines, i.e. (41 = γj,k − γj,k−1) for d =1. In matrix representation, the smooth function fj (Equation 3.5) will be:fj = (fj(z1,j), ..., fj(zn,j))′= Zjγj (3.5)Therefore, the semi-parametric representation in Equation 3.3 becomes:η = Xβ +Z1γ1 + ...+Zpγp (3.6)273.3. Mathematical formulation of geoadditive modelswhere Zj = Bj,k(zi,j) is a (n × mj ) design matrix and γj = (γj,1. . . γj,mj )′is a vector of regression coefficients. The penalized least squared criterion isgiven in the following equation (März et al., 2016):PLS(λ) = (y − η)′(y − η) +p∑j=1λjγ′jKdγj (3.7)where Kd = penalty matrix based on the d-th order differences. However,this approach does not consider the uncertainty related to the data and themodel itself. Furthermore, the minimization of the PLS (Equation 3.7) oftenfail in practice because no optimal solution for the λj exists or the compu-tational effort becomes intractable as the number of smooth function in themodel increases (Lang and Brezger, 2004). The development of computersand MCMC simulation made the Bayesian inference, an attractive way toanalyze complex statistical models (Fahrmeir et al., 2013).3.3.3 Bayesian Structured additive modelThe developed structured additive model in Equation 3.6 is flexibleenough to capture the uncertainty related to data and modeling. In theBayesian framework, the observed data are considered as random realiza-tions. Thus, the vectors of regression coefficients γj and β in Equation 3.6are modeled as random variables and appropriate prior distributions are as-signed. Non-informative priors are assumed for the parametric coefficientsβ, in the model, i.e., p(βr) ∝ const, r = 1. . . q (März et al., 2016; Lang andBrezger, 2004). The first or second order Gaussian random walks priors forthe semi parametric part γj are defined to replace the roughness penalty.Random walks(RM) priors are represented as in the following equations 3.8and 3.10:RW1 : γj,k = γj,k−1 + µj,k k = 2, ..,mj (3.8)RW2 : γj,k = 2γj,k−1 − γj,k−2 + µj,k k = 3, ..,mj (3.9)where µj,k ∼ N(0, τ2j ) = Gaussian error terms. In Bayesian approach, thequadratic penalty λjγ′jKdγj in (see Equation 3.7) is replaced by a joint mul-tivariate Gaussian smoothing prior distribution for the regression coefficientsγj :p(γj |τ2j ) =1(τ2j )rank(Kj )2exp(− 12τ2jγ′jKdγj)(3.10)283.3. Mathematical formulation of geoadditive modelswhere Kj = penalty matrix based on the d-th order difference and τ2j =variance parameter that control the smoothness of fj and corresponds tothe inverse of the smoothing parameter λj defined in the penalty term inthe frequentist approach.3.3.4 Geoadditive modelInformation about the geospatial location where the observation has beencollected is used as a surrogate variable representing unobserved covariatesand also accounting for spatial autocorrelation. The addition of this valu-able information to the structured additive model in Equation 3.3 with itsmatrix notation in Equation 3.6 become a Geoadditive regression model pre-sented in Equation 3.11. Spatial effects, in sewer pipes deterioration analy-sis, originate from correlated (load transfer, surface use, surface type) anduncorrelated (water main burst and leakage, ground disturbance, groundwa-ter level, ground conditions, soil backfill type) unobserved covariates. Thepredicted value is then given by the following equation:ηi = x′iβ + f1(zi1) + ...+ fp(zip) + fgeo(Si) (3.11)Thus, the geospatial effect on the pipes condition fgeo is split into twocomponents: the structured correlated effect fstruct and the unstructuredfunstruct, specific location effect (local heterogeneities), i.e. fgeo = fstruct +funstruct. The correlated spatial effect fstruct = (fstruct(S1)...fstruct(Sn))′ =Zstructγstruct is represented as follows: for each district s ∈ 1, . . . , S in thearea of interest (e.g. in a city, different communities may represent districts),a separate regression coefficient is estimated. The vector of regression coef-ficients γstruct = (γstruct(1)...γstruct(S))′ collects all distinct spatial effects.The (n×S) designed matrix Zstruct connects an observation i with the corre-sponding spatial effects. Gaussian Markov Random Field priors (Equation3.12) are assigned to the spatial regression coefficients γstruct. These priorsallow the districts in the neighborhood to have similar effects.γstruct(s)|γstruct(−s)∼N(1|N(s)|∑r∈N(s) γstruct(r),τ2struct|N(s)|), s=1...S (3.12)where γstruct(−s) = vector containing all the spatial effects except the onefor district s, and |N(s)| denotes the total number of neighbors that sharea common boundary with district s. The expected value of the regressioncoefficient γstruct, that is the mean value of the regression of the neighboringdistricts, is controlled by the variance τ 2struct and the inverse of |N(s)|.293.3. Mathematical formulation of geoadditive modelsThe joint prior of all spatial effects can be derived from the conditionaldistributions and can be represented as (März et al., 2016):p(γstruct(s)|τ2struct)∼ 1(τ2struct)rank(Kstruct)2exp(− 12τ2structγ′structKstructγstruct)(3.13)whereKstruct = the precision matrix containing the neighborhood informa-tion, i.e.,Kstruct[r, s] =−1 if districts s and r are neighbors|N(s)| if s = r0 otherwiseThe joint prior in Equation 3.13 induces a specific correlation structureand ensures spatial smoothness of the regression coefficients γstruct and lo-cal heterogeneities are correlated. Therefore, the unstructured componentfunstruct of the geospatial covariates are modeled as i.i.d Gaussian randomeffects γstruct|τ2struct ∼ N(0, τ2struct), s = 1...S. In the Bayesian frameworkapproach, the function in Equation 3.13 represents the joint multivariateprior distribution of the unstructured effect where Kstruct = I.With the assumption of a Gaussian condition mean response, i.e., y|η, σ2 ∼N(η, σ2I)the inference is based on a full Bayesian MCMC simulation, witha posterior given as:p (θ|y) ∼n∏i=1p(y|η, σ2)×p∏j=1p(γj |τ2j)p(τ2j)×[p(γstruct|τ2struct)p(τ2struct)p(γunstruct|τ2unstruct)p(τ2unstruct)] q∏r=1p (βr) p(σ2)(3.14)where θ = vector of all the model parameters. Details on the StructuredAdditive Regression (STAR) models can be found in März et al. (2016) andKneib and Fahrmeir (2007). R implementation is detailed in Umlauf et al.(2012).3.3.5 Variable selection and model developmentThe dependent variable used in this study is the pipe score rather thanthe ICG used in previous studies ((e.g. Caradot et al., 2018; Tran et al.,2009a)). Limitations in predictive models (e.g. binary response for logis-tic regression, reference state for multinomial regression) are overcome by303.3. Mathematical formulation of geoadditive modelsselecting a continuous dependent variable that will be converted to the qual-itative performance metric ICG. Three categories of covariates are includedin the regression model: (1) Physical data: material, length, diameter, age,depth, slope, residential and commercial service connections, (2) Mainte-nance data: repairs, flushes, cleaning, degrease, backups and root cuts and(3) Environmental data: geographical location of pipes into communities.Table 3.1 gives a brief description of the factors, used in this study, whichare assumed to have an influence on the sewer pipe deterioration in the cityof Calgary. Data are collected from different sources: (1) asset database(physical), (2) incident database (maintenance) and (3) inspection database(environment,defects and pipes’ scores). Available factors are classified intoqualitative and quantitative sets before the definition of the way each fac-tor influences the output response. All the continuous covariates: numberof root cuts, length, diameter, age, depth, slope, number of previous re-pairs, number of previous flushes, number of previous cleaning, number ofprevious degrease and number of previous backups are assumed to havenonlinear impacts on the response variable that is the pipe score. Main-tenance operations increase the pipes service life. However, some mainte-nance techniques (e.g. flushes, cleaning) may initiate erosion in the sewermaterial that will evolve with time. A P-spline based on a second orderrandom walk of degree 2 was assumed as prior distribution for the contin-uous variables. The material covariate is the only categorical variable inthis model and an ordinary least squares method is used to estimate thefixed effect for each material. The number of knots is set to 40 for diameter,age, spatial effects, flushes, cleaning, repairs, degrease and 20 for the rootcuts, slope, depth, backups. The interactions between age-repairs, length-diameter, cleaning-backups and slope-depth are included in the regressionmodel. A two-dimensional P-spline based on the tensor product of one-dimensional P-splines is set as their prior. The geospatial location of a pipewithin a district, contain information about unobserved covariates, similari-ties among pipes in the neighborhood and possible local heterogeneities. Inour approach, all the pipes of a district have the same identification number,which means they have the same characteristics of the unobserved covari-ates. Additionally, a possible dependency due to the proximity of pipes isconsidered, i.e., pipes in the neighborhood may show similar deteriorationpatterns because they are affected by the same magnitude of all the as-sumed factors including the unobserved factors. The geospatial covariateis composed of two components: the structured components whose prior isthe Gaussian Markov Random Field and the unstructured components thatare assigned a random effect. In structured additive regression models, the313.4. Wastewater system of the city of Calgaryposterior distribution is numerically intractable. The Markov Chain MonteCarlo (MCMC) simulation method allows the construction of a Markov chainwith the posterior as stationary distribution. The iterations of the transitionkernel of this Markov chain converge to the posterior yielding a sample ofdependent random numbers. After the convergence phase of the algorithm(burn-in), a thinning phase is applied to the Markov chain to reduce theautocorrelations. In the proposed framework, the response variable distri-bution is assumed to be Gaussian. Thus, the full conditional of the fixedeffects (linear part) and the nonlinear functions are multivariate Gaussianmaking the Gibbs sampler the most appropriate for the MCMC. The city ofCalgary has 301 communities representing the districts. The final proposedused model is:η = γ0 + γ1 ×Matcode+ γ2 × Length+ γ3 ×Diameter + γ4 ×Age+ γ5 ×Depth+ γ6 × Slope+ γ7 ×Rservs+ γ8 × Cservs+ γ9 × Flushes+ γ10 × repairs+ γ11 ×Rcuts+ γ12 ×Backups+ γ13 ×Degrease+ γ14 × Cleaning + γ15 ×Diameter × Length+ γ16 ×Depth× Slope+ γ17 × Cleaning ×Backups+ fstruct(district) + funstruct(district)(3.15)3.4 Wastewater system of the city of CalgaryThe city of Calgary is situated in Southern Alberta, Canada and hasa population of 1.2 million people. Its wastewater system is composed of79,923 sewer pipes (5545.9 km) (fig. 3.2), connecting three treatment facili-ties (Fish Creek, Pine Creek and Bonnybrook) to 312,243 residential homesand 7786 commercial, industrial and public buildings. 5.24% (299.5 km) ofpipes have their age above 65 years with 3.4% (188.6 km) above 100 yearsold. Different pipe materials have been used to build the system: asbestoscement (AC), concrete (CON), brick (BR), vitrified clay (VCT), steel (ST),cast iron (CI), corrugated Metal Pipes (CMP); polyvinyl chloride (PVC)and polyethylene (PE) sewer pipes. These materials are grouped into: (1)Cementitious: CON, AC; (2) Clay: BR, VCT; (3) Metallic pipes: ST, CI,CMP; and (4) Plastic: PE, PVC. Plastic and cementitious pipes represent89.4% of the total pipes’ length in the system. Before 1945, most of thepipes were Clay or Metallic. From 1945 to date, a predominance of Plasticand Cementitious pipes is observed in the data.323.4. Wastewater system of the city of CalgaryFigure 3.2: Wastewater system in the city of Calgary.Inspection data collection and processingSince early 1990, an inspection program using closed circuit television(CCTV) technique has been implemented in order to prioritize further in-spection, maintenance and replacement of pipes. The selection of pipes forinspection is based on their age, material and the expert knowledge. Outof 76380 pipes in the city of Calgary, 12662 (1188.2km i.e.; 16.6%) havebeen inspected and classified as follows: 68.2% Cementitious, 17.2% Clay,10.1 % metallic and 4.5% of Plastic). For older pipes, i.e.; installed before333.5. Results and discussion1940, only two groups of material are of concern in the inspection program:Clay and Metallic pipes. A replacement program, started in 1940, has beenintensified since 1960 with a high rate of replacement of Asbestos Cementand Metallic pipes with concrete and Plastic pipes. This is seen in fig. 3.3,where the distribution age for Cementitious pipes is between 0 and 55 andfor plastic between 0 and 45 years. The installation period has been reportedas important parameter that affects the sewer condition. It integrates theage and the quality of the material and the construction work (Baur andHerz, 2002; Davies et al., 2001b).The observed defects have been graded following the WRc protocol. Inthis protocol defects are categorized and assigned a score describing theirseverity and orientation. The pipe segment grade is given based on itshighest defect score that is converted into a crisp number varying from1 to 5 (see Table 2.1) representing the internal condition grading (ICG)(Khazraeializadeh et al., 2014; Rahman and Vanier, 2004).The selection of pipes to be inspected is mostly based on expert judg-ment, the pipe’s material and their age. For the city of Calgary, mostinspected pipes are located in the interior part of the city. Collected dataare summarized and presented in Fig. 3.3. Model’s input data are repre-sented in table (Table A.1) with the first column representing the dependentvariables while the subsequent columns are the independent covariates thatexplain the response score.3.5 Results and discussion3.5.1 Physical covariatesFour groups of material (cementitious, clay, metallic, and plastic) areconsidered in this study. The cementitious and clay pipes have low impactcompared to the metallic and plastic pipes groups (fig. 3.4a) . The metallicmaterial has the highest effect on the structural deterioration of sewer pipes.The corrosion might be the principal reason for the bad performance, i.e.,high impact on the structural deterioration. Ana et al. (2009) logicallyattributed the good performance of cementitious pipes to the fact that theyare constructed offsite in a controlled environment.343.5. Results and discussion040080012000 30 60 90Age (years)Count(a)0200040006000500 1000 1500Diameter (mm)Count(b)025050075010000 100 200Length (m)Count(c)050010001500200025005 10Depth (m)Count(d)010002000300040000 10 20 30Slope (%)Count(e)0200040001 2 3 4 5ICGCount(f)CementitiousClayMetallicPlasticFigure 3.3: Description of inspected pipes classified in 4 material groups:the cementitious, clay, metallic and plastic pipes (a) Age (years), (b) Diam-eter (mm), (c) Length (m), (d) Depth (m), (e) Slope (%), and (f) ICG353.5. Results and discussionTable 3.1: Covariates description.Covariates (Physical) DescriptionMaterial Designed material of pipes (categorical: 1= cementitious,2= clay, 3= metallic, 4= plastic)Age The difference between the inspection date and the installa-tion date (continuous)Length The manhole to manhole distance inspected (continuous)Diameter size of the pipes (continuous)Depth mean distance from the crown of the pipe to the groundsurface (continuous)Slope Angle between the pipes axis with the horizontal (continu-ous)Rservs Number of residential connections to the pipe (continuous)Cservs Number of commercial buildings connected to the pipe (con-tinuous)Covariates (Maintenance)Flushes Number of flushes done previously on the sewer pipe (con-tinuous)repairs Number of previous repairs on the sewer pipe (continuous)Rcuts Number of times, the roots have been cut from inside thepipe (continuous)Backups Number of times, there have been water backups in the sew-ers (continuous)Degrease Number of time, the maintenance team have degreased thesewer pipe (continuous)Cleaning Number of time, the sewer pipes have been cleaned (contin-uous)Covariates (Environmental)Geospatial location The geographic location of the sewer pipe. While it is widelyaccepted that pipes having the same characteristics deterio-rates at the same pace, there is a variation in the deteriora-tion across pipes in the same cohort but affected by differentenvironmental covariates such as the nature of the soil theyare buried in, the groundwater fluctuation, soil compaction,traffic on the ground, activities in the vicinity. These unob-served and unknown data have correlated and uncorrelatedeffects on the structural responseThis result is in agreement with previous studies that found the materialcovariate to be significant for drainage pipes (Micevski et al., 2002) and forwastewater sewer pipes (Salman, 2010; Ana et al., 2009). If no constructiondefects exist, the newly installed sewer pipe will have a period during whichno defects are observed during inspections. For the city of Calgary, thisperiod is approximately equal to 30 years (fig.3.4b). At 60 years old, the363.5. Results and discussionAge impact on the pipe score, that started increasing when the pipe was at20 years old, reaches a local maximum value.Between 60 and 100 years old, the Age impact decreases until 80 years,before its level increases significantly. Thus, the period between the localmaximum at 60 years old and the local minimum at 80 years, appears tobe the best moment for planning pipe replacement. The narrow credibleinterval is an indication of high density of data availability along all ages,from the age of 1 to 115 years. The increased level of impact of the age factoron the sewer structural condition have been reported (Ana et al., 2009; Baiket al., 2006).Small diameter pipes (Diameter ≤ 500mm) have higher impact on thedeterioration of sewers than large pipes (Diameter ≥ 500mm) (fig. 3.4c).Previous studies reported the same observation on different case studies(Salman, 2010; Ana et al., 2009; Baur and Herz, 2002; Davies et al., 2001b).Small size pipes deteriorate faster because inexperienced workers handle andpose them (Kley and Caradot, 2013; Davies et al., 2001b). Furthermore,their small moments of inertia make them less resistant to bedding move-ments. Large pipes get more attention because the consequences of theirfailure are high. In the city of Calgary, 82.3% of inspected pipes have theirdiameter below 500 mm. The length, similar to the Age, has an increasingnonlinear impact (fig. 3.4d). In WRc protocol, each defect observed on apipe segment is attributed a score.The condition of a sewer pipe is classified according to its most severedamage in the WRc protocol. Long pipes are likely to have more defects withdifferent severity. Thus, the probability of having defects with high scoresis higher in long sewer pipes than it is for short sewer pipes. Generally, forthe same diameter, long pipes expose larger areas to factors influencing thedeterioration than short pipes. In addition, the probability of long pipesbending is also elevated. The obtained results are contradicting the resultsby Baik et al. (2006) and are in accordance with the results presented bySalman (2010) and Ana et al. (2009).A sewer at shallow depth is subject to load cycles on the ground surfaceand the effect of seasonal variation of the soil moisture content (Fig. 3.4e).However, deep buried sewer pipes only support the weight of the backfillsoil and are not affected by high frequency of surface loads. This assump-tion is confirmed in the Calgary case study. Underground activities (miningblastings), can have impact on the presented curve (Fig. 3.4e). Salman(2010) found a contradictory conclusion for the depth covariate when ap-plying different deterioration models on a single case study. The depth wasstatistically significant for the multinomial logistic regression, while it was373.5. Results and discussionnot for the logistic regression. Ana et al. (2009) also found the depth covari-ate not significant using the logistic regression on the Leuven case study.(a)Cement Clay Metallic PlasticMaterial types-1001020Partial effect(b)20 40 60 80 100 Age (years)-2002040Partial effect(c)200 300 400 500 600 700 800 900Diameter (mm)-30-20-10010Partial effect(d)50 100 150 200Length (m)-505Partial effect(e)2 3 4 5 6 7 8Depth (m)-10-505Partial effect(f)-2 0 2 4 6 8 10 12Slope ( %)-20020Partial effect(g)0 5 10 15 20 25 30 35Residential connnections0510Partial effect(h)0 1 2 3 4 5 6 7Commercial connnections-50510Partial effectFigure 3.4: Semi-parametric effects of the physical covariates (a) Materialtypes, (b) Age (years), (c) Diameter (mm), (d) Length (m), (e) Depth (m),(f) Slope (%), (g) Residential connections, and (f) Commercial connections,with 80 % and 95 % credible interval.The Slope covariate is not usually included in deterioration studies. Ingravity sewers, low velocities, due to flat sewers, increases sediment deposi-tion that have negative effect on the structural condition of pipes. Sediment383.5. Results and discussiondeposit will increase the probability of production of corrosive gases (e.g.H2S), which increase the probability of internal corrosion in cementitiousand Metallic pipes. Moreover, the flow velocity will increase just after thesediment deposit with the possibility of creating erosion for cementitiousand Clay pipes. The results in Fig.3.4f confirms the nonlinear dependenceof the structural condition of sewer pipes on the slope. Baur and Herz(2002) argued that steeper pipes deteriorate slower than flat pipes. Whenthe number of connections (residential and commercial) to a pipe increases,the effects on the structural states of the sewers also increases. The increaseddischarge is responsible for new defects appearance (e.g.erosion, leakage atthe junctions).(a)0 5 10 15 20 25 30 35Number of Flushes-50510Partial effect(b)0 1 2 Number of Repairs-1001020Partial effect(c)0 5 10 15Number of Roots cuts-10010Partial effect(d)0 1Number of Backups-1000100Partial effect(e)0 1 2 3 4 5 6 7Number of Degrease actions-505Partial effect(f)0 5 10 15Number of Cleanings-20-10010Partial effectFigure 3.5: Semi parametric effect of maintenance covariates on the re-sponse variable: (a) Number of Flushes, (b) Number of Repairs, (c) Numberof Roots cuts, (d) Number of Backups, (e) Number of Degrease actions, and(f) Number of Cleanings.393.5. Results and discussion3.5.2 Maintenance covariatesMaintenance data are important in the assessment of the deteriorationof sewer pipes. These data play a double role in regression models:1. Memory of the process : as all the covariates,they allow the model topredict the condition of a pipe given previous maintenance works;2. Some maintenance activities may increase the likelihood of appearanceof new defects (e.g.; the flushing may initiate an erosion defect in aclay pipe).An activity in maintenance is scheduled when the structural and/or theoperational states reach a certain threshold. The objective of maintenance isto upgrade the pipe from its actual condition to a better condition. However,once flushes and repairs are executed on a sewer pipe, our results show anincreased impact on the structural deterioration of pipes (Fig. 3.5a-b). Thissituation is the same for the number of root cuts (Fig. 3.5c) that has thesame trend up to five (5) root cuts before it presents a declined effect withthe increase of the number of root cuts. More data are needed for this partto understand and evaluate the effect of root cuts above 5 cuts.The Backups (Fig. 3.5d) have a constant impact on the deterioration.This should be understood that more data are needed about backups andfor the results presented here, the backup is assumed to have a random effecton the deterioration. The degrease impact is increasing and more data willallow the assessment of the real trend of the covariates (Fig. 3.5e). Thenumber of cleanings (Fig. 3.5f) has a negative impact on the structuraldeterioration as expected. However, further investigations are needed witha increased size of data related to this activity. From the above analysis, itis shown that most of the factor influencing the deterioration of sewer pipeshave a nonlinear impact on the condition of sewer pipes.The definition of a complex model that accounts for both fixed and non-linear effects of the covariates is justified and it enhances the prediction ofstructural deterioration. Furthermore, the interactions between the covari-ates may have higher impact on the response variable than the covariatesthemselves. The next section presents the covariate interaction impacts onthe response variable.403.5. Results and discussion-300 15-20-102 100Covariates interactionSlope (%)Depth (m)4105206 0308 -5(a)(a) Interaction impact between Depthand Slope-200 200-15-10150-5Covariates interactionDiameter (mm) Length (m)0500 1005105001000(b)(b) Interaction impact between Diame-ter and Length-400 2-30-201.5-10Covariates interaction50Age (years) Repairs (count)01100.520100 0(c)(c) Interaction impact between Age andthe number of previous repairs-60 200-4-21500Covariates interactionLength (m)Age (years)250 1004650100 0(d)(d) Interaction impact between Age andLenghtFigure 3.6: Impact on the response of the interactions between the covari-ates.3.5.3 Covariate interactionsThe analysis of the interactions between covariates gives an indicator ofthe way independent variables are linked to the response variable. The inter-action is viewed here as the attenuation(intensification) of the effect of indi-413.5. Results and discussion-4000 2-2001.5100Covariates interactionRepairs (count)Flushes (count)12020030 0.540040 0(a)(a) Interaction impact between thenumber of previous flushes and repairs-20 1-1051Covariates interactionCleaning (count) Backups (count)0.51023154020(b)(b) Interaction impact between thenumber of previous cleaning and back-upsFigure 3.7: Impact of covariates’ interactions.vidual variables acting together on the output response value. Furthermore,when the interaction between two covariates is high, then the assumption oflinear dependency between these covariates with the response variable is nolonger plausible (Jaccard and Wan, 1995). The nonlinear effect of the depthcovariate is larger when the sewer is buried at shallow depth and decreasesas the depth increases (Figure 3.4e). However, the analysis of the interactionof the depth and the slope (Figure 3.6a) shows an increasing effect when thedepth increases. Covariates interaction (Figures 3.6 and 3.7) give details onthe variation of the individual covariate effects.For example, figure 3.6a shows that the presented effect of the depth,in figure 3.4e, is available only for the slope values below 10%. In addition,when the slope is greater or equal to 10%, the depth impact is reversed, anincreasing effect from shallow to deeper pipes. This is also observed for theslope where a steep slope have a high effect at certain values of depth. Thesame situation occurs in the evaluation of the interaction of the diameterand the length (Figure 3.6b) where the interaction between the diameterand the length of the pipes produce a high combined effect. The effect ofthe length have been modified by the diameter showing an increased effect ofthis latter for long pipes and small diameter. The high interaction impactsin (Figure 3.6) confirms the nonlinearirty of the effects of the covariates onthe structural deterioration of sewer pipes.423.5. Results and discussionIn the above mentioned results, only few of the influential factors, avail-able in the dataset, are used in the deterioration model. In order to accountfor the unobserved data, the geospatial information contained in the loca-tion of pipes is added to the modeling to increase its accuracy. The nextsection will present the obtained map representing the effects of unknowncovariates at different location of the city of Calgary and how this result canbe used in practice.2.5 0 2.5 5 7.5 10 km -9.7 - -5.6 -5.6 - -1.4 -1.4- 2.7 2.7 - 6.8 6.8 - 10.9 MarlboroughWoodbineFigure 3.8: Geospatial effect of the unobserved covariates on the expectedmean score of pipes.433.5. Results and discussion3.5.4 Geospatial effectsThe inclusion of geospatial effects of the unknown and unobserved co-variates in the development of structural deterioration models of sewer pipesis important in large buried water infrastructure where budget and timelimitations do not allow the inspection of all the pipes. The deteriorationpattern represented in the map (Fig. 3.8) cannot be described by the co-variates (continuous and categorical) alone. The map shows a high effect inthe central part of the network area with a peak value in the Marlboroughdistrict. This finding triggers questions on the causes that make pipes todeteriorate faster or slower from one place to another in the same networksystem. The search of additional covariates that will explain the deteriora-tion in the center of the city is necessary to support future decision making.Furthermore, the map is a useful tool that will be used by utility managersfor the prioritization of inspections and to focus maintenance tasks on areasthat are critical (fast deterioration). Decision makers will have a rapid viewon the areas that need their attention in the network.For illustration of the concept, we selected two districts (Marlboroughand Woodbine) that have the highest and the lowest geospatial effect onthe response variable in the city (Fig. 3.8). Then we assume two newhypothetical cementitious pipes with the physical characteristics given inTable 3.2. Predicted scores are converted into internal condition gradingfollowing WRc protocol as defined in Table 2.1. The following combinationof characteristics (short pipe-small diameter, short pipe-large diameter, longpipe-small diameter, long pipe–long diameter) are considered in the analysis.The minimum and maximum values of these characteristics are used for thediameter and length. The mean depth and slopes are used for both (Table3.2).The model is run for 120 years, with a time step of 10 years, and theresults are presented in Fig. 3.9. Our objective is to illustrate how pipessharing the same characteristics (this pipes will be considered to belong tothe same cohort, following previous studies) may have different deteriorationpatterns if they do not share the same geospatial location. The analysis ofthe results in Fig. 3.9 highlights the following:− For the same length of pipes, the smaller diameter (Fig. 3.9a) deteri-orates faster than the larger diameter (Fig. 3.9b). The reason is thefact that larger pipes are installed by experienced personnel with ahigher level of supervision while smaller pipes are not (Davies et al.,2001b). This confirms the results published in (Baur and Herz, 2002;Ariaratnam et al., 2001). However, it is in contradiction with the443.5. Results and discussionresults presented in Ana et al. (2009).− Longer pipes deteriorate (Fig 3.9c) faster that shorter pipes (Fig 3.9a).This results reproduced the result found by Ana et al. (2009) for thecity of Leuven in Belgium. They argued that this results is due tothe fact that the probability of having several defect in longer pipes ishigher than in short segments.− Two small size and long cementitious pipes (Fig 3.9c) installed thesame day one in the Marlborough district and the other one in theWoodbine district, the pipes in the Marlborough district will dete-riorate faster than the pipes in the Woodbine district. If pipes incondition 4 are considered as failed pipes (the minimum acceptableservice level of pipes in the system is fixed at the level condition 3),then the pipe installed in the Marlborough district will fail ten yearsbefore the pipe in the Woodbine. This results is very important sinceit will allow the municipality to increase the inspection frequency inthe district of Marlborough rather than in Woodbine. Moreover, for areplacement decision making based on sewer pipes age only, the pipesinstalled in Marlborough will reach their replacement age 10 years be-fore these in Woodbine. Thus, the future value of the required amountof money to replace one pipe today in Woodbine will allow a replace-ment of two pipes (for a 10% interest rate) considering the delay inthe deterioration in this area.− Two long and larger cementitious pipes installed in both places dete-riorates following the same curve as presented in Fig. 3.9d.3.5.5 Future condition predictionsThe actual and future structural condition of sewer pipes (both inspectedand uninspected) can be predicted using the geoadditive regression modelpresented above. Much research suggested a single deterioration curve usedto predict the internal condition states of all the pipes in cohorts or the entirenetwork. However, this study demonstrated that the geospatial effects onthe structural deterioration of sewer pipes vary from one location to another.Thus, similar pipes, i.e., pipes having the same physical characteristics, in-stalled in the same sewer network may present different deterioration rateif they are installed at locations where local heterogeneities are observed inthe network.453.5. Results and discussion0 20 40 60 80 100 120 Age (years)12345Performance(a)MarlboroughWoodbine0 20 40 60 80 100 120 Age (years)12345Performance(b)0 20 40 60 80 100 120Age (years)12345Performance(c)0 20 40 60 80 100 120Age (years)12345Performance(d)Figure 3.9: Future condition prediction of a new cementitious pipe installedin two different locations: Marlborough and Woodbine. (a) Small diameterand short length, (b) Large diameter and short length, (c) Small diameterand long length, and (d) Large diameter and long length.3.5.6 DiscussionThe above model results from 75% of data (training data). The valida-tion is obtained on the 25% testing set that gives a coefficient of determina-tion R2=0.89 and a Root Mean Squared Error (RMSE) of 17.33 (Fig. 3.10).The normalized RMSE for training and validation sets are 10% and 11%463.5. Results and discussionrespectively. The high value of RMSE is due to the missing information onthe replaced pipes that is captured in the proposed model by the geospatialcovariate. It should be noted that in many sewer pipes networks, databasesare not usually update in relation with the replaced pipes. (e.g. In the cityof Calgary, pipes with score values equal or above 165 only represent 2.5%of the data used to build the proposed model). Rapid and easy decisionsare based on the pipes conditions that are the transformation of scores intoordinal numbers following a given protocol.10 40 80 165 200Observed14070190330Predicted(a)R2=0.89Sewer scoresFitted curve1 2 3 4 5Observed12345Predicted(b)Sewer ConditionFitted curveFigure 3.10: Correlation curves between the predicted and observed pipes:(a) scores, and (b) conditions.Observed scores are transformed into condition states following WRcprotocol as presented in Table 2.1. Predicted scores are converted intocondition states after an optimization process that aims at minimizing theprediction error (RMSE) between the two representations (scores and con-dition) to obtain the same error value while varying the classes ranges (Fig.3.10b).The high correlation between the predictions and the observed scoresdemonstrates the following:1. Natural phenomena are nonlinear, and deterioration of sewer pipesshould include nonlinear relationships between the covariates and thescore that represents the internal condition of pipes;2. The inclusion of geospatial location allows accounting for unknownand unobserved covariates that may have significant influence of the473.6. Summarydeterioration. The correlation between the predicted and the observedcovariates confirms the complexity of the process.Table 3.2: Characteristics of new pipes installed at Marlborough and Wood-bine.CovariatesShort LongSmall Large Small LargeLength 2.53 2.53 264.38 264.38Material Cement Cement Cement CementDiameter 200 1800 200 1800Age 0 0 0 0Flushes 0 0 0 0Cleaning 0 0 0 0Degrease 0 0 0 0Roots 0 0 0 0repairs 0 0 0 0Replaced 0 0 0 0Slope 3% 3% 3% 3%Depth 4 4 4 4Backups 0 0 0 0Rservs 0 0 0 0Cservs 0 0 0 03.6 SummaryIn this chapter, an individual deterioration model is developed using aBayesian inference based on MCMC simulations. The model considered theimpacts of physical, maintenance and environmental factors on the struc-tural condition of sewer pipes using linear, nonlinear and geospatial effects.Geospatial autocorrelation and local heterogeneities embeds the unobservedcovariates that may have effects on the deterioration process.The results highlight the importance of considering a semi parametricmodeling approach as some of the continuous covariates (e.g., length, Age)have nonlinear effect on the structural states of the pipes. The constantform of effect (e.g., backups) is due to the limited available data. Once morebackups data are available, they can be easily incorporated into the modeland reduce the high uncertainty represented in the results. Additionally,483.6. Summarythe interactions between the covariates show an increased trend comparedto the separate effects. Furthermore, the Bayesian inference captures theuncertainty in the data. The spatial autocorrelation allows the detection ofspatial patterns in the data that can be used to identify additional covariatesrepresenting the local heterogeneities. Our results show a high rate of sewersdeterioration in the center of the network area with the highest and lowestrate identified in the Marlborough and Woodbine districts respectively. Thepipes in this area (in the majority, metallic, cement and clay pipes) are olderthan the newly installeed PVC pipes in the outer part. If sewers in condition4 and 5 are assumed as failed, the prediction model shows an earlier failure(10 years before) of a cemetitious pipe installed in the Marlborough than theone installed in Woodbine districts. This results will enhance a cost-effectivemanagement of water utilities for municipalities.At a practical point of view, this research produced a powerful tool toorient and guide the prioritization of inspections in the network area. A mapis a universal language tool, accessible to people from different personal andprofessional backgrounds. The geospatial effect map on the deteriorationof sewer pipes provide a sense of scale and distance of critical areas. Theregression model will allow planning for the time of future inspection andinterventions. Finally, this research showed that the designed data rep-resenting the physical data (e.g., length, material, age, depth, slope), themaintenance data and the geospatial location of the pipes can efficientlyrepresent a realistic deterioration model for all (inspected and uninspected)the pipes in the network. Such a model will serve both planning and oper-ations.49Chapter 4Geoadditive quantileregression model for sewerpipes deterioration usingboosting optimizationalgorithm4.1 BackgroundQuantiles go beyond the mean and provide a detailed information aboutcomplete conditional distribution instead of only the median (Zhang andTang, 2017; März et al., 2016; Waldmann et al., 2013; Fenske et al., 2011).Thepth quantile is the value that delineates a given proportion of set of values.For instance, the median quantile (50th quantile) divides an ordered set intotwo groups. In addition, the inherent robustness of quantiles reduces the in-fluence of outliers and extreme data on the model (Waldmann et al., 2013).An example of quantile is the median that is defined empirically as the valuewhere 50% of a random sample have smaller values and 50% of the samplehave greater values.The analysis of quantiles allows the assessment of the lower and upperquantile distribution of the response variable that may contain high riskypipes (the upper quantile contains pipes that have the high likelihood of fail-ure; the lower quantile may contain old pipes in good condition but havinghigh consequences of failure). Furthermore, the pipes attributes that areresponsible of the appearance of outliers may differ in the quantiles. Theidentification of these factors through appropriate modeling of the deteri-oration process will allow decision makers to anticipate the occurrence ofextremes deterioration patterns in pipes useful life. Statistically significantvariables, in regression models, are identified based on heuristic techniquessuch as stepwise selection that are not efficient. In addition, in frequentist504.2. Methodologybased statistical models, this approach has a risk of overconfident estima-tion of the output variable (Fragoso et al., 2018; Hofner et al., 2014). Shiauand Chen (2015) used quantile regression to model quantile dependent sed-iment rating curves. Their objective was the prediction of daily suspendedsediment load with a quantified uncertainty information. .The approach presented in (Balekelayi and Tesfamariam, 2019b) is mod-ified with the integration of linear components for continuous covariates, i.e.,the continuous covariates are allowed to have two types of impacts includ-ing the linear and the nonlinear effects modeled following the ordinary leastsquare and P-splines nonlinear smooth functions approaches respectively.Categorical covariates have only one type of impact (linear) to the pipe’sscore. The geospatial effects are evaluated using the Gaussian Markov ran-dom field(GMRF) and are allowed to have two components the structuredand unstructured effects. A Bayesian inference based on Markov ChainMonte Carlo is used to capture uncertainty propagation in the definition ofbase learners’ models. The response data ,defined as a continuous variable(pipes score obtained after grading observed defects following a given proto-col, see Marlow et al. (2007), is iteratively estimated through an optimizedprocess of learners selection.In the following subsections, an extension of this definition to other quan-tiles is presented for an application to the deterioration of sewer pipes usingboth available sewer pipes data (physical, operational and environmental).4.2 Methodology4.2.1 Structured additive quantile regressionFlexible models are needed to express complex nonlinear relationshipsbetween the regressors and quantiles responses variables. Moreover, thesemodels allow the addition of noise that account for over dispersion causedby unobserved heterogeneities and possible autocorrelation.Assume the observations Yi, xi, zi ,i = 1, · · · , n are elements of the in-spection database where Yi represents the pipe segment score, xi = (xi1, · · · , xiq)and zi = (zi1, · · · , zip) are vectors of categorical (e.g. material) and contin-uous covariates (e.g. age) respectively. The objective is to find a relationbetween the observations Yi and the predictions ηi (Equation 3.15)Yi = ηi + i ; i ∼ F (i|θ) ; i ∈ I (4.1)where i is a subset of 1 · · ·n, that is not necessary all latent ηi are observedthrough the data Yi. F is an unknown distribution function of error terms514.2. Methodologyi and may depend on some additional parameters θ. Equation 4.1 relatesthe observations Yi with the modeled predictions ηi.The predictions ηi areexpressed as presented in Equation 3.11.The expression in Equation 3.11 represents the basic model, composed ofthree parts: the usual parametric part (linear), the nonlinear part (smoothfunctions) and the surrogate geospatial effects part, that is used to predictsewer pipes scores. In the case where Yi belongs to an exponential familyand its mean is linked to the predicted ηi through a certain link function (e.g.Gaussian), a structured additive regression model can be used to calculateηi. However, the observed extreme values of pipes internal condition gradesled to the following assumption: the upper and lower quantiles of Yi maybe dependent on different covariates sets than the center (median). Thus,inference on the conditional quantile will provide a more complete descrip-tion of functional changes than focusing solely on the expected mean value.The general additive quantile regression model, derived from Equation 3.11,is given by the following equation (Waldmann et al., 2013):QYi|xi,zi(τ |xi, zi) = ητi = xTi βτ +p∑j=1fτj (zij) + bτi (4.2)where QYi|xi,zi(τ |xi, zi) is a conditional quantile response, ητi is the semi-parametric predictor, τ ∈ (0, 1) is the τ th quantile response, β is the vectorcoefficient of categorical covariates and f is the vector of smoothing func-tions for continuous and spatial covariates which are assumed to relate ina nonlinear way to the dependent quantile response. The conditional meanobtained for τ = 50% in Equation 4.2 is the Structured Additive Regres-sion model (STAR) (März et al., 2016; Kneib et al., 2009). Equation 4.2represents the Structured Additive Quantile Regression model. The τ thquantile in Equation 4.2 of the error distribution represented in Equation4.1 is zero (F−1(τ |θ) = 0) and the dependent variable is continuous. Thisproperty makes quantile regression interesting because the expert opinionon the prior distribution of error is no longer needed. Information aboutthe geospatial location of pipes can be incorporated in Equation 4.1 to buildGeoadditive Structured Quantile regression model (Equation 4.2).QYi|xi,zi(τ |xi, zi) = ητi = xTi βτ +p∑j=1fτj (zij) + bτi + fgeo,τ (Si) (4.3)The spatial effect fgeo has the same components as in Geoadditive regressionmodel.524.2. MethodologyFor linear quantile, the regression coefficients are estimated by minimiz-ing the asymmetrically weighted sum of absolute deviations (Koenker, 1994).An alternative representation of the Structured Additive Regression Quan-tile model (Equation 4.3) can be achieved via the following minimizationproblem:argminητn∑i=1ρτ (Yi − ητi) (4.4)whereρτ (Yi − ητi) ={τ |Yi − ητi| if (Yi − ητi) ≥ 0(τ − 1)|Yi − ητi| if (Yi − ητi) ≤ 0is the “check function”, i.e., a loss function for quantile regression prob-lem that is appropriate for decision making perspectives in sewer deteriora-tion. The estimation of the Structured Additive Quantile Regression modelis made in a fully Bayesian inferential framework. Three simulation ap-proaches are used to solve the Bayesian quantile inference in practice: theMarkov Chain Monte Carlo (MCMC), the Integrated Nested Laplace Ap-proximation (INLA) and the boosting algorithm. The performance of theseapproaches depends on the problem and is subjected to discussion. Yueand Rue (2009) compared MCMC and INLA and concluded that both areefficient and give reliable quantile inference. However, Mtambo et al. (2014)argued that INLA outperformed MCMC both inaccuracy and computationalspeed for large non-Gaussian response in quantile regression. In their com-parison, Yue and Rue (2009) also applied the boosting algorithm. Although,they used fixed parameters (cubic P-splines base learners with second orderdifference penalty and 20 inner knots), the range of the estimated errorswere the same as for the MCMC and INLA. The boosting algorithms arenovel statistical procedures that starts with sensible estimator or classifiernamed the learner and seeks to improve iteratively its performance on thetraining set (Fenske et al., 2011; Bühlmann and Yu, 2003). Thus, they allowconsistent and stable identification of the significant predictors for differentlevels of response variable (severe, lower, median) (Fenske et al., 2011). Themain advantage of the boosting algorithm is its verified convergence underweak conditions, such as limited information on the covariates in a regressionmodel. With less data on the extreme quantiles, both MCMC and INLAlooses their performance (Yue and Rue, 2009). For each continuous covari-ate, the estimation of the nonlinear part follows the principle in Equation3.4.534.2. Methodology4.2.2 Boosting algorithmThe goal of boosting algorithms is the accurate prediction of a responsevariable based on a set of covariates achieved by combining an ensemble ofdifferent “weak” statistical models, called base learners, that yields greaterprediction accuracy than the results of one single base learner only. A baselearner can be any kind of statistical regression tool where the responsevariable is modeled by one or more covariates, i.e., covariates base learner−−−−−−−→prediction of response. Typical examples of base learners are (univariate)linear regression models, classification and regression trees, or penalized re-gression splines (see Equation 3.4).In general, the goal of boosting is to minimize the expected loss functionin Equation 4.4 that can be rewritten in the following:η∗τ = argminητ E[L(Y, η)] (4.5)where Y is the response and η is the predictor of a regression model. L(Y, η)corresponds to the loss function defined in Equation 3.4. From the observa-tions (Yi;xi, zi), with i = 1 · · ·n; the expected loss in Equation 4.5 can bereplaced by the empirical risk defined in the following equation:E[L(Yτ , ητ )] =1nn∑i=1L(Yτi , ητi(xi, zi)) (4.6)where xi, zi are vectors of categorical (e.g. material) and continuous covari-ates (e.g. age) respectively.The advantage of the boosting algorithm is its ability to proceed to theselection of influential covariates in different quantiles while allowing forrealistic representation of the physical process under study. In addition,only one parameter (stopping criteria ) has to be tuned for avoiding overfitting. This parameter should be carefully selected to allow the selection ofthe most important covariates that best fit the negative gradient residualsand simultaneously prevent the overfitting (Algorithm 1 in Table 4.1).Boosting algorithm iteratively fits the gradient of the loss function tothe covariates. The stepwise increment of fˆ [m]j are small and the overallminimum is slowly approximated. At the same time, the additive struc-ture of the resulting model fit is conserved since the final aggregation ofthe additive predictor and its single component are strictly additive. Theloss function to be minimized, in the estimation part of the algorithm, is ex-pressed in the general form presented in Equation 4.4. The algorithm selectsthe most informative base learners (model components) that minimize the544.2. MethodologyTable 4.1: The gradient descent algorithm.Algorithm: Component-wise functional gradient descent boosting algorithm for struc-tured additive quantile regressionInitialization:After selection the stopping criteria mstop, the definition and initialization of the predictorare the next steps to consider. From Equation 4.5, the type of interaction of each covariateis defined and the model built. Set the iterator m = 0 and the initialization of the responseis done from suitable starting values such as the median of the response values Y1 · · ·Ynas offset, i.e., η[0]i = argminc∑ni=1 ρ0.5(Yi − c) , and fˆ [0]j = 0 for j = 1 · · · p.Iterationwhile m < mstopDo {Negative gradientm = m+ 1 (increment the iterator)Compute the negative gradient residuals of the loss function evaluated at the predictorvalues ηˆ[m−1]i (previous iteration estimated value)u[m]i = −∂∂ηL (Yi, η) |η=ηˆ[m−1]i i = 1 · · ·nFor quantile regression boostingu[m]i = −ρ′τ(Yi − ηˆ[m−1]i)=τ Yi − ηˆ[m−1]i ≥ 0τ − 1 Yi − ηˆ[m−1]i < 0EstimationFit all the base learners separately to negative gradient residuals and obtain, for each baselearner, the gˆ[m]j estimators of fˆ[m]j . Run an optimization process to estimate the bestfitting base learner gj∗ that minimizes the loss function below:j∗ = argminj[(u[m] − gˆ[m]j)T (u[m] − gˆ[m]j)]where u[m] = (u[m]1 , · · · , u[m]n )T is the vector of gradient residuals in the current iterationUpdateCompute the update for the nest fitting base learnerfˆ[m]j∗ = fˆ[m−1]j∗ + νgˆ[m]j∗where ν ∈ [0, 1] is a given step length.Keep all the other effects constant, i.e., set fˆ [m]j = fˆ[m−1]j for d 6= d∗Compute the ηˆ[m]i for i = 1 · · ·n}554.2. Methodologyloss function. Since each base learner is constructed from a single covariate,the variable selection process in boosting algorithm is very efficient becausethe non-informative covariates will not be updated (i.e. they will never bethe best fitting base learner in the optimization part of the algorithm) untilthe stopping criteria is reached. Thus, only influential base learners willappear in the final model. The step length factor ν is of minor effect on theaccuracy of the estimators if a sufficiently small number is selected (Fenskeet al., 2011). The optimal number of boosting iterations (also the influentialcovariates) for Structured Additive Quantile Regression models is obtainedby cross validation. The K-fold cross validation is used for the present study.In this approach, the data is split into two sets: the training and the test-ing sets. Boosting is estimated on the training set while the empirical risk(Equation 4.5) is evaluated on the testing set. The optimal number of boost-ing iterations is the point of minimal risk of the aggregated empirical risks.At that point, only the selected base learners are incorporated in the finalmodel used for predictions.The boosting technique will highlight the causing (influencing) attributesthat make extreme pipes condition to be observed in the network. The inher-ent variable selection property of boosting algorithm (also defined as com-ponents wise functional gradient descent boosting) make it a good choice toestimate quantile regression in sewer deterioration models. An unsupervisedapproach is defined where the continuous covariates have both types of im-pacts (linear, nonlinear) to the response pipe’s score. Parametric and nonparametric components are estimated following the ordinary least squareand P-splines nonlinear smooth functions approaches respectively. Categor-ical covariates, expressed as discrete variables, are assumed to have onlythe linear impact. The Geospatial effects are evaluated using the GaussianMarkov random field and are allowed to have two components (the correlatedand the random) effects as defined in the Geoadditive regression model. ABayesian inference based on Markov Chain Monte Carlo is used to captureuncertainty propagation in the construction of base learners’ models. Theresponse data, defined as a continuous variable (pipes score obtained aftergrading observed defects following the WRc protocol, see (Marlow et al.,2007)), is iteratively estimated through an optimized process of learnersselection.4.2.3 Model developmentAs for the Geoadditive model, the adopted response variable is the scoreof pipes following WRc protocol. The relationships between the pipe score564.3. Results and discussion(continuous variable) and the independent variables described in Table 3.1is established following the assumptions made in the previous paragraph.The final proposed used model is:ητ = a1 × (Age) + f(Age) + a2 × (Rservs) + f(Rservs) + a3 × (Cservs)+f(Cservs) + a4 × (Length) + f(Length) + a5 × (Diameter) + f(Diameter)+a6 × (Material) + a7 × (Flushes) + f(Flushes) + a8 × (Cleaning)+f(Cleaning) + a9 × (Degrease) + f(Degrease) + a10 × (Backups)+f(Backups) + a11 × (Roots) + f(Roots) + a12 × (repairs) + f(repairs)+a13 × (Replaced) + f(Replaced) + a14 × (Slope) + f(Slope)+a15 × (Depth) + f(Depth) +map(id, bnd = clgr) + rd(id, bnd = clgr)(4.7)where ai is a fixed parameter coefficient estimated for linear impact, f isthe smooth function expressing nonlinearity in the relationships, map is thestructured effect of the geospatial information and rd the random geospatialeffect. The boosting algorithm iteratively build each quantile model (hav-ing different base learners) by selecting and updating the more informativefactors. Its parameters are selected as follow: mstop = 30000 and the steplength ν = 0.25. The cross validation of the model is done over 25-foldsbootstrap and the last selected model has the covariates that are the mostinfluential at the stopping criteria for the quantile under analysis.4.3 Results and discussion4.3.1 Model Selected covariatesSeveral reasons may explain the appearance of extreme values: humanerrors in the interpretation of inspection data, the pipes have been replacedand the installation dates have not been updated, or some other reasons thatshould be investigated on the field. In the presented results, human causesof errors are not considered as sources of error and the assigned sewer pipescondition grades are assumed to reflect the real actual condition of pipes.574.3. Results and discussionIterationsRisk factor1 3752 8890 14490 20553 2661623456Figure 4.1: Optimal number of function evaluation to avoid overfitting inthe lower quantile.Three quantile regression models (percentiles) are evaluated in this study(5%, 50% and 95%). These quantiles are selected to evaluate and analyzethe factors that causes extremes values deterioration scores to appear inthe observed condition of sewer pipes after inspections campaigns. The twoextremes groups selected (5% and 95%) are important in the schedule of fur-ther inspections and maintenance plans: the lower quantile with aged pipesbut having low condition score, i.e. having good ICG and the upper quantilegroup, which include new pipes with high condition grading scores, i.e. hav-ing bad ICG. For each quantile model, the optimization process allows thereduction of the loss function, i.e. increase in the accuracy of the predictionand the selection of the most informative base learners (covariates).The minimimal empirical risk (Equation 4.5) is reached after 3675,18656and 20000 iterations for the lower (5th) median (50th) and upper (95th) per-centiles respectively. Fig. 4.1 gives an example for the lower quantile. Opti-mal risk is obtained through a 25 folds bootstrap cross-validation technique.At the minimal obtained risk (e.g. at 3675 iterations as shown in Fig.4.1),the variables that have been incorporated in the model are considered as themost influential, i.e. the most informative (Table 4.2). Their integration inthe model increases the accuracy of the predictions through the minimiza-584.3. Results and discussionTable 4.2: Influential covariates for each selected percentile.Covariates 5th percentile 50th percentile 95th percentileLinear Nonlinear Linear Nonlinear Linear NonlinearAge - - x x x xRservs - x x x xCservs - x x - x -Length - x - - - -Diameter - - - - x -Material x - x - x -Flushes - x x x - xCleaning - x - x - -Degrease - x - x - -Backups - x - x - -Roots - x - x - -repairs x x x x x xReplaced - - X - x -Slope - x - x - -Depth - x - x - -tion of the loss function as presented in the boosting algorithm (Table 4.1).Both types of relationships are iteratively included in the model. Thus, thefinal optimal model may have linear, nonlinear and geospatial effects of thecovariates on the output ICG response as presented in Table 2.1.Globally, it can be observed from Table 4.2, that the diameter does notinfluence the lower and 50th percentile. However, it has a linear influence atthe upper quantile. Large diameter sewer pipes increase the probability ofoccurrence of extreme high scores. Several studies considered a linear rela-tionship between the pipes condition (i.e., failure) and the diameter. Theyfound it as an influential factor that affect the deterioration of sewer pipes(Salman and Salem, 2011; Chughtai and Zayed, 2008; Baik et al., 2006; Tranet al., 2009a; Baur and Herz, 2002; Micevski et al., 2002; Ariaratnam et al.,2001). Some other studies found pipes with large diameters as having largeconsequences of failure due to the amount of flow they can carry (Zhao et al.,2001). However, none of these studies gave details on how this covariate actsupon the sewer pipe scores. It is shown here that the diameter factor influ-ences the observation of extreme high score values (upper quantile) of sewerpipes deterioration only. The length covariate is the only characteristic of594.3. Results and discussionsewer pipe segment that influence nonlinearly the lower quantile (Fig. 4.4a)and do not affect on the median and upper quantile. It has been reported inprevious studies that this covariate has an influence on the ICG. However,the precision on how this influence happens in not given (Kabir et al., 2018b;Salman and Salem, 2011).0 20 40 60 80 1000246810Age (years)(a)Partial effect on 50% quantile0 20 40 60 80 100010203040Age (years)(b)Partial effect on 95% quantile0 20 40 60 80 100−0.50.00.5Age (years)(c)Partial effect on 50% quantile0 20 40 60 80 100−2.0−1.5−1.0−0.50.00.51.01.5Age (years)(d)Partial effect on 95% quantileFigure 4.2: Age covariate impacts in different quantiles.The Age covariate only affects the median and upper quantiles. Mu-nicipalities mostly use Age covariate to support their decision making forinspections and budget planning. The following studies highlighted the in-fluence of the Age variable on the condition of sewer pipes (Salman and604.3. Results and discussionSalem, 2011; Younis and Knight, 2010; Ana et al., 2009; Chughtai and Za-yed, 2008; Baik et al., 2006; Ariaratnam et al., 2001). When analyzing sewerpipes in the lower quantile, the Age covariate may be misleading as decisionvariable. However, in the median and upper quantile, both linear and non-linear effects of Age are selected as influencing the predicted ICG of pipes(Fig. 4.2).0 10 20 30 400.000.010.020.030.04Number of residential connections(a)Partial effect on 50% quantile0 10 20 30 40−0.6−0.4−0.20.00.20.40.6Number of residential connections(b)Partial effect on 5% quantile0 10 20 30 40−6−4−20246Number of residential connections(c)Partial effect on 50% quantile0 10 20 30 40−4−2024Number of residential connections(d)Partial effect on 95% quantileFigure 4.3: Residential connection impacts in different quantiles.The lower quantile is affected by most of the independent variables exceptthe following: Age, Diameter and Replaced. However, the 50th percentile(expected mean regression) is not affected by the diameter and length vari-614.3. Results and discussionables. Finally, only three maintenance covariates influence the upper quan-tile predicted ICG, flushes that have a nonlinear effect, the repairs with bothtypes of relationships and the linear effect of Replaced.0 50 100 150 200 250−0.002−0.0010.0000.0010.002Length (m)(a)Partial effect on 5% quantile−0.050.000.050.10MaterialCementitious Clay Metallic Plastic(b)Partial effect on 5% quantile0510152025MaterialCementitious Clay Metallic Plastic(c)Partial effect on 50% quantile203040506070MaterialCementitious Clay Metallic Plastic(d)Partial effect on 95 % quantileFigure 4.4: Length and material impacts in different quantiles.The impacts of covariates to the sewer score in the lower quantile modeldo not exceed 1. Both covariates have either negative influence (meaningthe pipes is in the resistance period meaning the pipe is new and correctlyinstalled), either positive but below one. Negative values correspond tothe flat part of the bath-tube shape deterioration curve. Positive valuesdemonstrate the low influence of the selected covariates to the degradation624.3. Results and discussionof the sewer pipes’s conditions. In the median and upper quantiles, theeffects of some covariates go beyond 250 (e.g. impact of the number ofprevious repairs in the upper quantile)(Fig. 4.4,4.5,4.6).0 5 10 15 20 25−0.4−0.20.00.20.4Number of previous sewer cleaning(a)Partial effect on 5% quantile0 5 10 15 20 25−3−2−10123Number of previous sewer cleaning(b)Partial effect on 50% quantile0.0 0.5 1.0 1.5 2.0 2.5 3.0−0.06−0.04−0.020.000.020.040.06Number of previous backups(c)Partial effect on 5% quantile0.0 0.5 1.0 1.5 2.0 2.5 3.0−3−2−10123Number of previous backups(d)Partial effect on 50 % quantileFigure 4.5: Cleaning and backups impacts in different quantiles.The response variable is an additive combination of simple estimators(constant and varying parameters) representing the effect of the selectedcovariates to the deterioration process. For each covariate, the estimatorvalue is a combination of the two types of impacts (linear and nonlinear)included in the model (Fig. 4.8). Thus, the resulting covariate’s impact isa mixture of individual impacts and cannot be captured with a single type634.3. Results and discussionof relationship between the covariate and the output ICG variable whiledesigning the model. Fig. 4.8) is showing this type of impact for the ageand repairs covariates in the 50th and the 95th percentiles.0 5 10 15 20 25−0.050.000.05Number of previous sewer degrease(a)Partial effect on 5% quantile0 5 10 15 20 25−10−50510Number of previous sewer degrease(b)Partial effect on 50% quantile0 5 10 15 20−0.02−0.010.000.010.020.03Number of previous roots cut(c)Partial effect on 5% quantile0 5 10 15 20−1.0−0.50.00.51.0Number of previous roots cut(d)Partial effect on 50 % quantileFigure 4.6: Root cuts and degrease impacts in different quantiles.The boosting algorithm (see Table 4.1) selected influential parametersamong which the Age and repairs have both types of impacts to the responsescore of the sewer. The resulting effect (“combined effect”) shows that theAge effect (Fig. 4.8a) in the 50th percentile is mostly controlled by thelinear part. However, the nonlinear part should be included to make sureof a better representation of the overall covariate effect. On the other side,644.3. Results and discussionthe repairs covariate effect (Fig. 4.8c) is also a mixture of both linear andnonlinear when the number of repair is below 4. However, after 4 repairs ofa pipe, the total covariate effect is led by the nonlinear component.The inclusion in the model of either linear or nonlinear effect is in somecases the source of errors in the predictions of the output ICG. For theAge covariate, the contribution of the nonlinear part to its effect can benegligible. However, the differences related to the repairs covariates aremore significant.4.3.2 Covariates effects on the response variableIn additive models, each covariate’s impact on the response variable isestimated separately and the resulting response is a weighted addition of thecovariates’ effects. In this section, the covariates’ effects on scores of sewerpipes that representing the ICG are presented. Both quantiles are influencedlinearly and nonlinearly (Table 4.2). The lower quantile has the highestnumber of nonlinear factors than the median and upper quantiles. Moreover,the type of relationships (linear and nonlinear) between the response variableand the regressors added to their effect’s ranges confirm the complexity ofthe deterioration process of sewer pipes. These models trigger the needto search for more factors that have influence on the behavior of buriedsewer pipes in each quantile (lower, median, upper). Some of these factorsare unknown or others expensive to be acquired. Thus, the inclusion ofgeospatial information as a surrogate covariate partly solve the issue. Therepairs covariate has both types of relationships (linear and nonlinear) withthe pipes scores within all the selected quantile models (e.g. Fig. 4.8c-dshow both effects for the 50th and 95th percentile models). The linear effectof the repairs covariate has a negative slope for the lower quantile, whileit has a positive slope for the median and 95th quantiles. Thus, if onlythe linear model is considered, this result could lead to conclusions such asthe database may not be up-to-dated i.e. the number of repairs is kept inthe database while the pipes replacement is not updated. However, whenthe linear impact is coupled with the nonlinear, the resulting impact leadsto an effective quantification of the influence of the covariate (repairs) tothe deterioration of sewer pipes in the considered quantile (Fig. 4.8c-d).The median and upper quantile are more explicit because both linear andnonlinear are positive and influence the score positively.654.3. Results and discussion−5 0 5 10 15 20 25 30−0.10.00.10.20.3Number of residential connections(a)Partial effect on 5% quantile−5 0 5 10 15 20 25 30−2−10123Number of residential connections(b)Partial effect on 50% quantile2 4 6 8 10 12−0.015−0.010−0.0050.0000.0050.010Number of residential connections(c)Partial effect on 5% quantile2 4 6 8 10 12−4−2024Number of residential connections(d)Partial effect on 50 % quantileFigure 4.7: Slope and depth impacts in different quantiles.The 50th percentile, i.e. the normal (usual) expected mean regressionmodel, gives a balance between linear and nonlinear relationships. Finally,the extreme observed high scores, (in the upper quantile) are caused byonly few factors (Age, the number of residential connections, the number ofcommercial connections, Diameter, Material, the number of previous flushes,repairs and replacement) that influence linearly and/or nonlinearly the 95thpercentile (Table 4.2).664.3. Results and discussion0 20 40 60 80 10002468Age (years)Partial effect on the 50% quantile−0.50.00.5Combined(left axis)Linear(left axis)Nonlinear(right axis)(a)0 20 40 60 80 100010203040Age (years)Partial effect on the 95% quantile−2.0−1.5−1.0−0.50.00.51.01.5Combined(left axis)Linear(left axis)Nonlinear(right axis)(b)0 2 4 6 8020406080100Number of previous repairsPartial effect on the 50% quantile0204060Combined(left axis)Linear(left axis)Nonlinear(right axis)(c)0 2 4 6 8050100150200250300350Number of previous repairs−50050100150200250Combined(left axis)Linear(left axis)Nonlinear(right axis)(d)Partial effect on the 95% quantileFigure 4.8: Combined impacts in different quantiles.Material, Flushes and repairs covariates are the only factors that haveinfluence in the all three quantile regression models (Table 4.2). The metallicpipes have the highest impact on the ICG of sewer pipes in both quantiles.Other types of material have varying effects depending on the selected quan-tile (Fig. 4.4b-d). Metallic pipes and clay are the first material that havebeen used to install sewer in the city of Calgary. Progressively, they arereplaced by concrete and PVC. The obtained result is in accordance withthe material type (Fig. 3.3). They affect more the deterioration of sewersand are responsible of extreme values appearance. The geospatial location674.3. Results and discussionof these pipes in correlation with the output geospatial effect map should beanalyzed together with the covariates effects to understand the differencesin the deterioration.In additive models, each covariate is fitted to the output score (Figures4.9 and 4.10). The model minimizes the differences between the outputscore and its predicted value from each single covariate. Once a good fit isobtained for each covariate, the global output is a weighted sum of the fitof the covariates.lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll0 20 40 60 80 100050100150200250300 5%50%95%(a)Age (years)Pipe scorellllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll llllll0 50 100 150 200050100150200250300 5%50%95%(b)Length (m)Pipe scorellllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllll lll200 300 400 500 600 700050100150200250300 5%50%95%(c)Diameter (mm)Pipe scorellllllllllllllllllllllllllllllllllllllllllCementitious Clay Metallic Plastic050100150200250300 5%50%95%(d)MaterialPipe scoreFigure 4.9: Score prediction using pipe’s attributes.It can be seen from Figures 4.9 and 4.10 that the lower quantile is not684.3. Results and discussionsupported by enough data. Thus, the decision maker should in accordancewith the map effect provided in the next section investigate the delineatedareas to get more information that can support his decision. However, forthe median and upper quantiles, the figures show a good fit of the predictionsover the observations. It is therefore established that quantile regression isa very good tool for assessing the deterioration of sewer pipes. However,when looking into the response variable, it can be seen that its distributionis skewed to the left with a long tail to the right. Thus, the low quantile canbe captured when using the expected mean approach. The upper quantilethat have the highly risky pipes that should be prioritized for inspection andmaintenance in not captured and should be modeled separately.llllllllllllllllllllllllllllllllllllllllllllllllllllllllll0.0 0.2 0.4 0.6 0.8 1.00501001502002503005%50%95%(a)Number of previous backupsPipe scorelllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll0.0 0.5 1.0 1.5 2.00501001502002503005%50%95%(b)Number of previous repairsPipe scorellllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllll lllll0 5 100501001502002503005%50%95%(c)Slope (%)Pipe scorelllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllll lllllllll ll lll llllllllll1 2 3 4 5 6 7 80501001502002503005%50%95%(d)Depth (m)Pipe scoreFigure 4.10: Score prediction using maintenance and environmental factors.694.3. Results and discussion4.3.3 Spatial effectsMaps in Fig.4.11 are interesting source of information to support earlydecision making for inspection needs and search of more explanatory vari-ables that could better explain the undergoing deterioration of sewers ineach district of the city of Calgary. The area around the airport have thehighest effect on the observed condition scores (in the median and upperquantiles). Pipes in the designated area are made of concrete, i.e. cementi-tious. The following reasons may be the causes of high deterioration ratesin the area: (1) Rigid pipes subject to intermittent surface loading (due tofrequent take-off and landing of planes) will likely fail more than plastic orother material types in the outer areas of the city, (2) the soil chemistrycomposition may have compound that reacts with the cementitious pipesand reduces their thickness. An in-depth investigation will likely reveal themain causes of this elevated rate of deterioration. However, on the decision-making side, the inspection frequency in this area should be higher than inother areas of the city.−6.47 −6.21 −5.95(a)−7.43 0.26 7.95(b)17.5 20.1 22.7(c)Calgary airportFigure 4.11: Spatial effects for (a) lower quantile model, (b) 50th percentileand (c) upper quantile.The south west districts, where there is a mix of cementitious and plas-tic, present also a high rate of deterioration for both median and upperquantiles (Fig. 4.11a-b). The analysis of the linear effect of the materialalone for both quantiles shows that metallic pipes have the highest impactfactor to the deterioration of pipes (e.g. the impact of metallic pipes in themedian and upper quantiles is above 25 and 70 respectively, see Fig. 4.4).However, when it comes to the geospatial location of pipes, although the704.3. Results and discussionoldest group of pipes is the metallic and clay pipes (center of the network),the area presenting the high probability of having high deterioration scoreis the location where relatively new pipes (cementitious) are installed. Itshould be noticed that the median regression model (Fig. 4.11b) highlightsthe same area of high influence (with a tendency to focus on the center ofthe network where there are more older pipes: metallic and clays). Thereal representation of the critical area (near the airport) is obtained in theupper quantile model. Thus, the analysis with more quantiles allows todiscover other causes that may influence the deterioration pattern in thesystem and delineate critical areas. Furthermore, spatial effects maps showthe existence of autocorrelation between the districts. However, the effectof districts with white color is difficult to be interpreted since this may beonly the effects of local heterogeneities or missing data (e.g. there is notinspection data of pipes in the district that have been made available to themodel). Thus, for an effective decision making based on the single geospa-tial effect, early decision making on inspection priorities should be orientedtoward districts with high spatial effects and these districts with only localheterogeneities. Moreover, there is similarities between the districts effectson the 50th percentile and the upper quantile. Considering the ranges valuesof the geospatial effects, it can be observed that high geospatial effects areseen in the upper quantile.4.3.4 DiscussionQuantile regression modeling is effective way of addressing deteriorationof sewer pipes. The proposed model is robust against outliers that repre-sent a frequent issue in the development of statistical deterioration modelsfor sewer pipes. Quantile regression models allow to elucidate factors thatmake extremes values to be observed. Moreover, it gives a credible intervalin which the observed values are identified. This interval corresponds tothe limit range of the output variable that is a key element in the decision-making process. Accuracy in the prediction is gained not only throughacquisition of more information about contributing factors but also througha realistic representation of the way (linear, nonlinear) they influence theinternal condition grade. This study shows that it is more efficient to in-clude in the final model only the most informative covariates in the quantilemodel of interest. These covariates may differ from one quantile to an-other. Furthermore, the output maps highlight areas where further searchesof causing factors and pipes inspection should be prioritized. For inspectionprioritization, the areas where no information have been recorded (district714.4. Summarywhere only local heterogeneities are found) and district with high geospatialeffects are the areas of priority for future inspection campaigns. Regardingthe quantiles, the upper quantile is more informative on pipes having a highdeterioration rate and give a better representation of critical zones than thelower and median (50th) percentiles. From the analysis of the predictedICG (Fig 4.9 and 4.10), it can be seen that the distribution of the output isskewed to the left and considering only the median and the upper quantileswill be sufficient to give insights on the range of probable output response.4.4 SummaryIn this chapter, an individual deterioration model is developed using aBayesian quantile inference with boosting algorithm for variable selection.The model considered the effects of physical, maintenance and environmen-tal factors on the structural condition of sewer pipes using linear, nonlinearand geospatial effects on different quantiles (5%, 50% and 95%). The resultshighlight the importance of considering quantile semi parametric modelingapproach to identify the factors that make extreme ICG values to be ob-served. The advantage of the approach is the automatic selection of themodel complexity done by the boosting algorithm. The operator suggestsall possible types of impact the covariates may have on the response anditeratively the algorithm select only the components that better capturethe observed data. The lower quantile output has a complex relationshipwith high number of continuous variables because it is not supported bymore data. However, the median and upper quantiles are balanced withlinear and nonlinear relationships and capture most of the observed datathrough smooth functions and appropriately defined priors and paramet-ric coefficients. Furthermore, the Bayesian inference captures the uncer-tainty in the data through appropriate polynomials and degree selections.Spatial autocorrelation and local heterogeneities are introduced to captureunknown covariates that may have influence on the deterioration of sewerpipes. Younger sewer pipes located on the north-east (airport area) presentthe highest rate of deterioration compared to the metallic and clay pipeslocated in the center-west of the city area. Cyclic loading due to air trafficmay be the reason why plastic pipes are presenting this high deteriorationrate in the area. The proposed model is a cost-effective management toolfor water utilities in municipalities. The tool is flexible to allow the uses ofreduced number of sewer pipes attributes to estimate their condition anddelineates critical areas in the network. At practical point of view, this724.4. Summaryresearch presents a powerful tool to orient and guide the prioritization ofinspections in the network area. A map is a universal language tool, acces-sible to people from different personal and professional backgrounds. Thegeospatial effect maps on the deterioration of sewer pipes provide a sense ofscale and distance of critical areas. The decision makers will have to decideon different priorities focusing on the lower and upper quantiles for inspec-tions. The rehabilitation plan may be based on the 50th percentile. Finally,this research showed that the designed data representing the physical data(e.g., length, material, age, depth, slope), the maintenance data and thegeospatial location of the pipes can efficiently represent a realistic deteriora-tion model for all (inspected and uninspected) the pipes in the network andprovide the factors that are the most important in the deterioration pro-cess. Such a model will serve both planning and operations and will allowthe quantification of the risk taken in the decision making. This study showsthat for a detailed analysis of the factors that influences the deteriorationof sewer, i.e., factors that triggered the appearance of extremes values, thequantile regression is more appropriate than the expected mean regressionmodeling approach.73Chapter 5Critical componentsidentification using graphtheory5.1 BackgroundUrban water infrastructure systems (water supply, wastewater collection,and drainage systems) are essential to the health and security of populationsliving in modern societies. These infrastructure systems are composed of nu-merous components (e.g. pipes, pumps, valves) that are interconnected witheach other and together constitute the network system. Components of in-frastructure systems are subject to both gradual degradation over time aswell as extreme hazard events (e.g., earthquakes or hurricanes). Gradualdegradation, hazard events, or a combination of both can cause the fail-ure of individual components within these systems and therefore, throughthe interactions of components within and between systems, failures of theinfrastructure system as a whole to fulfill its functionAt a large-scale, urban water infrastructure management practices focuson the component level decision-making, i.e., analysis of individual com-ponent, deciding upon optimal actions for these components (potentiallyincluding inspection actions), and undertaking these actions without con-sidering their impacts on the entire water system. This atomistic view isalso observed in structural health monitoring where sensors are installedto monitor the states of individual components without translating the ac-quired information to the system level or prioritizing data collection basedon system level. It is important to develop effective system models andthe tools to use them for optimal planning. Network-based models are pre-sented here, as they are appropriate to the tasks of modeling uncertaintiesand interdependencies within infrastructure systems.745.2. Methodology5.2 MethodologyBoth urban water infrastructure systems (water supply, wastewater,uuban drainage) are formed of nodes connected trough pipes. Therefore,they can mathematically be represented as graphs and all the theory ofgraphs applied. The methodology (Figure 5.1) presented here is general forall urban water infrastructure systems (pressurized and free surface).Network selection (Graph and hydraulic representations)Hydraulic reliability assessment  Run an extended pressure driven hydraulic simulation with a single pipe failure For the failed pipe, compute the Water Shortage Ratio (WSR) Build an adjacency matrix A weighted by the computed pipes WSR WSR(i) = max A(i, ) , where i=1,…,n is the number of nodesTopological reliability assessment Compute the betweenness (Betw) Compute the Topological Information Centrality (TIC) Compute the Eigenvector centrality (EVC) Compute the Principal Component centrality (PCC)BBN based data fusion Compute the WSR_BBNCorrelation analysis Spearman test Moran indexGeographical Information System maps representation Interpolation of metrics scores heatmap representations for Prioritization for Inspection𝑊𝑆𝑅 𝑝𝑖𝑝𝑒𝑠 = 𝐷𝑖 ,𝑟𝑒𝑞𝑡 − 𝑞𝑖 ,𝑑𝑒𝑙𝑡𝐷𝑖 ,𝑟𝑒𝑞𝑡 𝑡𝑖 Figure 5.1: Proposed framework for critical component identification5.2.1 Hydraulic modeling of pressurized pipesObjective of WDSs is the delivery of water to customers at requiredpressure, quality, quantity and time. The reliability of wdn is assessed in755.2. Methodologyterms of the quantity and quality of water the distribution system is able toprovide over the demand period. The pressure available at nodes determinethe deliverable quantity of water with respect to the minimum requiredpressure computed as (Giustolisi et al., 2008):qti,del =0 if P ti,act < P ti,minDti,req(P ti,act−P ti,minP ti,req−P ti,min)( 1ni)if P ti,req > Pti,act ≥ P ti,minDit if Pti,act ≥ P ti,req(5.1)where t is the time (hours), qti,del = delivered amount of water within therange[0, Dti], P ti,act is the actual pressure at node i at time t, P ti,min is theminimum required pressure at the node i, P ti,req is the required pressure todeliver the water demand Dti,req at the node i, ni is the emitter exponent(empirical value between 0.5 and 2.5) and Dti,req is the water demand atnode i. The hydraulic reliability of the wdns, here called Water ShortageRatio (WSR), is represented as the ratio between the undelivered to thetotal required volumes of water over an extended period simulation. WSRmeasures the importance of the failed pipe j on the hydraulic reliability ofthe system (Eq. 5.2):WSR(j) =∑i∑t(Dti,req − qti,delDti,req)(5.2)where j = 1 · · ·m represent the failed pipe in the network, i = 1 · · ·n arethe nodes and t = 1 · · ·T the simulation time. The simulation process foreach pipe is carried out as described in Su et al. (1987). At the end ofthe simulation, each pipe is attributed the WSR value obtained after itsfailure representing its criticality. Then, an adjacency matrix weighted withthe computed criticality of the pipes is built. The nodes criticality index(WSR) are the maximum values of each row of the graph adjacency matrix.The defined WSR criticality index quantifies the failed component’s impacton the network level performance. High WSR indicate the importance isthe failed component in the system. The WSR metric is used as baseline inthis study, against which, the defined topological metric will be assessed.Herrera et al. (2015) weighted the shortest paths in wdns with a coeffi-cient representing the energy loss between two nodes. This coefficient is akey element in the computation of shortest paths-based centrality metricsand influences the hydraulic flow pattern in the network. Hazen-William765.2. Methodologyresistance coefficient is used to represent the energy loss as given in Eq. 5.3:Lw =( 10.670LC1.852D4.87)(5.3)where L is the length expressed in (m), C is the C-factor, D is the diameterof the pipe in (m). The number of geodesics in Eq. 5.5 is replaced with thesum of weights of the links in the path given in Eq. 5.3. Components withhigh Betweenness control the flow in the network and have great impact onthe topological reliability. The C-factor (Eq. 5.3) is a function of the age ofthe pipe and the water quality in the distribution system (Sharp and Walski,1988). For long period simulations (over years), the C-factor reduces andLw increases, hence, the flow in the network will no longer depend on thephysical distance L between the nodes but water will follow the less resistantpath which, influences the length of the shortest path between the nodes.Over one-week simulation (168 h), this factor can be considered as constantand the flow is controlled by the water demand fluctuations.The application of this methodology to gravitational sewer pipes is straight-forward. However, the loss of energy in pipes is captured trough the manningcoefficient of pipes rather than the Hazen-William resistance coefficient inEq. 5.3. The use of manning approach is motivated by the free surfaceflows that predominate the flows in gravitational sewer. Together with thehydraulic radius and the slope of the bed, the coefficient of manning thatrepresents the pipe’s wall roughness are used to determine the velocity ateach point (Eq.5.4). The obtained velocity is then converted into energy.For each pipe, the manning coefficient depends on a complex set of factorssuch as the pipe’s shape, the type of vegetation on the wall, the presence ofcracks, or any other type of defects. A new pipe will have a smaller manningcoefficient than an old pipe.V = R2/3S1/2n(5.4)where V is the velocity, R is the hydraulic radius, S is the bed slope and nis the manning coefficient.Chow (1959) proposed the manning’s n values for different pipe materi-als (see in Table 5.1). In this table, three values are given the minimum, thenormal and the maximum. From the equation 5.4, the minimum value cor-responds to low flows, high resistance of the pipe to the flow. The minimummanning value is attributed to old pipes or pipes presenting high densityof defects (e.g. deteriorated pipes). The maximum value is related to newpipes. The relation between the pipes condition and the manning coefficient775.2. Methodologyis not straightforward. In this study, the normal value is considered for theapplication of gravitational flows in sewer pipes. Higher inverse n valuesreduce the flows in pipe and increase the shortest path distance betweenthe nodes while lower values increases the flow and reduce the shortest pathdistance.5.2.2 Graph theoretical metricsA graph representationG(V,E) of urban water networks consist of a setof V vertices interconnected through edges E. The interconnection patternof a network with N vertices is characterized by an adjacency matrix A con-sisting of elements ai,j . Urban water networks are represented as undirectedgraphs because inside a single pipe, water can flow in both directions. Theadjacency matrix of undirected graphs is a real symmetric N × N matrixwith ai,j = 1 when there exist an edge connecting the vertex i to the vertexj. Self-loops ai,j = 0 or multiple links between two vertices i and j are notconsidered in this representation.The most used metric in the graph theory is the centrality metric. Itmeasures component’s importance by virtue of its central location (Ilyasand Radha, 2011) Two important concepts are used to define the centralitymetrics in graph theory:1. The proximity representing how a component is close to the others.Two metrics are defined in this group: degree centrality and closenesscentrality. The degree centrality or connectivity of a node i is thenumber of nodes that are interacting with it. It is the number ofedges incident with the node i. For directed graph, the definition ofindegree and outdegree is required. The closeness centrality quantifiesthe number of hops between nodes.2. In Urban water system, water flows from pumping stations and tanksto the customer’s homes or treatment plants following different paths.The followed path is not optimal since water will always flow throughthe less resistant path. In wastewater or storm water sewers pipes,where free surface flow usually occurs, flow restrictions due to defects(e.g. grease growth, sediment depot, root growth) increase the frictionlosses make water to search for least resistant paths too. The minimaldistance di,j between two vertices is called shortest path and can beused to characterize the internal structure of graphs. Several centralitymetrics characterizing networks are derived from the shortest path.785.2. MethodologyTable 5.1: Manning’s coefficient n for closed conduits flowing patly full(Chow, 1959).Type of Conduit and Description Minimum Normal MaximumBrass, smooth: 0.009 0.01 0.013Steel:Lockbar and welded 0.01 0.012 0.014Riveted and spiral 0.013 0.016 0.017Cast Iron:Coated 0.01 0.013 0.014Uncoated 0.011 0.014 0.016Wrought Iron:Black 0.012 0.014 0.015Galvanized 0.013 0.016 0.017Corrugated Metal:Subdrain 0.017 0.019 0.021Stormdrain 0.021 0.024 0.03Cement:Neat Surface 0.01 0.011 0.013Mortar 0.011 0.013 0.015Concrete:Culvert, straight and free of debris 0.01 0.011 0.013Culvert with bends, connections, and some debris 0.011 0.013 0.014Finished 0.011 0.012 0.014Sewer with manholes, inlet, etc., straight 0.013 0.015 0.017Unfinished, steel form 0.012 0.013 0.014Unfinished, smooth wood form 0.012 0.014 0.016Unfinished, rough wood form 0.015 0.017 0.02Wood:Stave 0.01 0.012 0.014Laminated, treated 0.015 0.017 0.02Clay:Common drainage tile 0.011 0.013 0.017Vitrified sewer 0.011 0.014 0.017Vitrified sewer with manholes, inlet, etc. 0.013 0.015 0.017Vitrified Subdrain with open joint 0.014 0.016 0.018Brickwork:Glazed 0.011 0.013 0.015Lined with cement mortar 0.012 0.015 0.017Sanitary sewers coated with sewage slime withbends and connections0.012 0.013 0.016Paved invert, sewer, smooth bottom 0.016 0.019 0.02Rubble masonry, cemented 0.018 0.025 0.03795.2. MethodologyThe degree centrality and the closeness centrality do not capture the struc-tural organization of network. They provide local information that is notuseful when considering the global network performance (Van Mieghem,2014).Four graph theoretic centrality metrics are described in the following:two based on the shortest path: Betweenness and Topological informationcentrality and two spectral metrics: eigenvector centrality and principalcomponents centrality.5.2.3 BetweennessThe Betweenness (Betw) represents the influence a component has overthe connectivity of all the other nodes in the network. A component hashigh Betw if the shortest paths (geodesics) between many pairs of the othercomponents in the graph pass through the considered component. Thus, theconnectivity of a network is negatively impacted if a component with highBetw fails. The failed component is critical to the performance (connectiv-ity) of the network. The Betw of a vertex k is the fraction of shortest pathsfrom the vertex i to the vertex j that pass through the vertex k over thetotal number of shortest paths between the vertices i and j. The expressionin 4.1 gives the Betw of a vertex k in the graph G(V,E).CBk =1(n− 1)(n− 2)∑i∈G,i 6=k∑j∈G,j 6=i,j 6=kni,j(k)ni,j(5.5)where ni,j is the number of geodesics edges going from i to j and the sameni,j(k) the number of geodesics going from i to j passing through kand n isthe number of vertices in the graph G(V,E) . Typically, Betw centrality isnormalized to [0, 1] range within a graph.5.2.4 Topological Information CentralityThe Topological information centrality (TIC) quantifies the relative changein the network global efficiency (performance) after the failure of one or mul-tiple components. The global efficiency is the average sum of the efficiencyof all the vertices pairs in the network and is expressed as follow (Crucittiet al., 2005, 2004):E[G] = 1n(n− 1)∑i 6=j∈G1di,j(5.6)where di,j is the shortest path between vertices i and j, and n is the numberof vertices in the graph G(V,E). The TIC of the component i is computed805.2. Methodologyas:TIC = E[G]− E[G′]E[G] (5.7)where the subgraph G′ is obtained after the failure of one or more compo-nents of the graphG, and TIC represent the impact of the failed componentson the global efficiency5.2.5 Eigenvector centralityThe eigenvector centrality of a vertex is a measure of the importanceof the vertex in the network considering all possible connections betweenvertices through the adjacency matrix.The spectrum of a graph better rep-resentation of topological characteristics Van Mieghem (2014). The networkcharacteristic equation is written as:λX = AX (5.8)where λ is the vector of eigenvalues,X the corresponding eigenvector matrixand A is the adjacency matrix. In undirected graphs,A is symmetrical andthe eigenvalues are real numbers. The components of the spectral radiusassociated eigenvector represent the Eigenvector centrality (EVC) scores ofthe graph’s vertices (Van Mieghem, 2014).The main drawback of EVC is the tendency the metric has to only iden-tify vertices that are connected to the highly connected vertices. Hence,EVC is suitable technique in small networks where the identification of onehub is sufficient to characterize the network. However,in large networks, theprobability of getting more than one important neighborhood is high. Itis crucial to identify other important neighborhoods to better characterizelarge infrastructure networks. Finding a trade-off between the cost of iden-tification of additional hubs and the supplemental information they revealmay be challenging.5.2.6 Principal components centralityThe Principal Component Centrality (PCC) represents the Euclideandistance/`2 norm of a vertex from the origin in a P-dimensional eigenspaceformed by the P most significant eigenvectors. This metric is able to identifyadditional important neighborhoods in large networks.Consider a graphG(V,E) and P ≤ n with n being the number of verticesin the graph G. The first P eigenvectors of the adjacency matrix An×n ofG form a matrix Xn×P . For P = 1, the PCC decomposition is a scaled815.2. Methodologyversion of EVC. Consider Λ = [λ1, λ2, · · · , λn]′ a vector of the adjacencymatrix eigenvalues. The vector CP whose components measure the PCC ofvertices in the graph G is evaluated as:CP =√(Xn×P Xn×P )(ΛP×1 ΛP×1) (5.9)The operator is the Hadamard (or entry wise product) operator. Theidentification of the P most significant eigenvectors passes by the observationof the phase angle (Equation 5.10) between the PCC and EVC (?).Φ(P ) = arccos( CP‖CP ‖) (5.10)where Φ(P ) is the angle between the PCC vector using P eigenvectors andthe first (spectral radius) eigenvector.The optimal number of eigenvectorsP to consider in the matrix X is reached when the relative PCC scores ofthe components cease to increase with the addition of more eigenvectors.Ilyas and Radha (2011) evaluated the effect of adding more componentsto X matrix and they concluded that the optimal number of features toadd is obtained when the phase angle value reaches it maximum and donot increase. The initial number of eigenvectors in X is randomly selectedbetween one and the total number of vertices in the network (for largenetworks a value of 100 is a good start).5.2.7 Bayesian belief network (BBN) based data fusionThe application of individual metrics on urban water infrastructure sys-tems lead to different classification of components. Moreover, none of themetric clearly identifies all the hubs determined using hydraulic simulationsmodels (baseline). For effective decision making, it is useful to aggregateinformation contained in each metric with the aim of increasing classifica-tion accuracy. A two layers classification structure is built in which the firstlayer is formed of four individual graph theoretical metrics and the second iscomposed of a combining module that transforms them into a single output(Castanedo, 2013). Two data fusion techniques are selected and applied inthe framework of this thesis: the Bayesian belief network approach (BBN)and the ordered Weight averaging (OWA).The information from the four topological metrics is clustered througha centralized architecture with the BBN method applied as the data fusiontechnique. Each topological metric provides an identity declaration E orhypothesis about the node’s importance based on the network topology and825.2. Methodologyits specific algorithm. The performance characteristics of each classificationtechnique provides estimates of the likelihood function, that is, the proba-bility P (E|Hi) that the technique will declare the node H to be in state E,given that the node is in fact type i. These declarations (evidences) are thencombined using Equation 5.11 to produce an updated, joint probability foreach entity Hi based on the technique’s classifications.P (Hi|E) = P (E|Hi))P (Hi))P (E) =P (E|Hi)P (Hi))∑P (E|Hi)P (Hi)) (5.11)where P (Hi|E) is the posterior probability that hypothesis Hi is true givenevidence E ;P (E|Hi) is the probability of observing evidence E given thatHiis true (sometimes referred to as the likelihood function);P (Hi) is the priorprobability that hypothesis Hi is true, and∑P (E|Hi)P (Hi)) is the prob-ability of observing evidence E given that hypothesis Hi is true, summedover all hypotheses i. Figure 5.2: Proposed data fusion technique using BBNFigure 5.2 represents the developed BBN for data fusion model thatcluster the four topological metrics, i.e. the nodes (Betweenness, Topologi-cal information centrality, Eigenvector centrality and Principal componentscentrality) defined in the previous subsection into a single graph theoretical835.3. Application to water supply in the city of Richmondmetric (WSR_BBN). For each node, the range of values have been dividedinto 10 states after expert knowledge. The aggregation of the topologicalmetrics through BBN will ensure capturing the uncertainty related to theflow pattern changes occurring in the network due to water demand fluctu-ations, energy loss variation and possible failure of pipes. The final modelis coupled with an excel file that run a visual macro to predict the outputWSR_BBN given the values of the other nodes as described in Demissieet al. (2015). The influence zones are calculated from individual scores usingthe inverse distance weighting interpolation method. Then, the delineatedzones of influences are projected on Geographical Information System (GIS)maps for visual analysis. The areas with high criticality are highlighted forprioritization of interventions. Figure 5.3: Richmond Water Supply Network5.3 Application to water supply in the city ofRichmondRichmond water distribution system, which is part of the Yorkshire watersupply in the UK (Van Zyl et al., 2004) is used as the case study (Fig. 5.3).It is a large wdn with 836 nodes, 1 reservoir, 6 cascading tanks, 948 pipes, 7pumps and 1 valve. The primary water source is the boreholes in the lowestzone (Catterick Bridges). Conditions of the pipes are not considered in thisstudy. The valve is ignored in the topological classification of nodes and isincluded in hydraulic simulations.For each simulation period, a single pipe failure is considered over therunning time as suggested by Ostfeld and Shamir (1993). When a pipe fails,water demand at nodes remains the same. The failed pipe is modeled asclosed pipe in the hydraulic model and simply removed from the graph inthe topological reliability model. The hydraulic simulation is performed on845.4. Results and Discussionsan extended period simulation (168 h) of a pressure driven EPANET modelto make sure the physical constraints (pipes capacity, pressure requirementsand water demand) are met. Moreover, a minimum pressure Pmin = 0mand a required pressure Preq = 5m to deliver the demanded quantity at anytime during the simulation for all the nodes in the network have been setin the hydraulic model Giustolisi et al. (2008); Van Zyl et al. (2004). Theflow-based scores WSR are computed from the Equations 5.1 and 5.2 usingthe output of the pressure based hydraulic simulation.At the same time, the topological metrics (Betweenness, Topologicalinformation centrality, eigenvector centrality and principal components cen-trality) are calculated using equations 5.5, 5.7, 5.8 and 5.9. The networkrepresentation as a graph is done following data in Tables 5.2 and 5.3. Theflow in pipes is directed by the avaialble energy at the nodes and the demandfluctuations that are represented in the Tables 5.2 and 5.4. The calculatedscores are normalized and reported on a GIS map. Then the influences zonesare computed for critical zone delineation using GIS. Furthermore, the scoresare ranked, and the Spearman correlation coefficients are computed for bothpairs.5.4 Results and DiscussionsIn this study, it is assumed that in normal operating conditions, the WSRindex equals zero for all the consumption nodes in the network. Thus, thecalculated WSR represents the network reliability against which the selectedtopological and defined aggregated metrics are evaluated. Furthermore, inaccordance with the findings in (Agathokleous et al., 2017) , the geospatialautocorrelation of all the metrics is computed and the ability of the proposedtopological reliability metric to capture the vulnerability of the considerednetwork is discussed.855.4. Results and DiscussionsTable 5.2: Example of Nodes’coordinates, base water demand and elevationin the city of Richmond.Node ID X Y Z Demand1 422347008 499939008 69 0.0012 417240000 501588000 183 03 417243008 501588000 183.82 04 417243008 501584000 183 05 417239008 501580000 183 06 417240000 501584000 186 07 417236000 501580000 183 08 417236000 501582272 183 09 422345984 499942016 68.85 0.17810 417480000 501463008 166.42 011 417483328 501462336 166.48 012 417639008 501302016 154 013 417732800 501317312 154 014 417808992 501116992 146 015 417860000 501088000 136.51 0.0316 418294016 500960000 126 017 418318016 500993984 126 018 418367008 501056992 126 019 418423008 501219008 132 020 421811008 500080992 64 0.32621 418387008 501212992 132 0.0222 418303008 501180000 132.2 0.0223 418326016 501272000 138 0.0324 418336000 501305984 139 0.0525 418440992 501265984 137 0.0326 418468992 501310016 137 0.0427 418350016 501361984 142 0.0928 418431008 501459008 139 0.1129 418488992 501360992 137 0.0430 418479008 501468992 140 0.0331 421324000 500147008 64 0.15232 418481984 501500992 141 0.0233 418535008 501516992 141.67 0.0134 418483008 501508992 141 0.0235 418532992 501524000 142 0.01865.4. Results and Discussions5.4.1 Hydraulic reliabilityRichmond wdn has a hybrid topology layout that is highly looped in theNorth-East Richmond and a tree like layout in the South and West of thecity. High-density population areas situated in the North-East of the wdnare identified as critical in the hydraulic reliability assessment (Fig. 5.4a). Inaddition to high redundancy (increased number of loops), the North-Eastarea is characterized by high base demand and high demand fluctuation(up to 2.96 times the base demand). This latter shows how uncertain thehydraulic topological flow pattern is in the network. In such wdn, the hy-draulic flow pattern cannot be captured by single graph topological metrics,unless at each time step, a reliable flow pattern is determined based on thewater demand pattern and the pressure distribution over the network. Innormal operating conditions, i.e., when no pipe failure has occurred in thesystem, the demand nodes located at higher elevations are the most criticalcomponents, because they may experience water shortage in case of pumpsfailure, empty tanks or unusual water demand fluctuation. However, whenrandom pipes failure may occur, any node in the network become at risk.In addition, the uncertainty in the definition of possible digraphs backupsincreases, because the failed pipes are not localized, and the new flow layoutof the network is unknown.5.4.2 Topological reliabilityShortest path-based metrics (betweenness: BETW and Topological in-formation centrality TIC) and spectral metrics (Eigenvector centrality: EVCand Principal components centrality: PCC) are used for this analysis. Inhighly redundant network (North-East Richmond wdn), the BETW of nodesis low because there is not much redundant ties between the nodes Borgattiand Everett (2006). For the same reason, the failure of a single pipe willnot have an increased impact on the efficiency of a highly redundant net-work. Thus, the Topological information centrality is not much affected bythe pipes failure in the North-East Richmond. The high number of inde-pendent pathways connecting nodes pairs in wdns infrastructures, with ahigh number of loops, significantly decreases the impact of the failure of thepipes in such network (Fig. 5.4b-c). Thus, the shortest path-based metricswill not capture the hydraulic topological changes in redundant network sys-tem and the information given is limited. However, in the South and Westparts of the city, where the network has a reduced number of loops, shortestpath metrics classified the majority of vertices, situated on the main line875.4. Results and DiscussionsTable 5.3: Example of links connectivity and characteristics.Link ID Node1 Node2 Length Diameter Roughness MinorLoss Status785 2 3 3 150 28 0 Open786 2 6 4 150 100 0 Open787 1 9 3 150 120 0 Open788 3 4 5 150 120 0 Open789 4 5 6 150 120 0 Open790 4 10 401 150 120 0 Open791 5 7 3 150 120 0 Open792 7 8 5 150 130 0 Open793 7 104 9 150 120 0 Open794 9 20 586 300 140 0 Open795 10 11 3 100 120 0 Open796 11 12 328 150 120 0 Open797 12 798 1 76 70 0 Open799 798 13 1 999 150 0 Open800 12 14 447 150 120 0 Open801 13 73 125 76 140 0 Open802 14 15 59 150 120 0 Open803 14 58 7 100 120 0 Open804 15 16 471 150 120 0 Open805 16 44 113 150 120 0 Open806 17 16 42 150 120 0 Open807 17 18 80 150 120 0 Open808 18 19 226 99 130 0 Open809 19 21 49 102 10 0 Open810 19 25 51 102 10 0 Open811 21 22 103 100 120 0 Open812 21 23 110 100 140 0 Open813 20 31 491 300 140 0 Open814 23 24 36 76 110 0 Open815 24 25 115 76 20 0 Open816 24 27 58 76 110 0 Open817 25 26 53 102 30 0 Open818 26 27 131 76 70 0 Open819 26 29 55 102 70 0 Open885.4. Results and DiscussionsTable 5.4: Example of hourly demand variation and characteristics in thecity of Richmond.Pattern ID 1 2 3 4 5 6Fac_1010 0.59 0.2 0.34 0.33 0.38 0.36Fac_1010 0.62 1.26 1.88 1.93 1.67 1.37Fac_1010 0.97 1.07 0.81 0.67 0.76 1.03Fac_1010 1.38 1.53 1.38 1.21 1.39 0.85Fac_1212 0.34 0.04 0.02 0.01 0.02 0.1Fac_1212 0.34 1.46 1.93 2.13 1.77 1.43Fac_1212 1.19 1.02 0.93 0.67 0.81 1.17Fac_1212 1.55 1.64 1.54 1.46 1.31 1.12Fac_1313 0.38 0.2 0.15 0.11 0.11 0.14Fac_1313 0.29 1.18 1.66 1.67 1.66 1.4Fac_1313 1.35 1.18 1.16 1.05 0.99 1.24Fac_1313 1.41 1.55 1.3 1.52 1.45 0.92Fac_1616 0.51 0.34 0.12 0.13 0.19 0.13Fac_1616 0.45 1.53 1.9 1.69 1.68 1.28Fac_1616 0.96 0.77 0.95 0.7 0.67 0.87Fac_1616 1.35 1.73 1.62 1.72 1.6 1.06Fac_2020 0.68 0.63 0.63 0.72 1.31 0.95Fac_2020 0.95 1.72 0.93 0.88 1.61 1.61Fac_2020 1.11 1.34 1.11 0.84 0.88 1.61Fac_2020 0.89 0.77 0.77 0.72 0.63 0.66Fac_2222 0.43 0.2 0.13 0.09 0.12 0.13Fac_2222 0.48 1.71 1.61 1.96 1.96 1.07Fac_2222 0.91 0.89 0.76 0.29 0.44 0.91Fac_2222 1.69 1.93 1.78 1.96 1.66 1.05Fac_2626 0.66 0 0.02 0 0 0Fac_2626 0.62 1.04 1.58 2.96 2.11 1.66Fac_2626 0.31 0.39 1.04 0.23 0.88 2.09Fac_2626 1.8 1.94 2.25 1.18 0.61 0.64Fac_2828 0.56 0 0.01 0 0 0Fac_2828 0.52 0.87 1.55 2.86 2.14 1.75Fac_2828 0.6 0.67 1.22 0.53 1.09 2.12Fac_2828 1.74 1.69 1.96 1.04 0.56 0.56Fac_44 0.1 0.1 0.1 0.1 0.1 0.1Fac_44 0.1 0.1 1.1 2.25 2.25 2.25Fac_44 2.25 2.25 2.25 2.25 2.25 2.25895.4. Results and DiscussionsTable 5.5: Spearman correlation coefficients and spatial autocorrelation ofthe metrics.BETW TIC EVC PCC WSR_BBN WSR Moran Index (P_value)BETW 1 0.86 0.06 -0.02 -0.61 -0.22 0.27 (0)TIC 1 0.05 0.03 -0.58 -0.2 0.26 (0)EVC 1 0.54 0.16 0.17 0.25(0)PCC 1 0.25 0.24 0.23 (0)WSR_BBN WSR 1 0.11 (0)connecting the sources to nodes in these areas as critical (Fig.5.4b-c).The low degree (degree≤2) components that form a single path (mainline) from the source of water (tank D in the Eastern Richmond) to tank E inthe Western area are topologically critical because all the paths connectingnodes in the North-East Richmond to nodes in the South-West pass throughthem. However, the unsupplied volume of water due to failure of pipes inthese areas is not elevated due to low occupancy of the areas and reducedwater demand. Thus, the failure in these areas will not affect significantlythe hydraulic reliability as defined in this study.The number of the most significant eigenvectors, in PCC evaluation,following Equation 5.10 is represented in Fig.5.5. From this figure, the valueof P to consider in PCC metric calculation (Equation 5.9) should be between3 and 8. This range is the transition between the sharp rise of the phase angle(from 0 to 3 eigenvectors) and the mid rise (8 to 100 eigenvectors). Thus,values below 3 does not capture all the hubs in the network and values above8 will introduce noise in the identification of hubs. The optimal number withreduced noise is 8 and that is the selected value for the computation of PCC.The spectral metrics (EVC and PCC) have a tendency to identify astopologically critical high degree nodes that are interacting with highly con-nected nodes. Thus, Spectral metrics will be efficient in highly looped net-works. In the Richmond wdn case study application, all the nodes identifiedas topologically critical, using spectral metrics, are in the North-East partsof the city (Fig. 5.4d-e). These metrics did not classify the low degree nodesin the South-West as critical. This result confirms that EVC is correlatedwith the degree centrality (Boccaletti et al., 2006).and the number of cy-cles present in the network Costa et al. (2007). In the large and complexRichmond network, the PCC metric identified two optimal hubs (Fig. 5.4e)rather than the single identified hub by the EVC. The hydraulic reliabilityidentified in the same region (North-East Richmond) the majority of criticalcomponents in the wdn.905.4. Results and Discussions a) Water shortage ratio (WSR) b) Betweenness (BETW) c) Topological information centrality (TIC) d) Eigenvector centrality (EVC) e) Principal components centrality (PCC) f) Aggregated metric using BBN (WSR_BBN) 109 3 1 0 1 0 1 0 1 0 100 5 Figure 5.4: Critical areas in the Richmond wdn.The graph topological centrality metrics are useful in the evaluation ofcritical components in large networks infrastructure. However, in wdns (Fig.5.4a-e), the visual evaluation of areas delimited using both four topological915.4. Results and Discussionsmetrics scores do not show strong correlation with critical areas identifiedwith hydraulic model assessment. Table 5.5 shows,in the WSR column, theSpearman correlation between the rankings of the nodes’ criticality indicesfor all the metrics. It is seen that the PCC has a strong positive correlation(0.24) with the baseline followed by the EVC (0.17). However, the between-ness and the Topological Information metric have both negative correlationwith the WSR baseline.0 20 40 60 80 1000.00.20.40.60.81.01.2Number of eigenvectors included in PCCPhase angleFigure 5.5: Phase angle variation between the PCC and the EVC.In wdns design process, it is usually assumed to increase the reliabilityof the system when there exist more than one path connecting the sourceto the consumption nodes. In practice, the presence of loops of networkgives to the network a certain level of reliability (Suribabu, 2017; Prasadand Park, 2004). On the other side, the spectral metrics are efficient whenredundant connectivity exist in the network and partly explains why thespectral metrics have good performance compared to shortest path-basedmetrics. Moreover, on the field, the location of water reservoirs and thegeospatial distribution of consumers constraints may reduce the possibilityof building loops leading to a hybrid (tree like and looped) network such as925.4. Results and Discussionsthe wdn in the Richmond city. In this case, it is important to couple bothmetrics the shortest path based and spectral metrics to ensure capturing allthe topological characteristics of the network. To deal with the flow patternchanges in the network, the aggregation method should be able to handle theuncertainty and increase the similarities between the identified topologicalcritical components and the hydraulic critical components.5.4.3 Data fusionThe combined topological metric (WSR_BBN) tool show a better cor-relation (0.37) with the baseline (Table 5.5) compared to 0.24 obtained withthe only PCC. The visual map (Fig. 4f) also shows that WSR_BBN iscapturing all the areas delineated using WSR performance indicator in theidentification of topological critical components and increases the similar-ity in the elements identified using both the topological and the hydraulicreliabilities metrics. Both, the visual map (Fig. 5.4f) and the Spearman cor-relation (Table 5.5) are better compared to individual topological metric.Agathokleous et al. (2017) quantified the spatial autocorrelation and thedispersion of vulnerable areas in subnetworks using the Moran Index. Thisindex together with the p-value allow them to conclude to the existence of acorrelation between the operation type of the network and its vulnerability.In this study, the same indicator is used to assess the spatial correlationbetween the baseline WSR and the topological and proposed aggregatedmetric. The last column in Table 5.5 gives the Moran Index of the usedmetrics.From values in the table, the low Moran Index of the WSR (0.11) in-dicate a highly vulnerable network with vulnerable areas spread all overthe network. This situation is well captured by the WSR_BBN that gives avalue of 0.9 close to WSR index. The topological metrics alone tend to iden-tify clustered vulnerable areas. This result is not the same as Agathokleouset al. (2017), because in their application, data related to pressure distri-bution and failure areas in the network allow them to build the real flowpattern in the network and determine betweenness centrality of a directedgraph. In this study, the basic assumption is the absence of operationaldata and thus operator should only rely on their knowledge of the topolog-ical pattern of the network and the design parameters that allow them todefine the hydraulic distances that is used to weight the paths in the twoshortest path-based metrics of an undirected graph. Thus, the aggregatedtopological metric can be used for early assessment of the reliability of wdnsto orient inspections. The tool allows a rapid update of the model through935.4. Results and Discussionshydraulic simulations and BBN-model run. The individual topological met-rics do not need update unless there is evidence of failed components.Table 5.6: Twenty most critical nodes rankings using the WSR as baseline.Nodes ID WSR BETW TIC EVC PCC WSR_BBN376 1 61 54 149 62 2378 1 62 456 142 25 1123 3 42 28 524 196 3124 3 48 237 438 171 31977 5 404 380 527 685 151992 5 555 502 470 695 17689 7 394 326 816 708 21690 7 409 358 848 717 21688 9 376 310 441 698 329687 10 344 283 315 688 185691 11 428 398 749 739 9606 12 230 249 46 53 21625 12 389 263 61 102 33627 14 421 300 77 167 21670 15 307 253 853 672 11671 15 325 262 757 687 11155 17 257 323 350 371 7157 17 267 339 348 386 762 19 403 302 284 442 963 19 482 355 440 462 21The developed tool, together with the other topological metrics, areused to identify the 20 critical nodes shown in Fig. 5.4a for the RichmondWDS. Results of the WSR and four topological metrics (BETW, TIC, EVC,PCC) are summarized in Table 5.6. From Table 5.6, it can be shown thatnone of the four topological metric correctly rank nodes in the first twentymost hydraulically critical components. The BBN clustered metric (Fig. 2,aggregated metric of BETW, TIC, EVC, PCC), correctly identified 12 outof 20 components (60% accuracy).When a failure occurs (e.g. population complaints for lack of water,pressure drops), the developed BBN metric tool will allow decision makersto start their search from the identified critical areas. This will save moneyand time to the municipality. Furthermore, the developed BBN tool is aperfect surrogate of wdn’s reliability metric. It helps localize and prioritize945.5. Summarycritical areas in the network in the absence of hydraulic data.5.5 SummaryThe reliability of wdns is an indicator that support decision making formaintenance, rehabilitation and replacement or inspection. In this study, thelack of operational data is overcome through the introduction of a topologicalreliability metric that is a Bayesian belief network based data fusion of infor-mation provided by individual graph theoretic metrics (Betweenness, Topo-logical information centrality metric, Eigeinvector and Principal ComponentCentrality). The resulting aggregated topological metric(WSR_BBN) is as-sessed against a defined Water Shortage Ratio (WSR) metric that repre-sents the water deficit in the network due to failure of its components. Theapplication of the approach to an exixting case study shows an increasedcorrelation (0.34) between the WSR and the WSR_BBN. In addition, thegeospatial autocorrelation of the two metrics are very closed as describedby their respective Moran Indices equal to 0.11 and 0.09 (Table 5.5). Theselow values of Moran Indices demonstrate the dispersion of vulnerable ar-eas in the network caused by the failure of its components. Furthermore,the p-values (0.00) indicate that the dispersion of the vulnerable areas isnot due to random effects. Additionally, the combined topological metric(WSR_BBN) identified 12 out of 20 most critical components (identifiedbased on the WSR indices) in a large hybrid wdn (Richmond wdn). There-fore, the WSR_BBN metric can be used as surrogate wdn reliability metricin the absence of operational data for both normal and abnormal condi-tions. The projection of WSR_BBN indices on a GIS map, for delineationof critical areas in large networks is practical and useful tool to support thedecision-making in wdn prioritization when financial or temporal constraintsexist.On the other side, the topological metrics calculated in large wastewa-ter are aggregated using the OWA approach to unified the decision supporttool and efficiently assist the management team. The decision maker’s at-titudes are considered and three different aggregated metrics are provided.The analysis of the aggregated metrics show significant improvement in theidentification of critical components from the conservative to the normativeattitude. However, the difference between the normative and the optimisticattitude is minimal and it is proposed to work with the normative attitudeas long as the hydraulic baseline is not variable to evaluate the normativeand the optimistic views.955.5. SummaryIn the last section, an operational risk index is determined for the pipesin the network. The actual condition of all pipes in the network is predictedusing deterioration models, then the criticality is coupled to the conditionthrough a BBN framework to define the risk of failure of pipes on the op-erational performance of the networked system. The defined risk index donot include the subjective consequences of failure such as the impact on thepopulation, on the economy for example. It only consider the failed pipe’seffect on the reliability of the network.96Chapter 6Risk and value ofInformation-based inspectionprioritization for largewastewater system6.1 BackgroundRisk management approach has been adopted in wastewater infrastruc-ture management to account for uncertainties and prevent catastrophic fail-ure of systems (Anbari et al., 2017; Baah et al., 2015; Salman and Salem,2011). Utility managers constantly search for optimal management policiesfor inspection and maintenance. However, the risk approach is limited whenit comes to the quantification of the risk itself (e.g. what is the acceptablelevel of risk?). In this case, the manager should make consistent use of allthe information available, including his(her) degree of belief in the possiblestates, the subsequent observed data and his(her) preferences among thevarious possible action/state pairs. In addition, the decisions are based onthe expected values of the corresponding consequences. Here consequencesare expressed in terms of cost. Pozzi and Der Kiureghian (2011) definedthree manager’s attitudes toward risk including a risk averse, risk neutraland risk affinitive agents. For example, a risk neutral decision maker willmake decision by maximizing the expected utility Eidsvik et al. (2015). Ineach attitude, there is a need for information that should be collected inorder to maximize the utility function. This latter is a mathematical ab-straction that support decision making by incorporating the decision maker’sattitude toward risk. Value of Information is a mathematical tool examiningthe changes in the probability of exceedance of a given policy target whennew information becomes available (Malings and Pozzi, 2018; Li and Pozzi,2017; Pozzi and Der Kiureghian, 2011). The concept incorporates expertjudgement to assess prior beliefs and quantify the uncertainties. Value of976.1. Backgroundinformation is a utility based metric that assesses the impact of data indecision making under uncertainties.Inspection data and developed sewer pipe deterioration models are in-tended as decision support tools for wastewater infrastructure managers toplan for maintenance, rehabilitation, repairs and future inspections. Acqui-sition of new data increases the accuracy of available information and devel-oped deterioration models. However, data acquisition has a subsequent costthat should be evaluated and limited at a certain level for a cost-effectivemanagement Straub (2014). If the type of data needed is covered in thedevelopment of deterioration models, the locations where these data shouldbe collected in the network are not much discussed. Existing deteriorationmodels should be updated with new data collected over the entire networkto increase their prediction capabilities. Updated and accurate deteriorationmodel guides toward an optimal allocation of available resources under ex-isting conditions with the aim of maximizing the network performance. Theoptimal allocation of resources includes the economic criteria in the decisionprocess to evaluate the importance of gathering new information.The quantification of the value of a piece of information depends on itsability to guide the decision process through an optimal and rational selec-tion of actions that lead in the desired direction Pozzi and Der Kiureghian(2011). In the absence of information about the structural condition of twopipes buried in the same network, a manager will prefer to inspect bothpipes. However, if a prior probabilistic performance model of these pipesestimates their probabilities of failure at 50% for the first and 5% for the sec-ond. Under the model classification error reduction approach, an inspectionshould be performed for the former pipe, since its state is the most uncer-tain, i.e., its state would only be correctly predicted 50% of the time, asopposed to 95% of the time for the other component. If a threshold is fixedat 50% probability of failure, then the former pipe should be replaced, andthe second pipe inspected to determine further actions. Inspection policyand further maintenance planning depend on the prioritization of informa-tion acquisition that is not considered in deterioration models.The concept of value of information measures the expected cost of man-aging the infrastructure system without and with the monitoring system(e.g. the deterioration model). This concept integrates the economic crite-ria and is more objective than traditional risk-based decision making. Thedecision maker’s attitude toward risk is an important parameter in the quan-tification of new information to be collected. For instance, a decision makercan adopt a risk averse attitude where the loss function is concave, a riskneutral with a linear function and risk-affinitive where the loss function is986.1. Backgroundconvex (Eidsvik et al., 2015).Individual deterioration models Geoadditive model with nonlinear effects included Bayesian Quantile Geoaditive regression modelCritical components identification Graph theoretic metrics (Betweenness, Topological Centrality, EVC, PCC)Sewer network infrastructure𝜂𝑖 = 𝒙𝑖′𝛽 + 𝑓1 𝑧𝑖1 + . . . + 𝑓𝑝 𝑧𝑖𝑝 + 𝑓𝑔𝑒𝑜 𝑠𝑖 1 Pipes characteristics (e.g.Diameter, Length, Material)Pipes score (after defects grading following WRc)Nodes connectivityLinks weighting factor calculation (includes Diameter, Length and Rugosity)Pipes scores Betw EVC PCCValue of Information Risk based prioritization BBN Framework ModelOWA(Betw, EVC,PCC)Economic criteria (Failure cost, Rehabilitation cost)Figure 6.1: Proposed framework for risk and value of information assess-mentFigure 6.1 shows the proposed framework for both risk assessment andvalue of information. These tools are independently used for pipe inspectionprioritization. To maximize overall life cycle benefit of urban water facili-ties and comply with the safety and environmental regulations, water utilitymanagers needs decision support tools for the planning, design, operationand management of urban water infrastructure. The incompleteness coupled996.2. Risk based approach methodologyto the uncertainty of the available information (e.g. soil properties, loading,material properties, future condition of sewer pipes and the deteriorationprocess) make the decision making process to be a decision problem subjectto uncertain information. The network component characteristics and thehistorical maintenance data enter the individual deterioration model to pre-dict a deterioration score. On the other side, the topology of the networkand the physical characteristics of pipes are considered in the graph-theoreticapproach to determine the importance of each components in the network.The importance is defined in terms of centrality metrics (Betw, EVC andPCC). These metrics are aggregated using the OWA approach into a singleand holistic metrics that is used, together with the pipe score, to evaluatethe risk of pipe failure.The value of information is obtained after including in the decision pro-cess the cost of actions taken but the decision maker. For instance, in thecase of inspection, only the inspection cost and the failure cost are includedin this research. These costs, together with the pipe scores, assign the valueof acquisition of new information from the site. The decision maker is gettinginformation about the pipe’s score from the deterioration model.6.2 Risk based approach methodologyPredictive models provide tools to support inspection, repair, rehabilita-tion and replacement of sewer pipes based solely on their structural condi-tion. However, the definition of maintenance plans include multiple criteria(e.g. hydraulic condition, water quality, complaints, structural condition,network reliability, costs, other works, risk) which cannot be compared (Røs-tum, 2000). The risk criterion is the mostly used and applied in this research(Baah et al., 2015; Salman and Salem, 2011).6.2.1 Ordered Weighted Averaging (OWA)The selection of most critical component based on information providedby graph-theoretical metrics can be posed as a multicriteria decision makingproblem where the alternatives are the components and the metrics are thecriteria. Almoghathawi et al. (2017) aggregated graph theoretical metricsinto a single and holistic metric using TOPSIS. TOPSIS weighting factorsare mostly subjectively selected based on the decision maker’s preferencefor one or another criterion. Balekelayi and Tesfamariam (2019a) applieda BBN based data fusion to aggregate four graph theoretical metrics inurban water distribution system. The developed metric captured all the1006.2. Risk based approach methodologyareas determined by the hydraulic baseline obtained after several hydraulicsimulations.The availability of validated hydraulic simulation models allows the useof BBN as data fusion technique. For wastewater systems, BBN based datafusion will require a well validated hydrodynamic model. The validationdepends on data (water levels, flows) measured on field. However, thesemeasurements are affected by time varying defects present in sewer pipes,due to their noraml deterioration, making hydrodynamic predictions veryuncertain. For instance, the evaluation of the flooded area due to the fail-ure of a pipe that has root intrusion using hydrodynamic model will overestimate the flow in the pipe if the root is not identified and properly repre-sented in the hydrodynamic model. This is the same for other defects suchas breakage, blockage or joint defects. The inflow-infiltration will make thesystem fail while the hydraulic simulation model may not be able to capturethe excess flow given the flow characteristics (wet or dry weather flow).When the baseline hydraulic model is not available, an objective aggre-gation technique that accounts for the decision maker’s attitude toward riskis desired. OWA is a flexible technique that aggregate individual metricsinto a single metric while accounting for the ranges of the individual metricstogether with the decision maker’s attitude (Tesfamariam et al., 2010).An OWA operator of dimension n is a mapping OWA : Rn → [0, 1] thathas an associated weighting vector W = (w1, w2, · · · , wn)T . The require-ments to be satisfied wj ∈ [0, 1], and ∑nj=1wj = 1. For a given vector ofpayoffs for n criteria (x1, x2, · · · , xn), the OWA aggregation is performed asfollows (Yager and Filev, 1999; Yager, 1988):OWA(x1, x2, · · · , xn) =n∑j=1bjwj (6.1)where bj is the jth largest element in the vector (x1, x2, · · · , xn), i.e., b1 ≥b2 ≥ · · · ≥ bn. The weights wj of OWA are not associated with any particularmetric xj ; rather, these are associated with the ordinal position of bj . OWAaggregation provides a nonlinear technique to combine individual metricsinto a single output. OWA is characterized by two basic functions associatedwith the weighting vector W : the orness and dispersion (Disp) or entropy.The following equations 6.2 and 6.3 give their expressions:orness(W ) = 1n− 1n∑i=1wi(n− i) (6.2)1016.2. Risk based approach methodologyDisp(W ) = −n∑i=1wi ln(wi) (6.3)where orness ∈ [0, 1]The degree to which the aggregation is like and or (or and) is character-ized by its orness. Therefore, when the orness function value is equal to 0,the OWA becomes a "minimum" operator and, conversely, when the valuepasses to 1, the operator becomes a "maximum" operator. The measure Dispprovides a degree to which the information is distributed and is bounded by0 ≤ (Disp) ≤ ln(n). For orness = 0 or 1, the dispersion becomes zero, andwhen wi = 1/n (like a uniform distribution), the dispersion is maximum, i.e.,ln(n).Various OWA weight generation methods have been proposed (Yager andFilev, 1999). O’Hagan (1988) proposed the most used procedure to generateweights under a predefined degree of orness. He set an optimization problemaiming at maximizing the dispersion function under the selected degree oforness and unit range of weights. The calculated weights are referred toas maximum entropy (ME) OWA weights Tesfamariam et al. (2010). Theobjective function and associated constraints can be written as: Objectivefunction:Max(Disp(W )) = Max(−n∑i=1wi ln(wi)) (6.4)subjected to :orness(W ) = 1n− 1n∑i=1wi(n− i) (6.5)and0 ≤ wi ≤ 1 ;n∑i=1wi = 1 (6.6)Tesfamariam et al. (2010) proposed a transformation of different ornessvalues into linguistic (e.g., “optimistic”, “moderately optimistic”, “norma-tive”, “moderately conservative” and “conservative”) degree of optimism ofa decision maker. Their approach in Table 6.1 is applied in this research.6.2.2 Risk evaluation for sewer pipesRisk perception greatly depends on the quality of information providedby the deterioration models. In engineering definition of risk, the likelihoodof failure is coupled with the consequence of failure to define the risk indexlevel. This approach is incomplete and actual trend of research is toward the1026.2. Risk based approach methodologyTable 6.1: Transformation of Linguistic Degree of Optimism to Orness Val-ues (Tesfamariam et al., 2010).Degree of optimism ornessOptimistic 0.9moderately optimistic 0.7normative 0.5moderately conservative 0.3conservative 0.1application of resilience that is considered to be effective Elms and Brown(2013). The definition of the consequence of failure is mostly subjective andthe weighting of the parameters depends on the selected approach Kabiret al. (2018a); Baah et al. (2015); Salman and Salem (2011). An operationalrisk index defined as the combination through a Bayesian belief network,of the likelihood of failure and the criticality of components as defined inchapter 5 is calculated and projected on GIS map for visualization. Theoperational risk index quantifies the effect the condition of the pipe and itsimportance on the system level operation. The calculated operational riskindex solves the limitation of the traditional risk index definition that donot include the impact of the failed pipe on the system level performance.Moreover, the rate of deterioration of pipes as presented in GIS maps (seefigures 4.11) is included in the risk model. This approach is innovative inthe way that two pipes in condition 3 and installed at two different locationsin the city, where the consequences of failure are assumed to be the same,will not have the same risk index at a given planning horizon if the rate ofdeterioration at the two locations are different or their criticality indices arenot equal. The pipe located where high deterioration rate is identified willdeteriorate faster than the pipe buried in low rate deterioration (benign)environment. Thus, the former pipe should be given high priority than thelater. The deterioration rate becomes an important decision parameter forthe planning of maintenance.The risk index is discretized in three levels (low, median and high). Thecriticality of the components are determined using graph theory and the finalaggregated metric is computed following the OWA approach. System failurescenarios are modeled using OWA approach. For each decision maker’sattitude a risk map is produced.1036.3. Methodology for the value of information6.3 Methodology for the value of information6.3.1 Decision treeIn the management and operation of existing wastewater, the large num-ber of alternatives actions a decision maker can take requires the definitionof a framework for systematic analysis of the corresponding consequences(e.g. what will be the effect of rehabilitation of a sewer pipe on the systemlevel performance?). Figure 6.2 presents a decision tree that convenientlyrepresent the decision problem in engineering in general. Each action lead todifferent states of nature with their consequences. The consequences are ei-ther expressed in monetary units or as utility function. The optimal decisionshould maximize the defined utility function (Straub, 2014).Not failedFailedInspectionNo InspectionInspection costCost of failureNo costFigure 6.2: Example of a simple decision tree for pipe inspectionInspection in large infrastructure systems should target pipes in bad con-dition in order to plan for their rehabilitation and replacement Ahmadi et al.(2016); Mancuso et al. (2016). Newly installed pipes (condition 1 and 2) andpipes in the failing mode (condition 5) will not provide useful information tosupport the decision making. Pipes in condition 5 should be replaced. In-formation about the condition of pipes is unknown or uncertain if obtainedafter running a deterioration model. Municipalities usually define a thresh-1046.3. Methodology for the value of informationold above which the level of service is not accepted by the population. Thus,pipes are classified into two groups: failed pipes those whose condition isabove the threshold amd no fail pipes those whose condition is below thethreshold. Mostly condition 3 (corresponding to the defect score of 80) isconsidered as a cutoff between the two groups. Whitout any information,the probability of failure of pipes is 50%. The decision maker has inspectiondata and know the condition of inspected pipes. Inspected pipes usually donot exceed 10-20% of pipes in the networks. Thus, deterioration models willbe used to get information about the 80% uninspected pipes. Both informa-tion (from inspection and deterioration models) will be used for planning offuture inspection.In the best case scenario, the decision maker need to inspect all thepipes in the network but, he is limited by the available budget and the timeto inspect large size networks. If he decides to inspect a pipe i, whatevercondition is the pipe, an inspection cost (C(I)) will be applied. However, ifthe pipe is not inspected, no cost is applicable unless the pipe has failed. Inthis latter case, a failure cost including the direct, indirect and social costswill be applied. Potential consequences are associated with different costs6.2. If the decision maker’s knows the exact probability of failure of thepipe, then his decision will be easy. However, in practice, the informationabout the probability of failure of pipes in the network is uncertain.A consistent analysis of such decision problem will use all the availableinformation including the degree of belief of the decision maker in the pos-sible state of nature of the pipes, the subsequent observed data and herpreferences among the various possible action/state pairs. The expectedvalues of the corresponding consequences will be the basis of the decisionmaking process.6.3.2 Decision-based on expected valuesLet consider a case where the decision maker should select between twoalternatives: inspection a1 and no inspection a2. Possible states of the pipebelong to the set ω = {0, 1}. The failure cost C(F ) is higher than theinspection cost C(I). The manager can take the risk of not inspecting thepipe and later spending C(F ) with the probability θ1 if the pipe is failed orspend nothing if the pipe is good. The consequence of inspecting the pipe(meaning the decision maker selects the alternative a1) is C(I).Before the true state condition of the pipe is known, the optimal decisiondepends upon the likelihood of the various conditions θ of pipe and theseriousness of the consequences: Inspection cost, Cost of failure and No1056.3. Methodology for the value of informationCost. The objective is the identification of the action that provide an optimalbalance between its implementation cost and the risk associated with thefailure of the system. A further analysis of the decision problem requires thenumerical assessment of the preferences of the decision maker. Eidsvik et al.(2015) proposed the following equation to represent the decision maker’sattitude toward risk:u(v) = α+ β × e−γv (6.7)where α and β are constant such that if γ > 0, then the decision maker isrisk averse and β < 0, whereas if γ < 0, the decision maker is risk seekingand β > 0. In the case where γ = 0, the decision maker is risk neutral andthe linear function should be applied:u(v) = v (6.8)In practice, the risk averse decision maker’s attitude is represented whenthe following values α = 1 and β = −1 are applied and the utility equationresults in the following:u(v) = 1− e−γv (6.9)The utility function u incorporates the decision maker’s preference intothe decision process to allow a consistent selection between the alternativesa1 and a2.The value of information quantifies the price at which the decision maker’sis indifferent between acquiring or not additional information. The indiffer-ence is characterized by the attitude of the decision maker toward risk asdefined in equation 6.6.When the information is available, the uncertainty is quantified beforemaking the decision. If x is observed and the alternative a1 is chosen, thenthe decision maker get a reward w and pays the cost P for certain andalso get the value v(x, a1) from the decision situation since E (v (x, a1) |x) =v(x, a1). The optimal alternative will be given by the following equationEidsvik et al. (2015) :a∗ (x) = arg maxa∈A {u (v (x, a) + w − P )} (6.10)If x is observed with the probability p(x), then, the expected utility foravailable information is given by :a∗ (x) =∑xmaxa∈A {u (v (x, a) + w − P )} × p (x) (6.11)The value of information is the cost P at which the expected utilities inequations 6.10 and 6.11 are equal as presented in the following equation:1066.3. Methodology for the value of information∑xmaxa∈A {u (v (x, a) + w − P )} × p (x) = maxa∈A {u (v (x, a) + w − P )}(6.12)The decision maker can select a1 over a2 only if the expected utilityE(u|a1) is greater than E(u|a1). The behavior of the decision maker iscrucial as described in Peterson (2017). For a risk neutral manager, onlyminimum cost can be paid. Thus, the rehabilitation of a sewer pipe can becarried out only if its cost is lower than the risk associated with the failure.In this perspective, the utility function can be expressed in terms of lossfunction that is given in the following equation Pozzi and Der Kiureghian(2012):C∗ = min(CR, P (F )× CF ) (6.13)where CR is the repair cost, P (F ) is the probability of failure of the pipe andCF the cost of failure. The deterioration model’s information is considered astest information and the manager is aware of possible state of the conditionof pipes.Model misclassification results into over or underestimation of the infor-mation provided. False alarms and silences should be quantified to evaluatethe importance of the classification model. The integration of the probabil-ity of occurrence of false alarms and false silence in the estimation of thevalue of information provided by the model is paramount. Although thisinformation is imprecise based on the accuracy of the model. Thus, basedon this imperfect information, the probability of obtaining an alarm fromthe model (test) is given by:P (A) = P (A|F )× P (F ) + P (A|U)× P (U) (6.14)P (S) = P (S|F )× P (F ) + P (S|U)× P (U) (6.15)where P (A) is the probability of getting an alarm from the model, P (A|F )is the probability of getting an alarm when the pipe has failed, P (A|U) isthe probability of getting an alarm while the pipe did not fail and P (U) =1 − P (F ). S is the silence of the model in these cases. The probability ofgetting a failed pipe can be updated using the Bayes’ rule as following:P (F |A) = P (A|F )× P (F )P (A) (6.16)P (F |S) = P (S|F )× P (F )P (S) (6.17)1076.4. Application to wastewater networkThen, after every inspection and the update of the model, the managerwill update his knowledge following these probability and orient his selec-tions.6.4 Application to wastewater networkThe wastewater system of the city of Calgary is represented as a graphand the methodology proposed in this chapter is applied to identify criticalareas in the network. The lack of hydraulic data (e.g. dry and wet weatherflow, runoff) do not allow to build a baseline as suggested for pressurizedflows. However, the decision maker’s attitudes (Table 6.1) are included inthe process through the OWA to identify boundaries of critical componentsin the large network.6.5 Results and Discussion6.5.1 Critical areas delineationHydrodynamic models are time consuming and several needed param-eters (e.g. dry weather flow production, slope change due to subsidence,inflow-infiltration due to joint defects, breakage, root intrusion) change withtime making difficult a correct estimation of sewerage flows in pipes. Even awell calibrated hydrodynamic model will give approximate location of criti-cal areas in the network because it does not incorporate defects that appearsin the pipes due to their structural deterioration.The city of Calgary’s wastewater system has several pipes installed 100years ago and not all of them have been inspected to assess their actualinternal conditions. Graph theory allows a mathematical abstraction ofthe network and does not require a lot of parameters to identify importantareas in complex networks. The application of graph theory to a large andcomplex network (76380 pipes for the city of Calgary) with several loopsis computationally expensive for shortest path-based metrics and requireadvanced processing of sparse matrices for the spectral metrics.The wastewater of the city of Calgary has a highly looped topology lay-out in the entire area of the city (3.2). Thus, from the definition of graphtheoretical metrics, the identification of critical components is not straightforward. The existing and ongoing deterioration states of some pipes donot allow a realistic determination of critical components using hydrody-namic simulation. 10 10% available inspection data of sewer pipes show the1086.5. Results and Discussion10Figure 6.3: Critical areas in the the city of Calgary estimated using thebetweenness centrality1096.5. Results and Discussion10Figure 6.4: Critical areas in the the city of Calgary estimated using EVCmetric1106.5. Results and Discussion10Figure 6.5: Critical areas in the the city of Calgary estimated using PCCmetric1116.5. Results and Discussion10Figure 6.6: Critical areas in the the city of Calgary estimated using con-servative OWA based data fusion1126.5. Results and Discussion10Figure 6.7: Critical areas in the the city of Calgary estimated using nor-mative OWA based data fusion1136.5. Results and Discussion10Figure 6.8: Critical areas in the the city of Calgary estimated using opti-mistic OWA based data fusion1146.5. Results and Discussionexistence of several defects inside pipes and these defects affect the flow ofsewerage Balekelayi and Tesfamariam (2019b). No hydrodynamic model hasbeen run for this study. All the performances (hydraulic and mechanical)are estimated using a single aggregated metric obtained using OWA. Theuncertainty in the identification of critical component is captured throughthe inclusion of the attitude of the decision maker toward risk in the datafusion technique. The changes in the importance of components due tothe changes in the flow directions and the pipes’ failure are also capturedthrough the attitudinal approach in OWA.While gravitational wastewater networks have a designed direction ofwater flows, the undirected representation of the wastewater networks isrecommended to capture undesired events such as blockage, breakage orany defects and their interaction in sewer pipes. For example, in a blockedpipe, wastewater accumulates then flows backward until it finds a least resis-tant path to flow again toward the treatment facility. The situation is worseif the blockage is coupled with other defects such as joint displacement al-lowing inflow-infiltration in the pipe upstream the blockage defect. Shortestpath-based metric (betweenness: BETW) and spectral metrics (Eigenvec-tor centrality: EVC and Principal components centrality: PCC) are usedfor this analysis. In highly redundant network (complex looped structure),the betweenness of nodes is low because there is not much redundant tiesbetween the nodes Borgatti et al. (1998).For the same reason, the failure of a single pipe will not have an in-creased impact on the performance of the network because the number ofindependent paths connecting different vertices is high. Three major axes,with high BETW, are identified in the city of Calgary (Fig 3). The firsttwo axes composed of high betweenness components go from the North andthe North-East of the city toward the Bonnybrook wastewater treatmentplant located in the central part of the city. This wastewater facility is rep-resented with the highest calculated betweenness (Figure 6.3). In the south,the Fish creek wastewater treatment plant is also showing a relatively highbetweenness and one major axis (composed with relatively high betweennesscomponents) is connecting all the small pipes in the area to the treatmentplant through the highlighted axes (Figure 6.3).From its definition, the BETW centrality metric captures the principallinks connecting the majority of nodes in the network. The high numberof independent pathways connecting node pairs in the network, coupledwith a high number of internal loops, significantly decreases the impactof the failure of the pipes in such network (Figure 6.3). Only trunks arehaving the high betweenness. The BETW centrality should be coupled with1156.5. Results and Discussionother metrics that are able to capture important components in the globalstructure of the network under study.Spectral metrics (EVC and PCC) have a tendency to identify as topolog-ically critical high degree nodes that are interacting with highly connectednodes. Thus, Spectral metrics will be efficient in highly looped networks.Figure 6.4 shows the EVC calculated for the wastewater of the city of Cal-gary. It is observed the following: Only the two wastewater treatment plantsincluding the Bunny creek and Pine creek facilities are identified as impor-tant in the network system. Although wastewater treatment facilities arecritical, EVC is not able to get information on the other critical componentsin the network. The objective of the analysis is the identification of othercomponents that are not directly identifiable as critical. The application ofPCC (Figure 6.5) allows to locate more hubs in the global structure of thelarge network.The number of the most significant eigenvectors, in PCC evaluation,following equation 5.10 is represented in Figure (6.9). From this figure, thevalue of P to consider in PCC metric calculation should be between 10.Thus, the values of P below 10 do not allow to identify all the importanthubs in the large network and values beyond this value, the identificationis perturbed by noise. There is no more useful information that will becollected in adding more eigenvectors to the X matrix beyond the optimalvalue 10.PCC metric determined from X matrix (76380 × 10) composed with10 eigenvectors (determined from Figure 6.9) expands the power of spec-tral metrics in the identification of critical components in large networks.The PCC metric identified all the most connected areas in the network(Fig. 6). The identified hubs include both three main treatment facilities(Bunny creek, Fish creek and Pine creek) and more other areas that couldnot be identified simply using EVC. The results obtained from the threegraph-theoretical metrics and the analysis of the complexity of the networkhighlight the important of aggregating the individual graph metrics togetherwith the aim of increasing the accuracy in the identification of critical com-ponents. In addition, the absence of hydrodynamic model as baseline forcomparison in the identification of critical components led to the applicationof OWA that include the decision maker’s attitude.1166.5. Results and DiscussionFigure 6.9: Phase angle between the PCC and the principal eigenvector(EVC)OWA aggregation allows the combination of different metrics determinedusing graph theory and increases the accuracy in the identification of criticalcomponents in large networked infrastructure. Five degree of optimism areconsidered: the conservative, the moderate conservative, the normative, themoderate optimistic and the optimistic attitudes (Table 6.1). The conser-vative attitude represents a decision maker that does not want to involvein large search of critical areas in the network. Only few optimal hubs areidentified for the conservative degree of optimism of the decision maker (Fig.6.6). The conservative attitude does not add more information compared toindividual graph metrics.In addition, some areas identified as critical by the BETW (figure.6.3)are not captured in this attitude. It is useful for the decision maker touse individual metrics rather than adding more computation required inthe conservative method. However, the identified areas are the optimum1176.5. Results and Discussionareas that should be regularly controlled to keep the system connected. Afailure in these areas will inevitably have consequences at the system levelperformance. Pipes in these areas should be hardened and the frequencyof inspection increased. The inspection frequency will also depend on thegeospatial effect of the highlighted areas as described by Balekelayi andTesfamariam (2019b).The normative attitude is more inclusive and captured all the areas de-limited by both three graph theoretical metrics. The normative attitude ap-pears to better highlight critical areas in large networks (figure 6.7). Whenthe access to financial resources is limited, this attitude is recommendablebecause it does not only capture all the areas delimited by individual graphmetrics, but also give realistic weights to the areas with the only highly crit-ical area located in the South of the city close to the pine creek wastewatertreatment facility.The optimistic attitude is capturing more areas than the normative (fig-ure 6.8). From table 3, it is noticed that the ranking of the components usingdifferent aggregation are the same compared to individual metrics and therank correlation between the normative and the optimistic OWA is 1. Thus,the suggestion of selecting the normative aggregation is justified.On the other side, it is observed the low correlation between the PCCand the aggregated metrics (Table 3). This is due to the topology of wastew-ater treatment of the city of Calgary. The system presents three main subnetworks connected to the three wastewater treatment facilities. The linksconnecting theses subgroups are therefore getting more importance sincethey are connecting multiple nodes. It results in a high betweenness forthese links while the spectral metrics do not capture them as critical be-cause they are not connected to nodes with high degree. However, ThePCC acts well in individual subgroup by identifying critical components inthese subnetworks. The aggregation results in a metric that capture all thecomponentsShortest path-based and spectral metrics defined in the methodologyare also applied to the sewer pipes system with the different resulting inthe definition of the energy loss. This latter is dependent of the manningcoefficient as presented in Table 5.1. Figure 6.3 shows the areas delimitedby the betweenness centrality. From its defintion, this metric captures theprincipal links connecting the majority of nodes in the network. However,the EVC metric (Figure 6.4) identified only two hubs. One hub (situated inthe centre of the network) is located in an area that have been identified ashaving a very high impact on the deterioration of sewer pipes in the networkas represented in (Figure 3.8). The implementation of PCC (Figure 6.5)1186.5. Results and Discussionallows to get more hubs as per its definition. None of the metric capturesall critical areas in the network. The analysis of figures 6.3-6.5 shows thatthere is not two metric that identify the same areas. It is therefore importantto consider each metric as source of information about critical areas in thenetwork and aggregate them in order to enhance the identification of criticalareas.The lack of hydraulic data do not allow us to build a supervised datafusion. The attitude of the decision makers plays a significant role in thedelineation of critical components in large infrastructure networks. Thus,the OWA technique is used to cluster the three metrics inot a single andholistic metric that will capture all critical areas in the network. From eachdegree of optimism of the decision maker (see Table 6.1), an aggregate metriccorresponding to its orness value is constructed. Only three critical maps,based on three degree of optimism (conservative, normative and optimistic)(see Figures 6.6,6.7 and 6.8) are presented in this research. It is observedthat the optimistic degree of the decision maker captured all the criticalareas delineated by the graph topological metrics. However, the normativedegree of optimism is indicated to be considered as reference because of thelack of baseline. The difference between the normative and the optimistic isthe values of indices only but they capture the same areas.6.5.2 Risk of pipes failureWhen the computed criticality indices are coupled with the probabilityof failure in a Bayesian belief network framework as stated in figure 6.1,different risks indices are calculated. Figure 6.6 gives critical areas identi-fied using the conservative degree of optimism of the decision maker. Thecalculated risk indices show that the decision maker minimizes the risk ofpipe failure and one third of pipes in the network are represented in lowrisk (Figure 6.10). This is not the real case because from the installationperiod data and the material of pipes installed on the network. The pipesin the outer part of the city are new pipes that have been installed after1960 and they are made of concrete or PVC. However, the pipes installed inthe center of the city are old and are mostly metallic and clay pipes. Themetallic pipes are in advanced deterioration state and should be identified ascritical for their future replacement. That is not the case when consideringthe conservative degree of optimism.The normative degree of optimism is represented in Figure 6.11. Theproduced map is in accordance with the material and age distribution inthe network. The majority of pipes are in median risk and few pipes are1196.5. Results and Discussioncategorized as in high risk. Cementitious and PVC pipes are categorized aslow risk pipes while metallic and clay are in median and high risk categories.The low risk pipes are younger than the high risk pipes.LowHighMediumLegendFigure 6.10: Risk map of sewer pipes in the city of Calgary following theconservative approach1206.5. Results and DiscussionLowHighMediumLegendFigure 6.11: Risk map of sewer pipes in the city of Calgary following thenormative approach1216.5. Results and DiscussionLowHighMediumLegendFigure 6.12: Risk map of sewer pipes in the city of Calgary following theoptimistic approachThe optimistic and normative views are closed to each other. The risk1226.5. Results and Discussionincrease due to the change of decision maker attitude is not captured in thecategorization of the output risk map (low, middle, high). The likelihood offailure remains the same in both views and only the criticality index changesfrom normative to optimistic attitude.The high risk pipes are found in areas where the majority of pipes areold (installed before 1960).The pipes in the North-East of the city are crit-ical and the area is found to have high deterioration rate (Figure 6.12). Inthis area, is constructed the Calgary international airport and the major-ity of pipes in the area are concrete pipes installed recently (after 1960).The high frequency of cyclic loading may be the reason behind the highvulnerability of the pipes in the area. Further investigations are needed toidentify the factors that should be added to the model to better capture thisheterogeneity.6.5.3 Example application of the risk approach in theprioritization of maintenanceIn the following example, pipes with highest risk are replaced with newpipes and in this research, the normative attitude of the decision makertoward risk is considered. However, the approach can be applied to all theattitude of the decision maker toward risk.In normative attitude, 4078 pipes are found to have high operationalrisk of failure in the city of Calgary. Assuming the decision maker plansto replace between 10 and 30% of high risk pipes. Three scenarios areconsidered in this example:the replacement of 10,20 or 30% of highly riskpipes. With 10% replacement, the comparison of maps in Figures 6.11 and6.13 do not show significant difference. However, it is observed that thereplaced pipes are located in critical areas delineated by both the graphtheoretical approach (Fig. 6.7) and the geospatial effect map (Fig. 3.8).1236.5. Results and DiscussionLowHighMediumLegendFigure 6.13: Changes in the normative risk map after 10% replacement ofhigh risk pipes1246.5. Results and DiscussionLowHighMediumLegendFigure 6.14: Changes in the normative risk map after 20% replacement ofhigh risk pipes1256.5. Results and DiscussionLowHighMediumLegendFigure 6.15: Changes in the normative risk map after 30% replacement ofhigh risk pipes1266.5. Results and DiscussionThe replacement of 20 and 30% of pipes leads to the same conclusionsas for the 10% replacement. However, 30% replacement allows to reducesignificantly the high risk pipes in the south of the city. The majority ofpipes in the central part of the city are metallic pipes. Metallic pipes con-tributed more to the deterioration of pipes in the city of Calgary (Fig. 3.4).The developed deterioration models plays a key role in the prioritization ofpipes replacement. The geospatial impact map provides critical informationinfluencing the prioritization of sewer pipes.Geoadditive models are effective in the delineation of critical areas thatrequire attention from the management. The identification of componentsthat affect the performance of the system ehance these areas. Finally, therisk based decision metric allows fast prioritization of inspection, mainte-nance and replacement as shown by the above replacement example.6.5.4 Probability of failureThe benefit of using advanced deterioration models is to be demonstratedin order to increase the confidence of utility managers towards simulationresults (Caradot et al., 2017). The identification of pipes for inspection ismostly based on expert knowledge and historical failure records. A consis-tent selection of pipes to be inspected is presented in this research. Fromthe deterioration models and future condition prediction results as presentedin Figure 3.9, the conditions of all the pipes in the network is predicted atdifferent planning horizons (actual, 25 and 50 years later). For each horizon,the predicted conditions are converted into the probability after fitting thepredicted scores to a log-normal distribution.The probability of failure is then input in the decision making process toevaluate the value of information provided by the deterioration models. Anexample of the probability of failure curve is given in figure 6.16 for pipesin the network after 25 years.1276.5. Results and Discussion0 50 100 150 200 250 300 350Pipe score00.10.20.30.40.50.60.70.80.91Probability of failureFigure 6.16: Probability of sewer pipes failure after 25 years6.5.5 Value of InformationThe decision maker will evaluate the accuracy of the deterioration modelto update his(her) prior knowledge in the decision process. The use of de-terioration model implicitly consider that the information provided to thedecision maker is imperfect and decisions should be made accordingly. Pre-vious assumptions hold (pipes in conditions above 3 are considered failed).The predicted and observed vectors are transformed into binary variableswith 0 representing the non-failed and 1 the failed pipes. The resulting con-fusion matrix, given in Table 6.2, allows the computation of model accuracyand different detection levels such as the probability of getting an alarmand the probability of getting a silence from the model. Among possibleactions, only the decision regarding the inspection of pipes is considered inthe application.1286.5. Results and DiscussionTable 6.2: Confusion matrix of the statistical deterioration model.N = 11189 Predicted non-failed Predicted failedObserved non-failed 9003 0Observed failed 41 2145 Figure 6.17: The value of information in the city of Calgary from nowThe developed model gives the following initial probabilities: P (A|F ) =0.981, P (A|U) = 0.0000453, P (S|F ) = 0 and P (S|U) = 1. The applicationof this methodology lead to the result presented in figure 6.17. The maps inthis figure show the level of deterioration of pipes and the value of informa-tion. It is seen that pipes in the south of the city will give more informationto prioritize inspection rather than pipes that are in failing states (condi-tion 4 and 5) situated in the center of the city. Pipes in the external partof the city are new pipes and do not have useful information to support theprioritization of inspection or maintenance. These pipes are classified withless value. It should be noticed that pipes in the center of the city can beinspected but they do not have priority in regards to pipes in the south. Inaddition, the decision maker should plan for their replacement and only few1296.5. Results and Discussioninspections. Figure 6.18: The value of information in the city of Calgary after 25 yearsAfter 25 years, given that no rehabilitation has been carried out, theresults show a reduction in the high value area because, the number offailed pipes is increasing and given the detection probability, the decisionmaker should concentrate his limited resoyrces to the inspection of pipesbetween the centre and the south of the city. Some interetsting regions areappearing in the north of the city giving an alarm that should be consideredfor inspection also. The pipes in the centre are not completely with the value0 but have a value that is greater than pipes between the extreme north andthe center. This highlights the importance of still inspecting these failedpipes.After 50 years, under the same assumption, the extend of pipes thatwill not add information is getting large and the pipes with supporting in-formation are reduced to a small area. At this level, the pipes in failingstates in the area of the airport (North-East) should be planned for replace-ment because from the developed deterioration models, that area has a highdeterioration rate.1306.6. Summary Figure 6.19: The value of information in the city of Calgary after 50 years6.6 SummaryThe developed tools provide consistent support for cost effective prior-itization of inspection of sewer pipes. The risk based decision making toolgives an operational risk that embed the condition state of the pipe, itsimportance in the network due to its location and the rate at which thepipe changes from one condition state to another. This later is beneficial forpipes that have high deterioration rate. In addition, the criticality metricdefined captures all possible changes in the importance of components inthe network. The developed risk decision tool allows fast updating of therisk maps once the deterioration state is calculated.On the other side, the VoI tool includes a loss (utility) function definedfor each component in the network and the economic criteria that constitutesa constraint in the selection of sewer pipe for inspection. Furthermore, thedeveloped VoI model is coupled with the deterioration model to estimatethe change in time of the VoI with only two possible alternatives for thedecision maker: inspection or not. Three different horizons are consideredin the planning : now, 25 and 50 years later.1316.6. SummaryThe application presented in this research restricts the actions of thedecision maker to the inspection of pipes. In a broad view, the wide rangeof possible decision maker actions will have an impact not only on the valueof information because the conditions will be changing after each decision,but also on the evolution of the probability of failure of pipes. Pipes thatare in the failing states (condition 4 and 5) are suggested for replacementand should not be included in the inspection planning.132Chapter 7Conclusions andrecommendations7.1 Summary and conclusionsThis research introduces advanced deterioration models for improvinginspection, maintenance, rehabilitation and repair of sewer pipes. The de-veloped models are based on structured additive regression techniques. Thecovariates are modeled with both linear and nonlinear relationships with thedependent variable. The quantile deterioration model automatically selectsthe significant base learners through an embedded optimization techniquewhile estimating the model’s parameters. In both models, the geospatiallocation of the pipe is introduced as a surrogate covariate to capture infor-mation about the unobserved and unknown variables. A Bayesian inferenceframework is considered to reduce uncertainties in model’s parameters. Thecovariates are represented as random variables and appropriate prior distri-butions are accordingly defined. For example, first and second random walkspriors are defined for the P-splines smooth functions of continuous covariatesin the structured additive regression models. Results shows a good perfor-mance of the developed models with a coefficient of determination equal 0.89for the expected mean deterioration model approach. Another advantage of-fered by the developed models is the definition of the entire distribution ofthe output response that gives a good measure of the uncertainty in theresponse variable.On the other side, the estimation of the magnitude of the effects ofthe covariates provides a basis to improve the management by deciding onfactors that should be controlled or improved to avoid rapid deteriorationof sewer pipes.The second objective of this research is the identification of critical com-ponents in large infrastructure using simple graph theoretic metrics. Thegraph metrics are limited in their definition and do not capture the dynamicsoccurring in the network. Data fusion techniques based on Bayesian belief1337.2. Originality and contributionsnetworks and Ordered Weighted Averaging are applied to multiple graphmetrics to aggregate them into a single and holistic metric. The proposedmetric is able to capture the effects of both types of failure in urban waterinfrastructure networks: the hydraulic and mechanical failures.The results of the first and second objectives are used to prioritize thepipes inspection and maintenance using Bayesian belief networks. Finally,a the value of information gained throughout the simulation models is eval-uated and projected on maps to orient future inspections.7.2 Originality and contributionsThis thesis research is the first to apply structured additive nonlinearregression models to develop accurate individual sewer pipes. In addition,the application of the optimization in boosting algorithm to select the in-fluential attributes and the use of geospatial location of pipes as surrogatevariable representing the unknown covariates are novel approaches that en-hance the prediction of sewer pipes. Furthermore, the developed geospatialmap is original approach to support early decision making for prioritizationof inspection. On the other side, the lack of operational hydraulic data (flow,pressure) is no longer a stopping criterion. The performance of large net-worked urban water infrastructure systems can be assessed using from theirtopological pattern. Data fusion techniques based on Bayesian inference andOrdered Weighted Averaging are introduced to ameliorate the graph theoret-ical based assessment of critical components in large infrastructure systems.Resulting metrics are effective because they rank the components nearly asthe baseline hydraulic models and efficient because the long and fastidioushydraulic simulations are avoided. Finally, the expensive optimization oflife cycle cost to prioritize pipes renewal is replaced by a more effective andflexible BBN that will not only account for the uncertainty in the predic-tions but will also include the rate of the deterioration as a component inthe risk approach that is traditionally based on the likelihood of failure andthe consequence of failure only. The proposed research tool can be appliedto both types of urban water infrastructures (wastewater, water distributionand drainage systems). The produced maps are easy to interpret and can beused by operational teams on field. All the applications are done on the cityof Calgary sewer data with the emphasis that the geospatial informationplays a crucial role in the development of increased accurate deteriorationsewer pipes. Specifically, the contributions of this research are summarizedas:1347.3. Limitations1. Develop an enhanced nonlinear individual sewer pipes regression modelthat includes geospatial information as a surrogate covariate represent-ing the unknown and unobserved covariates.2. Develop quantile-based deterioration model to allow the analysis ofthe identification of factors that are responsible of the occurrence ofextreme conditions in the deterioration process.3. Develop a graph theoretic based model to predict the topological per-formance of large infrastructure systems and identify the componentsthat are critical in a scarce operational data environment.4. Develop a Bayesian belief network to conduct a risk-based prioritiza-tion of sewer pipes based on their criticality, the likelihood of failureand the rate of deterioration5. Develop a sewer network level performance metric evaluation modelto allow decision making at strategic and tactical levels.7.3 LimitationsSome limitations can be raised in the thesis:1. The geospatial information is used as surrogate covariate. However,due to the replacement effort taken by the city of Calgary, inspectedpipes are clustered in the center of the city and pipes in the externalpart of the city have not been inspected. Therefore, predictions inthese zones are mostly dependent on the correlation. We have pro-posed to prioritize these areas for future inspections.2. The developed deterioration models are based on pipes’ features (phys-ical, environmental, maintenance) and the output is the scores givenby the operator. Mostly, the scores given in WRc are related to theactions to be done on the pipes rather its condition. It is proposed inthis thesis to develop a new conditional assessment model for sewerpipes that account for observed defects and gives the condition. Suchmodels will give important input for the models developed in this the-sis.3. The TIC is computed on an iterative process. This is fastidious andlimited by the size of the available RAM of computers.1357.4. Recommendations7.4 RecommendationsThis study developed two deterioration models and proposed a surrogateapproach to identify critical components in large infrastructure networks.The assigned criticalities are coupled with the condition states of pipes toprioritize sewer pipes for inspection and maintenance. The following recom-mendations may apply :1. In the statistical models, pipes geospatial location is considered interms of district. Future work may consider the exact coordinates ofpipes and use the krigging approach to compute the spatial correlation.This will enhance the deterioration model.2. Large infrastructure networks should be clustered into small networksand build an hierarchical decision making.136BibliographyAbraham, D. M. and Wirahadikusumah, R. (1999). Development of pre-diction models for sewer deterioration. In Lacasse, M. and (Eds), D. V.,editors, Proceedings of the 8th Conference Durability of Building Materialsand Components, volume 8, pages 1257–1267, Ottawa.Agathokleous, A., Christodoulou, C., and Christodoulou, S. E. (2017).Topological robustness and vulnerability assessment of water distributionnetworks. Water Resources Management, 31(12):4007–4021.Ahmadi, M., Cherqui, F., Aubin, J.-B., and Le Gauffre, P. (2016). Sewerasset management: impact of sample size and its characteristics on thecalibration outcomes of a decision-making multivariate model. Urban Wa-ter Journal, 13(1):41–56.Alegre, H. and Coelho, S. T. (2012). Infrastructure asset management ofurban water systems. In Water Supply System Analysis-Selected Topics.InTech.Almoghathawi, Y., Barker, K., Rocco, C. M., and Nicholson, C. D. (2017).A multi-criteria decision analysis approach for importance identificationand ranking of network components. Reliability Engineering & SystemSafety, 158:142–151.Ana, E. and Bauwens, W. (2010). Modeling the structural deterioration ofurban drainage pipes: the state-of-the-art in statistical methods. UrbanWater Journal, 7(1):47–59.Ana, E., Bauwens, W., Pessemier, M., Thoeye, C., Smolders, S., Boonen,I., and De Gueldre, G. (2009). An investigation of the factors influencingsewer structural deterioration. Urban Water Journal, 6(4):303–312.Anbari, M. J., Tabesh, M., and Roozbahani, A. (2017). Risk assessmentmodel to prioritize sewer pipes inspection in wastewater collection net-works. Journal of environmental management, 190:91–101.137BibliographyAriaratnam, S. T., El-Assaly, A., and Yang, Y. (2001). Assessment of infras-tructure inspection needs using logistic models. Journal of InfrastructureSystems, 7(4):160–165.Baah, K., Dubey, B., Harvey, R., and McBean, E. (2015). A risk-basedapproach to sanitary sewer pipe asset management. Science of the TotalEnvironment, 505:1011–1017.Baik, H.-S., Jeong, H. S., and Abraham, D. M. (2006). Estimating transitionprobabilities in markov chain-based deterioration models for managementof wastewater systems. Journal of water resources planning and manage-ment, 132(1):15–24.Balekelayi, N. and Tesfamariam, S. (2019a). Graph-theoretic surrogate mea-sure to analyze reliability of water distribution system using bayesianbelief network-based data fusion technique. ASCE-Journal of Water Re-sources Planning and Management, 145(8):1–10.Balekelayi, N. and Tesfamariam, S. (2019b). Statistical inference of sewerpipes deterioration using bayesian geoadditive regression model. ASCE-Journal of Infrastructure System.Baur, R. and Herz, R. (2002). Selective inspection planning with ageingforecast for sewer types. Water Science and Technology, 46(6-7):389–396.Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U.(2006). Complex networks: Structure and dynamics. Physics reports,424(4-5):175–308.Borgatti, S. P. and Everett, M. G. (2006). A graph-theoretic perspective oncentrality. Social networks, 28(4):466–484.Borgatti, S. P., Jones, C., and Everett, M. G. (1998). Network measures ofsocial capital. Connections, 21(2):27–36.Bühlmann, P. and Yu, B. (2003). Boosting with the l 2 loss: regres-sion and classification. Journal of the American Statistical Association,98(462):324–339.Caradot, N., Riechel, M., Fesneau, M., Hernandez, N., Torres, A., Sonnen-berg, H., Eckert, E., Lengemann, N., Waschnewski, J., and Rouault, P.(2018). Practical benchmarking of statistical and machine learning mod-els for predicting the condition of sewer pipes in berlin, germany. Journalof Hydroinformatics, page jh2018217.138BibliographyCaradot, N., Sonnenberg, H., Kropp, I., Ringe, A., Denhez, S., Hartmann,A., and Rouault, P. (2017). The relevance of sewer deterioration mod-elling to support asset management strategies. Urban Water Journal,14(10):1007–1015.Carlsson, C., Fullér, R., and Fullér, S. (1997). Owa operators for doctoralstudent selection problem. In The ordered weighted averaging operators,pages 167–177. Kluwer Academic Publishers.Castanedo, F. (2013). A review of data fusion techniques. The ScientificWorld Journal, 2013.Chow, V. T. (1959). Open-channel hydraulics. Caldwell. New Jersey, USA:The Blackburn Press.Chughtai, F. and Zayed, T. (2008). Infrastructure condition prediction mod-els for sustainable sewer pipelines. Journal of Performance of ConstructedFacilities, 22(5):333–341.Compare, M., Mancuso, A., Laakso, T., Salo, A., Zio, E., et al. (2015).Identification of the most critical pipes in the presence of imprecise in-formation. In 25th European Safety and Reliability Conference, ESREL2015, pages 2717–2722. CRC Press/Balkema.Costa, L. d. F., Rodrigues, F. A., Travieso, G., and Villas Boas, P. R.(2007). Characterization of complex networks: A survey of measurements.Advances in physics, 56(1):167–242.Crucitti, P., Latora, V., and Marchiori, M. (2005). Locating critical linesin high-voltage electrical power grids. Fluctuation and Noise Letters,5(02):L201–L208.Crucitti, P., Latora, V., Marchiori, M., and Rapisarda, A. (2004). Error andattack tolerance of complex networks. Physica A: Statistical mechanicsand its applications, 340(1-3):388–394.Davies, J., Clarke, B., Whiter, J., and Cunningham, R. (2001a). Factorsinfluencing the structural deterioration and collapse of rigid sewer pipes.Urban water, 3(1-2):73–89.Davies, J., Clarke, B., Whiter, J., Cunningham, R., and Leidi, A. (2001b).The structural condition of rigid sewer pipes: a statistical investigation.Urban Water, 3(4):277–286.139BibliographyDel Giudice, G., Padulano, R., and Siciliano, D. (2016). Multivariate prob-ability distribution for sewer system vulnerability assessment under data-limited conditions. Water Science and Technology, 73(4):751–760.Demissie, G., Tesfamariam, S., and Sadiq, R. (2015). Considering soil pa-rameters in prediction of remaining service life of metallic pipes: Bayesianbelief network model. Journal of Pipeline Systems Engineering and Prac-tice, 7(2):04015028.Deuerlein, J., Wolters, A., Roetsch, D., and Simpson, A. R. (2009). Reliabil-ity analysis of water distribution systems using graph decomposition. InWorld Environmental and Water Resources Congress 2009: Great Rivers,pages 1–11.di Nardo, A., Giudicianni, C., Greco, R., Herrera, M., and Santonastaso, G.(2018). Applications of graph spectral techniques to water distributionnetwork management. Water, 10(1):45.Diao, K., Farmani, R., Fu, G., and Butler, D. (2014). Vulnerability assess-ment of water distribution systems using directed and undirected graphtheory. In 11th International conference on Hydroinformatics.Dirksen, J., Clemens, F., Korving, H., Cherqui, F., Le Gauffre, P., Ertl,T., Plihal, H., Müller, K., and Snaterse, C. (2013). The consistency ofvisual sewer inspection data. Structure and Infrastructure Engineering,9(3):214–228.Dong, J., Zhuang, D., Huang, Y., and Fu, J. (2009). Advances in multi-sensor data fusion: Algorithms and applications. Sensors, 9(10):7771–7784.Duchesne, S., Beardsell, G., Villeneuve, J.-P., Toumbou, B., and Bouchard,K. (2013). A survival analysis model for sewer pipe structural deterio-ration. Computer-Aided Civil and Infrastructure Engineering, 28(2):146–160.Dunn, S. and Wilkinson, S. M. (2012). Identifying critical components ininfrastructure networks using network topology. Journal of InfrastructureSystems, 19(2):157–165.Eidsvik, J., Mukerji, T., and Bhattacharjya, D. (2015). Decision analysis,page 63–104. Cambridge University Press.140BibliographyElms, D. G. and Brown, C. B. (2013). Intuitive decisions and heuristics–an alternative rationality. Civil Engineering and Environmental Systems,30(3-4):274–284.Fahrmeir, L., Kneib, T., Lang, S., and Marx, B. (2013). Regression: models,methods and applications. Springer Science & Business Media.Fenske, N., Kneib, T., and Hothorn, T. (2011). Identifying risk factors forsevere childhood malnutrition by boosting additive quantile regression.Journal of the American Statistical Association, 106(494):494–510.Fragoso, T. M., Bertoli, W., and Louzada, F. (2018). Bayesian model av-eraging: A systematic review and conceptual classification. InternationalStatistical Review, 86(1):1–28.Fuchs-Hanusch, D., Friedl, F., Möderl, M., Sprung, W., Plihal, H.,Kretschmer, F., and Ertl, T. (2012). Risk and performance oriented sewerinspection prioritization. In World Environmental and Water ResourcesCongress 2012: Crossing Boundaries, pages 3711–3723.Gedam, A., Mangulkar, S., and Gandhi, B. (2016). Prediction of sewerpipe main condition using the linear regression approach. Journal of Geo-science and Environment Protection, 4(05):100.Giustolisi, O., Savic, D., and Kapelan, Z. (2008). Pressure-driven demandand leakage simulation for water distribution networks. Journal of Hy-draulic Engineering, 134(5):626–635.Hahn, M. A., Palmer, R. N., Merrill, M. S., and Lukas, A. B. (2002). Ex-pert system for prioritizing the inspection of sewers: Knowledge baseformulation and evaluation. Journal of Water Resources Planning andManagement, 128(2):121–129.Halfawy, M. R., Dridi, L., and Baker, S. (2008). Integrated decision sup-port system for optimal renewal planning of sewer networks. Journal ofComputing in Civil Engineering, 22(6):360–372.Halfawy, M. R., Dridi, L., and Baker, S. (2009). A multi-objective optimiza-tion decision support model for renewal planning of sewer networks. InProceedings of international stormwater and urban water systems model-ing conference, pages 1–14.141BibliographyHarvey, R. R. and McBean, E. A. (2014). Comparing the utility of decisiontrees and support vector machines when planning inspections of linearsewer infrastructure. Journal of Hydroinformatics, 16(6):1265–1279.Hernández-Perdomo, E., Rocco, C. M., and Ramirez-Marquez, J. E. (2016).Node ranking for network topology-based cascade models–an orderedweighted averaging operators’ approach. Reliability Engineering & SystemSafety, 155:115–123.Herrera, M., Abraham, E., and Stoianov, I. (2015). Graph-theoretic surro-gate measures for analysing the resilience of water distribution networks.Procedia Engineering, 119:1241–1248.Hofner, B., Mayr, A., Robinzonov, N., and Schmid, M. (2014). Model-based boosting in r: a hands-on tutorial using the r package mboost.Computational statistics, 29(1-2):3–35.Howard, R. A. (1966). Information value theory. IEEE Transactions onsystems science and cybernetics, 2(1):22–26.Ilyas, M. U. and Radha, H. (2011). Identifying influential nodes in onlinesocial networks using principal component centrality. In 2011 IEEE In-ternational Conference on Communications (ICC), pages 1–5. IEEE.Infrastructure, C. (2016). Canadian infrastructure report card-informing thefuture.Jaccard, J. and Wan, C. K. (1995). Measurement error in the analysis of in-teraction effects between continuous predictors using multiple regression:Multiple indicator and structural equation approaches. Psychological bul-letin, 117(2):348.Kabir, G., Balek, N. B. C., and Tesfamariam, S. (2018a). Consequence-basedframework for buried infrastructure systems: A bayesian belief networkmodel. Reliability Engineering & System Safety, 180:290–301.Kabir, G., Balek, N. B. C., and Tesfamariam, S. (2018b). Sewer struc-tural condition prediction integrating bayesian model averaging withlogistic regression. Journal of Performance of Constructed Facilities,32(3):04018019.Kabir, G., Demissie, G., Sadiq, R., and Tesfamariam, S. (2015a). Integratingfailure prediction models for water mains: Bayesian belief network baseddata fusion. Knowledge-Based Systems, 85:159–169.142BibliographyKabir, G., Tesfamariam, S., Francisque, A., and Sadiq, R. (2015b). Evalu-ating risk of water mains failure using a bayesian belief network model.European Journal of Operational Research, 240(1):220–234.Kabir, G., Tesfamariam, S., Loeppky, J., and Sadiq, R. (2015c). Integrat-ing bayesian linear regression with ordered weighted averaging: Uncer-tainty analysis for predicting water main failures. ASCE-ASME Journalof Risk and Uncertainty in Engineering Systems, Part A: Civil Engineer-ing, 1(3):04015007.Kabir, G., Tesfamariam, S., and Sadiq, R. (2015d). Predicting water mainfailures using bayesian model averaging and survival modelling approach.Reliability Engineering & System Safety, 142:498–514.Kadan, O. and Manela, A. (2018). Estimating the value of information. TheReview of Financial Studies, 32(3):951–991.Kapelan, Z., Banyard, J. K., Randall-Smith, M., and Savić, D. A. (2011).Asset planning and management. In Water distribution systems, pages227–261. Thomas Telford Ltd.Keisler, J. M. and Brodfuehrer, M. (2009). An application of value-of-information to decision process reengineering. The EngineeringEconomist, 54(3):197–221.Khazraeializadeh, S., Gay, L. F., and Bayat, A. (2014). Comparative analy-sis of sewer physical condition grading protocols for the city of edmonton.Canadian Journal of Civil Engineering, 41(9):811–818.Kleiner, Y. (2001). Scheduling inspection and renewal of large infrastructureassets. Journal of infrastructure systems, 7(4):136–143.Kleiner, Y., Sadiq, R., and Rajani, B. (2006). Modelling the deterioration ofburied infrastructure as a fuzzy markov process. Journal of Water Supply:Research and Technology-AQUA, 55(2):67–80.Kley, G. and Caradot, N. (2013). Review of sewer deterioration models.Kneib, T. and Fahrmeir, L. (2007). A mixed model approach for geoadditivehazard regression. Scandinavian Journal of Statistics, 34(1):207–228.Kneib, T., Hothorn, T., and Tutz, G. (2009). Variable selection and modelchoice in geoadditive regression models. Biometrics, 65(2):626–634.143BibliographyKoenker, R. (1994). Confidence intervals for regression quantiles. In Asymp-totic statistics, pages 349–359. Springer.Korving, H., Van Noortwijk, J. M., Van Gelder, P. H., and Clemens, F. H.(2009). Risk-based design of sewer system rehabilitation. Structure andInfrastructure Engineering, 5(3):215–227.Lang, S. and Brezger, A. (2004). Bayesian p-splines. Journal of computa-tional and graphical statistics, 13(1):183–212.Laxminarayan, R. and Macauley, M. K. (2012). The value of information:methodological frontiers and new applications in environment and health.Springer Science & Business Media.Leon, D. D., Lopez, A., and Esteva, L. (2015). Value of information onthe risk/benefit of infrastructure under strong winds in mexico. In 12thInternational Conference on Applications of Statistics and Probability inCivil Engineering, ICASP12.Li, S. and Pozzi, M. (2017). Parametric analysis of value of information formonitoring infrastructure components. In The 11th International Work-shop on Structural Health Monitoring, volume 1, pages 1306–1313, Stan-ford.Li, S. and Pozzi, M. (2019). What makes long-term monitoring convenient:A parametric analysis of value of information in infrastructure mainte-nance. Struct Control Health Monit.Luque, J. and Straub, D. (2019). Risk-based optimal inspection strategiesfor structural systems using dynamic bayesian networks. Structural Safety,76:68–80.Malings, C. A. (2017). Optimal Sensor Placement for Infrastructure SystemMonitoring using Probabilistic Graphical Models and Value of Informa-tion. PhD thesis, Carnegie Mellon University.Malings, C. A. and Pozzi, M. (2018). Value of information in spatio-temporalsystems: Sensor placement and scheduling. Reliability Engineering andSystem Safety, 172:45–57.Mancuso, A., Compare, M., Salo, A., Zio, E., and Laakso, T. (2016). Risk-based optimization of pipe inspections in large underground networks withimprecise information. Reliability Engineering & System Safety, 152:228–238.144BibliographyMarlow, D., Heart, S., Burn, S., Urquhart, A., Gould, S., Anderson, M.,Cook, S., Ambrose, M., Madin, B., and Fitzgerald, A. (2007). Condi-tion assessment strategies and protocols for water and wastewater utilityassets.Marlow, D. R., Boulaire, F., Beale, D. J., Grundy, C., and Moglia, M.(2010). Sewer performance reporting: factors that influence blockages.Journal of Infrastructure Systems, 17(1):42–51.März, A., Klein, N., Kneib, T., and Musshoff, O. (2016). Analysing farm-land rental rates using bayesian geoadditive quantile regression. EuropeanReview of Agricultural Economics, 43(4):663–698.Marzouk, M. and Omar, M. (2013). Multiobjective optimisation algorithmfor sewer network rehabilitation. Structure and Infrastructure Engineer-ing, 9(11):1094–1102.Mashford, J., Marlow, D., Tran, D., and May, R. (2010). Prediction of sewercondition grade using support vector machines. Journal of Computing inCivil Engineering, 25(4):283–290.Memarzadeh, M. and Pozzi, M. (2016). Value of information in sequen-tial decision making: Component inspection, permanent monitoring andsystem-level scheduling. Reliability Engineering & System Safety, 154:137– 151.Micevski, T., Kuczera, G., and Coombes, P. (2002). Markov model for stormwater pipe deterioration. Journal of infrastructure systems, 8(2):49–56.Miller, A. C. (1975). The value of sequential information. ManagementScience, 22(1):1–11.Mohammed, A. U., Zayed, T., Moselhi, O., , and Alhawari, A. (2015). Re-liability analysis of water distribution networks using minimum cut setapproach. In 11th International Construction speciality Conference, Van-couver 2015, pages 1–12.Mtambo, O., Masangwi, S. J., and Kazembe, L. (2014). Analysis of child-hood stunting in malawi using bayesian structured additive quantlie re-gression model. International Journal of Statistics and Applications 4 (3),pages 161–171.145BibliographyO’Hagan, M. (1988). Aggregating template or rule antecedents in real-timeexpert systems with fuzzy set logic. In Twenty-second Asilomar conferenceon signals, systems and computers, volume 2, pages 681–689. IEEE.Ostfeld, A. (2001). Reliability analysis of regional water distribution sys-tems. Urban Water, 3(4):253–260.Ostfeld, A. (2004). Reliability analysis of water distribution systems. Journalof Hydroinformatics, 6(4):281–294.Ostfeld, A. (2005). Water distribution systems connectivity analysis. Jour-nal of water resources planning and management, 131(1):58–66.Ostfeld, A. (2012). Optimal reliable design and operation of water distribu-tion systems through decomposition. Water Resources Research, 48(10).Ostfeld, A., Kogan, D., and Shamir, U. (2002). Reliability simulation ofwater distribution systems–single and multiquality. Urban Water, 4(1):53–61.Ostfeld, A. and Shamir, U. (1993). Incorporating reliability in optimal de-sign of water distribution networks—review and new concepts. ReliabilityEngineering & System Safety, 42(1):5–11.Perelman, L. and Ostfeld, A. (2011). Topological clustering for water distri-bution systems analysis. Environmental Modelling & Software, 26(7):969–972.Peterson, M. (2017). An Introduction to Decision Theory. Cambridge Uni-versity Press.Pozzi, M. and Der Kiureghian, A. (2011). Assessing the value of informa-tion for long-term structural health monitoring. In Health monitoring ofstructural and biological systems 2011, volume 7984, page 79842W. Inter-national Society for Optics and Photonics.Pozzi, M. and Der Kiureghian, A. (2012). Assessing the value of alternativebridge health monitoring systems. In In 6th International Conference onBridge Maintenance, Safety and Management, IABMAS.Prasad, T. D. and Park, N.-S. (2004). Multiobjective genetic algorithmsfor design of water distribution networks. Journal of Water ResourcesPlanning and Management, 130(1):73–82.146BibliographyQuimpo, R. G. and Shamsi, U. M. (1991). Reliability-based distributionsystem maintenance. Journal of Water Resources Planning and Manage-ment, 117(3):321–339.Quirk, L., Matosb, J., Murphya, J., and Pakrashi, V. (2018). Visual inspec-tion and bridge management. Structure and InfraStructure engineering,14(3):320–332.Rahman, S. and Vanier, D. (2004). An evaluation of condition assessmentprotocols for sewer management. Technical Report Report Number B-5123.6, National Research Council of Canada Research Report.Rajani, B. and Tesfamariam, S. (2004). Uncoupled axial, flexural, and cir-cumferential pipe soil interaction analyses of partially supported jointedwater mains. Canadian geotechnical journal, 41(6):997–1010.Røstum, J. (2000). Statistical modelling of pipe failures in water networks.PhD thesis, Norwegian University of Science and Technology.Roth, P. M., Hirzer, M., Köstinger, M., Beleznai, C., and Bischof, H. (2014).Mahalanobis distance learning for person re-identification. In Person re-identification, pages 247–267. Springer.Sadiq, R. and Tesfamariam, S. (2007). Probability density functions basedweights for ordered weighted averaging (owa) operators: An exampleof water quality indices. European Journal of Operational Research,182(3):1350–1368.Salman, B. (2010). Infrastructure management and deterioration risk assess-ment of wastewater collection systems. PhD thesis, University of Cincin-nati.Salman, B. and Salem, O. (2011). Risk assessment of wastewater collec-tion lines using failure models and criticality ratings. Journal of PipelineSystems Engineering and Practice, 3(3):68–76.Sharp, W. W. and Walski, T. M. (1988). Predicting internal roughness inwater mains. Journal-American Water Works Association, 80(11):34–40.Sheridan, T. B. (1970). On how often the supervisor should sample. IEEETransactions on Systems Science and Cybernetics SSC, 6(2):140–145.Shiau, J.-T. and Chen, T.-J. (2015). Quantile regression-based probabilisticestimation scheme for daily and annual suspended sediment loads. WaterResources Management, 29(8):2805–2818.147BibliographyShinstine, D. S., Ahmed, I., and Lansey, K. E. (2002). Reliability/availabilityanalysis of municipal water distribution networks: Case studies. Journalof water resources planning and management, 128(2):140–151.Shuang, Q., Liu, Y., Tang, Y., Liu, J., and Shuang, K. (2017). Systemreliability evaluation in water distribution networks with the impact ofvalves experiencing cascading failures. Water, 9(6):413.Sousa, V., Matos, J. P., and Matias, N. (2014). Evaluation of artificial intel-ligence tool performance and uncertainty for predicting sewer structuralcondition. Automation in Construction, 44:84–91.Sterling, R., Wang, L., and Morrison, R. (2009). Rehabilitation of wastewa-ter collection and water distribution systems: State of technology reviewreport. US Environmental Protection Agency, Edison, NJ.Straub, D. (2014). Value of information analysis with structural reliabilitymethods. Structural Safety, 49:75–85.Su, Y.-C., Mays, L. W., Duan, N., and Lansey, K. E. (1987). Reliability-based optimization model for water distribution systems. Journal of Hy-draulic Engineering, 113(12):1539–1556.Suribabu, C. (2017). Resilience-based optimal design of water distributionnetwork. Applied Water Science, 7(7):4055–4066.Syachrani, S., Jeong, H., and Chung, C. (2013). Advanced criticality assess-ment method for sewer pipeline assets. Water Science and Technology,67(6):1302–1309.Syachrani, S., Jeong, H. S., and Chung, C. S. (2011). Dynamic deteriorationmodels for sewer pipe network. Journal of Pipeline Systems Engineeringand Practice, 2(4):123–131.Tanyimboh, T. and Templeman, A. (1993). Calculating maximum entropyflows in networks. Journal of the Operational Research Society, 44(4):383–396.Tesfamariam, S., Sadiq, R., and Najjaran, H. (2010). Decision making underuncertainty - an example for seismic risk management. Risk Analysis,30(1):78–94.Tolson, B. A., Maier, H. R., and Simpson, A. R. (2001). Water distribu-tion network reliability estimation using the first-order reliability method.148BibliographyIn Bridging the Gap: Meeting the World’s Water and Environmental Re-sources Challenges, pages 1–10.Torres, J. M., Duenas-Osorio, L., Li, Q., and Yazdani, A. (2016). Exploringtopological effects on water distribution system performance using graphtheory and statistical models. Journal of Water Resources Planning andManagement, 143(1):04016068.Tran, D., Perera, B., and Ng, A. (2009a). Comparison of structural deteri-oration models for stormwater drainage pipes. Computer-Aided Civil andInfrastructure Engineering, 24(2):145–156.Tran, H. D. (2007). Investigation of deterioration models for stormwaterpipe systems. PhD thesis, Victoria University.Tran, H. D., Perera, B., and Ng, A. (2009b). Markov and neural networkmodels for prediction of structural deterioration of storm-water pipe as-sets. Journal of Infrastructure Systems, 16(2):167–171.Tung, Y.-K. (1985). Evaluation of water distribution network reliability.In Hydraulics and hydrology in the small computer age, pages 359–364.ASCE.Umlauf, N., Adler, D., Kneib, T., Lang, S., and Zeileis, A. (2012). Structuredadditive regression models: An r interface to bayesx. Technical report,Working Papers in Economics and Statistics.Van Mieghem, P. (2014). Graph eigenvectors, fundamental weights andcentrality metrics for nodes in networks. arXiv preprint arXiv:1401.4580.Van Riel, W., Langeveld, J., Herder, P., and Clemens, F. (2014). Intuitionand information in decision-making for sewer asset management. UrbanWater Journal, 11(6):506–518.Van Zyl, J. E., Savic, D. A., and Walters, G. A. (2004). Operational opti-mization of water distribution systems using a hybrid genetic algorithm.Journal of water resources planning and management, 130(2):160–170.Waldmann, E., Kneib, T., Yue, Y. R., Lang, S., and Flexeder, C. (2013).Bayesian semiparametric additive quantile regression. Statistical Mod-elling, 13(3):223–252.Wright, L. T., Heaney, J. P., and Dent, S. (2006). Prioritizing sanitary sew-ers for rehabilitation using least-cost classifiers. Journal of infrastructuresystems, 12(3):174–183.149BibliographyXu, C. and Goulter, I. C. (1998). Probabilistic model for water distribu-tion reliability. Journal of Water Resources Planning and Management,124(4):218–228.Yager, R. R. (1988). On ordered weighted averaging aggregation operatorsin multicriteria decisionmaking. IEEE Transactions on systems, Man,and Cybernetics, 18(1):183–190.Yager, R. R. and Filev, D. P. (1999). Induced ordered weighted averagingoperators. IEEE Transactions on Systems, Man, and Cybernetics, PartB (Cybernetics), 29(2):141–150.Yang, S.-L., Hsu, N.-S., Louie, P. W., and Yeh, W. W. (1996). Waterdistribution network reliability: Connectivity analysis. Journal of Infras-tructure Systems, 2(2):54–64.Yang, Y. (1999). Statistical models for assessing sewer infrastructure in-spection requirements. Master’s thesis, University of Alberta.Yazdani, A. and Jeffrey, P. (2011). Complex network analysis of waterdistribution systems. Chaos: An Interdisciplinary Journal of NonlinearScience, 21(1):016111.Yazdani, A. and Jeffrey, P. (2012). Water distribution system vulnerabilityanalysis using weighted and directed network models. Water ResourcesResearch, 48(6).Yokota, F. and Thompson, K. M. (2004). Value of information analysisin environmental health risk management decisions: Past, present, andfuture. Risk Analysis, 24(3):635–650.Younis, R. and Knight, M. A. (2010). A probability model for investigatingthe trend of structural deterioration of wastewater pipelines. Tunnellingand Underground Space Technology, 25(6):670–680.Yue, Y. and Rue, H. (2009). Bayesian inference for structured additive quan-tile regression models. Norwegian University for Science and Technology.Zhang, Y. and Tang, N. (2017). Bayesian empirical likelihood estimationof quantile structural equation models. Journal of Systems Science andComplexity, 30(1):122–138.150BibliographyZhao, J. Q., McDonald, S. E., and Kleiner, Y. (2001). Guidelines for condi-tion assessment and rehabilitation of large sewers. Technical report, In-stitute for Research in Construction, National Research Council Canada,Ontario, Ottawa.Zhou, Y. (2018). Deterioration and Optimal Rehabilitation Modelling forUrban Water Distribution Systems. CRC Press.151Appendix152Appendix ATable: Example of data usedto build deterioration modelsInformation collected after inspection campaigns are arranged into tablewhere each row gives the score attributed to the pipe after the analysis of theobserved defects, its physical characteristics (e.g. length, diameter, mate-rial), its historical maintenance works (flushes, root cuts, degrease, backups,repairs) and its location in a given district.All these factors are expressed in terms of covariates to explain the at-tributed score. The location covariates (Table A.1) are integers representingthe code given to the district where the pipe is buried. The Matcode is alsoan integer (going from 1 to 4) representing the four groups of pipe materialsin the sewer system of the city of Calgary.Rows with missing data are removed from the analysis. In addition, forthe development of the expected mean deterioration model, extreme val-ues are removed from the analysis using the Mahalanobis distance. Detailsabout this metric can be found in Roth et al. (2014). This approach helpsdetect outliers that have great influence on the regression coefficient andsmooth functions. However, the development of geoadditive quantile regres-sion models did not consider the use of this metric.153Appendix A. Table: Example of data used to build deterioration modelsTableA.1:Exampleofdatausedtobuilddeteriorationmodels.ScoreAgeRservsCservsLengthMatcodeDiameterFlushesCleaningDegreaseBackupsRootsRepairsReplacedSlopeDepthPeopleDistrict50597196.6185230052100100.3443.6311311031100118.7965120030000100.993.1301838081161115.6783220013141114100.4482.7681311033200140.0989125010000000.8723.5602384026100132.9044120022000000.7492.63019110330077.0867130042014005.7524.301888059210105.21662500170000000.2252.96382101900164.803260004000000.1744014012048140119.7864120020100000.7893.4421855046130113.0101120030000200.7853.23918080104110134.52691250282000100.2621.3337990280085.624125010000000.4313.90429052110130.5146125013003000.9013.233117224611114.5073120010000000.7463131661026170112.3744120020000000.7433.15191404510062.2921125030000000.1163.230191120489088.3739125047103000.1583.627240120527065.3939120050101000.71321802533059.1443120030001000.7832.69801023140124.4712120010001001.9923.8422841048150130.45171250230001000.573.545160104371114.901120030100001.52623113340912071.6099220000000002.0474.1619710230094.4315120014101001.9534.508810371038.5418120040101000.8383.531141668035162.0316220020000101.13.579257102909128.96511200415009010.8653.6901174067151104.4885220027002001.6982.9581024010210061.1737220032000000.4872.93087154Appendix BExample code for statisticaldeterioration modell i b r a r y (R2BayesX)setwd ( " d i r " )## Read the datadat<−read . datadat <− dat [ complete . c a s e s ( dat ) , ]Sx <− cov ( dat )ColM <−colMeans ( dat )## Mahalanobis d i s t ancedat$mahal <− mahalanobis ( dat ,ColM , Sx )alpha=0.001## C r i t i c a l d i s t anc e from Chi squaredc r i t d i s t<−qch i sq (1−alpha , df= nco l ( dat )−1)## Cleaning the datadat <− dat [ dat$mahal < c r i t d i s t , ]dat<−dat [ ,− nco l ( dat ) ]dat <− data . frame ( dat , id = as . f a c t o r ( dat\$ D i s t r i c t ) )dat$Matcode<−as . f a c t o r ( dat$Matcode )smpsize <− f l o o r ( 0 . 75 ∗ nrow ( dat ) )## se t the seed to make your p a r t i t i o n r ep r oduc t i b l es e t . seed (123)t r a i n_ind <− sample ( seq_len ( nrow ( dat ) ) , s i z e = smpsize )t r a i n <− dat [ t r a i n_ind , ]t e s t <− dat [− t r a i n_ind , ]## Read boundary f i l ec l g r <− read . bnd ( " c l g r . bnd " )## rep l a c e d i s t r i c t names with i n t e g e r s ( g e o s p a t i a l data )N <− l ength ( c l g r ) ; n <− N∗5names ( c l g r ) <− 1 :N## Build the model155Appendix B. Example code for statistical deterioration model## Model with non l i n e a r e f f e c tf <− Score ~ sx (Matcode ) + . . . + sx ( id , bs = " re " )r <− bayesx ( f , method = "MCMC" , . . . , data = t r a i n )save ( r , f i l e=" c l g r_bayesX . RData " )156
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Advanced deterioration models for wastewater inspection prioritization
Text