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Advanced deterioration models for wastewater inspection prioritizationNgandu Balekelayi, PhD Candidate

Dr. Solomon Tesfamariam, Professor

School of Engineering, University of BritishColumbia, Okanagan

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Advanced deterioration models for wastewater inspection prioritization

Ngandu BalekelayiDr. Solomon Tesfamariam

School of Engineering, University of British Columbia

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CONTENT

❑Introduction

❑Sewer pipes deterioration

❑Risk based decision making

❑Value of information for prioritization of inspection

❑Conclusion

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INTRODUCTION

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INTRODUCTION

❑ Wastewater networks systems (sewers):

• important and expensive municipal infrastructure assets

• Critically support the quality (health, economy) of life of citizen

❑ 27% of sewer pipes in Canada are in fair to poor condition representing a

total replacement cost of CAD 24billion (Canada Infrastructure Report 2016)

❑ Limited access to financial resources and stringent regulations

❑ Prioritization of inspection to cope with financial and service level

requirements

Vojinovic, Z., and Abbott, M. B. (2012). Flood risk and social justice.

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INTRODUCTION

Kley, G., and Caradot, N. 2013. “Review of sewer deterioration models—project SEMA”—Technical report prepared for Kompetenzzentrum Berlin GmbH. Veolia Water, Berlin

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INDIVIDUAL DETERIORATION MODEL

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NONLINEAR MODELING

❑Semi parametric model :

𝜂𝑖 = 𝛽0 + 𝛽1𝑥𝑖1 +⋯+ 𝛽𝑞𝑥𝑖𝑞 + 𝑓1 𝑧𝑖1 + . . . + 𝑓𝑃 𝑧𝑖𝑝

❑P-spline : use of local polynomials in each interval

𝑓𝑗 𝑧𝑖,𝑗

= 𝛾𝑗,1 + 𝛾𝑗,2𝑧𝑖,𝑗 +⋯+ 𝛾𝑗,𝑙𝑗+1𝑧𝑖,𝑗𝑙𝑗+ 𝛾𝑗,𝑙𝑗+2 𝑧𝑖,𝑗 − 𝜉𝑗,2 +

𝑙𝑗+⋯+ 𝛾𝑗,𝑙𝑗+ℎ𝑗−1 𝑧𝑖,𝑗 − 𝜉𝑗,ℎ𝑗−1 +

𝑙𝑗

Where 𝑧𝑖,𝑗 − 𝜉𝑗,𝑘 +𝑙𝑗= ൝ 𝑧𝑖,𝑗 − 𝜉𝑗,𝑘

𝑙𝑗𝑖𝑓 𝑧𝑖,𝑗 ≥ 𝜉𝑗,𝑘

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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GEOADDITIVE REGRESSION MODEL

❑Geospatial location as surrogate covariate• Variable location is added to the model to represent unknown variables

𝜂𝑖 = 𝜂𝑖𝑙𝑖𝑛𝑒𝑎𝑟 + 𝑓1 𝑧𝑖1 + . . . + 𝑓𝑃 𝑧𝑖𝑝 + 𝑓𝑔𝑒𝑜 𝑠𝑖

where 𝑠𝑖 represent the membership of an observation to a given region S

• Neighborhood : common boundaries

Z 𝑖, 𝑠 = ቊሻ1 𝑖𝑓 𝑦𝑖 𝑤𝑎𝑠 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑖𝑛 𝑟𝑒𝑔𝑖𝑜𝑛 𝑠 (𝑖. 𝑒. , 𝑆𝑖 = 𝑆1

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Source: Fahrmeir et al. (2015)

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Application to large sewer network

𝜂= 𝛾0 + 𝛾1 ∗ 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝛾2 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ + 𝛾3 ∗ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 + 𝛾4 ∗ 𝐴𝑔𝑒 + 𝛾5 ∗ 𝐷𝑒𝑝𝑡ℎ + 𝛾6 ∗ 𝑆𝑙𝑜𝑝𝑒 + 𝛾7∗ 𝑅𝑠𝑒𝑟𝑣𝑠 + 𝛾8 ∗ 𝐶𝑠𝑒𝑟𝑣𝑠 + 𝛾9 ∗ 𝐹𝑙𝑢𝑠ℎ𝑒𝑠 + 𝛾10 ∗ 𝑅𝑒𝑝𝑎𝑖𝑟𝑠 + 𝛾11 ∗ 𝑅𝑐𝑢𝑡𝑠 + 𝛾12 ∗ 𝐵𝑎𝑐𝑘𝑢𝑝𝑠 + 𝛾13∗ 𝐷𝑒𝑔𝑟𝑒𝑎𝑠𝑒 + 𝛾14𝐶𝑙𝑒𝑎𝑛𝑖𝑛𝑔𝑠 + 𝛾14 ∗ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ + 𝛾15 ∗ 𝐷𝑒𝑝𝑡ℎ ∗ 𝑆𝑙𝑜𝑝𝑒 + 𝛾16 ∗ 𝐶𝑙𝑒𝑎𝑛𝑖𝑛𝑔∗ 𝐵𝑎𝑐𝑘𝑢𝑝𝑠 + 𝑓𝑠𝑡𝑟𝑢𝑐𝑡 𝑑𝑖𝑠𝑡𝑟𝑖𝑐𝑡 + 𝑓𝑢𝑛𝑠𝑡𝑟𝑢𝑐𝑡 𝑑𝑖𝑠𝑡𝑟𝑖𝑐𝑡

Balekelayi N and Tesfamariam S. (2019): “Statistical inference of sewer pipes deterioration using Bayesian geoadditive regression model” ASCE, Journal of Infrastructure systems (in press).

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Partial effects , model validation and predictions

Balekelayi N and Tesfamariam S. (2019): “Statistical inference of sewer pipes deterioration using Bayesian geoadditive regression model” ASCE, Journal of Infrastructure systems (in press).

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Visualization of the geospatial effects

Balekelayi N and Tesfamariam S. (2019): “Statistical inference of sewer pipes deterioration using Bayesian geoadditive regression model” ASCE, Journal of Infrastructure systems (in press).

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TOPOLOGICAL RELIABILITY AND CRITICAL COMPONENTS ASSESSMENT

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Implementation on large sewer network

❑No hydrodynamic model available

❑Pipes defects are not considered in validated models

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Graph theory

Balekelayi, N. and Tesfamariam, S (2019): “Graph theoretic surrogate measure to analyzereliability of water distribution system using Bayesian belief network-based data fusiontechnique” ASCE's Journal of Water Resources Planning and Management (in press)

❑Centrality metrics:

1. Betweenness : 𝐶𝑘𝐵 =

1

𝑛−1 𝑛−2σ𝑖 ∈𝐺,𝑖 ≠𝑘σ𝑗 ∈𝐺 ,𝑗 ≠𝑘,𝑗≠𝑖

𝑛𝑖𝑗 𝑘

𝑛𝑖𝑗

2. Topological centrality :

• Network efficiency: 𝐸 𝐺 =1

𝑛(𝑛−1ሻσ𝑖 ≠𝑗 ∈𝐺

1

𝑑𝑖𝑗

• Topological centrality : 𝑇𝐼𝐶 =𝐸 𝐺 −𝐸 𝐺′

𝐸 𝐺

3. Eigenvector centrality: 𝜆𝑋 = 𝐴𝑋

4. Principal component centrality: 𝐶𝑃 =

(𝑋𝑛 × 𝑃 ⊙ 𝑋𝑛 × 𝑃ሻ(Λ𝑃 × 1 ⊙Λ𝑃 × 1ሻ

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Implementation on large sewer network

❑Hydraulic distance:

𝑉 =1

𝑛𝑅ℎ

ൗ2 3 𝑖 ൗ12

𝑅ℎ =𝐴

𝑃

𝐿ℎ = 𝑛𝐿

❑Topological metrics : Betw, EVC, PCC

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Data fusion technique

❑Ordered Weighted Averaging (OWA) based data fusion

❑Objective function :

𝑀𝑎𝑥 𝐷𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛 𝑊 = 𝑀𝑎𝑥 −

𝑖=1

𝑛

𝑤𝑖𝑙𝑛 𝑤𝑖

subjected to:

𝑜𝑟𝑛𝑒𝑠𝑠 𝑊 =1

𝑛 − 1

𝑖=1

𝑛

𝑤𝑖 𝑛 − 𝑖

and

0 ≤ 𝑤𝑖 ≤ 1;

𝑖=1

𝑛

𝑤𝑖 = 1

Balekelayi N and Tesfamariam S.: “Graph-theoretic surrogate measure to analyze theperformance of wastewater system using Ordered Weighted Averaging fusion technique”(under internal review).

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Data fusion technique : linguistic degree of optimism

Tesfamariam, S., Sadiq, R., and Najjaran, H. (2010). Decision making under uncertainty - Anexample for seismic risk management. Risk Analysis, 30(1), 78–94.

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Topological reliability and critical components

Betweenness EVC

2020

Topological reliability and critical components

PCC

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Topological reliability and critical components

Conservative Normative

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Topological reliability and critical components

Optimistic

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RISK-VALUE OF INFORMATION BASED INSPECTION PRIORITIZATION FOR LARGE SEWER PIPES

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❑Risk definition incompleteness (likelihood x consequence)

❑Pipe location contributes to its risk

Risk assessment

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Risk based decision making

Likelihood of failureConsequence of failure

Risk map

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Value of information

Decision tree

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Value of information

Probability of getting an alarm during a testing

Probability of getting a silence during a testing

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Value of information

Loss function

𝐶𝑡𝑟𝑢𝑡ℎ∗ = 𝑃 𝐹 . 𝐶𝑅

Expected cost of the test

Value of Information VoI

𝑉𝑜𝐼 = 𝐶𝑡𝑟𝑢𝑡ℎ∗ − 𝐶∗

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Value of information : Wastewater application

Deterioration model

Probability of failure

Economic criteria

Value of Information

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Value of information : Now

Likelihood of failure

Value of Information

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Value of information after 25 years

Likelihood of failure

Value of Information

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Value of information after 50 years

Likelihood of failure

Value of Information

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❑Advanced deterioration model with geospatial information

❑Risk based decision making (rate of deterioration factor)

❑Value of information for inspection prioritization

Conclusion

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Thanks

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