A Survival Analysis Model for Sewer Pipe Structural Deterioration

Abstract: The structural state of sewer systems is often quantified using condition classes. The classes are based on the severity of structural defects observed on individual pipes within the system. Here, a survival analysis model was developed to predict the overall structural state of a sewer network based on camera inspection data from a sample of pipes in the system. The convolution product was used to define the survival functions for cumulative staying times in each condition class. An original calibration procedure for the sewer deterioration model was developed to overcome the censored nature of data (left censored and right censored) available for the calibration of sewer deterioration models. The exponential and Weibull functions were used to represent the distribution of waiting times in each deterioration state. Cross‐validation tests showed that the Weibull function led to greater uncertainty than the exponential function for the simulated proportion of pipes that are in a deteriorated state. Using various sample sizes for model calibration, these cross‐validation tests also showed that the model's results are robust to smaller calibration sample sizes. This confirms the model's potential for predicting the overall state of deterioration of a sewer network when only a small proportion of the pipes have been inspected.     

Prediction models for sewer infrastructure utilizing rule-based simulation

Management of infrastructure projects is becoming increasingly challenging due to inherent uncertainties. The most effeective way to deal with uncertainty is to collect supplementary information and knowledge. When expensive or infeasible, quantification of uncertainty may be performed using analytical or simulation techniques. The City of Edmonton, Canada has approximately 4600 km of sewer pipes in the combined, sanitary, and storm sewer local systems with uncertainty issues related to deterioration. The City has taken a proactive approach with respect to sewer rehabilitation, as it is more cost-effeective to repair a defective pipe prior to failure rather than after a collapse. This article demonstrates an approach for predicting the condition of a sewer pipe and the related cost of rehabilitation, given the limited data. Three models are described in this article that are developed to assist the City of Edmonton to effeectively plan maintenance expenditure. Each model uses a combination of rule-based simulation and probability analysis to assist in the planning of future expenditures for sewer maintenance, thereby producing an invaluable planning tool.     

The relevance of sewer deterioration modelling to support asset management strategies

Deterioration modelling can be a powerful tool to support utilities in planning efficient sewer rehabilitation strategies. However, the benefits of using deterioration models are still to be demonstrated to increase the confidence of utilities toward simulation results. This study aims at assessing the performance of a statistical deterioration model to estimate the current condition and predict the future deterioration of a sewer network. The prediction quality of the deterioration model GompitZ has been assessed using the extensive data-set of 35,826 inspections performed in the city of Braunschweig, Germany. The performance of the statistical model has been compared with the performance of a simple model based only on the condition of observed sewers. Results show that the statistical model performs much better than the simple model for simulating the deterioration of the network. The findings highlight the relevance of using modelling tools to simulate sewer deterioration and support strategic asset management.     

Multiobjective optimisation algorithm for sewer network rehabilitation

Understanding of deterioration mechanisms in sewers helps asset managers in developing prediction models for estimating whether or not sewer collapse is likely. Effective utilisation of deterioration prediction models along with the development and use of life cycle maintenance cost analysis contribute to reducing operation and maintenance costs in sewer systems. This article presents a model for life-cycle maintenance planning of deteriorating sewer network as a multi-objective optimisation problem that treats the sewer network condition and service life as well as life-cycle maintenance cost (LCMC) as separate objective functions. The developed model utilises Markov chain model for the prediction of the deterioration of the network. A multi-objective genetic algorithm is used to automatically locate an appropriate maintenance scenario that exhibits an optimised tradeoff among conflicting objectives. Monte Carlo simulation is used to account for LCMC uncertainties. The optimisation algorithm provides an improved opportunity for asset managers to actively select near-optimum maintenance scenario that balances life-cycle maintenance cost, condition and service life of deteriorating sewer network. A case study is used to demonstrate the practical features of developed methodology.     

A qualitative analysis of early defects present in PVC-U sewers but not observed in rigid pipes

The objective of the study was to analyze early defects in PVC-U sewer pipes that are not observed in rigid pipes. Field investigations were conducted on newly laid PVC-U sewer pipes in more than a dozen cities in Poland using CCTV equipment and a special device for measuring deflections. The analysis focused on qualitative data concerning defects observed in PVC-U sewers. Three types of defects, i.e. dents, deflections and buckling, were thoroughly analyzed to determine whether trenchless rehabilitation of such pipes is possible and to improve the existing sewer deterioration models. The major conclusions concern the types, sizes and frequencies of defects in PVC-U pipes, their causes, and the possibility of future rehabilitation as well as the improvement in the deterioration models.     

Prediction models for serviceability deterioration of stormwater pipes

Reducing the number of annual blockages and the consequential flooding events is one of the most important tasks for stormwater pipe infrastructure managers in Australia. Blockages are more likely to occur with pipes experiencing serviceability deterioration, resulting in a reduction of hydraulic capacity. When changing from a problem-based approach to a proactive maintenance and rehabilitation (M&R) approach, the asset managers need predictive information on the serviceability condition of pipes in order to firstly prepare the necessary resources from limited annual budgets and, secondly, to allocate these resources for the maintenance of the deteriorated pipes as precisely as possible. This paper investigates the application of a Markov model and an ordinal regression model for predictions of serviceability deterioration of stormwater pipes. The first model provides the prediction at a network level, which satisfies the first requirement, and the second model predicts serviceability condition for individual pipes, given the attributes of the pipes, in order to satisfy the second requirement. Both models are calibrated using Bayesian inference and Markov Chain Monte Carlo (MCMC) simulation techniques on a dataset supplied from the City of Greater Dandenong, Australia.     

Simulation-based deterioration patterns of water pipelines

Water pipelines deteriorate overtime due to several distressing factors. To keep water pipelines in good condition, municipalities need to use reliable and credible deterioration models and inspection plans to better manage their rehabilitation and maintenance. Thus, this paper presents the development of deterioration models and patterns of water pipelines. The deterioration models consider different water pipe sizes and materials as well as different surrounding environmental conditions which affect their deterioration rates. As a prerequisite to the development of such deterioration models, a condition assessment model for water pipelines was first developed. Questionnaires were distributed among experts to determine the weights of the factors affecting water pipeline conditions using the fuzzy analytic network process. Monte-Carlo simulation was used to account for the large uncertainties of the calculated weights in the development of the condition assessment model. The validation of the model, which was performed using historical data, yielded an average validity percentage of 93.59%. The developed models are expected to help municipalities and decision makers to accurately plan for future water pipelines maintenance and rehabilitation activities based on their different deterioration patterns. It takes into consideration both the uncertainties at the initial stage and those accumulated during the calculation process.     

Improving the reliability of a Bridge Management System (BMS) using an ANN-based Backward Prediction Model (BPM)

The slow adoption of Bridge Management Systems (BMSs) and its impractical future prediction of the condition rating of bridges are attributed to the inconsistency between BMS inputs and bridge agencies' existing data for a BMS in terms of compatibility and the enormous number of bridge datasets that include historical structural information. Among these, historical bridge element condition ratings are some of the key pieces of information required for bridge asset prioritisation but in most cases only limited data is available.

This study addresses the abovementioned difficulties faced by bridge management agencies by using limited historical bridge inspection records to model time-series element-level data. This paper presents an Artificial Neural Network (ANN) based prediction model, called the Backward Prediction Model (BPM), for generating historical bridge condition ratings using limited bridge inspection records. The BPM employs historical non-bridge datasets such as traffic volumes, populations and climates, to establish correlations with existing bridge condition ratings from very limited bridge inspection records. The resulting model predicts the missing historical condition ratings of individual bridge elements. The outcome of this study can contribute to reducing the uncertainty in predicting future bridge condition ratings and so improve the reliability of various BMS analysis outcomes.     

UNCERTAINTIES OF ASPHALT LAYER THICKNESS DETERMINATION IN FLEXIBLE PAVEMENTS-INFLUENCE DIAGRAM APPROACH

The thickness of pavement layers is an important parameter used in Pavement Management Systems (PMS). Thickness data are used for pavement condition assessment, performance predictions, selection of maintenance strategies and rehabilitation treatments, basic quality assessment, and as input to overlay thickness design. Pavement thickness is usually determined from direct testing such core samples, nondestructive testing such as radar, or historical records such as pavements network database. This paper proposes the use of Bayesian Influence Diagrams as a tool in providing a probabilistic model for thickness determination procedure in flexible pavements. The Bayesian Influence Diagram Model is presented as a framework for addressing uncertainties involved in capturing quantitative and qualitative information in the asphalt layer thickness determination procedures. The model is also used to perform value of information analysis in the determination of pavement layer thickness. The Influence Diagram representation facilitates the assessment of coherent prior distributions and makes it easier for knowledge engineers and other decision makers to express and understand more general kinds of dependency and independency assumptions.     

Sensitivity of uncertainties in performance prediction of deteriorating concrete structures

Deterioration models for the condition and reliability prediction of civil infrastructure facilities involve numerous assumptions and simplifications. Furthermore, input parameters of these models are fraught with uncertainties. A Bayesian methodology has been developed by the authors, which uses information obtained through health monitoring to improve the quality of prediction. The sensitivity of prior and posterior predicted performance to different input parameters of the deterioration models, and the effect of instrument and measurement uncertainty, is investigated in this paper. The results quantify the influence of these uncertainties and highlight the efficacy of the updating methodology based on integrating monitoring data. It has been found that the probabilistic posterior performance predictions are significantly less sensitive to most of the input uncertainties. Furthermore, updating the performance distribution based on ‘event’ outcomes is likely to be more beneficial than monitoring and updating of the input parameters on an individual basis.     

An evaluation of a sanitary sewer system using a computer model

The purpose of this study was to (1) provide the city of West Lafayette, Indiana, USA, with an analysis and evaluation of its sanitary sewer system and (2) make recomendations for improving the existing system and any modifications necessary for accomodating future growth within the service area. Using a computer model, virtually every sewer line within the city and Purdue University was modelled. The computer model was calibrated for dry weather flow using water use records, while wet weather flows were checked against field observations. The analysis included both the present condition and future growth projections. The unique aspects of this study include the use and enhancement of a comprehensive, user-friendly computer program that models the stormwater runoff component and provides easy calibration and verification.     

Calibration of hydrodynamic model-driven sewer maintenance

Sewer performance is typically assessed using hydrodynamic models assuming the absence of in-sewer defects. As a consequence, hydraulic performance calculated by models is likely to be overestimated, while the real hydraulic performance of the sewer system remains unknown. This article introduces the concept of ‘hydraulic fingerprinting’ based on model calibration to identify in-sewer defects affecting hydraulic performance. Model calibration enables detection of changes in hydraulic properties of the sewer system. Each model calibration results in a set of model parameter values, their uncertainties and residuals. The model parameter values also incorporate the antecedent condition of the catchment of the event calibrated and are therefore less suitable to identify in-sewer defects. The residuals on the other hand, and more specifically their absolute values, statistical properties and the correlation between residuals at different monitoring locations are suitable as indicators of the occurrence of in-sewer defects. This allows the application of ‘hydraulic fingerprinting’ based on model calibration, where the ‘fingerprint’ is defined by the model parameters and the residuals. The concept of ‘fingerprinting’ is demonstrated for the combined sewer system ‘Tuindorp’ (Utrecht, the Netherlands). The results show that ‘hydraulic fingerprinting’ can be a powerful tool for directing sewer asset management actions.     

Evaluation of calibration efficacy under different levels of uncertainty

This paper examines how calibration performs under different levels of uncertainty in model input data. It specifically assesses the efficacy of Bayesian calibration to enhance the reliability of EnergyPlus model predictions. A Bayesian approach can be used to update uncertain values of parameters, given measured energy-use data, and to quantify the associated uncertainty. We assess the efficacy of Bayesian calibration under a controlled virtual-reality setup, which enables rigorous validation of the accuracy of calibration results in terms of both calibrated parameter values and model predictions. Case studies demonstrate the performance of Bayesian calibration of base models developed from audit data with differing levels of detail in building design, usage, and operation.     

Probabilistic capacity model and fragility estimates for composite floor systems subjected to column loss

This paper presents probabilistic capacity models for composite floor systems subjected to column loss. The probabilistic capacity models are formulated by adding explanatory terms to an existing deterministic model. The explanatory terms are selected to correct the bias in deterministic capacity model. After that, virtual experiment data generated from finite element simulations are used to calibrate the model parameters. The finite element models consider the effect of axial loading on steel connection and the slab membrane action. The calibration of model parameters is conducted using the Bayesian inference approach. As an application and validation of the probabilistic capacity models, fragility analyses of typical composite floor systems are carried out. The developed fragility curves are compared with those from finite element analysis cooperated with Monte Carlo simulation. The comparison results show that the proposed capacity models are considered reasonable in predicting the resistance capacity of the composite floor and seek a compromise between model accuracy and computational efficiency. The proposed capacity models can be used to carry out a rapid fragility analysis against progressive collapse.     

A method to consider replaced pipes in modeling of sewer pipe deterioration

Statistical models that predict the deterioration of sewer pipes are useful for planning financial resources required for sewer renewal. Usually, data that are available to calibrate these models solely concern pipes that are still in place, leading to underestimated deterioration rates. A new method is proposed to consider possible past replacement of pipes in the statistical modeling of their deterioration. The proposed method considers the aging of pipes, simulated with a Cox model, and their probability to be replaced separately. Application to a synthetic sewer network, for which it was assumed that information regarding all pipe replacements over the lifetime of the network was available, showed that the proposed method allows for improved predictions of the sewer deterioration model, when compared to predictions of a model calibrated without considering the information about replaced pipes.     

基于随机多项式展开的流固耦合非饱和土坡概率反分析

降雨入渗条件下非饱和土坡流固耦合作用复杂,具有高度非线性的特点,一般采用数值方法模拟。数值模型计算量大已成为监测数据概率反分析的重要制约因素。提出一种基于随机多项式展开(PCE)的概率反分析方法。该方法采用随机多项式展开构建土性参数与数值模型响应的显式函数,作为概率反分析中原数值模型的代替模型,与基于贝叶斯理论和马尔可夫链蒙特卡罗(MCMC)模拟的概率反分析方法相结合,从而有效提高非饱和土坡流固耦合参数概率反分析的效率。通过降雨入渗非饱和土坡算例研究,结果表明,与基于数值模型的常规随机反分析相比,两种方法在后验分布统计值、95%置信区间等结果非常接近,基于PCE的概率反分析计算效率显著提高,结果可靠。     

Statistical comparison of the performance of data-based models for sewer condition modeling

Abstract

The present article proposes a methodology to consider the uncertainty intrinsic to data-based models when comparing their performance. The goal is to provide a quantification of the variability of this type of models due to the random nature of the calibration process and enable a statistical comparison of the models’ performance when attempting to identify the best. The methodology proposed doesn’t provide an alternative metric to determine the models’ performance, but it expands the traditional deterministic comparison to a stochastic comparison. The methodology builds on the current standard approach for developing data-based model and its application is demonstrated to model sewer condition using data from 4 trunk sewers of the SANEST – Saneamento da Costa do Estoril sewer system, corresponding to 25?km of sewer pipes. The data-based models were developed using artificial neural networks, support vector machines, bootstrapping aggregation and least squares support vector machines. For the case study, the highest and average misclassification performance records are similar for all models (23% to 24% and 31% to 33%, respectively) but the lowest performance varied more significantly (39% to 62%). This demonstrates that selecting a model based on its maximum single realisation performance alone may be misleading.     

A Bayesian network model to assess the public health risk associated with wet weather sewer overflows discharging into waterways

Overflows from sanitary sewers during wet weather, which occur when the hydraulic capacity of the sewer system is exceeded, are considered a potential threat to the ecological and public health of the waterways which receive these overflows. As a result, water retailers in Australia and internationally commit significant resources to manage and abate sewer overflows. However, whilst some studies have contributed to an increased understanding of the impacts and risks associated with these events, they are relatively few in number and there still is a general lack of knowledge in this area. A Bayesian network model to assess the public health risk associated with wet weather sewer overflows is presented in this paper. The Bayesian network approach is shown to provide significant benefits in the assessment of public health risks associated with wet weather sewer overflows. In particular, the ability for the model to account for the uncertainty inherent in sewer overflow events and subsequent impacts through the use of probabilities is a valuable function. In addition, the paper highlights the benefits of the probabilistic inference function of the Bayesian network in prioritising management options to minimise public health risks associated with sewer overflows.     

A hierarchical Bayesian framework for calibrating micro-level models with macro-level data

Owners of housing stocks require reliable and flexible tools to assess the impact of retrofits technologies. Bottom-up engineering-based housing stock models can help to serve such a function. These models require calibrating, using micro-level energy measurements at the building level, to improve model accuracy; however, the only publicly available data for the UK housing stock is at the macro-level, at the district, urban, or national scale. This paper outlines a method for using macro-level data to calibrate micro-level models. A hierarchical framework is proposed, utilizing a combination of regression analysis and Bayesian inference. The result is a Bayesian regression method that generates estimates of the average energy use for different dwelling types whilst quantifying uncertainty in both the empirical data and the generated energy estimates. Finally, the Bayesian regression method is validated and the use of the hierarchical Bayesian calibration framework is demonstrated.