A Bayesian Approach for Active Fault Isolation with an Application to Leakage Localization in Water Distribution Networks

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Abstract

This thesis describes the application of a stochastic active fault diagnosis method for localising leaks in a Water Distribution Network (WDN) under parametric uncertainty, in order to localise leaks faster and more reliable compared to non-invasive state-of-the-art methods. Output residual Probability Distribution Functions (PDFs) for a discrete set of leak hypotheses are constructed by smoothing out the realisations resulting from Monte Carlo simulations of a non-linear hydraulic model by means of Kernel Density Estimation (KDE). Active pressure control inputs are designed to minimise the probability of misisolation aka the Bayes error. Where Pressure Reducing Valves (PRVs) usually regulate pressure at a minimum level, we show that they can also be used to enhance leakage diagnosis. During night time, when user demands are low, the control inputs are iteratively updated according to some objective function that aims to maximise the sum of stochastic distances between residual PDFs, weighed with their corresponding likelihood, whereas the likelihood vector itself is updated in a Bayesian classification framework. Stochastic distances are calculated using a stochastic metric that quantifies the overlap between residual PDFs. The algorithm is applied to the Hanoi benchmark network for different intensities of parametric uncertainty. Improvements in performance are observed in comparison to a passive cutting-edge counterpart method.