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

This article proposes an active fault isolation method for application to water distribution networks (WDNs) to localize leaks. The method relies on the classification of observed outputs to a discrete set of hypothetical faults. Due to parametric uncertainties, the outputs are random vectors that follow unknown probability distribution functions (PDFs). The output PDFs corresponding to the considered faults are approximated using smooth kernel density estimation (SKDE). They are used to calculate the posterior probability of each hypothesis, given the observed outputs, by applying Bayes’ rule. The difficulty to classify observed outputs to the right fault comes from the overlap between output PDFs. An active algorithm is introduced that proactively minimizes the joint overlap between the output PDFs by designing optimal control inputs. Due to physical limitations on control inputs and depending on the intensity of uncertainties, full separation, and hence fault isolation, cannot be guaranteed for a single observed output. Therefore, subsequent observations are used in an iterative framework, where the posterior probabilities of the previous time step serve as the prior probabilities for the next time step. The method is applied to locate leaks in a benchmark WDN for different levels of uncertainty in customer water demand and leakage magnitude. Improvements in the performance are observed in comparison to the best considered passive method from literature.