Theoretical Aspects of Water Distribution Leak Localization

QC 20240830

Abstract

Leak management is a critical task in water distribution system operations. Leakages account for substantial water losses, wasting energy and monetary resources, and reducing consumer capacity. Furthermore, leaks can lead to hazardous situations with, on the one hand, undermined and water-damaged infrastructure and, on the other, the risk of pollution and disease spread. In this licentiate thesis, we deal with leak localization in light of new communicating hydraulic sensors.

Leak localization, traditionally requiring cumbersome manual labor, can be automated by properly analyzing measurements from smart sensors. Numerous elaborate methods have been developed for this task. Many leak localization algorithms were designed for and tested in a specific steady-state network flow simulation model. This is the model used in the popular simulation tool EPANET, on which, for example, the BattLeDIM competition was based. Our focus is also on this model. However, instead of only developing new algorithms, we take a step back and delve into often overlooked questions regarding the theoretical foundations of algorithmic leak localization. 

The thesis is based on three articles designated one chapter each. In addition, before the technical chapters, a mathematical modeling chapter serves to unify the presentation. Our modeling goes beyond the common practice of considering only node leakages by introducing notation for leakages that can occur anywhere along any pipe in the network.

First, we consider a single pipe scenario, which was only previously treated under full model knowledge. We analyze how we can simultaneously learn an uncertain model and estimate a leakage position. Given a particular model parameterization, the problem takes a \emph{bilinear} form. We consider specific solution methods for the bilinear parameter estimation problem. We derive theoretical convergence rates for these. We also investigate the practical performance through an EPANET simulation and discuss the reasons for the observed results. 

Then, we scale the considered network to a set of parallel pipes. In this setting, we state which sensors are necessary to localize the leakage. We notice the risk of finding multiple plausible leakage positions among the parallel pipes. We investigate ways to get around this pitfall. 

Finally, we move on to whole networks. We derive structural conditions to guarantee successful leak localization. Our conditions are general and thus an improvement compared to the standard simulation testing procedure on specific hydraulic states. 

With the presented results, we hope to bring insight that can be used to develop more robust and trustworthy leakage localization algorithms. 

urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-352339