A Graph Partitioning Algorithm for Leak Detection in Water Distribution Networks

Abstract: Leak detection in urban water distribution networks (WDNs) is challenging given their scale, complexity, and limited instrumentation. We present an algorithm for leak detection in WDNs, which involves making additional flow measurements on-demand, and repeated use of water balance. Graph partitioning is used to determine the location of flow measurements, with the objective to minimize the measurement cost. We follow a multi-stage divide and conquer approach. In every stage, a section of the WDN identified to contain the leak is partitioned into two or more sub-networks, and water balance is used to trace the leak to one of these sub-networks. This process is recursively continued until the desired resolution is achieved. We investigate different methods for solving the arising graph partitioning problem like integer linear programming (ILP) and spectral bisection. The proposed methods are tested on large scale benchmark networks, and our results indicate that on average, less than 3% of the pipes need to be measured for finding the leak in large networks.