A graph partitioning algorithm for leak detection in water distribution networks

•A multi-stage graph partitioning for leak detection in water distribution networks using flow balances proposed.•Multi-objective mixed integer linear program for graph partitioning formulated.•Approximation algorithm for graph partitioning based on spectral bisection proposed.•Leak location identified using a minimum number of additional flow measurements.

Urban water distribution networks (WDNs) are large scale complex systems with limited instrumentation. Due to aging and poor maintenance, significant loss of water can occur through leaks. We present a method for leak detection in WDNs using repeated water balance and minimal use of additional off-line flow measurements. A multi-stage graph partitioning approach is used to determine where the off-line flow measurements are to be made, with the objective of minimizing the measurement cost. The graph partitioning problem is formulated and solved as a multi-objective mixed integer linear program (MILP). We further derive an approximate method inspired by spectral graph bisection to solve the MILP, which is suitable for very large scale networks. The proposed methods are tested on large scale benchmark networks, and the results indicate that on average, flows in less than 3% of the pipes need to be measured to identify the leaky pipe or joint.