Linear Programming Models for Leak Detection and Localization in Water Distribution Networks

This study examined the benefits and limitations of formulating linear programming models for water distribution network leak detection and localization considering sequences of demands. First, the consistency of sensitivity matrixes for different demand magnitudes and spatially varying nodal demands was investigated to determine if different sensitivity matrixes are needed for each time step and to determine the demands to use for computing the gradient matrixes. Then several unconstrained and constrained models were developed and their detection and localization performance was evaluated for a network in Austin, Texas. To constrain the failure location in time and space, binary (zero-one) integer linear programming (BILP) was used. A set of threshold-based detection rules was applied to test for the anomalies in the time series, and they were compared for a range of realistic leak sizes. Based on the numerical results, the best optimization model was identified considering multiple detection metrics (detection effectiveness, efficiency, and localization). The best BILP model that constrains leak locations spatially and temporally outperformed the unconstrained model in detecting and locating relatively small leaks.