Pressure-Leak Duality for Leak Detection and Localization in Water Distribution Systems

Water utilities are challenged to reduce their water losses through detecting, localizing, and repairing leaks as quickly as possible in their aging distribution systems. In this work, we solve this challenging problem by detecting multiple leaks simultaneously in a water distribution network for the Battle of the Leak Detection and Isolation Methods. The performance of leak detection and localization depends on how well the system roughness and demand are calibrated. In addition, existing leaks affect the diagnosis performance unless they are identified and explicitly represented in the model. To circumvent this chicken-and-egg dilemma, we decompose the problem into multiple levels of decision-making (a hierarchical approach) where we iteratively improve the water distribution network model and so are able to solve the multileak diagnosis problem. First, a combination of time series and cluster analysis is used on smart meter data to build patterns for demand models. Second, point and interval estimates of pipe roughnesses are retrieved using least squares to calibrate the hydraulic model, utilizing the demand models from the first step. Finally, the calibrated primal model is transformed into a dual model that intrinsically combines sensor data and network hydraulics. This dual model automatically converts small pressure deviations caused by leaks into sharp and localized signals in the form of virtual leak flows. Analytical derivations of sensitivities with respect to these virtual leak flows are calculated and used to estimate the leakage impulse responses at candidate nodes. Subsequently, we use the dual network to (1) detect the start time of the leaks, and (2) compute the Pearson correlation of pressure residuals, which allows further localization of leaks. This novel dual modeling approach resulted in the highest true-positive rates for leak isolation among all participating teams in the competition.