Localizing leakage hotspots in water distribution networks via the regularization of an inverse problem

The ill-posed inverse problem for detecting and localizing leakage hotspots is solved using a novel optimization-based method which aims to minimize the difference between hydraulic measurement data and simulated steady states of a water distribution network. Regularization constrains the set of leak candidate nodes obtained from a solution to the optimization problem. Hydraulic conservation laws are enforced as nonlinear constraints. The resulting nonconvex optimization problem is solved using smooth mathematical optimization techniques. The solution identifies leakage hotspot areas, which can then be further investigated with alternative methods for precise leak localization. A metric is proposed to quantitatively assess the performance of the developed leak localization approach in comparison with a method that uses the sensitivity matrix. In addition, we propose a strategy to select the regularization parameter when large-scale operational networks are considered. Using two numerical case studies, we demonstrate that the proposed approach outperforms the sensitivity matrix method, with regards to leak isolation, in most single leak scenarios. Moreover, the developed method enables the localization of multiple simultaneous leaks