Wasserstein-Enabled Leaks Localization in Water Distribution Networks

Leaks in water distribution networks are estimated to account for up to 30% of the total distributed water; moreover, the increasing demand and the skyrocketing energy cost have made leak localization and adoption ever more important to water utilities. Each leak scenario is run on a simulation model to compute the resulting values of pressure and flows over the whole network. The values recorded by the sensors are seen as features of one leak scenario and can be considered as the signature of the leak. The key distinguishing element in this paper is to consider the entire distribution of data, representing a leak as a probability distribution. In this representation, the similarity between leaks can be captured by the Wasserstein distance. This choice matches the physics of the system as follows: the equations modeling the generation of flow and pressure data are non-linear. The signatures obtained through the simulation of a set of leak scenarios are non-linearly clustered in the Wasserstein space using Wasserstein barycenters as centroids. As a new set of measurements arrives, its signature is associated with the cluster with the closest barycenter. The location of the simulated leaks belonging to that cluster are the possible locations of the observed leak. This new framework allows a richer representation of pressure and flow data embedding both the modeling and the computational modules in a space whose elements are discrete probability distribution endowed with the Wasserstein distance. Experiments on benchmark and real-world networks confirm the feasibility of the proposed approach.