A Leak Localization Algorithm in Water Distribution Networks Using Probabilistic Leak Representation and Optimal Transport Distance.

Leaks in water distribution networks are estimated to account for up to 30% of the total distributed water: the increasing demand, and the skyrocketing energy cost have made leak localization and adoption even 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 recorded values are seen as the signature of one leak scenario. The key distinguishing element in the present paper is the representation of a leak signature as a discrete probability distribution. In this representation the similarity between leaks can be captured by a distance between their associated probability distributions. This maps the problem of leak detection from the Euclidean physical space into a space whose elements are histograms, structured by a distance between histograms, namely the Wasserstein distance. This choice also matches the physics of the system: indeed, the equations modelling the generation of flow and pressure data are non-linear. Non-linear data structure is better represented by the Wasserstein distance than by the Euclidean distance. The signatures obtained through the simulation of a large set of leak scenarios are non-linearly clustered according in the Wasserstein space using Wasserstein barycenters as centroids. As a new set of sensor measurements arrives, the related signature is associated to 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 theoretical and computational framework allows a richer representation of pressure and flow data embedding both the modelling and the computational modules in the Wasserstein space whose elements are the histograms endowed with the Wasserstein distance. The computational experiments on benchmark and real-world networks confirm the feasibility of the proposed approach.