State Estimation and Leakage Detection in Water Distribution Networks Using Constrained Zonotopes

State estimation in water distribution networks (WDNs) is a challenging task due to the scarcity of measurements and the presence of several modeling uncertainties. In the literature, pseudo-measurements are often required to obtain an observable model for state estimation, which are highly uncertain and mostly represented by bounded sets. This article proposes two new methods for set-based state estimation in WDNs, considering unknown-but-bounded measurement and model uncertainties to calculate bounds on the system states. A new interval method is proposed based on iterative computation of tight enclosures of the nonlinear head-loss functions, and bounding the solution of the algebraic equations using rescaling. This method, referred to as iterative slope approximation and rescaling (ISAR), is mildly more conservative than the iterative hydraulic interval state estimation (IHISE) method previously proposed by the authors, but significantly more computationally efficient. However, since intervals are not capable of capturing the dependencies between state variables, we propose the use of constrained zonotopes (CZs) as an additional step to both IHISE and ISAR. This yields two new algorithms for set-based state estimation of WDNs, capable of capturing the dependencies between hydraulic states, which result in sets with significantly smaller volumes than intervals. The benefits of CZs are also highlighted when the new enclosures are used for leakage detection. These provide higher leakage detection rates compared to intervals, as demonstrated in two case studies using benchmark WDNs.