Interval State Estimation of Hydraulics in Water Distribution Networks

Water distribution networks are critical infrastructure systems, which are required to reliably deliver water to consumers. Hydraulic state estimation of flows and pressures is key for the efficient and dependable operation of water systems. However, in practice,  hydraulic state estimation is a challenging task due to the scarcity of sensors compared to system states and the presence of several modeling uncertainties. It is a common practice for historical data to be used in the place of missing measurements, however the lack of a statistical characterization for the error of these measurements results in having no knowledge of the state estimate error magnitude. This paper presents a methodology for generating hydraulic state bounding estimates by modeling measurement and parametric uncertainties as intervals. The resulting nonlinear interval hydraulic equations are re-formulated using bounding linearization, a technique that restricts the nonlinearities within a convex set, and solved using linear optimization. An iterative procedure improves the bounding linearization, converging to the tightest possible bounds. Simulation results demonstrate that the proposed methodology produces tight state bounds and can be successfully used to detect water leakages in the network.