Probabilistic State Estimation in Water Networks

Abstract

State estimation (SE) in water distribution networks (WDNs), the problem of estimating all unknown network heads and flows given select measurements, is challenging due to the nonconvexity of hydraulic models and significant uncertainty from water demands, network parameters, and measurements. To this end, a probabilistic modeling for SE in WDNs is proposed. After linearizing the nonlinear hydraulic WDN model, the proposed probabilistic SE (PSE) shows that the covariance matrix of unknown system states (unmeasured heads and flows) can be linearly expressed by the covariance matrix of three uncertainty sources (i.e., measurement noise, network parameters, and water demands). Instead of providing deterministic results for unknown states, the proposed PSE approach: 1) regards the system states and uncertainty sources as random variables and yields variances of individual unknown states; 2) considers thorough modeling of various types of valves and measurement scenarios in WDNs; and 3) is also useful for uncertainty quantification, extended period simulations, and confidence limit analysis. The effectiveness and scalability of the proposed approach are tested using several WDN case studies.