Online state estimation in water distribution systems via Extended Kalman Filtering

Operators of water distribution systems (WDSs) need continuous and timely information on pressures and flows to ensure smooth operation and respond quickly to unexpected events. While hydraulic models provide reasonable estimates of pressures and flows in WDSs, updating model predictions with real-time sensor data provides clearer insights into true system behavior and enables more effective real-time response. Despite the growing prevalence of distributed sensing within WDSs, standard hydraulic modeling software like EPANET do not support synchronous data assimilation. This study presents a new method for state estimation in WDSs that combines a fully physically-based model of WDS hydraulics with an Extended Kalman Filter (EKF) to estimate system flows and heads based on sparse sensor measurements. To perform state estimation via EKF, a state-space model of the hydraulic system is first formulated based on the 1-D Saint-Venant equations of conservation of mass and momentum. Results demonstrate that the proposed model closely matches steadystate extended-period models simulated using EPANET. Next, through a holdout analysis it is found that fusing sensor data with EKF produces flow and head estimates that closely match ground truth flows and heads at unmonitored locations, indicating that state estimation successfully infers internal hydraulic states from sparse sensor measurements. These findings pave the way towards real-time operational models of WDSs that will enable online detection and mitigation of hazards like pipe leaks, main bursts, and hydraulic transients.