Scalable online constrained state estimation for digital twin applications in water distribution systems.

Reliable operation of water distribution systems (WDSs) requires continuous information on system-wide pressures and flow rates. State estimation (SE) is a widely used approach to infer these unmeasured states by combining hydraulic model predictions with sensor measurements. However, SE for WDSs remains challenging due to limited sensor data, discrepancies between observed and modeled system conditions, nonlinear hydraulic behavior, discrete operational states introduced by control devices, and the large scale of real-world systems. This study presents a constrained state estimation (CSE) framework that extends the Extended Kalman Filter for pressure estimation in complex WDSs. The proposed approach enhances conventional SE by extending the state-space formulation to include control valves and enforcing physical and operational boundary constraints during both the prediction and correction steps. These advances enable the direct assimilation of measurements from sources, tanks, and control devices into the hydraulic model, yielding physically consistent system states. The framework is evaluated using two real WDSs, one employing synthetic sensor data and the other incorporating real sensor measurements. Results demonstrate that the CSE achieves significantly improved pressure estimates across the entire system compared to the unconstrained SE baseline. Furthermore, by leveraging reduced hydraulic models that preserve system pressure behavior while simplifying system topology, the framework achieves over 99% reduction in runtime with minimal accuracy loss, enabling near real-time scalability. This work advances efficient, scalable, real-time state estimation within the broader context of operational WDS digital twins.