Adaptive Calibration of Nodal Demands of Water Distribution System by Extended Kalman Filter and Prior Information of Demand Pattern

The extended Kalman filter (EKF) method has been widely used in adaptive calibration of model parameters of water distribution systems (WDS), comprising the prediction module and correction module. In the adaptive calibration of nodal water demand of WDS model by EKF, the 24-hour time-varying patterns of nodal water demand usually have not been considered. This study investigates the influence of the demand patterns on the adaptive calibration of nodal water demand using an improved EKF approach by considering demand patterns (EKF-P). At the initial time step t1, model parameters of WDS were firstly calibrated by weighted least-squares (WLS) method. For the adaptive calibration of nodal demands at the subsequent time steps, the 24-hour demand patterns of user nodes were integrated as prior information to estimate nodal demands in the prediction module of EKF-P, and then the measurement data were utilized in the correction module to determine the final estimation of nodal demand. The EKF-P method was implemented in benchmark WDSs to verify its efficiency compared with the EKF and inferred measurement Kalman filter (IMKF) method. The results show that the Nash-Sutcliffe efficiency (NSE) of time-varying nodal demand curves was improved by {0.40, 0.35} through the EKF-P method, compared to {EKF, IMKF} method. The prior information on the time-varying demand pattern essentially provides general constraints to the adaptive calibration of water demand of the vast user nodes in the WDS model. Therefore, the EKF-P method can provide better performance and robustness.