Water demand dynamic estimation in water distribution network hydraulic models based on Kalman filter
[Objective]Nodal water demand dynamic estimation is the main task in the dynamic update of a water distribution network hydraulic model.The data assimilation method based on the extended Kalman filter(EKF)has been widely adopted in dynamic verification and estimation of hydraulic model parameters for pipeline networks.However,the nodal water demand can be divided into different patterns according to user types.Ignoring the influence of demand patterns can cause unreasonable results.Accordingly,this study investigates the effect of demand patterns on the nodal water demand dynamic estimation by the EKF.Additionally,this study proposes an improved extended Kalman filter(IEKF)method and analyzes the main parameters affecting estimation accuracy by comparing different methods.[Methods]The EKF obtains the dynamic water demand of the model through the estimation of multiple time steps,each of which comprises the prediction and correction steps.In the initial time step,the demands are calibrated using an iterative calibration model to avoid state parameter error transmission.In the prediction step,a 24-h demand pattern is adopted as a priori information to predict the nodal water demand at time step t+1 with the demand estimation result at time step t.In the correction step,the nodal demand predicted at time step t+1 is corrected by using the measurement data at time step t+1.The abovementioned steps lead to the IEKF.Aiming at the key parameters in the calculation process,including system noise,measurement noise,and sampling interval,the adaptability of several data assimilation algorithms,including EKF and inferred-measurement Kalman filter(IMKF),is analyzed under different parameter settings.The root mean square error(RMSE)and mean absolute percentage error(MAPE)are used to evaluate the accuracy of the results.Additionally,the Nash-Sutcliffe efficiency(NSE)coefficient is introduced to evaluate the similarity between the demand estimation curves and their corresponding demand patterns.The robustness of the IEKF to errors in the demand estimation curves is also analyzed by establishing an error condition.[Results](1)Compared with the EKF and IMKF,the MAPE obtained by the IEKF is 15.93％and 12.20％ lower,respectively.Additionally,the NSE coefficient of the demand estimation curve is improved by 0.40 and 0.35,respectively.The computation time of the IEKF is similar to that of the EKF and is 99.8％ lower compared with the IMKF.(2)The IEKF can adapt to larger sampling intervals,offering more advantages over the EKF and IMKF for larger sampling intervals.(3)Within the 24-h estimation period,the IEKF suffers smaller errors at all sampling intervals,and the demand estimation curves match the real demand pattern curves.Compared with the EKF and IMKF,IEKF can more accurately capture the demand change and is robust to the demand pattern curve errors in a priori information.[Conclusions]The proposed IEKF uses demand patterns of different user types as a priori information,and NSE coefficient is introduced to assess the similarity between the demand estimation curves and real demand patterns,which improves the accuracy of dynamic estimation of nodal water demand using data assimilation algorithms.In the estimation of nodal water demand,considering the user water consumption patterns can significantly improve the computational accuracy of the EKF method.
water distribution networkmodel calibrationwater demand estimationwater demand patternextended Kalman filter(EKF)
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维普
