An enhanced dynamic soft sensor–based online estimation of missing data for water distribution system with inherent disturbances

Abstract

Interruption of water supply is an unfavourable event in water distribution system (WDS). The interruptions are mainly due to water hammer (WH) transients that are caused by sudden pump/valve failures. In this paper, the effects of hammer are mathematically realized considering the effect of valve coefficient integrated with the system. Due to economic and technical limitations, the system is generally equipped with some obsolete instruments for continuous monitoring, which creates a missing data problem. The problem of missing data estimation could be addressed using a novel customized Kalman filter (CKF), a customized version of conventional Kalman filter (KF) based on process model. Initially, to avoid the intricacies of obtaining the optimal estimates of missing instants, the vacancies in the data are filled assigned by the average values of available adjacent data. The measured quantities are considered distorted with state-, input-dependent and independent uncertainties. The effect of WH on a prototypical WDS is studied for different modes of operation, and the missing data points are reconstructed for regular and irregular sampled data set using the proposed CKF. The performance of the proposed algorithm is also compared with the conventional extended Kalman filter (EKF). The study indicates that the proposed missing data estimation algorithm is highly reliable to identify the missing instances in the states of distribution system.