Statistical performance analysis of transient-based extended blockage detection in a water supply pipeline

The aim of the present research is to quantify the maximum feasible accuracy (location and size) for the transient-based blockage detection in a water supply pipeline. Owing to the randomness of transient measurements, a performance bound for the extended blockage detection exists which estimated parameters cannot exceed. The Cramér-Rao lower bound (CRLB) theorem is utilized to compute the lower bound variance of noise-induced estimation errors. It gives the minimum mean square error of any estimator according to information obtained from measurements and quantified by Fisher information. The Fisher information matrix is computed using direct differentiation of the compatibility equations obtained by the method of characteristics. The influence of relevant physical parameters including valve closure time, measurement time length and noise level on the best possible localization of blockage is investigated. The connection between the signal bandwidth, noise level and the performance limit is quantified for a typical case study. The results demonstrate trade-off between the size and the location/length of blockage estimates subject to different maneuver times, roughly offering half the wave speed times maneuver duration as the resolution limit.