Uniformly optimal multi-sensor design in pipe networks for transient-based leakage localization

The design of sensor placement in water supply pipe networks for the purpose of transient-based leakage localization is investigated. Each sensor is placed at where the Fisher information of measurement concerning leaks is maximized; equivalently, the Cramér–Rao lower bound (CRLB) representing the lower limit of leak localization error is minimized. An explicit algorithm for computing the CRLB with respect to leak parameters in a general pipe network is developed. The presence of leak is considered as stochastic and modeled in a probabilistic framework by assuming that the leak location follows a probabilistic distribution with a support on the whole network. The optimal distribution of the sensors is then computed via a quasi-Monte-Carlo simulation, where the expectation of the CRLB of leak localization error is minimized. The proposed sensor placement methodology is optimal uniformly over all the leak localization methods, all the potential sensor locations and all the situations of leaks. Four examples from a simple single-pipe system to a complex pipe network are presented to illustrate the proposed methodology.