Optimal sensor placement for leak location in water distribution networks based on graph learning algorithm

The effective monitoring of urban water distribution networks (WDNs) relies heavily on pressure sensor placement. Nevertheless, a WDN may consist of hundreds of nodes, and it is not economically feasible to install sensors at each node. Therefore, how to identify an optimal location for sensor placement becomes a crucial issue. We use graph signal processing to analyze the pressure signals and introduce a framework for optimal sensor placement specifically designed for pressure signals. To address the limitation that pressure signals cannot be sampled directly, we propose a method to convert the signal into a band-limited signal that meets the requirements. Central to the method is learning a graph Fourier operator, and the effectiveness of the proposed method is proved theoretically. The graph Fourier operator enables the pressure data to become a smooth graph signal with variations in its topology. In addition, we design a graph filter based on the energy of the signal and obtain a band-limited signal that meets the requirements. To ensure the selection of representative nodes, we use a noise-robust graph sampling method to obtain the sensor node. Our method is further evaluated using the pressure data from Anytown versus Net3, showing strong performance in leak identification and signal reconstruction capabilities.