Sensor placement for leak localization in water distribution networks based on graph sampling method

Abstract

Abstract The sensor placement is an important research issue for monitoring water distribution networks (WDN). Due to the natural graphical structure of the WDN, it is advantageous to use graph sampling theory for selecting monitoring nodes in the WDN. But the existing graph sampling theory is only applied to processing the band-limited signal, and the pressure data of WDN is a non-band-limited signal. This paper is devoted to solving this problem. The paper proposes an approximate conversion method from non-band-limited signal to band-limited signal and gives an optimal spectrum threshold formula. The threshold formula is applied to perform spectral screening in the graph frequency domain and to convert a non-band-limited signal into a band-limited signal. The band-limited signal retains the major frequency components of the original signal and ignores the frequency components of smaller values. The paper performs graph sampling of the obtained band-limited signal and obtains sampling nodes that can perfectly recover the band-limited signal. The sampling node is used as the monitoring node of the WDN to obtain comprehensive information about the WDN. Our method compares numerically with two methods of optimizing sensor placement. The experiment results demonstrate the effectiveness of the proposed method.