Sensor placement method for water distribution networks based on sampling of non-bandlimited graph signals

Monitoring water distribution networks (WDNs) requires careful consideration of sensor placement, which is essential for obtaining comprehensive information about the network. A natural graphical structure underlies WDN, making graph sampling theory advantageous for selecting monitoring nodes. However, graph sampling theory is only applied only to restrictive band-limited signals, while the pressure data of WDN is a restrictive non-band-limited signal. To address this issue, this paper presents an approximate conversion method for transforming non-band-limited signals into band-limited signals, accompanied by an optimal spectrum threshold formula. This formula is used to perform spectral screening in the graph frequency domain, effectively converting non-band-limited signals into band-limited signals that preserve the major frequency components while ignoring smaller-value frequency components. By sampling band-limited signal, we identify sampling nodes that perfectly recover the signal. These sampling nodes act as monitoring nodes that can perform a comprehensive inspection of the WDN and accurately locate leaks. The accuracy of our method in recovering the signal and locating the leak is demonstrated by comparing it with two existing sensor placement optimization methods.