Bridging hydraulics and graph signal processing: A new perspective to estimate water distribution network pressures

The low spatial density of monitored nodal pressures (nodal heads) has already become a bottleneck restricting the development of smart technologies for water distribution networks (WDNs). Inferring unknown nodal heads through available WDN information is an effective way to bypass data limitations, but an accurate and easy-to-implement method is still absent. For general WDNs, the spatial distribution of nodal heads is approximately 'smooth' as there are few dramatic head changes. If heads can be divided into components with different spatial varying speeds, then they can be approximated by a few slow varying components. On this basis, a graph-based head reconstruction (GHR) method is proposed, which employs graph signal processing technologies to reconstruct the slow varying parts to estimate unknown nodal heads. Four metrics are proposed to bridge WDN hydraulics and signal processing to quantify the similarity of adjacent nodal heads, which enhance the smoothness of heads over the graph, and thus increase estimation accuracy. GHR was tested with different parameter settings and compared with other head estimation methods. Results showed that GHR has less restrictive parameter requirements compared with hydraulic simulation, and outperforms traditional data interpolation methods with better accuracy. At a larger looped network under potential model uncertainties and measurement errors, GHR still accurately estimated the heads for more than 10,000 unknown nodes, achieving a mean absolute error of 0.13 m using only 100 pressure meters. Thus the proposed method provides an efficient, robust, and convenient way to estimate unknown nodal heads in WDNs.