Graph Signal Processing Techniques for Estimating Nodal Heads in Water Networks

<p dir="ltr">This study investigates the performance, in terms of the accuracy and robustness, of four graph signal processing (GSP)-based nodal head estimation techniques for water distribution networks (WDNs), including Graph Head Reconstruction (GHR), Graph Head Reconstruction Stable (GHR-S), Graph Total Variation Minimization (GTVM), and Mean Percolation Head Reconstruction (MPHR). The algorithms were tested under optimal and random sensor locations, with network parameter uncertainties represented by random weights. Under the optimal location scenario, all GSP techniques generally exhibited robustness to parameter uncertainties. However, under the random location scenario, GTVM and MPHR demonstrated greater accuracy and robustness to sensor location variations, as reflected by their small average Mean Absolute Errors (MAEs) and low standard deviation values.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>