A convenient and stable graph-based pressure estimation methodology for water distribution networks: Development and field validation

Accurate estimation of unknown nodal pressures (nodal heads) is necessary for efficient operation and man-agement of water distribution networks (WDNs), but existing methods such as hydraulic simulation and data interpolation can hardly reconcile estimation accuracy with model construction and maintenance costs. Recent developments in graph signal processing (GSP) techniques provide us with new tools to utilize information in WDN hydraulics and available measurements. In a pilot study, a graph-based head reconstruction (GHR) method was proposed, which used GSP to reconstruct the spatially slow-varying parts of nodal heads from a limited number of field measurements to approximate original heads. GHR has illustrated the effectiveness and ease of implementation of GSP-based methods. However, due to the ill-conditioning reconstruction process and inherent uncertainties, GHR may show unstable results with large errors if pressure meters are not installed at specific optimized locations, which limits its applicability. To solve this problem and discover a stable and convenient method that can support a wider range of applications, a graph-based head reconstruction method with improved stability (GHR-S) is proposed. GHR-S utilizes a rough estimation of unknown pressures as pseudo measurements, which provide additional constraints and avoid the occurrence of unreasonable results during the reconstruction process. A middle-sized network with synthetic data illustrates the stability, convenience, and accuracy of GHR-S with arbitrary meter locations and uncalibrated model parameters. GHR-S is also applied to a large real-life network with field measurements, and successfully estimates the unknown pressures of 83,000 nodes with only 58 measurements, showing its effectiveness in practical engineering.