SBLR: A high-accuracy graph signal processing algorithm for nodal head reconstruction in water networks

In water distribution networks, pressure monitoring in terms of the nodal head values, is essential to provide insights into the operational state of the network and to optimize performance. Installing pressure sensors at pipe junctions is usually practically challenging and costly. Nodal heads at most locations are usually estimated using measurements from the sensors at limited number of locations. This task can be formulated as a problem in signal reconstruction, where the nodal head is considered as the graph signal. In this work, we develop a graph signal processing based algorithm for nodal head reconstruction. The algorithm is developed in the graph spectral domain, but can be implemented in the vertex domain, without the need for performing eigendecomposition. The algorithm exploits the smoothness assumption that is usually observed with steady-state nodal heads, but is also able to deal with any low level high-frequency information that may be present in the signal. Extensive performance evaluation of the proposed algorithm using realistic water network model and comparison with other algorithms is presented in this work.