Weighted spectral clustering for water distribution network partitioning

Abstract

In order to improve the management and to better locate water losses, Water Distribution Networks can be physically divided into District Meter Areas (DMAs), inserting hydraulic devices on proper pipes and thus simplifying the control of water budget and pressure regime. Traditionally, the water network division is based on empirical suggestions and on ‘trial and error’ approaches, checking results step by step through hydraulic simulation, and so making it very difficult to apply such approaches to large networks. Recently, some heuristic procedures, based on graph and network theory, have shown that it is possible to automatically identify optimal solutions in terms of number, shape and dimension of DMAs. In this paper, weighted spectral clustering methods have been used to define the optimal layout of districts in a real water distribution system, taking into account both geometric and hydraulic features, through weighted adjacency matrices. The obtained results confirm the feasibility of the use of spectral clustering to address the arduous problem of water supply network partitioning with an elegant mathematical approach compared to other heuristic procedures proposed in the literature. A comparison between different spectral clustering solutions has been carried out through topological and energy performance indices, in order to identify the optimal water network partitioning procedure.

Review of the Quantitative Resilience Methods in Water Distribution Networks

“…The first step is clustering, which aims to define the network subsets. Among the various clustering methods are breadth-first search [119], depth-first search [137], K-shortest paths [75], spectrum clustering algorithms [144,145], and multi-level-recursive algorithm [146]. The second step is division, which partitions the network by inserting flow meters or valves.…”

“…The second step is division, which partitions the network by inserting flow meters or valves. Heuristic optimization techniques such as genetic algorithms [145,147] can minimize the economic investment while maximizing the hydraulic performance. Combined resilience metrics reflect the pressure and flow requirements.…”

Partition of Water Distribution Networks into District Metered Areas Using a Graph Theoretical Approach

“…Kozelj et al [7] presented a case of applying combined weights from two different parameters: pipe diameter and downstream nodal head. Di Nardo et al [8,9] showed that the unweighted spectral partitioning outperformed tested weights for presented case studies by producing solutions with fewer inter-cluster links. The proposed weight cases form previous studies are the following: (unweighted), (pipe diameter), 1⁄ (reciprocal value of pipe length), 5 ⁄ (pipe hydraulic conductance),…”

“…Kozelj et al [7] proposed weighted spectral partitioning for DMA design, which also included hydraulic parameters in the partitioning process. Three different weighted spectral clustering methods were compared by Di Nardo et al [8]. Opposing to the previous research, their results go in favour of unweighted partitioning.…”

“…represent the minimum and the average expected implementation costs for each pipe and were selected because the cost plays an important role in the selection of the final solution. The diameter dependent information for gate valve and flow meter costs was taken from Di Nardo et al [8].…”