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. 2017;2(1):19.
doi: 10.1007/s41109-017-0033-4. Epub 2017 Jun 30.

Weighted Spectral Clustering for Water Distribution Network Partitioning

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Free PMC article

Weighted Spectral Clustering for Water Distribution Network Partitioning

Armando Di Nardo et al. Appl Netw Sci. .
Free PMC article

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.

Keywords: Laplacian spectrum; Spectral clustering; Water network partitioning; k-means.

Figures

Fig. 1
Fig. 1
First 10-smallest eigenvalues of unweighted graph Laplacian matrix
Fig. 2
Fig. 2
Node coordinates in the eigenspace of the first 3-smallest eigenvectors of the diameter-weighted graph L rw Laplacian matrix
Fig. 3
Fig. 3
Parete WSN partitioning in 4-DMA for the unweighted graph adjacency matrix: clustering phase (a) and dividing phase (b)
Fig. 4
Fig. 4
Parete WSN partitioning in 4-DMA for the conductance-weighted graph adjacency matrix and L rw Laplacian: clustering phase (a) and dividing phase (b). Flow meters are represented by rectangles while gate valves with the double triangle

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