New modularity-based approach to segmentation of water distribution networks

Complex and/or large size water distribution networks (WDNs) require the division of the hydraulic system into modules in order to simplify the analysis and the management tasks. In the modern science of networks, the modularity index has been proposed in order to detect communities, i.e., groups/clusters of nodes characterized by stronger inter-connections. The modularity index is a measure of the strength of the network division into communities and it is maximized in order to identify them. Therefore, the division into modules of WDNs, also named segmentation, could be performed by using the modularity index as metric in order to identify cluster of nodes. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems, which are infrastructure networks. In fact, the division into modules for infrastructure networks, although it can be based on the identification of clusters of nodes, is not aimed at investigating network features. Differently, the aim is the practical issue of simplifying system analysis, planning and management; therefore, the division is constrained by the technical needs. Accordingly, in the present work the classic modularity index is firstly presented. Successively, it is tailored and modified for WDNs. Furthermore, a multi-objective strategy for optimal segmentation is presented and discussed also using a real test network. The optimization framework is based on the maximization of the WDN-oriented modularity-based index versus the minimization of the cost of newly installed devices in order to obtain network segments. Those are a set of optimal divisions into modules of the hydraulic system which are the basis for an integrated, dynamical planning.