Modularity Index for Optimal Sensor Placement in WDNs

The division of water distribution networks (WDNs) in districts/modules for optimal placement of flow/pressure observations is a relevant issue for different management tasks. In fact, the division of hydraulic systems in districts allows simplifying technical tasks related to analysis and planning activities. Starting from the modularity index, i.e., the most used metric to measure the propensity of the network to be divided into modules, the optimal monitoring design proposes scenarios of optimal placement of flow and pressure meters. This way, each module results bounded by a subset of observations, guarantying the information about flow (i.e., mass balance) and pressure (i.e., energy balance) at the boundary cuts/nodes of each district of the network. Starting from the infrastructure segmentation-oriented modularity index as metric for WDN segmentation and the infrastructure sampling-oriented modularity index as metric for the sampling design, an integrated planning strategy for WDNs monitoring is here proposed, in order to increase service reliability and quality. The strategy is based on a multi-objective optimization that minimizes the number of devices, flow or pressure meters, and maximizes a specific tailoring modularity index, for segmentation and sampling design, respectively. The strategy allows dividing the network into integrated district and pressure monitoring areas, and flexibility is implemented by searching for nested districts.