Orazio Giustolisi

A novel infrastructure modularity index for the segmentation of water distribution networks

The search for suitable segmentations is a challenging and urgent issue for the analysis, planning and management of complex water distribution networks (WDNs). In fact, complex and large size hydraulic systems require the division into modules in order to simplify the analysis and the management tasks. In the complex network theory, modularity index has been proposed as a measure of the strength of the network division into modules and its maximization is used in order to identify community of nodes (i.e., modules) which are characterized by strong interconnections. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems as infrastructure systems. To this aim, the classic modularity index has been recently modified and tailored for WDNs. Nevertheless, the WDN-oriented modularity is affected by the resolution limit stemming from classic modularity index. Such a limit hampers the identification/design of small modules and this is a major drawback for technical tasks requiring a detailed resolution of the network segmentation. In order to get over this problem, we propose a novel infrastructure modularity index that is not affected by the resolution limit of the classic one. The rationale and good features of the proposed index are theoretically demonstrated and discussed using two real hydraulic networks.

Network structure classification and features of water distribution systems

The network connectivity structure of water distribution systems (WDSs) represents the domain where hydraulic processes occur, driving the emerging behavior of such systems, for example with respect to robustness and vulnerability. In complex network theory (CNT), a common way of classifying the network structure and connectivity is the association of the nodal degree distribution to specific probability distribution models; and during the last decades, researchers classified many real networks using the Poisson or Pareto distributions. In spite of the fact that degree-based network classification could play a crucial role to assess WDS vulnerability, this task is not easy because the network structure of WDSs is strongly constrained by spatial characteristics of the environment where they are constructed. The consequence of these spatial constraints is that the nodal degree spans very small ranges in WDSs hindering a reliable classification by the standard approach based on the nodal degree distribution. This work investigates the classification of the network structure of twenty-two real WDSs, built in different environments, demonstrating that the Poisson distribution generally models the degree distributions very well. In order to overcome the problem of the reliable classification based on the standard nodal degree, we define the “neighborhood” degree, equal to the sum of the nodal degrees of the nearest topological neighbors (i.e., the adjacent nodes). This definition of “neighborhood” degree is consistent with the fact that the degree of a single node is not significant for analysis of WDSs. This article is protected by copyright. All rights reserved.

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.