Twin-Hierarchy Decomposition for Optimal Design of Water Distribution Systems

This paper proposes a methodology to decompose water distribution systems (WDSs) into a twin-hierarchy pipeline structure consisting of backbone mains and community feeders. The method has three steps: (1) clustering analysis; (2) vulnerability analysis; and (3) identification of backbone mains and community feeders. After decomposition, analysis of a whole complex WDS could be simplified to that of smaller subsystems formed by either backbone mains or community feeders. The method enables the analysis of all communities independently without physical division of the WDS. It is applied to an optimal-design problem of the C-Town network defined in the literature. The problem is to find the best tradeoff between reducing background leakage and minimizing capital and operational costs. The final solution has a total annual cost of 1.19 million Euro with 54% operational costs and 46% capital costs, respectively. The decomposition process is also consistent with engineering practice on leakage control since one practical strategy is to divide the WDSs into metered zones. Other possible applications of the twin-hierarchy decomposition are further discussed.