Quantifying Hierarchical Indicators of Water Distribution Network Structure and Identifying Their Relationships with Surrogate Indicators of Hydraulic Performance

Abstract

Enhancing the performance of water distribution networks (WDNs) on a day-to-day basis or under extreme disturbances is an utmost priority for utilities. Previous research has characterized the structure of WDNs in the pipe–junction or segment–valve representation to gain insight on various aspects of their performance; however, the research on characterizing WDN structure in a hierarchical representation and its relationship with performance is lacking. Two key physical properties of WDNs are loops and pipe diameters that are organized in a hierarchical way. Novel indicators have been created to quantify the network hierarchy related to these key properties in other spatial flow distribution networks: loop nestedness and pipe diameter gradation along flow paths. The goal of this study is to adopt such indicators to characterize the hierarchy of WDNs and evaluate its relationship with WDN performance. This study applies a hierarchical decomposition process to model the relationships among loops as a tree network for quantifying loop nestedness. Flow paths of monotonically increasing and decreasing pipe diameters are traced to quantify pipe diameter gradation. Statistical distributions are approximated for these two indicators. Then, relationships between these network hierarchy indicators and two performance indicators (measuring path redundancy and power surplus) are identified. For 15 benchmark networks, this study finds the statistical distributions representing loop nestedness and pipe diameter gradation closely follow a power law. Results suggest that gradual pipe diameter gradation along flow paths and high loop nestedness increase WDN path redundancy, and gradual pipe diameter gradation increases WDN power surplus. The study demonstrates that the hierarchical analysis of WDNs can significantly supplement traditional topological analyses in explaining WDN performance.