Modular interdependency analysis for water distribution systems

Complexity in water distribution systems (WDSs) poses a challenge for analysis and management of the systems. To reduce the complexity, the recent development of complex network science provides a system decomposition technique that converts a complex WDS with a large number of components into a simple system with a set of interconnected modules. Each module is a subsystem with stronger internal connections than external connections. Thus far, the topological features of the modular structure in WDS have been extensively studied but not the behavioural features, e.g. the hydraulic interdependencies among modules. Therefore, this paper aims to quantitatively measure and graphically visualize the module interdependency in WDSs, which helps understanding the behavioural complexity of WDSs and thus various WDS analyses, such as pipe maintenance, model calibration, rehabilitation, and District Metered Areas planning. Specifically, this study first identifies the WDS's modular structure then measures how changes in the state of one module (i.e. any single pipe failure or perturbed demand within each module) affect the state of another module. Modular interdependencies are summarized in an interdependency matrix and visualized by the digraph. Four real-world systems are analysed, and three of them shows low interdependencies among most of the modules and there are only a few critical modules whose status changes will substantially affect a number of other modules. Hence, highly interconnected topologies may not result in strong and complex module interdependency, which is a fact that simplifies several WDS analysis for practical applications as discussed in this paper.