Fractality in water distribution networks: application to criticality analysis and optimal rehabilitation

Fractals have been identified as a common feature in many natural and artificial networks that exhibit self-similarity of the topological patterns, i.e. different parts of the system have similar structures to each other as well as to the whole system. This study investigates the fractality in water distribution networks (WDNs) and the application of the fractal property in WDNs analysis. Specifically, we explore the existence of fractal topological patterns in eight real-world WDNs of different complexities by using the box-covering algorithm. The results demonstrate all of the studied WDNs are fractal. Moreover, the application of the fractal property is demonstrated via critical pipe identification and optimal rehabilitation of benchmark real-world WDNs. All results show that the fractal-based approach can achieve better or equally good solutions compared with conventional methods in a much more efficient way, e.g. via automation of some processes or significant reduction in the search space/components to consider.