ABSTRACT

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.

摘要

分形已被确定为许多自然和人工网络中的一个共同特征，这些网络表现出拓扑模式的自相似性，即系统的不同部分彼此以及整个系统具有相似的结构。本研究调查了配水网络 (WDN) 中的分形以及分形属性在 WDN 分析中的应用。具体来说，我们通过使用框覆盖算法探索了八个不同复杂度的现实世界 WDN 中分形拓扑模式的存在。结果表明所有研究的 WDN 都是分形的。此外，分形属性的应用通过关键管道识别和基准现实世界 WDN 的最佳修复得到证明。