Integrating entropy theory and cospanning tree technique for redundancy analysis of water distribution networks

Abstract

A large number of recent studies have addressed the redundancy evaluation of Water Distribution Networks (WDNs) from a hydraulic perspective. There already exist a few topological redundancy metrics, which address very basic structural characterizations of networks and therefore fail to realistically capture the inherent topological redundancy. To remedy this weakness, we introduce, for the first time, a two-tiered approach to evaluate the redundancy of WDNs. Tier one is supported by the cospanning tree technique which offers a novel method to measure the local redundancy of pipes. Tier two uses the results of the level one and posits the informational entropy theory as a tool to measure the global redundancy of networks. An attempt has been made to generate a new robustness index as a measure to quantify the redundancy. The proposed redundancy index can be interpreted as a measure of distance from the maximum possible redundancy. In order to demonstrate the proposed method, the paper presents two case studies, a hypothetical network and a real world WDN of an Australian town. Comparison of the presented method with conventional redundancy measures reveals the superiority of the proposed redundancy method.