Reliability analysis for water supply networks based on pipeline dual graph model

Abstract:

A novel water supply network model, pipeline dual graph (PDG), is proposed for structure measurement and robustness analysis of water supply networks using complex network theory. If water pipes of same diameter and material are sequentially connected in rather small angle changes, this model takes them as a unified entity called pipeline. A PDG is an undirected graph constructed by taking every pipeline as a node and inserting a link between two nodes corresponding to a couple of intersected pipelines. Structure measurement for 3 Chinese cities' water supply networks shows that pipeline dual graphs are scale-free networks. Attack simulations using 3 strategies based on scale-free network robustness analysis methods were designed and conducted. Experimental results indicated that structural change processes of these networks were similar under different attack strategies, which all consisted of the initial phase, the splitting phase and the collapsing phase. However, every network entered the splitting phase and the collapsing phase at a distinctly different speed. Among the 3 strategies, the strategy based on node degree had the greatest impact on water supply networks, followed by the strategy based on betweenness, while random attacks had the least influence. Highly connected pipelines are critical and vulnerable components. Structure measurement and attack simulations prove that spectral gap and node removal rate while entering the splitting phase can be adopted as important indicators for evaluating the reliability of water supply networks. The proposed reliability analysis method based on PDG model can be used to guide design and operation of water supply networks.