基于管线对偶图模型的供水管网可靠性分析

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

为了利用复杂网络理论对供水管网进行结构测度和鲁棒性分析,提出一个新的管网模型——管线对偶图模型.该模型将顺序相连、无大角度转折的同口径同材质管段序列看作统一实体,即管线.将管线抽象为节点,两相交管线对应的节点用边相连,由此形成的无向图即为管线对偶图.使用这一模型对3个城市的供水管网进行结构测度,结果显示,管线对偶图具有明显的无标度特性.利用无标度网络鲁棒性分析方法中的模拟攻击方法,使用3种攻击策略进行实验.结果表明,管网在不同攻击策略下结构变化规律呈现较强的相似性,都会经过初始期、分裂期和崩溃期3个阶段;不同的攻击策略下供水管网进入分裂期和崩溃期的进程差异明显;基于节点度的攻击策略对管网的影响最大,基于节点介数中心性其次,随机攻击对管网的影响最小,高度连接的管线是供水管网中关键和脆弱的部分.对结构测度和模拟攻击的结果进行分析,发现谱隙和进入分裂期的去点率可作为衡量供水管网可靠性的重要指标.针对管线对偶图模型提出的可靠性分析方法可以用于指导供水管网的设计和运维.

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.