基于路径熵的长距离输水系统脆弱性研究

为定量分析长距离输水系统的脆弱性,综合运用图论和信息熵理论,建立长距离输水设施系统脆弱性计算模型。首先,根据输水系统拓扑结构网络图,分析长距离输水系统特征,阐明输水系统脆弱性产生机理;其次,依据水流不确定性,提出输水系统路径熵概念,定义最大路径熵,计算相对路径熵,表达输水系统脆弱度;最后,运用深度优先算法(DFS)对节点按离水源距离由近到远进行分层排序,借助序贯方法逐层逐点对模型进行求解。工程案例表明:该输水系统整体脆弱度为0.237 7,可靠性高;节点14脆弱性最小,脆弱度为0.047 0;脆弱度大于0.500 0的节点有6个,应重点监控并优化。本方法为长距离输水线路设计和确定重点监控对象提供决策支持。

Path entropy-based study on vulnerability of long-distance water conveyance system

In order to quantitively analyze the vulnerability of long-distance water conveyance system，a model for calculation of the vulnerability of long-distance water conveyance system is established through comprehensive application of graph theory and information entropy theory. Firstly，the characteristics of the long-distance water conveyance system is analyzed according to network topology structure of it，thus expounds the generating mechanism of the vulnerability of the water conveyance system. Secondly，the concept of the path entropy of the water conveyance system is proposed according to the uncertainty of the water flow，and then the maximum path entropy is defined and the relative path entropy is calculated for expressing the vulnerability of the water conveyance system. Finally，the stratified ranking is made on the nodes according to the distances from near to far to the water source with the algorithm of depth-first-search（DFS），while the model is stratifiedly solved node by node by means of the sequential analysis method concerned. The relevant engineering case shows that the overall vulnerability of the water conveyance system is 0.237 7 with a high realibility，while the minimum vunerability is found at the node 14 and the vulnerability is 0.047 0. Moreover，the vunerabilities of 6 nodes are over 0.500 0，which are necessary to be emphatically monitored and optimized. Generally，this method provides a deision-making support for the design of long-distance water conveyance route as well as the determination of the key monitoring objects.