配水管网水力学动态中心性度量
Dynamic Centrality Measures for Water Distribution Network Hydraulics
- Vanderbilt University（范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对配水管网脆弱性分析忽略动态特性的问题，提出基于控制理论中心性度量的脆弱性向量方法，结合动态与拓扑识别关键管道，以优化维护优先级。
AI中文摘要：
配水管网（WDNs）易受各种故障影响，包括但不限于人为错误、网络攻击和网络改造，因此有必要对配水管网进行脆弱性分析。图论中心性度量——作为中心性度量的一类主要方法——旨在仅根据网络组件在输入变化时对配水管网拓扑的影响（即关键性）对其进行排序，而忽略了配水管网的动态特性。为克服这一局限性，本文采用一种控制理论中心性度量方法，通过同时纳入配水管网的动态特性和拓扑结构，识别网络中影响最大和最小的管道。首先，给定一个由非线性微分代数方程（NDAEs）建模的配水管网，其中瞬态流动动力学作为微分方程（DE），水质量守恒作为代数方程（AE），并将管道流量视为状态空间（SS）表示的状态，我们提取一个在平衡（即稳态）流量向量附近由线性常微分方程（LODEs）建模的线性化系统。其次，将管道流量视为状态空间节点（状态），我们引入一种基于节点中心性的度量，即\textit{脆弱性向量（VV）}，以根据管道在输入变化时对配水管网动态特性和拓扑的影响对其进行排序。特别是，通过这种基于中心性的方法可以识别网络中影响最大和最小的管道。这使水工程师能够更好地理解配水管网的脆弱性，并有效地将维护和运营工作优先集中于配水管网中影响最大的管道上。
英文摘要：
Water distribution networks (WDNs) are susceptible to various failures, including but not limited to human errors, cyber-attacks, and network modifications, necessitating the vulnerability analysis of WDNs. Graph-theoretic centrality measures---as a main class of centrality measures---aim to rank the network components solely based on their influence (i.e., criticality) on the WDN topology in the case of input changes, while overlooking the WDN dynamics. To overcome such a limitation, this paper uses a control-theoretic centrality measure to identify the network's most and least influential pipes in WDNs, by simultaneously incorporating the dynamics and topology of the WDN. First, given a WDN modeled by nonlinear differential-algebraic equations (NDAEs) consisting of transient flow dynamics as differential equation (DE) and conservation of water mass as algebraic equation (AE) and considering the pipe flow rates as states of the state-space (SS) representation, we extract a linearized system modeled by linear ordinary differential equations (LODEs) around the equilibrium (i.e., steady) flow rate vector. Second, treating pipe flow rates as SS nodes (states), we introduce a node centrality-based measure, namely \textit{vulnerability vector (VV)}, to rank the network pipes based on their influence on the dynamics and topology of the WDN in the case of input changes. In particular, the network's most and least influential pipes can be identified through such a centrality-based approach. This enables water engineers to understand the WDN's vulnerability better and effectively prioritize the maintenance and operational efforts on the most influential pipes within the WDN.
