Water distribution networks (WDNs) are vital infrastructures in cities. However, reports about urban WDNs incidents that result in major system breakdowns and water outages are not uncommon, which repeatedly highlights the urgency of addressing vulnerability challenges of WDNs. This study aims to propose a new method for system-level, scenario-independent vulnerability assessment of WDNs, which considers the uncertainty in various failures that may happen in the system. The proposed method is developed based on the notion that the vulnerability of WDN is largely determined by its heterogeneity in node importance, which impacts how likely system malfunction or breakdown would happen should a small amount of nodes be attacked. Accordingly, the proposed method uses a set of indicators to measure the functional, structural and overall importance of each node in WDN, and introduces a novel network entropy model to measure the heterogeneity of importance of these nodes. The proposed method then assesses the systemic vulnerability of WDN, by benchmarking its current entropy against the entropies associated with the least and most vulnerable states of the system. The efficacy of the proposed method is demonstrated in a case study, in which the assessment yielded by the proposed method was found theoretically reasonable as well as consistent with actual conditions of the case WDN.

供水网络（WDN）是城市中至关重要的基础设施。但是，关于城市WDN事件导致重大系统故障和水中断的报道并不少见，这再次突显了解决WDN脆弱性挑战的紧迫性。本研究旨在为WDN的系统级，与场景无关的漏洞评估提出一种新方法，该方法考虑了系统中可能发生的各种故障的不确定性。提出的方法是基于以下概念开发的：WDN的漏洞很大程度上取决于其节点重要性的异质性，这影响了如果攻击少量节点，系统发生故障或崩溃的可能性。因此，建议的方法使用一组指标来衡量功能，WDN中每个节点的结构和总体重要性，并引入了一种新颖的网络熵模型来衡量这些节点重要性的异质性。然后，提出的方法通过将WDN的当前熵与与系统的最低和最脆弱状态相关的熵进行基准测试，从而评估WDN的系统脆弱性。在案例研究中证明了所提出方法的有效性，在该案例研究中，从理论上发现了所提出方法产生的评估是合理的，并且与案例WDN的实际情况一致。通过将其当前熵与与系统的最弱状态和最脆弱状态相关的熵进行基准测试。在案例研究中证明了所提出方法的有效性，在该案例研究中，从理论上发现了所提出方法产生的评估是合理的，并且与案例WDN的实际情况一致。通过将其当前熵与与系统的最弱状态和最脆弱状态相关的熵进行基准测试。在案例研究中证明了该方法的有效性，在该案例研究中，从理论上发现了该方法产生的评估结果是合理的，并且与案例WDN的实际情况相符。