Water distribution networks (WDNs) are critical infrastructure for communities. The dramatic expansion of the WDNs associated with urbanization makes them more vulnerable to high-consequence hazards such as earthquakes, which requires strategies to ensure their resilience. The resilience of a WDN is related to its ability to recover its service after disastrous events. Sound decisions on the repair sequence play a crucial role to ensure a resilient WDN recovery. This paper introduces the development of a graph convolutional neural network-integrated deep reinforcement learning (GCN-DRL) model to support optimal repair decisions to improve WDN resilience after earthquakes. A WDN resilience evaluation framework is first developed, which integrates the dynamic evolution of WDN performance indicators during the post-earthquake recovery process. The WDN performance indicator considers the relative importance of the service nodes and the extent of post-earthquake water needs that are satisfied. In this GCN-DRL model framework, the GCN encodes the information of the WDN. The topology and performance of service nodes (i.e., the degree of water that needs satisfaction) are inputs to the GCN; the outputs of GCN are the reward values (Q-values) corresponding to each repair action, which are fed into the DRL process to select the optimal repair sequence from a large action space to achieve highest system resilience. The GCN-DRL model is demonstrated on a testbed WDN subjected to three earthquake damage scenarios. The performance of the repair decisions by the GCN-DRL model is compared with those by four conventional decision methods. The results show that the recovery sequence by the GCN-DRL model achieved the highest system resilience index values and the fastest recovery of system performance. Besides, by using transfer learning based on a pre-trained model, the GCN-DRL model achieved high computational efficiency in determining the optimal repair sequences under new damage scenarios. This novel GCN-DRL model features robustness and universality to support optimal repair decisions to ensure resilient WDN recovery from earthquake damages.

中文翻译：

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用于弹性配水网络修复决策的图卷积网络-深度强化学习模型

配水网络 (WDN) 是社区的关键基础设施。与城市化相关的 WDN 的急剧扩张使它们更容易受到地震等后果严重的灾害的影响，这需要确保其复原力的策略。WDN 的弹性与其在灾难性事件后恢复服务的能力有关。关于修复顺序的合理决策对于确保弹性 WDN 恢复起着至关重要的作用。本文介绍了图卷积神经网络集成深度强化学习 (GCN-DRL) 模型的开发，以支持优化修复决策，以提高地震后 WDN 的弹性。首创WDN弹性评估框架，整合震后恢复过程中WDN性能指标的动态演化。WDN 性能指标考虑了服务节点的相对重要性以及震后用水需求得到满足的程度。在这个 GCN-DRL 模型框架中，GCN 对 WDN 的信息进行编码。服务节点的拓扑和性能（即需要满足的水的程度）是GCN的输入；GCN 的输出是每个修复动作对应的奖励值（Q 值），这些奖励值被输入到 DRL 过程中，以从大动作空间中选择最佳修复序列，以实现最高的系统弹性。GCN-DRL 模型在一个试验台 WDN 上进行了演示，该试验台经受了三种地震破坏情景。将 GCN-DRL 模型的修复决策性能与四种传统决策方法的性能进行比较。结果表明，GCN-DRL模型的恢复序列实现了最高的系统弹性指标值和最快的系统性能恢复。此外，通过使用基于预训练模型的迁移学习，GCN-DRL 模型在确定新损伤场景下的最佳修复序列时实现了高计算效率。这种新颖的 GCN-DRL 模型具有稳健性和通用性，可支持最佳修复决策，以确保 WDN 从地震破坏中恢复。