A Method for Evaluating Recovery Strategies for Cascade Failures of Metro Networks
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摘要: 恢复策略效果评估对地铁网络级联失效事件后的应急修复决策有着重要作用，关系到地铁网络运营安全水平。针对地铁网络级联失效现象，从系统韧性角度提出了1种恢复策略效果评估方法。建立了基于地铁节点客流分布特征的恢复节点分配函数，将恢复策略融入级联失效过程，构建了带恢复策略的网络级联失效模型。采用网络效率与连通性能表征系统机能，引入系统机能曲线量化系统韧性，利用Python仿真评估了随机恢复、重要度优先恢复和节点度优先恢复3种恢复策略的效果。以西安市轨道交通网络为对象开展仿真实验，结果显示：在单一策略效果评估时，节点恢复比例的增大可以提高恢复策略效果，表现为抵抗与恢复阶段更低的系统损伤值与更快的恢复速率。而在不同策略效果比较时，重要度优先恢复策略表现最佳，2类韧性指标均值较节点度优先恢复分别提升了11.9%及3.4%，比随机恢复分别提升了7.6%和1.2%。相比传统模型，提出的模型在失效蔓延速度、系统性能变化与实际交通级联失效过程拟合效果更佳。研究表明：在地铁网络级联失效的影响下，采用重要度优先恢复策略并增加节点恢复比例可以达到更优的恢复效果。仿真结果能够更加准确地描述突发扰动事件对系统性能的影响过程，为实际地铁网络级联失效现象的预防和恢复策略决策提供了参考依据。Abstract: The effectiveness of recovery strategies plays a vital role in emergency response after cascading failures take place in a metro network, which is closely related to its operation safety. To address the cascading failures in metro networks, a method for evaluating the efficiency of recovery strategies is proposed from a system resilience perspective. A function for allocating recovery nodes is established based on the characteristics of the distribution of passenger flows at metro stations. And a model of network cascade failure with recovery strategy is developed by integrating the recovery strategy into the cascade failure process. Then, network efficiency and connectivity are used to characterize system functionality, and a system functionality curve is introduced to quantify system resilience. The effectiveness of three recovery strategies, including random recovery, importance priority recovery, and degree priority recovery, are evaluated through Python simulations which are carried out based on the metro network in the city of Xi'an. The results indicate that increasing the node recovery ratio enhances the efficacy of recovery strategies in a singular strategy effectiveness assessment. This enhancement manifests as a reduction in system damage during the resistance and recovery phases, accompanied by an accelerated recovery rate. By comparing different strategies, the strategy of importance priority recovery outperforms the degree priority recovery and the random recovery. Two resilience indicators of the importance priority recovery are 11.9% and 3.4% greater than degree priority recovery, respectively; and 7.6% and 1.2% greater than random recovery, respectively. Compared to traditional models, the proposed model exhibits better goodness of fit for the speed of propagation failure, change of system performance, and process of actual traffic cascading failure. It suggests that under the influence of cascading failures in metro networks, better recovery results can be achieved by adopting an importance priority recovery strategy and increasing node recovery proportion. The simulation results accurately represent the impact of depict disturbance on system performance, aiding decision-making for preventing and recovering from cascading failures in metro networks.
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图 3 不同网络节点恢复比例网络效率变化情况
Figure 3. Network efficiency for different network node recovery ratios changes
图 4 不同网络节点恢复比例网络正常节点比例变化情况
Figure 4. Different network node recovery ratio network normal node ratio change
图 5 不同恢复策略网络效率韧性变化情况
Figure 5. Network efficiency resilience with different recovery strategies change
图 6 不同恢复策略下网络连通韧性变化情况
Figure 6. Network connectivity toughness under different recovery strategies change
表 1 典型节点指标特性
Table 1. Typical node metrics characteristics
典型节点 初始荷载 节点度 节点重要度 所属线路 北大街 245 502 4 0.1508 1、2号线 通化门 160 250 4 0.2119 1、3号线 钟楼 70 489 2 0.0257 2号线 汉城南路 10 540 2 0.0931 5号线 
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表 2 典型节点不同节点恢复概率下韧性指标
Table 2. Resilience index under different node recovery probabilities of typical nodes
节点 RE RN p = 0 p = 1/8 p = 1/4 p = 3/8 p = 1/2 p = 0 p = 1/8 p = 1/4 p = 3/8 p = 1/2 北大街 0.219 0.650 0.673 0.709 0.726 0.487 0.836 0.889 0.919 0.947 通化门 0.215 0.653 0.722 0.754 0.784 0.497 0.845 0.906 0.941 0.944 钟楼 0.247 0.657 0.681 0.763 0.847 0.520 0.851 0.906 0.930 0.973 汉城南路 0.237 0.684 0.714 0.908 0.908 0.563 0.856 0.979 0.946 0.989
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表 3 网络级联时序
Table 3. Timing sequence of cascading failures in network
站点 站点性质 无恢复 带恢复策略时间步 失效时时刻/s 恢复策略 达最大损伤时刻/s 恢复时刻/s 北大街 最大荷载换乘车站 23 C2 11 31 C3 9 30 C4 8 21 通化门 最大节点度换乘车站 25 C2 12 32 C3 10 32 C4 9 22 钟楼 最大荷载非换乘车站 24 C2 10 31 C3 9 31 C4 9 19 汉城南 较大节点度非换乘车站 29 C2 6 33 C3 11 17 C4 4 17
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表 4 不同节点被攻击后的韧性值（部分）
Table 4. Resilience values of different nodes after being attacked (partial)
韧性 网络指标 随机恢复 节点度恢复 重要度恢复 荷载 节点度 重要度 RE RN RE RN RE RN 通化门 160 250 4 0.211 0.625 0.906 0.723 0.920 0.663 0.920 北大街 245 502 4 0.150 0.605 0.893 0.674 0.890 0.666 0.917 科技路 70 739 4 0.128 0.625 0.902 0.685 0.899 0.687 0.935 南稍门 111 231 4 0.041 0.632 0.901 0.702 0.906 0.855 0.972
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