A Study on the Vulnerability of Multilayer Subway Networks Based on the SPM and DQN

To address the escalating vulnerability of metro systems under multiple perturbations—including extreme rainfall, equipment failures, and passenger surges—this study tackles several limitations in existing research: the predominant focus on single-layer topology, the neglect of cross-layer coupling effects between physical facilities and functional systems, the lack of dynamic global information in critical node identification, and the insufficient consideration of network clustering characteristics in cascading failure analysis. Drawing on complex systems theory, this study constructs a physical–functional bilayer coupled network model, proposes three improved Deep Q-Network algorithms for identifying cross-layer critical nodes, and introduces a cluster-augmented sandpile model to simulate the differentiated propagation of cascading failures. An empirical case study of the Zhengzhou Metro network demonstrates that the constructed bilayer network exhibits scale-free properties, that the improved DQN algorithms significantly outperform classical benchmarks—including degree centrality, betweenness centrality, closeness centrality, and the greedy algorithm—in sequential disruption efficiency, and that the safety tolerance coefficient and limit coefficient exert substantial regulatory effects on network vulnerability. The methodological framework developed herein—integrating bilayer coupled modeling, deep reinforcement learning-based critical node identification, and cluster-augmented sandpile cascading failure analysis—provides a transferable technical pathway for vulnerability assessment of multilayer coupled networks, with its applicability validated through the Zhengzhou case.