A Bidirectional Closed-Loop Coupled SD–BN Model for Metro Rainstorm Disaster Chains: Supporting Sustainable Urban Rail Infrastructure Resilience

As cities advance toward the UN Sustainable Development Goals (SDGs) for resilient, low-carbon urban transport systems, protecting underground metro infrastructure from climate-driven flood risks has become a core priority for sustainable urban operation. Given the complex nature of metro rainstorm disaster chains—characterized by the interplay of continuous evolution, discrete transitions, and probabilistic uncertainty—a single model is insufficient to fully capture their evolutionary process. This study proposes a bidirectional closed-loop coupled model integrating System Dynamics (SD) with Bayesian Networks (BNs), where SD variables are discretized and fed into the BN at each time step, and BN inference results dynamically adjust SD control parameters in the form of risk levels. A three-tier recursive CPT calibration method, combining maximum likelihood estimation, Laplace smoothing, and physical logical constraints, is developed based on 47 historical accident cases with a 13-node network. The model is validated using the Qingdao Metro “July 23” flooding incident. Results show that, compared to the unidirectional coupling model, the closed-loop model dramatically reduces peak station hall water accumulation, shortens operational disruption, and lowers peak passenger retention under idealized instantaneous-response conditions. Specifically, peak station hall water accumulation is reduced by 14.7%, operational disruption duration is shortened from 5.55 h to 0.05 h (99.1% reduction), and peak passenger retention falls from 2790 to 40 passengers (98.6% reduction). These values are controlled model-internal scenario outputs, and are not directly generalizable to other metro systems without local recalibration and empirical validation. The closed-loop mechanism primarily accelerates post-peak risk decline and shortens high-risk exposure duration, rather than suppressing peak risk levels. The core contribution of this work is the transferable bidirectional coupling framework and small-sample CPT calibration workflow, which provides a quantitative basis for dynamic risk assessment and adaptive emergency response in metro flood management—supporting sustainable urban mobility aligned with SDG 11 (sustainable cities and communities) and SDG 13 (climate action).