Resilience Quantification and Recovery Prediction of Highway Toll-Station Nodes Under Rainfall Disturbances

Frequent rainfall events threaten expressway operations, and toll stations, as critical network nodes, are vulnerable to functional degradation and cascading effects. However, existing traffic resilience studies mainly focus on urban road networks or static assessments, making it difficult to characterize the resilience evolution, recovery process, and predictability of toll-station nodes. This study proposes a resilience quantification and recovery prediction method for expressway toll-station nodes under rainfall disturbances. By integrating multi-source meteorological data, neighborhood propagation relationships, and network topology, a three-level resilience quantification framework is developed across the functional, neighborhood, and network layers. A piecewise exponential function is used to model the damage–valley–recovery process of node resilience and to extract parameters including damage depth and recovery rate. Focusing on the recovery stage, a node recovery prediction model is constructed by combining resilience sequences, meteorological disturbance features, and dual-graph spatial relationships, while dual-graph convolution and long short-term memory (LSTM) are used to capture the spatiotemporal evolution of node recovery. Results show that the proposed method quantifies toll-station node resilience, captures its staged evolution, and effectively predicts recovery. Baseline, cross-scene, and ablation results confirm the value of multi-source feature fusion and dual-graph propagation, supporting the sustainable operation of expressway systems under rainfall disturbances.