Multi-step prediction of daily vessel lock-waiting time in cascade navigation hubs using a hybrid deep learning framework

High-intensity operation of continuous cascade navigation hubs can lead to ship lockage congestion; however, existing research remains insufficient in the advance prediction of congestion states over consecutive future periods. Taking the Three Gorges–Gezhouba cascade navigation hub as the study area, this study formulates lockage congestion as a daily-scale, multivariate, multi-step time-series prediction task with a prediction horizon of 1–7 days. Operational mechanism-informed features are constructed, and a prediction framework integrating Langevin equation-based evolution, a bidirectional temporal convolutional network, a bidirectional gated recurrent unit, and an attention mechanism (LEE-BiTCN-BiGRU-Attention) is proposed. Specifically, BiTCN extracts local temporal fluctuations, BiGRU captures long-range dependencies, a self-attention mechanism strengthens the identification of key time steps, and LEE searches for the optimal hyperparameter combination of the model. The results show that the method achieves an R 2 of 0.9525 and an R M S E of 16.47 h for the pooled multi-step prediction results of the upstream and downstream test sets, and its multi-step prediction accuracy in both navigation directions outperforms that of the comparison models. SHapley Additive exPlanations (SHAP) analysis indicates that the previous backlog dominates short-term predictions, while the influence of ship scale and seasonal characteristics gradually strengthens in medium- and long-term predictions, providing a quantitative reference for navigation scheduling and early warning.