The residual ratio of ultimate bending moment is a critical indicator for hull structural safety assessment of damaged ships. In maritime emergency scenarios, the empirical formula method has insufficient prediction accuracy, while nonlinear finite element (FE) simulation bears prohibitive computational cost. To address this limitation, we propose a rapid surrogate model for predicting the residual ultimate bending moment ratio of side-damaged ships. The model integrates a lightweight one-dimensional U-Net (1D U-Net) for nonlinear feature extraction and multi-scale feature fusion and a fuzzy inference module for embedding engineering prior constraints. Trained on a 1D structured dataset generated via the modified Smith method (covering multiple damage conditions, hogging and sagging), the model achieves an overall mean absolute error (MAE) of 1.79% and root mean squared error (RMSE) of 2.39% on the test set. It outperforms empirical formulas in accuracy with ultra-short inference time, far lower computational cost than FE simulation, and provides engineering interpretability via activated fuzzy rules. This work offers an efficient alternative tool for rapid safety assessment of damaged hull structures.
Li et al. (2026) studied this question.