Objective Traditional numerical simulation methods based on hydrodynamics for calculating ship parametric roll encounter challenges such as high computational costs, demanding operational requirements, and limited coverage of loading conditions. To address these issues, this study proposes an integrated machine learning surrogate model that combines feature physicalization reconstruction, agglomerative hierarchical clustering (AHC), and an improved random forest (RF) algorithm for efficient prediction of ship parametric roll amplitude.

Method AHC is utilized to compress feature dimensions, thereby reducing model complexity and computational cost, while particle swarm optimization (PSO) is employed for global optimization of RF hyperparameters.

Results The validation results based on hydrodynamic numerical simulation data under multiple operating conditions of a large container ship indicate that, compared to the generalized regression neural network (GRNN) and the unoptimized RF model, the proposed model (AHC-PSO-RF) shows an average improvement of 5.84% and 0.27% in the coefficient of determination (R²) and an average reduction of 59.28% and 10.69% in the root mean square error (RMSE) when predicting roll amplitudes under head and following seas in two wave directions, indicating superior prediction accuracy. And the average calculation time per loading condition is reduced by 84.5% compared to the hydrodynamic numerical simulation method, offering significant efficiency advantages in batch prediction tasks.

Conclusion These results confirm the model's practical engineering value as an efficient alternative solution.