Numerical-simulation-driven three-degree-of-freedom ship motion prediction under varying sea states using a parallel spatio-temporal deep-learning network

Accurate prediction of ship motion under complex sea states is essential for motion compensation control, offshore operation safety, and maritime risk assessment. In this study, a numerical-simulation-driven prediction framework is developed for three-degree-of-freedom (3-DOF) ship motions, including surge, pitch, and yaw. First, the JONSWAP wave spectrum is adopted to construct nine representative sea state conditions with different significant wave heights and peak periods. Based on these wave environments, ANSYS is employed to simulate the 3-DOF motion responses of a moored ship, and nine corresponding motion datasets are generated. To capture the nonlinear, nonstationary, and strongly coupled characteristics of ship motion sequences, a parallel deep-learning network integrating CNN-AdaptiveGCN-ST-Mamba and CNN-TCN-CrossAttention branches is proposed. In this architecture, CNN modules extract local temporal features, AdaptiveGCN models the dynamic coupling relationships among different degrees of freedom, ST-Mamba captures long-range temporal dependencies, and TCN extracts multiscale short-term motion patterns. Furthermore, bidirectional cross-attention is introduced to fuse complementary features from the two parallel branches, while a Horizon Query Decoder is used to achieve non-autoregressive multi-step prediction. A composite loss function combining mean squared error and first-order difference error is designed to improve both amplitude accuracy and trend continuity. Experimental results on nine sea state datasets show that the proposed model achieves stable convergence and superior prediction performance compared with CNN-AdaptiveGCN-ST-Mamba, CNN-TCN-CrossAttention, and CNN-BiLSTM-Attention models. The proposed method obtains lower MAE and RMSE values and maintains high coefficient-of-determination values across all datasets, demonstrating its effectiveness in predicting 3-DOF ship motions under varying sea states. The results indicate that the proposed framework can provide reliable predictive information for subsequent ship motion compensation and maritime operational safety assessment.