An Investigation of PSO-Optimized LSTM–Transformer Hybrid Model for Multi-Step Ship Motion Prediction

The advantages of hybrid models for time series forecasting have received significant attention, and several studies focus on and test their application in the seakeeping of ship motions. A hybrid model integrating an LSTM encoder and Transformer decoder (LT) is introduced to overcome the limitation of individual LSTM and Transformer: initially, the seakeeping response of the KCS ship was simulated by ANSYS-AQWA considering the sea state 3 and 4 simultaneously and established a dataset; secondly, three standalone baseline models (LSTM, Transformer, and TCN), and two hybrid models, LT and LT, with PSO-optimized hyperparameters (P-LT) were constructed and trained to forecast the seakeeping performance of ships with multiple steps of 30, 60 and 90; finally, the comparison between solo and hybrid models was made by different steps on RMSE, MAE and NRMSE evaluations to prove the advancement of LT and P-LT models. The P-LT hybrid model achieved consistent accuracy improvements compared with the best-performing individual models across different ship motions. Notably, RMSE reductions were observed at all prediction horizons (30, 60, and 90 steps), with maximum improvements reaching 13.54% for rolling, 11.83% for pitching, and 12.87% for heaving motions. This study provides both theoretical and practical support to ship motion prediction and demonstrates the potential of the proposed study as an effective engineering product for enhancing safety in ship operation.