Prediction of Marine Shaft Centerline Trajectories Using Transformer-Based Models

The accurate prediction of marine shaft centerline trajectories is essential for ensuring the operational performance and safety of ships. In this study, we propose a novel Transformer-based model to forecast the lateral and longitudinal displacements of ship main shafts. A key challenge in this prediction task is capturing both short-term fluctuations and long-term dependencies in shaft displacement data, which traditional models struggle to address. Our Transformer-based model integrates Bidirectional Splitting–Agg Attention and Sequence Progressive Split–Aggregation mechanisms to efficiently process bidirectional temporal dependencies, decompose seasonal and trend components, and handle the inherent symmetry of the shafting system. The symmetrical nature of the shafting system, with left and right shafts experiencing similar dynamic conditions, aligns with the bidirectional attention mechanism, enabling the model to better capture the symmetric relationships in displacement data. Experimental results demonstrate that the proposed model significantly outperforms traditional methods, such as Autoformer and Informer, in terms of prediction accuracy. Specifically, for 96 steps ahead, the mean absolute error (MAE) of our model is 0.232, compared to 0.235 for Autoformer and 0.264 for Informer, while the mean squared error (MSE) of our model is 0.209, compared to 0.242 for Autoformer and 0.286 for Informer. These results underscore the effectiveness of Transformer-based models in accurately predicting long-term marine shaft centerline trajectories, leveraging both temporal dependencies and structural symmetry, thus contributing to maritime monitoring and performance optimization.