Dynamic chaos unveiled: enhancing ship’s attitude time series prediction through spatiotemporal embedding and improved transformer model

During ship operations at sea, the vessel’s attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship’s attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.