Physics-Informed Enhanced TCN-Transformer Hybrid Model for Predicting Moored Vessel Motion Responses

Abstract

Under environmental loads, moored vessels experience complex six-degree-of-freedom (6-DOF) motions, directly affecting port operation safety and efficiency. Accurate and efficient prediction of vessel motion responses is essential for dynamic assessment and risk early warning. However, the strong nonlinearity, multi-DOF coupling, and multi-time-scale characteristics of vessel-mooring line-fender systems pose significant challenges to prediction accuracy and reliability. To address these issues, this study proposes a physics-informed enhanced TCN-Transformer hybrid model (PITT), which integrates the physical constraints of physics-informed neural networks with the temporal feature extraction capabilities of TCN and Transformer. By embedding the governing equations of 6-DOF vessel motion into the loss function, PITT captures multi-scale dynamic characteristics while maintaining physical consistency. The model is trained on simulation data from three operating conditions and compared with several machine learning methods. Results show that PITT achieves superior overall performance. In the time domain, it accurately reproduces vessel motion responses, reducing the average relative error by approximately 10%–38% compared with TCN-Transformer and LSTM-Transformer. In the frequency domain, it effectively captures dominant frequency characteristics and spectral energy distribution, with yaw-related errors reduced by approximately 71% and 40%, respectively. Condition-wise testing on an unseen operating condition demonstrates strong generalization capability, while tests with three levels of Gaussian white noise confirm its robustness under noisy conditions. Overall, PITT provides accurate, efficient, and robust prediction of complex coupled vessel motions. Note to Practitioners—Excessive vessel movement during port loading due to wind, waves, and currents often forces costly work stoppages. While fast prediction is needed for decision support, pure simulation is too slow, and standard machine learning can produce physically unreliable results. We address this by developing a prediction model that embeds fundamental vessel motion physics directly into a neural network. This hybrid method provides operators with a fast, dependable forecast of six-degree-of-freedom motions. Our tests show it reduces prediction error by 10–50% for complex motions like yaw and roll compared to conventional data-driven methods. The key practical contribution is a more trustworthy, real-time risk assessment tool to help port managers decide whether to suspend or continue cargo operations safely. Current limitations include reliance on simulation data for a single vessel type. Future work will integrate real sensor data and cargo handling effects. Beyond ports, this physics-guided method can also support motion forecasting for offshore installation and floating wind platforms.