Comparative Study of Machine Learning Models for Instantaneous Wave-Height Estimation Using Three-Degree-of-Freedom Ship Motion Responses

To address the high deployment cost, insufficient local coverage, and limited timeliness of conventional wave-observation methods in onboard real-time applications, this study conducts a comparative investigation of centre-of-gravity-equivalent instantaneous wave-height estimation models based on three-degree-of-freedom ship motion responses under the framework of the wave buoy analogy (WBA). The heave, roll, and pitch responses of a 1:2 scaled Series 62 4667-1 planing craft model in regular head seas are used as inputs, while the synchronous instantaneous wave-height signal measured by a wave probe near the centre of gravity is used as the label. A unified protocol is established with consistent inputs, labels, window construction, data partitioning, and evaluation metrics. Six models, namely SVR, TCN, LSTM, CNN-LSTM, Transformer, and LSTM-MHA, are compared and validated using STAR-CCM+ numerical simulation data and towing-tank experimental data. The results indicate that, in the simulated case of H = 0.10 m and T = 1.5 s, LSTM-MHA achieves the highest estimation accuracy, with RMSE and R² values of 0.001231 and 0.997848, respectively, but it also has the largest model size and computational cost. In comparison, TCN achieves near-optimal accuracy with a smaller parameter count and lower inference latency, and shows stable performance across multiple conditions. The towing-tank experimental results further show that both LSTM-MHA and TCN clearly outperform the SVR baseline. Overall, accuracy in the simulation domain, robustness in the towing-tank experimental domain, and cross-domain generalisation capability are not fully consistent. Therefore, the selection of onboard instantaneous wave-height estimation models should jointly consider estimation error, model complexity, computational latency, window length, and practical deployment requirements.