Parameter Identification of Ship Response Model Based on an Improved Physics-Informed Neural Network

Objective To address the problems of limited training samples and strong noise interference in parameter identification of ship maneuvering motion models, a ship motion identification method based on a Fourier-feature and gated-residual Physics-Informed Neural Network (FGR-PINN) is proposed. Methods To improve the insufficient representation of high-frequency dynamic features and the limited training stability of standard PINNs under physical constraints, Fourier feature mapping is introduced to enhance high-frequency feature representation, and a gated residual network is constructed to improve gradient propagation. Automatic differentiation is adopted to compute state derivatives and avoid noise amplification caused by numerical differentiation. Based on this framework, the parameters of the first-order nonlinear Nomoto model are identified. Validation experiments under different noise levels and training data volumes are conducted in zigzag simulation and towing tank test scenarios using a Mariner cargo ship and an unmanned experimental vessel. Results The results show that the proposed method achieves high-accuracy identification of ship motion model parameters and exhibits good adaptability to noise interference and small-sample conditions. In the noise-level tests of the simulation and towing tank experiments, the best modeling performance is obtained at noise amplitudes of 5% and 10%, respectively. In the training-data-volume tests, the best performance is achieved when the training data volume is 60% and 70%, respectively. Compared with SVR and SINDy, the proposed method shows stronger anti-noise capability and better adaptability to sparse samples while maintaining modeling accuracy. Conclusion The proposed method is suitable for ship maneuvering motion modeling under limited-sample and noisy conditions, and provides an effective approach for high-accuracy and robust identification of ship motion models with potential engineering value.