Objectives  Predicting heave motion is helpful for improving the performance of the heave compensator and reducing the disturbance of waves on operating equipment. To improve the accuracy and stability of the heave prediction model, a real-time prediction method for ship heave motion is proposed in this paper.

  Methods  Based on the Nonlinear Autoregressive with eXogeneous inputs (NARX) neural network, a single sea-state prediction model is established. The simulated heave motion of the vessel is obtained using the Marine Systems Simulator software tool to verify the model. The prediction model based on NARX is compared with prediction models based on Kalman and BP. On this basis, a multi sea-state prediction model is established by improving the single sea-state model.

  Results  The prediction accuracy requirements of the multi sea-state prediction model are satisfied, and its stability is better than the single sea-state model, with a maximum prediction error of less than 10⁻⁴ magnitude in the range of sea state from 2 to 5.

  Conclusions  The simulation results verify the good adaptability of the NARX neural network to the complex wave environment. Its prediction speed and accuracy are higher than the common back-propagation neural network and the traditional filtering method. It still maintains high prediction accuracy under high sea state.