Aiming at the requirements of the real-time and accurate prediction of ship maneuvering motion, this paper investigates the prediction of ship maneuvering motion in regular waves using gray-box modelling to improve the accuracy.

A maneuvering motion equation is proposed to reveal the known movement mechanism. The hydrodynamic forces in calm water are approximated using the Taylor series expansion, and the second-order steady wave drift forces are estimated using empirical formulas, thereby obtaining the mathematical model for predicting ship maneuvering motion in regular waves. To promote the precision of the hydrodynamic expression, the Fourier transform method is adopted to separate the data of the maneuvering and seakeeping motions. A model for hydrodynamic correction and second-order steady wave drift forces is developed on the basis of the maneuvering motion and deep neural network (DNN) data, then submitted into the mechanistic equation of maneuvering motion. Finally, an gray-box modelling incorporation mechanism and data for predicting ship maneuvering motion in regular waves is established.

Taking the Office of Naval Research Tumblehome (ONRT) as an example, the maneuvering motion is predicted with the adoption of the mathematical model and gray-box model respectively. For all simulated cases, the simulation of the unit time step costs 2–3 ms on average, and the average error between the results of the gray-box model and experiments is 94.83%, with the accuracy promoted by an average of 4.50% compared with the mathematical model.

Gray-box modelling can be recognized as an efficient method for predicting ship maneuvering motion, laying a foundation for the real-time prediction of maneuvering motion in real marine environments.