Abstract: To address the precise modeling problem of highly nonlinear ship rolling motion, a data-driven modeling method based on Koopman operator was proposed. Firstly, based on the random wave model and the ship rolling dynamics model, the ship rolling dynamics model under random waves was established. Secondly, the extended dynamic mode decomposition (EDMD) method was used to approximate the Koopman operator, and a high-dimensional linear model of ship rolling was established. After determining the basis function used by the high-dimensional linear model and the spatial dimension of system lifting, data-driven modeling was carried out based on the ship rolling data obtained by Matlab Simulink simulation. The experimental results show that the established Koopman linear model is significantly better than the three models of local linearization, feedback linearization, and unscented Kalman filter in terms of tracking accuracy for ship roll angle and roll angular velocity, and the calculation speed of the model is significantly improved. The research results in this paper provide certain technical support for the application of the high-dimensional linear control fitting method in ship attitude stability control.

Key words: ship rolling, linear model, Koopman operator, data-driven