Time series prediction of ship course keeping in waves using higher order dynamic mode decomposition

A novel reduced-order model (ROM) based on higher order dynamic mode decomposition (HODMD) is proposed for the time series prediction of ship course-keeping motion in waves. The proposed ROM is validated by using the data of course-keeping tests of an ONR tumblehome ship model. First, modes are decomposed from the model test data by standard DMD and HODMD, and the dominant modes are selected according to the energy index. Then, the decomposed dominant modes are used to reconstruct and predict the dynamics of ship motion. The dynamic characteristics in the dynamical systems are revealed according to the energy index, growth rates, and frequencies of the decomposed modes. In addition, the effects of the tunable parameter in HODMD on prediction accuracy and computational times are analyzed by a parametric study. The prediction results by HODMD show better agreement with the model test data than those by standard DMD.