Time-series forecasting of ships maneuvering in waves via dynamic mode decomposition

Abstract

A data-driven and equation-free approach is proposed and discussed to forecast responses of ships maneuvering in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear finite-dimensional representation of a possibly nonlinear system dynamics by means of a set of modes with associated oscillation frequencies and decay/growth rates. This linear representation is entirely derived from available data and does not require the knowledge of the underlying system equations, which are and remain unknown. Based on the linear representation, DMD allows for short-term future estimates of the system state, which can be used for real-time prediction and control. Here, the objective of the DMD is the analysis and forecast of the trajectories/motions/forces of ships operating in waves, offering a complementary efficient method to equation-based system identification approaches. Results are presented for the course keeping of a free-running naval destroyer (5415M) in irregular stern-quartering waves and for the free-running KRISO Container Ship performing a turning circle in regular waves. Results are overall promising and show how DMD is able to identify the most important modes and forecast the system state with reasonable accuracy upto two wave encounter periods.