  A data-driven and equation-free approach is proposed and discussed to model
ships maneuvers 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. DMD also allows for short-term future estimates of the
system's 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 (KCS) 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's state with reasonable accuracy
up to two wave encounter periods.
