Adaptive dynamic mode decomposition for data-driven prediction of ship manoeuvring dynamics using windowed least squares

Dynamic Mode Decomposition (DMD), a data-driven method, is used to obtain a linear approximation of ship manoeuvring dynamics. The Esso Osaka tanker is used, with training data from a 30 ° − 30 ° zigzag manoeuvre and circling motions using a nonlinear mathematical model. Existing DMD-based ship manoeuvring models are static, the linear operator is identified once from training data and held fixed during simulation, so prediction accuracy degrades once the vessel's state departs from the training manifold, and no prior study has proposed or systematically tuned an online correction for this effect. To address this gap, an adaptive extension of DMD is developed and its parameters are characterised as a function of manoeuvre severity. The resulting DMD model is validated through independent zigzag tests at 10 ° − 10 ° and 30 ° − 30 ° rudder angles. The static DMD model accurately reproduces the ship's behaviour for prediction horizons up to t ≈ 150 s , after which accumulated prediction error causes progressive deterioration in prediction accuracy in velocity states and trajectory, particularly at large rudder angles where nonlinear hydrodynamic coupling is significant. This threshold ( t ≈ 150 s , corresponding to approximately 0.36 ship lengths of travel and 19 % of one 30 ° − 30 ° zigzag oscillation period) reflects the vessel, speed, and manoeuvre considered in this study and is not proposed as a general property of DMD-based ship motion prediction. To overcome this, an adaptive extension is proposed in which the four output rows of the linear operator corresponding to surge velocity, sway velocity, yaw rate, and heading angle are updated at a specific time step using a sliding window of recent snapshot pairs solved via batch least squares. A parameter study over window sizes of [ 10 − 200 ] and update intervals from 1 to 150 steps, identifies, through a qualitative trade-off assessment rather than a formal optimality criterion, a window size of 100 and an update interval of 150 steps as a robust configuration. The study confirms that adaptive DMD parameter selection must be manoeuvre-specific when operating across a wide range of rudder angles.