Model-free system identification of surface ships in waves via Hankel dynamic mode decomposition with control

This work introduces and evaluates Hankel Dynamic Mode Decomposition with control (Hankel-DMDc) and its Bayesian extension as model-free, data-driven approaches for system identification and prediction of surface-ship motions in waves. Using limited input-output data from free-running simulations of the 5415M hull in sea state 7 beam-quartering seas at Froude number 0.33, reduced-order models (ROMs) are built by treating rudder angle and wave elevation as control inputs, and augmenting the system with time-delayed states and inputs. A systematic design-of-experiments explores 294 hyperparameter combinations, statistically validating over 300 model runs to identify robust configurations. Over a 15-wave prediction window, deterministic Hankel-DMDc achieves average NRMSE below 8 %, amplitude error below 0.9 %, and Jensen-Shannon divergence (JSD) below 5 %. The Bayesian extension treats hyperparameters as uniformly distributed random variables and propagates uncertainty via Monte Carlo sampling, improving performance to NRMSE below 7 %, amplitude error below 0.8 %, and JSD below 4 %, while also providing confidence intervals. Predictions remain stable with no degradation over time, and predicted distributions closely match high-fidelity data (average JSD 1 %). The proposed ROMs require under 1 s to train and 0.04 s per 15-wave prediction, demonstrating suitability for real-time digital twins and onboard decision support in nonlinear seakeeping conditions.