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

TL;DR

This work develops a model-free framework for identifying and predicting surface-ship motions in irregular waves using Hankel-DMDc, augmented with a Bayesian extension for uncertainty quantification. By time-delay-embedding the state and inputs, the approach captures nonlinear dynamics with a compact ROM that remains computationally efficient. Applied to the 5415M hull in severe sea state, the deterministic Hankel-DMDc achieves accurate short-term predictions, while the Bayesian variant provides robust uncertainty bounds and improved distributional fidelity, validated against CFD data. The results suggest potential for real-time ship-safety assessment, operational planning, and digital-twin applications, with future directions including stability enforcement and sea-state interpolation to extend applicability across conditions.

Abstract

This study introduces and compares the Hankel dynamic mode decomposition with control (Hankel-DMDc) and a novel Bayesian extension of Hankel-DMDc as model-free (i.e., data-driven and equation-free) approaches for system identification and prediction of free-running ship motions in irregular waves. The proposed DMDc methods create a reduced-order model using limited data from the system state and incoming wave elevation histories, with the latter and rudder angle serving as forcing inputs. The inclusion of delayed states of the system as additional dimensions per the Hankel-DMDc improves the representation of the underlying non-linear dynamics of the system by DMD. The approaches are statistically assessed using data from free-running simulations of a 5415M hull's course-keeping in irregular beam-quartering waves at sea state 7, a highly severe condition characterized by nonlinear responses near roll-resonance. The results demonstrate robust performance and remarkable computational efficiency. The results indicate that the proposed methods effectively identify the dynamic system in analysis. Furthermore, the Bayesian formulation incorporates uncertainty quantification and enhances prediction accuracy. Ship motions are predicted with good agreement with test data over a 15 encounter waves observation window. No significant accuracy degradation is noted along the test sequences, suggesting the method can support accurate and efficient maritime design and operational planning.

Figures (18)

• Figure 1: Setup and notation for the current test case
• Figure 2: Visualization of the computational grid on the 5415M hull in TEMPEST.
• Figure 3: System identification with Hankel-DMDc, conceptual scheme.
• Figure 4: System identification with Hankel-DMDc, modeling approach sketch.
• Figure 5: Hankel-DMDc, box plot of error metrics over the validation set for tested $l_{tr}$ and $l_{d_x}$ with $l_{d_u}/\hat{T}=0$. Diamonds indicate the average value of the respective configuration.