Multi-Resolution Koopman-Based Modal Decomposition for Maneuvering Trend Extraction in Wave-Disturbed Ship Motion

Abstract

Accurate separation of maneuvering dynamics from wave-induced oscillations remains a fundamental challenge in the analysis of ship motion under stochastic sea conditions. Conventional filtering approaches typically rely on predefined frequency cutoffs and often fail to provide physically interpretable decompositions when multiple dynamical time scales are strongly coupled. This study introduces a multiresolution, Koopman-based modal decomposition framework for maneuvering trend extraction using Dynamic Mode Decomposition (DMD). The proposed methodology integrates sliding-window analysis, Hankel time-delay embedding, and multiresolution DMD (mrDMD) to construct localized spectral representations of nonlinear ship dynamics. Within this framework, low-frequency Koopman modes are associated with invariant subspaces governing maneuvering behavior, while higher-frequency modes capture wave-induced oscillatory components. The approach is validated on experimental multi-degree-of-freedom ship motion data under stochastic wave excitation obtained from the DaRUS repository. Motion components, including surge, sway, roll rate, yaw rate, and roll angle, are analyzed using windowed Hankel–mrDMD, and maneuvering trends are reconstructed via projection onto low-frequency Koopman subspaces. Quantitative evaluation using the Spectral Energy Separation Ratio (SESR) and Reconstruction Consistency Metric (RCM) demonstrates consistent separation of slow and fast dynamics, significant attenuation of high-frequency energy, and high reconstruction fidelity. Compared to classical spectral filtering techniques, the proposed method yields smoother trend estimates and enhanced physical interpretability, supported by measurable improvements in spectral energy separation and reconstruction consistency across all motion components, while preserving essential maneuvering characteristics. The proposed framework establishes a fully data-driven, operator-theoretic approach for multiscale ship motion analysis and provides a foundation for short-term prediction and reduced-order modeling of marine dynamical systems.

Keywords

Ship maneuvering / Koopman operator / Dynamic mode decomposition / Multiresolution DMD / Hankel embedding / Multiscale dynamics / Ship motion analysis

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