Estimating semi-stationary sea states through wavelet-based adaptive segmentation of ship motions

Environmental information is essential for the safety of marine operations, with waves constituting the dominant external excitation acting on floating structures. The wave buoy analogy (WBA) estimates the on-site wave energy spectrum from ship motion responses and offers a cost-effective, flexible complement to satellite observations, wave-rider buoys, and ship-borne radar. In practice, however, ocean waves exhibit pronounced temporal evolution. Approximating them as stationary over fixed windows (commonly of approximately 30 minutes) neglects this time dependence, introduces bias into the response spectra, and can substantially amplify estimation errors in the associated ill-posed inverse problem.

This paper therefore introduces the concept of semi-stationary evolutionary sea states, in which piecewise stationary regimes are connected by gradual transitions to represent continuously varying wave parameters, and develops a wavelet-based adaptive segmentation algorithm. The algorithm analyses ship motion response spectra under an explicit time–frequency trade-off, detects environmental transitions, and estimates directional wave spectra on comparatively coherent segments. Numerical simulations in a dynamic positioning setting indicate that the proposed approach tracks sea-state evolution more robustly than fixed-window baselines. Ideal response amplitude operators (RAOs) are assumed in the present study; the treatment of RAO uncertainty, for example via criteria related to the restricted isometry property, is identified as a direction for future research.