Sea-State-Conditioned Motion Response of Berthed Ships Using Field Measurements from Multiple Vessels and Berths

Field measurements of ship motions at berth are often sparse, heterogeneous, and collected across multiple vessels and locations, limiting the applicability of conventional multivariate response-modelling approaches. This study presents a statistical framework for analysing sea-state-conditioned motion responses of berthed ships using hourly field data from multiple vessels and berth locations with incomplete overlap between Degrees of Freedom (DoF). Each motion DoF is analysed independently and conditioned on the corresponding sea-state parameters, primarily significant wave height (Hs), peak wave period (Tp), and wave direction. A quality-control procedure that combines physical plausibility checks and robust regression is used to identify and remove inconsistent response–sea-state pairs while preserving the dominant response structure. Sea-state-conditioned motion response envelopes are derived by binning observations in sea-state space and computing representative and conservative statistics, including the median and upper-percentile responses. The results show a consistent increase in motion variability with increasing across all DoFs. Quantitative envelope metrics reveal that surge exhibits the strongest translational sensitivity to wave height, while roll displays the largest normalised motion coefficient, indicating strong amplification relative to wave height. Rotational motions, particularly roll and yaw, exhibit the largest envelope spreads and strongest directional dependence, whereas heave shows comparatively compact and monotonic behaviour consistent with direct wave excitation. Quadratic envelope fits further indicate that motion responses are not purely linear in Hs, with roll, yaw, and surge exhibiting clear superlinear growth in typical response levels. In contrast, extreme responses to heave and sway exhibit greater curvature in the upper-percentile envelopes. To support physical interpretation, synthetic sea surface elevations are generated for representative quality-controlled sea states using a spectral random-phase approach. Validation confirms that the generated sea states reproduce the prescribed spectral characteristics and statistical wave parameters, providing realistic time-domain representations of the sea surface. An ablation study further demonstrates the robustness of the proposed framework by quantifying the effect of individual methodological components, showing that the quality-control and sea-state conditioning stages are essential for reducing response dispersion and obtaining stable motion envelopes. Overall, the proposed methodology preserves most available field data, avoids restrictive assumptions about DoF simultaneity, and provides a transparent framework for extracting engineering-relevant response characterisation from heterogeneous berth-monitoring datasets. The approach offers a practical basis for assessing berth operability and evaluating motion risk under real-world sea conditions.