Seakeeping has been precisely estimated on the basis of the potential theory and tank tests. However, motion characteristic, etc. of a full-scale ship is not usually verified due to the fact the wave displacement cannot be measured in actual seas. To solve this problem, the authors constructed auto-regressive and moving average (ARMA) models of ship motions by approximation of the theoretical frequency response functions. These were based on the 2-Degree-of-Freedom (2-DOF) motion equations of heave and pitch modes, and the coupled longitudinal motions were considered. The obtained models can predict ship motions by a summation of radiation terms and diffraction terms. Since time-series data of wave displacement are not available for the full-scale ship problems, we proposed to identify only the coefficients of radiation terms by regarding the coefficients of diffraction terms as known. This model was realized as a state-space model, and parameters were identified by the ensemble Kalman filter.


In recent years, ship performance in actual seas has focused on, to reduce the environmental burden and realize autonomous ships. Especially, if the ship motion characteristics in actual seas are clarified, the ship states can be visualized by digital twin technologies, etc. in realtime, which will be useful for safety operations. To predict ship motions against waves, the ship motion parameters such as added-mass and damping coefficient are necessary. These parameters have been precisely estimated on the basis of the potential theory and tank tests. On the other hand, it is impossible to measure "wave information" such as the wave displacements and the wave exciting forces in actual seas, since irregular waves come from all of the directions against a ship. Therefore, these are not usually evaluated directly in actual seas, there are only a few studies that have examined the full-scale ship motion characteristics. In addition to waves, loading conditions and aging effects are expected to affect the ship motion in actual seas, so evaluating the seakeeping of full-scale ships only from the time-series data of ship motions is practical from the viewpoint of ship engineering.

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