In this study, a new technique to estimate directional wave spectra with respect to encounter waves of ships based on ship motions data is introduced. Firstly, the ship motion is analyzed by a Time Varying AutoRegressive modeling procedure, and cross spectra of the ship motion data is obtained. And then, based on the estimated instantaneous cross spectra, directional wave spectra with respect to the encounter wave are estimated by a state-space modeling procedure every time step. The proposed method is verified by numerical experiments.


If it is possible to understand a directional-frequency characteristic of ocean waves which is called directional wave spectra onboard every time step, it is very useful for ship operators to remain a ship safety. However, in general a mechanical measurement of ocean waves onboard is not carried out from the view point of benefits by costs. On the other hands, as a method to understand directional wave spectra, an inverse estimation procedure from spectra of ship motions in ocean waves has been focused on. As these procedures, Extended Maximum Likelihood Estimation method (Hirayama, 1987), Bayesian method (Iseki and Ohtsu, 1994), Time Varying Bayesian method (Terada and Iseki, 2002; Iseki, 2004), Extended Maximum Entropy method (Yoshimoto and Watababe, 1994), NonLinear Programming method (Saito and Maeda, 1998) and Exhaustive search method (Nihei et al., 2010) are mainly proposed in Japan. In these methods exception of Time Varying Bayesian method, if measured ship motions are nonstationary, then the correct estimation calculation cannot implement because the calculated spectra for ship motions is based on a stationary frequency analysis. And also, concerning to Time Varying Bayesian method, a complex calculation is required due to a linearization of a nonlinear equation for estimation of directional wave spectra and a robust estimation cannot implement against changes of ship speeds.

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