Motion-based Wave Estimation By a Bayesian Inference Method: a Procedure For Pre-defining the Hyperparameters

Wave estimation based on the motions of a vessel has been recently discussed by several researchers and a Bayesian inference method seems to be one of the most promising alternatives for such task. In the Bayesian approach, however, a certain number of (hyper)parameters must be adjusted for each estimation. In the version adopted in this paper, two parameters control the smoothness of the estimated spectrum in respect to frequency and direction. In principle, the best option for the hyperparameters depends on the characteristics of the waves to be inferred and, therefore, this poses the secondary problem of defining the best adjustment for these parameters. One option is to employ an information criterion (such as Akaike's Bayesian information criterion - ABIC) in order to perform this adjustment. However, several studies point out that using fixed hyperparameters increases drastically the computational efficiency of the algorithm and since ABIC has been shown not to always provide the optimum estimate (e.g. (Iseki, 2011)), this paper proposes an alternative approach for preestablishing the values of the hyperparameters. The methodology is based on a sensitivity analysis on the errors of the estimation with respect to the calibration of the parameters, performed for various wave conditions and for different drafts of the vessel. This analysis is carried out through numerical simulations of the ship response for different theoretical sea spectra. Variations in wave height, peak period, mean direction and directional spreading are taken into account. A criterion is then proposed for choosing the most appropriate values of the hyperparameters based solely on the vessel draft and on the mean period of the recorded motions. Results show that, by following this approach, one may define a suitable choice of the parameters prior to the wave estimation, thus reducing the computational effort without significantly increasing errors in the estimations.