Introducing two hyperparameters in Bayesian estimation of wave spectra

Abstract

Abstract. An estimate of the on-site wave spectrum can be obtained from measured ship responses by use of Bayesian modelling, which means that the wave spectrum is found as the optimum solution from a probabilistic viewpoint. The paper describes the introduction of two hyperparameters into Bayesian modelling so that the prior information included in the modelling is based on two constraints: the wave spectrum must be smooth directional-wise as well as frequency-wise. Traditionally, only one hyperparameter has been used to control the amount of smoothing applied in both the frequency and directional ranges. From numerical simulations of stochastic response measurements, it is shown that the optimal hyperparameters, determined by use of ABIC (a Bayesian Information Criterion), correspond to the best estimate of the wave spectrum, which is not always the case when only one hyperparameter is included in the Bayesian modelling. The paper includes also an analysis of full-scale motion measurements where wave spectra estimated by the Bayesian modelling are compared with results from ocean surface measurements by satellite and from a wave radar. The agreement is found to be reasonable.

Motion-based wave estimation: Small-scale tests with a crane-barge model

“…Wave spectrum is estimated from the recorded vessel motions by means of a Bayesian inference method, originally proposed by Iseki & Ohtsu [2] and later refined by Nielsen [8]. The method that is employed in this paper follows closely the one proposed by Nielsen, except for the set of motions that is adopted as input for the estimations: as explained in the introduction, the roll motion is disregarded here due to the strong nonlinearities that affect the transfer function of this motion with respect to the incident waves.…”

“…Most of the previous work is focused on the problem of ships with forward speed and a good perspective on the state-of-the-art of this problem may be found in references [1][2][3][4][5][6][7][8]. The present paper, on the other hand, deals with the possibility of estimating the directional wave spectrum from the motions recorded aboard a stationary vessel, such as, for example, an FPSO (Floating Production Storage and Offloading) unit or a pipe-laying barge.…”

Fault Isolation and Quality Assessment for Shipboard Monitoring

“…In case sea state estimation is conducted by a ship-wave buoy analogy e.g. [2], [3], it is sufficient to use three different ship responses and usually we have more at our disposal.…”

“…Since all the measurements have been taken on the ship, the frequency of encounter should be considered only. As already mentioned, in case sea state estimation is conducted by a shipwave buoy analogy [2], [3], it is sufficient to use three different ship motions (or responses). Therefore, it would be convenient to have expressions that relate three different ship responses, which is readily obtained from Eqs.…”

A Study on Parametric Wave Estimation Based on Measured Ship Motions

“…In the literature there are studies (2,3,4,5,6) concerning the estimation of sea state parameters using measured ship responses (e.g. motion data) where the ship, to make an analogy, acts as a wave rider buoy and for this reason the methodology is called the 'wave buoy analogy'.…”