Toshio Iseki

Bayesian estimation of directional wave spectra based on ship motions

Abstract New techniques are introduced into the Bayesian modeling procedure to estimate directional wave spectra based on ship motion data. In the proposed method, the triple-valued function problem in following seas is strictly taken into account and the optimum solution is obtained from the stochastic viewpoint. In order to examine the reliability of the proposed method, towing tank experiments and onboard experiments were carried out. Using the proposed method, it is shown that the directional wave spectra can be estimated from the vector-valued time series recorded on a running ship even in following seas.

Extended Bayesian Estimation of Directional Wave Spectra

The Bayesian modelling procedure has been extended to estimate time-varying directional wave spectra. In the proposed method, the hull of a ship is regarded as a wave sensor and the time history data of ship motions is analyzed to evaluate cross spectra. In this concept, a special attention should be paid to changes of the directional wave spectrum because the ship is moving and the location at sea is changing continuously. Therefore, the extended Bayesian estimation is based on the cross spectra evaluated at different times and the fluctuation of wave spectrum is taken into account. In order to examine the reliability of the proposed method, data of onboard experiments were analyzed. Comparisons between the results of the proposed method and visual observations show good agreements.© 2004 ASME

Real-Time Analysis of Higher Order Ship Motion Spectrum

The real-time algorithm of higher order spectral analysis is proposed in order to investigate the non-linear and non-stationary ship motions. The algorithm is based on the time-varying vector auto-regressive (TVVAR) modeling and can be considered as an extension of the instantaneous cross spectral analysis. The TVVAR model is fitted to the data using the Kalman filter algorithm and the instantaneous higher order spectra can be evaluated by using the TVVAR coefficients. In order to examine the validity of the proposed algorithm, numerical simulations of the real-time estimation of higher order spectra was carried out based on the full scale ship motion data. The accuracy of the proposed algorithm was investigated by comparing with the stationary analysis based on the FFT. Furthermore, the algorithm was extended to the trispectral analysis and a result was shown to demonstrate the usefulness of the proposed algorithm.Copyright

Estimation of Sea State Parameters From Measured Ship Responses: The Bayesian Approach With Fixed Hyperparameters

The paper deals with estimation of sea state parameters on the basis of time histories of ship responses. The focus is on the Bayesian estimation concept, where the outcome is controlled by a set of hyperparameters, which theoretically must be optimised to provide the optimum solution in terms of sea state parameters. The paper looks into the possibility of fixing the hyperparameters since this will increase the computational efficiency of the method. Sensitivity studies with respect to the hyperparameters are made for both synthetic data and full-scale data.Copyright

Real-Time Estimation of Directional Wave Spectra Using Non-Stationary Ship Motion Data

The Bayesian modeling procedure is modified for real-time estimation of directional wave spectra using non-stationary ship motion data. The assumption of stationary stochastic processes is applied to the seaway, but not to ship response because it also depends on ship maneuvers. Ship response is strongly affected by changes in the encounter angle and frequency of waves. Therefore, it is need to be a real-time algorithm that can deal with non-stationary stochastic processes and estimate the directional wave spectra. In the proposed algorithm, the iterative calculations of the non-linear equations were optimized and the convergence was not achieved at every time step, but was achieved gradually over several time steps. In order to examine the reliability of the proposed method, real-time estimation was conducted by using the data of onboard experiments. Comparisons between the results of the proposed algorithm and a wave monitoring radar system show good agreements.Copyright

BLIND ESTIMATION OF A SHIP'S RELATIVE WAVE HEADING

This article proposes a method to estimate a ship’s relative heading against the waves. The procedure relies purely on shipboard measurements of global responses such as motion components, accelerations and the bending moment amidships. There is no particular (mathematical) model connected to the estimate, and therefore it is called a ’blind estimate’. The approach is in this introductory study tested by analysing simulated data. The analysis reveals that it is possible to estimate a ship’s relative heading on the basis of shipboard measurements only.

A Study on Akaike’s Bayesian Information Criterion in Wave Estimation

A feasibility study of Bayesian wave estimation was carried out to investigate the relationship between the minimum Akaike’s Bayesian information criterion (ABIC) and the estimated wave parameters. The ship response functions, which were used for the Bayesian wave estimation together with the ship motion cross spectra, were simply modified and compared with the normal response functions in connection with the accuracy of estimated wave parameters. Moreover, the concept of the ABIC surfaces was introduced to investigate the optimum estimates from the stochastic viewpoint and the physical viewpoint. As the result, it was revealed that the minimum ABIC did not always provide the best estimates from the viewpoint of wave estimation and the simply modified response functions could reduce the estimating errors in some cases. The reasons were considered that the estimating error at the sharp peak of response amplitude operators was closely related to existence of the local minima of the ABIC surface and the simply modified response functions had some effects to make the ABIC surface smoother. It is pointed out as the conclusion of this report that any estimating errors of the ship response functions were not considered in the Bayesian modeling.Copyright

The Wave Buoy Analogy: Analysis of Synthetic Data by Bayesian Modelling

The paper presents results of the wave buoy analogy applied to synthetic data including measurement noise (white noise). The wave buoy analogy is of particular interest in the context of on-site wave estimations to be used in onboard decision support systems. In the study, Bayesian modelling is introduced as the underlying methodology. The analysis concerns an LNG vessel with forward speed and estimations are made of a rather comprehensive set of wave excitations. In general, reasonable agreements with the true wave parameters are observed. The paper forms parts of the background of another paper, Nielsen and Iseki [17], submitted also to OMAE 2010.Copyright

Instantaneous Spectral Analysis of Non-Stationary Ship Motion Data

The time varying coefficient vector autoregressive (TVVAR) modeling is applied to the cross-spectral analysis of non-stationary ship motion data. Introducing the instantaneous response, a vector autoregressive model can be reduced to simple time varying coefficient autoregressive (TVAR) models for each ship motion and the required CPU time is effectively reduced. The TVVAR model and stochastic perturbed difference equations are transformed into a state space model. The vector-valued unknown coefficients can be evaluated and the instantaneous cross spectra of ship motions can be calculated at every moment. The results showed good agreements with one of the TVAR modeling and also with the stationary autoregressive (SAR) modeling analysis under stationary conditions. Furthermore, the instantaneous relative noise contribution was also estimated using the TVVAR coefficients and illustrated how the structure of a spectrum changed according to the ship manoeuvres for the first time. Optimum order of the model and Akaike’s information criterion were also examined for several changes of parameters. Moreover, it is confirmed that the TVVAR modeling can estimate the instantaneous cross spectra and relative noise contribution of ship motions even under non-stationary conditions.Copyright

Estimation of Directional Wave Spectra Using Ship Motion Data

In rough seas, it is very important for mariners to grasp the sea state around the ship and to secure the safety of the hull and cargo by suitable maneuvers, such as changing the course, slowing down the speed and so on. The difficulty of decision making for these maneuvers arises from the relation between the safety and the cost of the voyage. Therefore the mariners are required to have profound knowledge concerning the sea-keeping characteristics of the ship.