Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection

In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.

A mixture of linear-linear regression models for a linear-circular regression

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modelling approach of a wrapped normal distribution that describes angular variables and angular distributions and advances them for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a nonparametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.

A Practical Spectral Fatigue Analysis Procedure for Topside of Floating Offshore Structures in West Africa

In most offshore projects recently ordered, spectral fatigue analysis is required for design integrity. However, the spectral fatigue analysis is very complicated to implement since it has many variations for parameters and forms of input data, and the classification and commercial software packages are exposing limit to support all those variations. A topside fatigue analysis for a FPSO design in West Africa is one of such a challenging project due to the fact that the specification of the project requires spectral fatigue analysis considering 3-peak Ochi-Hubble wave spectrum, Wrapped normal wave spreading and sea state data with 3 wave components, main swell, secondary swell and wind sea. In this study, a practical spectral fatigue analysis procedure is introduced in order to implement the fatigue analysis using a commercial program SACS. Applying adaptive cosine spreading wave distribution which can approximate Wrapped normal wave spreading is devised for each sea state and the comparison between two wave spreading is carried out. Finally, the proposed methodology is justified by analyzing the characteristics of the sea state in West Africa.

Response Sensitivity to Swell Spectra Off West Africa

Both hindcast and measured wave data were used to establish various descriptions of the swell spectra off West Africa in the West Africa Swell JIP (WASP). The effect on system responses of the various data types and swell spectral descriptions has been estimated. The response of single degree of freedom oscillators to wave spectra can be used to produce maximum responses as a function of natural period and damping, analogous to the approach used in earthquake engineering. The results can be used to gain insight into the sensitivity of floating systems to the swell characteristics of the location and also to the differences between hindcast and measured data sets. Extreme values of system response can be calculated and used to estimate design spectra, by scaling the measured or hindcast spectrum that produced the largest response. The sensitivity of the responses of floating systems to various simplifications of the hindcast spectra was evaluated by calculating the responses of an FPSO and CALM buoy for a location off Nigeria and southern Angola. It was found that there is little loss of accuracy if the hindcast spectra are decomposed into a maximum of two partitions, one of which may be a wind-sea, and the swell partitions are described with a lognormal function, the wind-sea partition with a JONSWAP-Glenn frequency function, and the directional spreading with a wrapped normal function, together with parametric forms for the widths of the lognormal and wrapped normal functions. As a consequence it is concluded that the parametric forms for the swell frequency and direction spreading can be used in design.