Improved environmental contour methods based on an optimization of hybrid models

Abstract Estimation of the extreme values of ship and offshore platform responses such as bending moment and mooring tension is important in terms of structural design. Among several such methods, long-term and short-term analyses normally have been used in the industry. In general, long-term relative to short-term analysis is more precise but more time-consuming, because it takes into account all observed sea states. The environmental contour method, which performs a short-term analysis under a few important environmental conditions with an accuracy similar to that of long-term analysis, has been used as an alternative approach. There are several joint distribution models of significant wave height and peak period for environmental contour lines, but it is not known exactly which model most accurately represents actual environmental conditions. A marginal distribution of H s and a conditional distribution of T p , which generally are recommended in the rules and standards, have difficulties in drawing contour lines depending on the field. For the three-parameter Weibull distribution of H s , a proper parameter estimation method should be selected among the several methods according to the observed data, and the distribution parameter of T p has too little data to fit the given model. Another marginal distribution model is a bivariate lonowe (LOgNOrmal and WEibull) hybrid model of H s with two distributions that allow for easy and unique estimation of parameters from any data [ 1 ]. The process of obtaining the distribution parameters from the existing hybrid model is clarified through the optimization process presented in this paper. And outlier technique is adopted to reduce the influence of some atypical data caused by small samples and, thereby, improve the accuracy of the T p fitted result. The contour line through this proposed procedure predicts the extreme value similarly to the three-parameter Weibull distribution model, but it can be rather easily drawn. It is shown that the procedure proposed in this paper can be an effective method for drawing of environmental contour lines using any observed sea states.

[1]  Luis Volnei Sudati Sagrilo,et al.  On the long-term response of marine structures , 2011 .

[2]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[3]  Elzbieta M. Bitner-Gregersen,et al.  Joint distributions for significant wave height and wave zero-up-crossing period , 1990 .

[4]  Erik Vanem,et al.  Joint statistical models for significant wave height and wave period in a changing climate , 2016 .

[5]  R. Montes-Iturrizaga,et al.  Development of environmental contours using Nataf distribution model , 2013 .

[6]  Muhammad Akram,et al.  Comparison of Estimators of the Weibull Distribution , 2012 .

[7]  Enrique Castillo.  Extreme value theory in engineering , 1988 .

[8]  Rola M. Musleh,et al.  Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study , 2014, Reliab. Eng. Syst. Saf..

[9]  Arvid Naess,et al.  Chapter 5 – Probabilistic Design of Offshore Structures , 2005 .

[10]  Carlo De Michele,et al.  Extremes in Nature : an approach using Copulas , 2007 .

[11]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[12]  Teri A. Crosby,et al.  How to Detect and Handle Outliers , 1993 .

[13]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[14]  Philip Jonathan,et al.  Joint modelling of extreme ocean environments incorporating covariate effects , 2013 .

[15]  Sverre Haver,et al.  Wave climate off northern Norway , 1985 .

[16]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[17]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[18]  S. Haver,et al.  Environmental contour method: An approximate method for obtaining characteristic response extremes for design purposes Sverre Haver & Kjersti Bruserud, Statoil ASA Gro Sagli Baarholm, Det Norske Veritas , 2013 .

[19]  Harvey J. Motulsky,et al.  Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate , 2006, BMC Bioinformatics.

[20]  Michael C. Johnson,et al.  Some uncertainties associated with wind and wave description and their importance for engineering applications , 2014 .

[21]  Dragan Jukić,et al.  Total Least Squares Fitting the Three-Parameter Inverse Weibull Density , 2010 .

[22]  Jonathan A. Tawn,et al.  A conditional approach for multivariate extreme values (with discussion) , 2004 .

[23]  Ole David Økland,et al.  Combining contours of significant wave height and peak period with platform response distributions for predicting design response , 2010 .

[24]  Ove T. Gudmestad,et al.  Estimation of extreme significant wave heights and the associated uncertainties: A case study using NORA10 hindcast data for the Barents Sea , 2016 .

[25]  Philip Jonathan,et al.  Joint modelling of wave spectral parameters for extreme sea states , 2010 .

[26]  Dag Myrhaug,et al.  Statistical properties of successive wave heights and successive wave periods , 2004 .

[27]  Bent Natvig,et al.  A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations , 2013 .

[28]  S. Haver,et al.  Environmental Contour Lines: A Method for Estimating Long Term Extremes by a Short Term Analysis , 2008 .

[29]  Dragan Jukić,et al.  Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start , 2009 .

[30]  Elzbieta M. Bitner-Gregersen,et al.  Environmental Description For Long-Term Load Response of Ship Structures , 1995 .

[31]  Yi Zhang,et al.  Long-term performance assessment and design of offshore structures , 2015 .