Comparing different approaches to environmental contours for offshore wind turbine extreme response analysis

Abstract

For marine structures subjected to combined wind and wave loads, predicting the long-term extreme response corresponding to a certain return period is an important aspect during the design stage. Generally, a full long-term analysis (FLTA) is recognized as a highly accurate method to determine the long-term extreme responses. FLTA integrates all the short-term extreme responses with their corresponding occurrence probability of environmental conditions. Therefore, this approach is very time-consuming and inefficient, especially for complex marine structures. Therefore, the environmental contour method (ECM) is proposed as a more efficient alternative method for predicting the long-term extreme response of offshore structures. The traditional environmental contour is obtained using the joint distribution of mean wind speed, significant wave height, and spectral peak period. This method has been used extensively on marine structures subjected to wave loads with reasonable numerical accuracy. It decouples the response with the environmental variables and uses the largest most probable short-term response evaluated along with the environmental contour corresponding to a given return period or exceedance probability to represent the extreme response. However, for offshore wind turbines which are subjected to combined wind and wave loads, the ECM performs poorly on wind-induced responses (under wind only or combined wind and wave load conditions). This is due to the non-monotonic behavior of the wind-induced responses resulted from the control system of the wind turbine. The ECM will cause the deviation of the critical environmental conditions between the identified environmental contour and the realistic case. The modified environmental contour method (MECM) is proposed and developed to deal with such a system whose response changes discontinuously due to variations in the operating conditions with additional environmental contours taken into consideration. It is seen that environmental contour plays an important role in the application of both the ECM and the MECM. A set of environmental conditions are selected along the target contour to perform short-term response analysis for the determination of the long-term extreme response. Traditionally, the environmental contour is established based on the inverse first-order reliability method (IFORM) by Rosenblatt transformation with response excluded as a variable. Since this traditional method involves the transformation of the standard normal variables and original physical space which is related to the FORM-approximation closely, a possible over-or underestimation of failure probability may be induced. Another method to obtain environmental contour is the inverse second-order reliability method (ISORM). The ISORM approximates the failure surface by a quadratic function at the design point in standard normal space instead of a linear function in the IFORM. The result of contour based on the ISORM always being conservative, which cannot be ensured by the traditional IFORM method. The highest density region method (HDRM) is to define the environmental contour as the boundary, along which the joint probability density function (PDF) of the environmental variables is a constant. This method solves the contour in the original physical space and can be used in high-dimension conditions. Applying the environmental contour method and modified environmental contour method based on the IFORM, the ISORM, and the HDRM allows to predict the extreme response. The MECM results are much better than the results from the ECM according to safety requirements in the design stage. When applying the environmental contour method, the inverse second-order reliability method to obtain contour is recommended. The ISORM contour is more conservative than the traditional inverse first-order reliability method but the numerical analysis is more stable than the highest density region method in three dimensions, while when applying the modified environmental contour method, the traditional inverse first-order reliability is preferred because of its simplicity and time-efficiency in the calculation.