The copula-based environmental contour approach in the existing literature is only ‘partially’ non-parametric. Theoretically, the derived environmental contours from this ‘non-parametric’ copula-based approach will still be somewhat rigid. Optimally, the environmental contours for a specific ocean site should be developed based on a joint model of the environmental variables and the joint model should be directly estimated by a two-dimensional non-parametric approach. In this study, the use of a bivariate kernel density estimation approach for generating environmental contours is proposed. The advantages of the proposed new method were validated using two calculation examples based on measured wave data at two offshore locations. It was found, in a wave energy converter (WEC) application example, that the design value will increase by 23.4% if the proposed method is used in comparison to using the technique based on the non-parametric Gumbel copula environmental contour method. It was also concluded that the design value will increase by 15.98% if the proposed method is used in comparison to using the technique based on the non-parametric Clayton copula environmental contour method. The calculation results in this paper clearly demonstrate that the proposed new method can be used to effectively forecast the extreme dynamic responses of WECs.

中文翻译：

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一种预测波浪能转换器极端动态响应的新方法

现有文献中基于 copula 的环境轮廓方法只是“部分”非参数化。从理论上讲，从这种基于“非参数”连接词的方法导出的环境轮廓仍然有些僵硬。最佳情况下，应基于环境变量的联合模型开发特定海洋站点的环境等值线，并且应通过二维非参数方法直接估计联合模型。在这项研究中，提出了使用双变量核密度估计方法来生成环境等高线。所提出的新方法的优点通过基于两个海上位置的测量波浪数据的两个计算示例得到验证。发现在波浪能转换器 (WEC) 应用示例中，设计值将增加 23。与使用基于非参数 Gumbel copula 环境轮廓方法的技术相比，如果使用所提出的方法，则为 4%。还得出结论，与使用基于非参数 Clayton copula 环境等值线方法的技术相比，如果使用所提出的方法，设计值将增加 15.98%。本文的计算结果清楚地表明，所提出的新方法可以有效地预测 WEC 的极端动态响应。