基于C藤Copula的多维随机环境变量极限状态曲面

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摘要针对联合分布模型较为复杂时Rosenblatt变换难以实施的现状，提出了基于C藤Copula的多维随机变量极限状态曲面计算公式及数值算法。在该方法中联合分布模型由C藤Copula建立，Rosenblatt变换以二维Copula偏导数的形式表达，采用数值算法求解。结合观测数据研究了平均风速、有效波高和谱峰周期的极限状态曲面，提出了根据极限状态曲面等值线确定风浪参数组合值，并讨论了不同Copula的影响。结果表明，C藤Copula在局部和整体上均能最优表达变量间的相关结构，更适用于建立多维随机变量的联合分布模型；基于C藤Copula的极限状态曲面能有效表达二维变量间的相关结构，其等值线的外包络是二维极限状态曲线；与风浪参数极值相比，根据等值线确定的组合值在保证多维变量各自及联合重现期的前提下有所降低，可使结构设计更加经济合理。

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	涂志斌1
	姚剑锋1
	黄铭枫2
	楼文娟2

关键词 ： C藤Copula, 联合分布模型, 极限状态曲面, 等值线, 风浪参数组合

Abstract：A formula and its numerical algorithm based on C-vine Copulas for environmental surface of dimensional random variables was developed to overcome the difficulty when Rosenblatt transformation was implemented with complex joint distribution model. In this formula joint distribution model was constructed by C-vine Copulas, Rosenblatt transformation was expressed as partial derivative of two dimensional Copula function and solved by numerical algorithm. Environmental surface of mean wind speed, significant wave height and peak spectral wave period, which were derived from an observation record, was constructed by this formula. Furthermore, a method of determining combination values of wind and wave variables based on level curves of environmental surface was proposed, and its influence caused by different Copulas was also discussed. The results show that it is more suitable for C-vine Copulas, which is optimal to express the correlation ship for random variables in local and general, to constructed joint distribution models. The correlation ship for two random variables can be simultaneously expressed by environmental surface based on C-vine Copulas as the level curves of environmental surface are contained within the boundary of 2D contour line. The combination values of wind and wave variables determined by level curves that whose return periods of respective and joint variables are ensured can be reduced compared to their extremes, making structural design more economical and reasonable.

Key words： C-vine Copulas joint distribution model environmental surface level curves combination of wind and wave variables

收稿日期: 2020-08-31 出版日期: 2022-04-15

引用本文:

涂志斌1，姚剑锋1，黄铭枫2，楼文娟2. 基于C藤Copula的多维随机环境变量极限状态曲面[J]. 振动与冲击, 2022, 41(7): 53-61.
TU Zhibin1, YAO Jianfeng1, HUANG Mingfeng2, LOU Wenjuan2. Environmental surface of multi-dimensional random variables based on C-vine Copulas. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(7): 53-61.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I7/53

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