中国机械工程

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考虑参数相关性的结构二阶可靠性分析方法

姜潮;邓青青;张旺   

  1. 湖南大学汽车车身先进设计制造国家重点实验室,长沙,410082
  • 出版日期:2016-11-25 发布日期:2016-11-23
  • 基金资助:
    国家自然科学基金资助项目(51222502,11172096);湖南省杰出青年基金资助项目(14JJ1016) 

Second Order Reliability Method of Structures Considering Parametric Correlations

Jiang Chao;Deng Qingqing;Zhang Wang   

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082
  • Online:2016-11-25 Published:2016-11-23
  • Supported by:

摘要: 提出了一种基于vine copula函数的二阶可靠性分析方法(VC-SORM),为存在复杂多维相关性的结构可靠性分析提供了有效手段。通过vine copula函数将随机向量多维概率分布函数转换为多个二维copula函数,基于极大似然估计法和AIC信息准则对各二维copula函数进行最优化选择,从而构建出联合概率分布函数,并进行一阶可靠性分析;在一阶可靠性分析的基础上,对功能函数进行二阶近似,获得精度更高的可靠性分析结果。最后通过两个数值算例验证了该方法的有效性。

关键词: 结构可靠性, vine copula函数, 二阶可靠性分析方法, 参数相关性

Abstract: A vine copula based second order reliability method(VC-SORM) was proposed to deal with reliability analysis problems with complex multidimensional correlated variables. The multidimensional probability distribution function was converted into two-dimensional copula functions using vine copula function. The maximum likelihood estimation method and the AIC information criterion(Akaike information criterion) were used to identify the optional two-dimensional copulas. Then the joint probability distribution function was built and the first order reliability results were obtained. Based on the first order reliability results, a reliability results with higher accuracy were obtained using the second order approximation. Finally, two numerical examples were provided to verify the effectiveness of the method.

Key words: structural reliability, vine copula(VC) function, second order reliability method, parametric correlation

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