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。
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.