Abstract: When solving structural reliability-based design optimization problems with nonlinear correlation， current method for correlated variables might lead to inaccurate optimization results in some situations. Based on Copula function， this paper proposed a method to serve as an effective tool for structural reliability-based design optimization problems where nonlinear correlation existed. The proposed method estimated the parameters of alternative Copula functions according to known samples and selected the optimal Copula function by AIC criterion. Therefore， joint distribution function of variables was established to solve structural reliability-based design optimization problems. Finally， two numerical problems were used to demonstrate the validity of proposed method. Influences on optimization results caused by different Copula were also discussed.

Key words: Copula function, structural reliability-based design optimization, correlation, AIC criterion

摘要： 在求解具有非线性相关性结构的可靠性设计优化问题时，现有的相关性处理方法在某些情况下可能会得到精度较低的优化结果。基于Copula函数提出了一种可靠性优化设计方法，用于求解存在非线性相关性结构的可靠性优化设计问题。该方法根据已知的样本对各备选Copula函数进行参数估计，并根据AIC准则选出最优Copula函数。根据最优Copula函数，构建联合概率分布函数，最后求解结构可靠性优化设计问题。通过两个数值算例验证了该方法的有效性，并讨论了不同Copula函数对优化结果的影响。

关键词: Copula函数, 结构可靠性优化设计, 相关性, AIC准则