非高斯荷载作用下结构微小失效概率的估计方法

Estimation Method for Small Failure Probabilities of Structures under Non-Gaussian Loads

本文提出了一个估计非高斯荷载作用下结构体系微小失效概率的有效方法.该方法由两个解耦的分析过程组成:第一个过程由移位广义对数正态分布模型估计结构非高斯反应的边缘分布函数,对于移位广义对数正态分布模型的参数估计采用两水准方法;第二个过程由Copula函数估计结构非高斯反应的联合分布函数,通过该联合分布函数的尾部得到结构体系的微小失效概率.非高斯地震荷载作用下六层抗弯钢框架的微小失效概率算例分析表明,本文所提方法能精确估计结构体系的微小失效概率,其计算效率比目前普遍采用的Monte Carlo模拟方法高5~10倍.

This paper aims to propose an efficient method to estimate the small failure probabilities of structures under non-Gaussian loads. The method consists of two decoupling modeling processes： the first one is to model the tails of the marginal distributions of responses of structures under non-Gaussian loads by using the shifted generalized lognormal distributions（SGLDs） based on the two level method, and the second one is to model the tails of the joint distributions of the non-Gaussian responses of interest by using the Copulas based on the obtained marginal distributions and the dependent coefficients of the responses. In this way, the small failure probabilities of structures under non-Gaussian loads can be estimated. The reliabilities of a six-story steel-frame structure under action of random earthquake load are analyzed in the paper, which demonstrates that the tail of the joint distribution function of the failure probability of the structural system can be accurately estimated and the efficiency of the proposed method is 5 times to 10 times higher than the commonly used Monte Carlo method. Therefore, the proposed method has a broad prospect for practical applications.