Abstract: When dealing with the problems of non-normality, multi-variables, small failure probability, and nonlinear performance functions, it was difficult to pursue satisfactory accuracy with low cost by means of traditional structural reliability solution methods. In order to overcome the shortcomings of existing methods, an adaptive subdivision-importance sampling method for solving structural reliability was proposed by organically combining universal generating function, adaptive subdivision method and importance sampling. According to the adaptive subdivision theory, the critical region was subdivided to reduce the discrete interval length, and the random variables were subdivided nonuniformly and adaptively by the backward recursion operation to obtain the probability of the failure region and the subdivided critical region, and the structure universal generating function of the critical region might be obtained by means of combination operations. The failure probability of the critical region was mainly obtained by employing the important sampling for the hot focal elements. The sum of the failure probabilities of the failure region and the critical region were the estimate of the structural failure probability. The examples indicate that the errors of the new method are significantly less than that of traditional methods. Additionally, the computational efficiency is improved with the help of importance sampling.

Key words: structural reliability, universal generating function, adaptive subdivision, critical focal element, importance sampling

摘要： 传统的结构可靠度求解方法在处理呈非正态、多变量、小失效概率以及功能函数非线性的问题时，很难以较低成本获得满意的精度。为克服现有方法的不足，将通用生成函数、自适应细分原理和重要抽样技术相结合，提出结构可靠度求解的自适应细分重要抽样法。根据自适应细分原理，对临界域进行细分，减少离散区间长度，通过递归操作对随机变量进行非均匀自适应细分，得到失效域概率以及细分后的临界域，并由复合运算获得临界域的结构通用生成函数。临界域失效概率由针对域内热点焦元的重要抽样技术获得，失效域概率与临界域失效概率之和即为结构失效概率估计值。算例分析表明，新方法的计算误差明显小于传统方法，同时借助重要抽样技术提高了计算效率。

关键词: 结构可靠度, 通用生成函数, 自适应细分, 临界焦元, 重要抽样