Abstract: An efficient method for solving the failure probability function was proposed to address the difficulties of solving the failure probability function in reliability optimization design, such as complexity and large amount of computation. The basic idea of the proposed method was to utilize the adaptive Kriging method to construct a local surrogate model of the full space of input variables at the failure boundary. The local surrogate model was then combined with the Monte Carlo simulation method to calculate the failure probability of the structures under the specified distribution parameter samples. The functional relationship between the sample points of the distribution parameters and the structural failure probability was then fitted by the Kriging method. Finalization of the implicit function of the failure probability function expressed in terms of the Kriging model. In order to test the accuracy and efficiency of the proposed method, two examples were given to compare the computational results of the proposed method with those of the existing methods for solving failure probability functions. The results of examples show that the proposed method is suitable for solving complicated functional function problems and significantly reduces the amount of computation while satisfying the accuracy requirements.

Key words: structural reliability, failure probability function, adaptive Kriging method, surrogate model

摘要： 针对可靠性优化设计中失效概率函数求解复杂、计算量大等问题，提出一种求解失效概率函数的高效方法。所提方法的基本思路是利用自主学习Kriging方法构造输入变量全空间在失效边界处的局部代理模型，进而通过该局部代理模型结合Monte Carlo模拟法计算在指定分布参数样本下结构的失效概率，然后基于Kriging方法拟合分布参数样本点与对应结构失效概率之间的函数关系，最终建立用Kriging模型表达的失效概率函数的隐式函数。为了检验所提方法的精度和效率，给出了两个算例，对比了所提方法与已有的求解失效概率函数方法的计算结果。算例结果表明，所提方法适用于求解复杂的功能函数问题，并在满足精度要求的基础上显著降低了计算量。

关键词: 结构可靠性, 失效概率函数, 自主学习Kriging方法, 代理模型