一种基于失效概率相对误差估计的可靠性分析方法

为更高效地分析复杂机械结构的可靠性，提出了一种新的基于Kriging模型和失效概率相对误差估计的自适应分析方法.采用泊松二项分布的近似正态分布推导了样本符号不确定区域内真实失效样本数的取值范围，并通过引入比例因子重新定义取值下限，以确保真实失效样本数准确落在确定的区间内，进而给出了一种更精确的失效概率相对误差的估计.采用学习函数U实现自适应试验设计.通过两个算例验证失效概率相对误差估计和自适应分析方法的准确性、通用性及高效性，结果表明:本文方法不仅能准确估计失效概率的相对误差，而且显著减少了功能函数的调用次数.

A Reliability Analysis Method Based on Relative Error Estimation of Failure Probability

To analyze the reliability of complex mechanical structures more efficiently， an innovative adaptive analysis method is proposed based on the Kriging model and the relative error estimation of failure probability. The range of the number of actual failure samples in the region where the signs of samples are uncertain is derived using the normal distribution that approximates to the Poisson binomial distribution. The lower limit of the range is redefined by introducing a scale factor to ensure that the number of actual failure samples can accurately fall within the range. Then， a more accurate estimation of relative error of failure probability is provided. The adaptive design of experiments is implemented by the learning function U. Two examples are employed to verify the accuracy， generality and efficiency of the presented relative error estimation of failure probability and the adaptive analysis method. The results indicate that the as-introduced approach can not only accurately estimate the relative error of failure probability， but also significantly decrease the calls to performance function.