基于Kriging和Monte Carlo的动态可靠性算法

Time-Dependent Reliability Algorithm Based on Kriging and Monte Carlo

首次穿越法可以得到失效概率随时间的变化,但是计算复杂提高计算成本.拟静态法计算量较小但是只能得到给定时间段对应的失效概率值,不能得到其变化趋势.针对以上问题,本文结合Kriging模型和Monte Carlo方法提出一种动态可靠性分析方法AK-MCS-T.AK-MCS-T即拥有拟静态法计算量小的优点又可以给出失效概率随时间变化情况.为提高Kriging模型精度,AK-MCS-T提出一种新的选点准则.新的选点准则不仅考虑到样本点处基于Kriging模型的响应估值符号判断错误的概率,还考虑了该样本点对应的概率密度.同时,为保证方法计算结果的准确性,AK-MCS-T提出了新的学习停止条件.最后通过腐蚀梁结构和悬臂管结构证明了新方法的高效性和准确性.

The first outcrossing method can get the change of failure probability with time,but the calculation is complex and may call for more cost.The quasi-static method requires a smaller amount of calculation,but it can only get the failure probability value corresponding to a given period of time,and cannot obtain its change trend.In view of the above problems,AK-MCS-T,a time-dependent reliability analysis method is proposed by combining the Kriging model and the Monte Carlo method.It not only has the advantage of small calculation amount of the quasi-static method,but also can give the change of failure probability with time.AK-MCS-T proposes a new selection criterion for the Kriging model which not only considers the probability of wrong judgment of response evaluation value based on the Kriging model at a sample point,but also considers the probability density corresponding to this sample point.At the same time,a new learning stopping condition is proposed to ensure the accuracy of AK-MCS-T.Finally,the effectiveness and accuracy of the new method are proved by two examples:acorroded beam structure and a cantilever tube structure.