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工程结构的功能函数大多数具有隐式非线性程度高的特点,且失效概率较小,需要复杂的有限元分析计算。针对工程实际中大量存在的小失效概率问题,本文提出了基于主动学习Kriging模型和子集模拟方法相结合的可靠度分析方法——AK-SS。AK-SS方法有子集模拟求解小失效概率和主动学习的Kriging模型代替真实功能函数的优势。该方法首先采用Kriging模型代替真实功能函数,通过主动学习方法逐步扩充实验设计点,逐步改善Kriging模型的精度;然后利用子集模拟方法的基本思路,通过引入合理的中间失效事件计算小失效概率。结果表明,AK-SS方法在保证结果精度的同时减少了功能函数的评估次数,对于工程实际中具有隐式功能函数的小失效概率计算问题具有较强的应用前景。
Most of the structural function functions have the characteristics of high degree of implicit nonlinearity, and the failure probability is small, which requires complex finite element analysis and calculation. Aiming at the problem of small failure probability existing in engineering practice, this paper proposes a reliability analysis method based on active learning Kriging model and subsets simulation method - AK-SS. AK-SS method has the advantages of subset simulation to solve the small failure probability and active learning Kriging model instead of the real function. Firstly, the Kriging model was used instead of the real function, and the active learning method was used to gradually expand the experimental design points to improve the accuracy of the Kriging model step by step. Then, the basic idea of the subset simulation method was used to calculate the probability of small failure by introducing reasonable intermediate failure events. The results show that the AK-SS method can reduce the number of evaluation of functional functions while ensuring the accuracy of the results and has a strong application prospect for the calculation of small failure probability with implicit functional in engineering practice.