基于新学习函数与收敛准则的改进AK-MCS方法

Improved AK-MCS method based on new learning function and convergence criterion

在对AK-MCS方法进行误差分析的基础上,结合Kriging模型更新对误差的影响,提出了一种新的学习函数及收敛准则.首先,基于Kriging模型的统计特性,进行AK-MCS方法预测失效概率的误差分析;然后,根据训练样本更新对误差贡献的影响,给出考虑区域影响的学习函数,并根据误差贡献的影响差异提出训练样本选择的两步法;接着,综合考虑可靠度分析精度与模型收敛的稳定性,提出一种兼顾误差与失效概率的收敛准则,形成改进的AK-MCS可靠度分析方法;最后,通过4个算例验证了本文方法适用于处理高度非线性、多失效域、较高维度以及有限元工程问题,并且具有较高的精度、效率与稳定性.

On the basis of error analysis of the AK-MCS method and considering the impact of Kriging model updates on errors,a new learning function and convergence criterion were proposed.Firstly,according to statistical properties of Kriging model,the error analysis of the AK-MCS method for predicting failure probability was performed.Secondly,due to influence of adding training sample on the error contribution,a learning function considering regional influence was proposed,and then a two-step method for selecting training sample was presented,in which the differences of both deterministic error and statistical one for different training samples were involved.Thirdly,considering accuracy of reliability and stability of model convergence,a convergence criterion was proposed.Combining the new strategy for selecting training sample and the new convergence criterion,an improved AK-MCS for reliability analysis was presented.Finally,several examples were employed to verify the applicability of the proposed method for problems concerning high nonlinearity,multiple failure domains higher dimensionality and finite element engineering problems,what is more,the results showed that the method is of high accuracy,efficiency and stability.