一种用于结构可靠性分析的Kriging学习函数

发布时间：2018-10-18 14:54

【摘要】：为提高基于Kriging模型的结构可靠性分析方法的效率,分析现有学习函数的不足,提出一种新的自适应学习函数VF.该学习函数同时考虑学习点的Kriging方差和联合概率密度函数值对失效概率估计精度的影响,避免对概率密度函数值过小的区域抽样造成的样本点浪费,提高了学习效率.根据Monte Carlo方法生成大量候选样本点,定义学习函数最大值点为最佳样本点;提出一种适合该学习函数的学习停止条件,既保证失效概率的精度又保证学习选点次数较少;分析两个数值算例.结果表明:与其他方法相比,所提出方法能够在较少样本数量的情况估计出较准确的失效概率值,其在迭代收敛速度、准确性及稳定性方面都具有较好的效果,且该方法能够应用于工程中隐式且非线性程度较高情况.
[Abstract]:In order to improve the efficiency of structural reliability analysis method based on Kriging model and analyze the deficiency of existing learning function, a new adaptive learning function VF. is proposed. The learning function takes into account the influence of the Kriging variance of the learning point and the value of the joint probability density function on the estimation accuracy of the failure probability. It avoids the waste of the sample points caused by the sampling of the region where the probability density function value is too small and improves the learning efficiency. According to the Monte Carlo method, a large number of candidate sample points are generated, and the maximum point of learning function is defined as the best sample point, and a learning stopping condition suitable for the learning function is proposed, which ensures both the accuracy of failure probability and the number of learning points selection. Two numerical examples are analyzed. The results show that compared with other methods, the proposed method can estimate more accurate failure probability values in the case of fewer samples, and has better results in terms of iterative convergence speed, accuracy and stability. The method can be applied to the case of high nonlinear degree and implicit expression in engineering.
【作者单位】：东北大学机械工程与自动化学院;
【基金】：国家科技重大项目(2013ZX04011-011)
【分类号】：TB114.3

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