一种用于结构可靠性分析的Kriging学习函数

摘要

To improve the efficiency of Kriging based structural reliability analysis, a new adaptive learning function VF is proposed after analyzing the weakness of existing learning functions. The learning function VF combines variance and joint probability density function both of which can affect the accuracy of estimated failure probability. This method can avoid wasting samples caused by sampling in the area where the value of joint probability density function is low, and increase learning efficiency. Firstly, a large number of candidate sample points are generated by Monte Carlo method, and the point that maximizes the proposed learning function value is defined as the best one. Secondly, a suitable stopping condition is proposed, which can not only ensure the accuracy of failure probability but also reduce iterations dramatically. Finally, two numerical examples are analyzed to show that the proposed method requires fewer calls to the performance function than other methods and it has high convergence speed, good accuracy and stability. And the method can be used in engineering problems with implicit and high nonlinear performance function.%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.