基于优化样本点的双重Kriging模型的重要性测度求解方法

A Double Kriging Model Method Based on Optimization Sample Points for Importance Measure Analysis

针对工程实际中极限状态函数往往是隐式的问题,提出了基于优化样本点的双重Kriging模型的重要性测度求解方法。该方法首先以少量初始样本点建立基本变量与响应值间的Kriging代理模型,通过全局优化的方法寻优找到Kriging预测值不确定性较大的点,并将其加入到初始样本点,从而在尽量少样本点的情况下建立满足精度的Kriging代理模型。该方法将基本变量与功能函数值以及基本变量与条件失效概率间的隐式关系以Kriging代理模型替代,在保证精度的情况下大大降低了矩独立的基本变量对失效概率重要性测度求解过程的计算量,数值算例和工程算例说明了该方法的工程适用性和可行性。

For the engineering problems involving implicit limit state functions, a double Kriging model method based on optimization sample points for importance measure analysis is discussed in this paper. Firstly, in this method, a small amount of initial sample points are employed to build the Kriging surrogate model which relates the basic variables to the response. Then the subsequent points with relatively high uncertainty can be added to the sam- ple points with global optimization method. Finally, the Kriging surrogate model can give fairly good accuracy with a minimum number of sample points. The relationship between the basic variables and the response function and that between the basic variables and the conditional probability of failure are substituted by Kriging models ; so the com- putation cost of the importance measure is reduced largely. To illustrate the engineering applicability and feasibility of the method, numerical and engineering examples are provided and discussed.