POINT ESTIMATION FOR STATISTICAL MOMENTS BASED ON THE BIVARIATE DIMENSION-REDUCTION MODEL AND KRIGING APPROXIMATION

When estimating statistical moments for complex random systems, the bivariate dimension-reduction method can alleviate the curse of dimension to some extent. However, there are many bivariate component functions for high-dimension random systems. It makes the estimation unfeasible. An efficient point estimation for moments is proposed, in which the dimension-reduction model is modified by the Kriging approximation model. Considering the characteristics of function approximation and the abscissas of numerical integration, a "star" shape point-selection strategy is proposed. Based on this point-selection strategy, a Kriging approximation model of the bivariate component function is developed. By replacing each bivariate component function in the bivariate dimension-reduction model for the original function or its moment function with their corresponding Kriging approximations, two modified methods for the moment estimation are presented. The efficiency and accuracy of the proposed methods are verified by several examples. The results show that the Kriging approximation of the bivariate component function based on the "star" shape point-selection strategy has higher accuracy. Correspondingly, the statistical moment estimation of the proposed methods has comparable accuracy with the existing methods, while fewer function evaluations are required.