范文亮, 袁满, 刘润宇, 杨晓阳, 李正良. 基于双变量降维模型和Kriging近似的统计矩点估计法[J]. 工程力学, 2020, 37(12): 171-179. DOI: 10.6052/j.issn.1000-4750.2020.02.0096
引用本文: 范文亮, 袁满, 刘润宇, 杨晓阳, 李正良. 基于双变量降维模型和Kriging近似的统计矩点估计法[J]. 工程力学, 2020, 37(12): 171-179. DOI: 10.6052/j.issn.1000-4750.2020.02.0096
FAN Wen-liang, YUAN Man, LIU Run-yu, YANG Xiao-yang, LI Zheng-liang. POINT ESTIMATION FOR STATISTICAL MOMENTS BASED ON THE BIVARIATE DIMENSION-REDUCTION MODEL AND KRIGING APPROXIMATION[J]. Engineering Mechanics, 2020, 37(12): 171-179. DOI: 10.6052/j.issn.1000-4750.2020.02.0096
Citation: FAN Wen-liang, YUAN Man, LIU Run-yu, YANG Xiao-yang, LI Zheng-liang. POINT ESTIMATION FOR STATISTICAL MOMENTS BASED ON THE BIVARIATE DIMENSION-REDUCTION MODEL AND KRIGING APPROXIMATION[J]. Engineering Mechanics, 2020, 37(12): 171-179. DOI: 10.6052/j.issn.1000-4750.2020.02.0096

基于双变量降维模型和Kriging近似的统计矩点估计法

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

  • 摘要: 对复杂随机系统进行统计矩分析时,双变量降维近似模型一定程度上可以缓解“维数灾难”。但当系统维数较高时,双变量分量函数较多,计算量仍然较大。为此,该文将降维近似和Kriging代理模型有机结合起来,提出了一类高效、合理的改进点估计法。充分考虑函数逼近和数值积分中积分点的特点,提出了“米”字形的选点策略,并基于此发展了双变量分量函数的Kriging近似模型;将此近似模型用于原函数和矩函数的双变量降维近似模型中双变量分量函数的近似,分别建立了基于原函数近似和矩函数近似的统计矩改进点估计法;通过多个算例对该文提出方法进行了效率和精度的分析。算例分析结果表明:基于“米”字形选点策略的双变量分量函数的Kriging近似具有较高的精度;相比于已有的基于双变量降维近似模型的统计矩点估计法,建议方法仅需较少的结构分析即可达到与已有方法相当的精度,能更好地体现精度和效率的平衡。

     

    Abstract: 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.

     

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