基于Kriging模型和代理抽样的分布参数不确定性灵敏度分析方法

doi:10.3901/JME.2024.08.370

摘要/Abstract

摘要： 针对结构系统输入变量分布参数具有不确定性的情况，为衡量分布参数不确定性对系统输出性能统计特征值的影响，以输出期望和方差为例，建立分布参数对输出性能均值和方差影响的全局灵敏度指标。为克服分布参数灵敏度指标计算量大而导致工程实际难以接受的问题，通过建立分布参数和输出统计特征值之间的Kriging模型，解决分布参数灵敏度分析计算量随输入变量及其分布参数维度增加呈指数形式增长的问题，又引入代理抽样概率密度函数对输入变量进行高效抽样，解除求解输出统计特征值时的计算量对输入变量分布参数维度的依赖性。数值和工程算例结果表明，所提方法能够在保证计算精度的同时，大大降低分布参数灵敏度分析的计算量。

关键词: 分布参数不确定, 灵敏度分析, Kriging代理模型, 代理抽样概率密度函数

Abstract: For structural system involving inputs with distribution parameter uncertainty, sensitivity indices which can evaluate the effect of uncertain distribution parameters on the statistical eigenvalues of the structural output response are firstly established by taking the output expectation and variance as examples. Then, to overcome the problem that the computational cost of the sensitivity indices is normally too prohibitive to be accepted for the engineering problem, a newly efficient algorithm is proposed for sensitivity analysis in the presence of distribution parameters uncertainty. In the proposed algorithm, the Kriging model between the distribution parameters and the statistical eigenvalues of the structural output response are established, which can solve the problem that the computational cost of the sensitivity analysis increases exponentially with the increase of the dimensions of the input variables and their distribution parameters. Furthermore, by introducing a ‘surrogate sampling probability density function (SS-PDF)’ to sample the input variables efficiently in the process of establishing the Kriging model, the dependency of the computational cost of the output statistical eigenvalues on the dimensionality of the distribution parameters of the input variables is further released. The results of numerical and engineering examples show that the proposed methods require substantially less computation effort while ensuring the calculation accuracy.

Key words: distribution parameter uncertainty, sensitivity analysis, kriging model, surrogate sampling probability density function

中图分类号:

TB114

程洪鑫, 李璐祎, 周长聪. 基于Kriging模型和代理抽样的分布参数不确定性灵敏度分析方法[J]. 机械工程学报, 2024, 60(8): 370-383.

CHENG Hongxin, LI Luyi, ZHOU Changcong. Method for Sensitivity Analysis of the Uncertain Distribution Parameters Based on Kriging Model and Surrogate Sampling[J]. Journal of Mechanical Engineering, 2024, 60(8): 370-383.

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