应用数学和力学2025，Vol.46Issue(7)：855-866,12.DOI:10.21656/1000-0887.450093
结构非Gauss随机响应分析的混沌响应面法研究
A Chaotic Response Surface Method for Non-Gaussian Stochastic Analysis of Structural Responses
摘要
Abstract
A chaotic response surface method was proposed to improve the computational efficiency and accu-racy of the traditional response surface method for stochastic analysis of structural responses involving non-Gaussian random variables.Firstly,the non-Gaussian response variable was expanded by a hybrid generalized polynomial chaos constructed according to the probability distribution function types of the basic random varia-bles.Secondly,the candidate probability collocation points in the non-Gaussian probability space were deter-mined through the combination of the roots of the 1D generalized polynomial chaos with the next higher order,then the probability optimal collocation points in the non-Gaussian probability space were picked out based on the full row rank principle of the coefficient matrix.Finally,the unknown coefficients of the proposed response surface were determined by means of the least squares method.Comparison of examples shows that,the pro-posed method requires fewer collocation points and lower expansion orders,and achieves higher calculation ac-curacy and efficiency than those of the traditional response surface methods.关键词
响应面法/广义混沌多项式/非Gauss/最优概率配点Key words
response surface method/generalized polynomial chaos/non-Gaussian/optimal probability collo-cation point分类
建筑与水利引用本文复制引用
李朝阳,许玉佼,杨绿峰..结构非Gauss随机响应分析的混沌响应面法研究[J].应用数学和力学,2025,46(7):855-866,12.基金项目
国家自然科学基金(重点项目)(51738004) （重点项目）
广西科技计划项目(桂科AD23026265) （桂科AD23026265）
