胡 冉, 李典庆, 周创兵, 陈益峰. 基于随机响应面法的结构可靠度分析[J]. 工程力学, 2010, 27(9): 192-200.
引用本文: 胡 冉, 李典庆, 周创兵, 陈益峰. 基于随机响应面法的结构可靠度分析[J]. 工程力学, 2010, 27(9): 192-200.
HU Ran, LI Dian-qing, ZHOU Chuang-bing, CHEN Yi-feng. STRUCTURAL RELIABILITY ANALYSIS USING STOCHASTIC RESPONSE SURFACE METHOD[J]. Engineering Mechanics, 2010, 27(9): 192-200.
Citation: HU Ran, LI Dian-qing, ZHOU Chuang-bing, CHEN Yi-feng. STRUCTURAL RELIABILITY ANALYSIS USING STOCHASTIC RESPONSE SURFACE METHOD[J]. Engineering Mechanics, 2010, 27(9): 192-200.

基于随机响应面法的结构可靠度分析

STRUCTURAL RELIABILITY ANALYSIS USING STOCHASTIC RESPONSE SURFACE METHOD

  • 摘要: 提出了考虑变量间相关性的随机响应面法,采用正交变换解决随机响应面法输入随机变量间相关性问题。推导了4阶和5阶Hermite随机多项式展开的解析表达式。编写了基于C#语言的随机响应面法计算程序。最后采用算例证明了随机响应面法在结构可靠度分析中的有效性。结果表明,提出的随机响应面法能够有效地分析输入随机变量间相关性的可靠度问题。3阶随机响应面法的计算精度在大多数情况下可以满足结构可靠度分析的需要,而且计算效率较高。但是随着变量间相关性的增加,4阶或5阶随机响应面法才能保证足够的计算精度。概率配点数目为随机多项式待定系数数目的两倍并不总能保证足够的计算精度,一般来说,配点数目要大于两倍待定系数的个数才能保证随机响应面法足够的计算精度。

     

    Abstract: This paper aims to propose a stochastic response surface method considering correlated input random variables. The orthogonal transform is adopted to treat the correlated random variables in stochastic response surface method. Explicit polynomials are derived for the forth-order and fifth-order Hermite polynomial chaos expansions of random variables. A C#-language based computer program WHUSRSM (Wuhan University Stochastic Response Surface Method) is developed. Four examples are selected to illustrate the application of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can estimate the structural reliability involving correlated random variables efficiently. A third-order stochastic response surface method is reasonably accurate to calculate failure probabilities between 10-3 and 10-4. However, a fourth-order or fifth-order Hermite polynomial chaos expansions should be used for cases with high dependency between input random variables. The number of collocation points equaling twice the number of unknown coefficients does not ensure the accuracy. In general, it is recommended that the number of collocation points should be at least two times of the number of unknown coefficients of the Hermite polynomial chaos expansion.

     

/

返回文章
返回