吴帅兵, 李典庆, 周创兵. 结构可靠度分析中变量相关时三种变换方法的比较[J]. 工程力学, 2011, 28(5): 41-048,.
引用本文: 吴帅兵, 李典庆, 周创兵. 结构可靠度分析中变量相关时三种变换方法的比较[J]. 工程力学, 2011, 28(5): 41-048,.
WU Shuai-bing, LI Dian-qing. COMPARISON AMONG THREE TRANSFORMATION METHODS FOR STRUCTURAL RELIABILITY ANALYSIS WITH CORRELATED VARIABLES[J]. Engineering Mechanics, 2011, 28(5): 41-048,.
Citation: WU Shuai-bing, LI Dian-qing. COMPARISON AMONG THREE TRANSFORMATION METHODS FOR STRUCTURAL RELIABILITY ANALYSIS WITH CORRELATED VARIABLES[J]. Engineering Mechanics, 2011, 28(5): 41-048,.

结构可靠度分析中变量相关时三种变换方法的比较

COMPARISON AMONG THREE TRANSFORMATION METHODS FOR STRUCTURAL RELIABILITY ANALYSIS WITH CORRELATED VARIABLES

  • 摘要: 介绍了Orthogonal变换、Rosenblatt变换和Nataf变换三种变换方法的基本原理,并比较了三种变换方法的优缺点及其适用范围。采用算例详细地比较了三种变换方法对可靠度结果的影响。结果表明,Nataf变换和Orthogonal变换的根本区别在于Nataf变换考虑了相关变量变换到相关标准正态空间后相关系数的变化,两种变换可靠指标的差值与变量的变异系数、变量间相关系数以及变量的分布类型都有关系,变量变异系数的影响尤为明显。采用FORM方法计算可靠指标时,Rosenblatt变换的不同变量顺序的可靠指标是不同的。当变换后的独立标准正态空间中功能函数曲线或曲面验算点处非线性程度很高时,采用三种变换时,FORM方法均不能准确地估计可靠指标。鉴于Nataf变换同时具有计算精度高和适用范围广两个优点,结构可靠度计算时宜优先采用。

     

    Abstract: This paper aims to compare three most representative transformation methods, namely, Orthogonal transformation, Rosenblatt transformation, and Nataf transformation, for structural reliability analysis with correlated variables. Firstly, the above three transformation methods are introduced. Then, the merits and applicable conditions for the considered three methods are compared. Finally, three examples are employed to compare the reliability results using the three transformation methods. The results indicate that the essential difference between the Nataf transformation and the Orthogonal transformation is that the former can take the reduced covariance matrix of correlated standard normal variables into consideration. The difference between the reliability indexes for the Nataf transformation and the Orthogonal transformation depends on the coefficients of variation, correlation coefficients, and distribution types associated with input variables, especially for coefficients of variation of the input variables. For different orderings of input variables, the reliability indexes using the Rosenblatt transformation can differ significantly when FORM is used to calculate the reliability index. After transformed into independent standard normal space using the considered three transformation methods, the performance function becomes highlynonlinear, which further impair the accurate estimation of the reliability index when FORM is used. It is recommended that the Nataf transformation be used for reliability analysis involving correlated input variables due to its accuracy and applicability.

     

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