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工程力学  2014 

考虑相关性的Rackwitz-Fiessler随机空间变换方法

DOI: 10.6052/j.issn.1000-4750.2013.04.0353

Keywords: 随机空间变换,Rackwitz-Fiessler方法,Nataf-Pearson方法,等概率变换,线性相关系数

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Abstract:

从新的角度对传统Rackwitz-Fiessler随机空间变换方法(R-F法)进行了多方位的阐释。首先,给出传统R-F法的描述并从几何角度分析R-F法与等概率变换的关系;然后,证明R-F法的正变换过程符合等概率变换而逆变换过程却不符合,但却可看作等概率变换的一次近似;其次,提出一种等价的R-F条件,为清晰的阐释R-F法中变量相关性的变化情况提供新思路;之后,指出R-F法的变量相关性变化情况同Nataf-Pearson方法(N-P法)一致;最后,比较考虑相关性变化的R-F法和N-P法的计算量,指出两者在单个迭代步中计算量基本一致且可通过算法优化实现;另外对R-F法与线性N-P法的也作了比较。算例表明:正确考虑相关性变化的R-F法可以得到同N-P法一致的结果。

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