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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。
In a new perspective, the traditional Rackwitz-Fiessler method for random space transformation (R-F method) is explained in many aspects. First of all, the description of the traditional RF method is given and the relationship between the RF method and the equal-probability transform is analyzed from the geometrical point of view. Then, it is proved that the positive transform process of the RF method conforms to the equal-probability transform and the inverse transform process does not conform, Secondly, an equivalent RF condition is proposed to provide a new idea for the clear explanation of the change of the correlation of the variables in the RF method. After that, it is pointed out that the variation of the correlation of the variables in the RF method is the same as that of the Nataf-Pearson method (NP method). Finally, the computational complexity of the RF method and the NP method considering the correlation change is compared. It is pointed out that the computations of the two methods are basically the same in a single iteration step and can be optimized by the algorithm. In addition, Also made a comparison. The example shows that the R-F method, which correctly considers the change of correlation, can obtain the same result as the N-P method.