In this paper, an efficient and explicit technique is proposed for transforming correlated non-normal random variables into independent standard normal variables based on the three-parameter (3P) lognormal distribution. In contrast with the classic Nataf transformation, the derived equivalent correlation coefficient in non-orthogonal standard normal space of the proposed transformation is expressed as an explicit formula, thereby avoiding tedious iteration algorithm or multifarious empirical formulas. Meanwhile, the applicable range of the original correlation coefficient is determined based on fundamental properties of the proposed expression of correlation distortion and the definition of correlation coefficient. The proposed transformation requires only the first three moments (i.e., mean, standard deviation, and skewness) of basic random variables, as well as their correlation matrix. Therefore, the proposed transformation can also be applied even when the joint distribution or marginal distributions of the basic random variables are unknown. Several numerical examples are presented to demonstrate the user-friendliness, efficiency, and accuracy of the proposed transformation applied in structural reliability analysis involving correlated non-normal random variables.

本文提出了一种有效且显式的技术，用于基于三参数（3P）对数正态分布将相关的非正态随机变量转换为独立的标准正态变量。与经典的Nataf变换相反，在所提出的变换的非正交标准正态空间中得出的等效相关系数表示为一个显式公式，从而避免了繁琐的迭代算法或多种经验公式。同时，基于所提出的相关失真表达的基本性质和相关系数的定义来确定原始相关系数的适用范围。拟议的转换仅需要前三个矩（即均值，标准差，和偏度），以及它们的相关矩阵。因此，即使基本随机变量的联合分布或边际分布未知，也可以应用所提出的变换。给出了几个数值示例，以证明在涉及相关非正态随机变量的结构可靠性分析中应用的拟议转换的用户友好性，效率和准确性。