An exponential normal transformation using the first three moments with application to structural reliability analysis
提出一种显式指数形式的正态变换方法，仅需随机变量的前三阶矩即可实现正态化，克服了现有方法因含根号、分母或对数项导致的数学限制，数值算例表明其适用范围更广且精度更高。
• Provide a practical tool for reliability analysis with unknown distributions. • Proposed normal transformation is formulated in an explicit exponential form. • Obtain the parameters directly using the first three moments without calculations. • Proposed transformation can encompass all possible realizations of random variables. • Numerical examples are illustrated to validate the proposed transformation. In practical engineering, the probability distributions of random variables are often unknown, making normal transformations using Rosenblatt or Nataf transformations unfeasible. To address this issue, the third-moment transformations based only on the first three moments have been proposed for structural reliability analysis. However, the expressions for these third-moment normal transformations involve the square root, denominator term, or logarithmic term, which introduce mathematical constraints and restrict their applicability. To overcome these mathematical constraints, this study proposes an explicit exponential third-moment normal transformation that covers a broad class of random variables. The determination of the proposed normal transformation begins with a predefined exponential form, from which the specific expression is derived based on the Taylor series expansion and the existing normal transformations. Subsequently, the coefficients of this expression are estimated through a trial-and-error process using numerous datasets, which are generated by averaging the results of existing normal transformations across a range of skewness levels. The five numerical examples demonstrate that the proposed exponential normal transformation not only extends the range of applications but also outperforms existing third-moment normal transformations in terms of accuracy.