Normalization of correlated random variables in structural reliability analysis using fourth-moment transformation

Zhao Hui Lu, Chao Huang Cai, Yan Gang Zhao, Yu Leng, You Dong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

31 Citations (Scopus)


In this paper, a fourth-moment transformation technique is proposed to transform correlated nonnormal random variables into independent standard normal ones. The procedure mainly includes two steps: First, the correlated nonnormal random variables are transformed into correlated standard normal ones using the fourth-moment transformation, where the complete mathematical formula of the correlation coefficient in standard normal space, i.e., equivalent correlation coefficient, is proposed and the upper and lower bounds of original correlation coefficient are identified to ensure the transformation executable; Second, the correlated standard normal random variables are transformed into independent standard normal ones using Cholesky decomposition. For the cases of original correlation matrix with very small eigenvalues, the equivalent correlation matrix might become a nonpositive semidefinite matrix. A recently developed method for solving the problem is adopted to make Cholesky decomposition ready. A first-order reliability method (FORM) for structural reliability analysis involving correlated random variables is developed using the proposed transformation technique. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method for structural reliability assessment considering correlated random variables.

Original languageEnglish
Article number101888
JournalStructural Safety
Publication statusPublished - Jan 2020


  • Correlated random variables
  • Equivalent correlation coefficient
  • Fourth-moment transformation
  • Normal transformation
  • Structural reliability

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Safety, Risk, Reliability and Quality


Dive into the research topics of 'Normalization of correlated random variables in structural reliability analysis using fourth-moment transformation'. Together they form a unique fingerprint.

Cite this