COMPARISON AMONG THREE TRANSFORMATION METHODS FOR STRUCTURAL RELIABILITY ANALYSIS WITH CORRELATED VARIABLES

This paper aims to compare three most representative transformation methods, namely, Orthogonal transformation, Rosenblatt transformation, and Nataf transformation, for structural reliability analysis with correlated variables. Firstly, the above three transformation methods are introduced. Then, the merits and applicable conditions for the considered three methods are compared. Finally, three examples are employed to compare the reliability results using the three transformation methods. The results indicate that the essential difference between the Nataf transformation and the Orthogonal transformation is that the former can take the reduced covariance matrix of correlated standard normal variables into consideration. The difference between the reliability indexes for the Nataf transformation and the Orthogonal transformation depends on the coefficients of variation, correlation coefficients, and distribution types associated with input variables, especially for coefficients of variation of the input variables. For different orderings of input variables, the reliability indexes using the Rosenblatt transformation can differ significantly when FORM is used to calculate the reliability index. After transformed into independent standard normal space using the considered three transformation methods, the performance function becomes highlynonlinear, which further impair the accurate estimation of the reliability index when FORM is used. It is recommended that the Nataf transformation be used for reliability analysis involving correlated input variables due to its accuracy and applicability.