An efficient hybrid reliability analysis method for structures involving random and interval variables

This paper presents a hybrid reliability analysis method for structures involving random and interval variables. Firstly, the original performance function is approximated as the product of a series of univariate functions based on the multiplicative dimensional reduction method. Secondly, weight-point estimation is employed to calculate the first and second moments of all univariate functions with random variables. Thirdly, the second-order Taylor expansion is applied to the univariate functions involving interval variables for solving their maximum and minimum values. Lastly, the relationship between the upper and lower bounds of the failure probability and the upper and lower bounds of the product of the interval univariate function is derived. As the upper and lower bounds of the failure probability are derived analytically on the basis of the first two moments obtained by combining the multiplicative dimensional reduction model with the interval of the product of all interval univariate functions, the proposed method avoids the optimization analysis process completely and is very efficient. The accuracy and efficiency of the proposed method are verified by two numerical examples and a practical engineering problem involving finite element analysis.