Iteration algorithm for propagation of mixed uncertainties in reliability analysis

For structural reliability problems simultaneously involving random variables, interval variables and fuzzy variables, an iteration algorithm is proposed to deal with the propagation of uncertainties. Corresponding to assumed membership value in the membership level interval [0,1], the membership interval of fuzzy variables can be obtained. After the fuzzy variables and the interval variables' effects on the extreme value of performance function are alternately and iteratively analyzed with the random variables' effects on statistical properties of the performance function, converged design point can be calculated, and the reliability can be as well calculated by the fourth moment algorithm based on the point estimate method. Finally the membership function of the reliability can be solved. Owing to the faster convergence of the iteration algorithm, the efficiency of the proposed algorithm is highly improved compared to the conventional numerical simulation method. And the adoption of fourth moment method proves much better in accuracy than only applying first order reliability method in the iteration algorithm. After the basic concept and process of the proposed algorithm is detailed, several numerical and engineering examples are studied to demonstrate its advantage both in efficiency and accuracy.