Reliability analysis methods for mixed uncertainties in structural system with multiple modes

For structural system with multiple modes simultaneously involving random variables, interval variables and fuzzy variables, a logical deduction algorithm is proposed to deal with propagation of uncertainties. Corresponding to assumed membership level in the membership level interval [0,1], the membership interval of fuzzy variables can be obtained. Firstly the fuzzy variables and the corresponding design points that optimize the respective mode will be calculated by iteration. Secondly, with the logical deduction, the interval of upper bound and lower bound of the system reliability with multiple modes can be solved by the fourth moment algorithm based on the point estimate, then the average of the interval will be used to approximate the true value of the upper bound and lower bound. Several numerical examples are presented to demonstrate the proposed method's advantages both in efficiency and accuracy.