Structural reliability analysis with fuzzy random variables using error principle

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve the accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of error propagation. Firstly, fuzzy variables are transformed into uncertain interval variables according to the fuzzy decomposition theorem. Secondly, by using the error transfer principle, the sigk. function is introduced into the reliability function to approximate the step function, and a structural reliability error analysis model based on the direct integration method is established. On this basis, the equivalent error of the fuzzy variable is determined by traversing the interval value of the membership function at [0, 1] level cut set, and then the structural reliability interval values corresponding to each cut set are obtained. The examples are investigated to demonstrate the efficiency and accuracy of the proposed method, which provides a feasible way to analyze and calculate the structural reliability with uncertain variables such as fuzzy random variables, random variables and fuzzy variables.