In real world application of structural reliability analysis some random variables contains two types of random and epistemic uncertainty, while in classic methods of structural reliability only the random uncertainty is considered completely. Therefore in order to have a reliable estimation of structural safety, random variables should cover both random and epistemic uncertainty. In this paper, modeling of epistemic uncertainty of random variables has been brought in to focus. Hybrid random variables are simulated using fuzzy numbers. A new alpha level set optimization approach applying particle swarm optimization technique was addressed in order to determine the minimum and the maximum members of reliability index interval. Importance sampling technique was used for reliability analysis to decrease the computational effort. Three numerical examples were given to illustrate the accuracy and efficiency of the proposed method. Results showed that the proposed method was more efficient compared to the alternative search approaches thorough low computational burden.
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