An Equivalent Method for Fuzzy Reliability Analysis

Abstract

Traditional structural reliability analysis reveals that the structure is safe if the stress is less than the strength, otherwise the structure fails. However there is a doubt what will happen if the stress is slightly less or more than the strength. Additionally, the situation will be more complex if the failure threshold is also uncertain with respect to time. In this regard, fuzzy reliability theory has been developed and using $\lambda$ -level cutting method can deal with this problem well. But sometimes it is computationally expensive. So this paper proposed a novel reliability analysis method based on the concept of entropy to calculate the fuzzy reliability. By means of the invariance of entropy, that is, fuzzy entropy of the original fuzzy variable equals to probabilistic entropy of the equivalent random variable, fuzzy variable can be transformed into normal random variable. Accordingly, fuzzy reliability analysis is turned into classical reliability analysis, and the well-established theories of probability can be used to calculate the structural reliability. The rationality of the equivalent transformation is also proved in this paper. The proposed method is not only applicable to normal membership function but applicable to any other type of membership functions as well. Two example problems are analyzed to illustrate the applicability of the proposed method. Also $\lambda$ -level cutting method is used for comparison. From the obtained results it can be concluded that the proposed method owns higher efficiency with almost the same accuracy.