A novel evidence-based fuzzy reliability analysis method for structures

Epistemic uncertainties always exist in engineering structures due to the lack of knowledge or information, which can be mathematically described by either fuzzy-set theory or evidence theory (ET) In this work, the authors present a novel uncertainty model, namely evidence-based fuzzy model, in which the fuzzy sets and ET are combined to represent the epistemic uncertainty. A novel method for combining multiple membership functions and a corresponding reliability analysis method is also developed. In the combination method, the combined fuzzy-set representations are approximated by the enveloping lines of the multiple membership functions (smoothed by neglecting the valleys in the membership functions curves) and the Murphy’s average combination rule is applied to compute the basic probability assignment for focal elements. Then, the combined membership function is transformed to the equivalent probability density function by means of a normalizing factor. Finally, the Markov Chain Monte Carlo (MCMC) subset simulation method is used to solve reliability by introducing intermediate failure events. A numerical example and two engineering examples are provided to demonstrate the effectiveness of the proposed method.