Saddlepoint approximation based line sampling method for uncertainty propagation in fuzzy and random reliability analysis

Abstract

For structural system with random basic variables as well as fuzzy basic variables, uncertain propagation from two kinds of basic variables to the response of the structure is investigated. A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation (SA) based line sampling method. In the presented method, the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership functions. In the value domain of the fuzzy basic variables corresponding to the given membership level, bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random variables. In this way the uncertainty of the basic variables is propagated to the safety measurement of the structure, and the fuzzy membership function of the reliability is obtained. Compared to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables, the presented method can considerably improve computational efficiency with acceptable precision. The presented method has wider applicability compared to the transformation method, because it doesn’t limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing process. Additionally, the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable, which isn’t suitably approximated by the existing transformation methods. Several examples are provided to illustrate the advantages of the presented method.