Reliability analysis of structures with fuzzy and non-probabilistic hybrid variables

For the reliability analysis of structures in the case of coexistence of fuzzy and non-probabilistic uncertainties, the hybrid analysis model was transformed into non-probabilistic analysis models at different membership values distributed in the interval [0,1] continuously based on the decomposition principle of fuzzy mathematics theories. An algorithm for determining the minimum/maximum of the structural performance function was presented to overcome the complexity in calculating the non-probabilistic reliability based on the optimization strategy dimension by dimension, by which the determination of the extreme values was converted to that of the extreme point vectors of the performance function. The quantification of the fuzziness in structural reliability was accomplished with the membership function of the structural reliability obtained by traversing the membership value in the interval[0,1]. The reasonability of the presented method was proved by two engineering applications and the merits of high accuracy and efficiency suggest a feasible way for the reliability analysis and optimization of complicated engineering structures.