A non-probabilistic reliability analysis method with the fuzzy failure criterion

In engineering practice, the failure boundary of structures is not usually distinct due to some ambiguous information, which brings a tricky challenge to reliability assessment. The fuzzy theory is introduced to solve it with the traditional probability assessment method. For the non-probabilistic reliability system, however, this problem tends to be at a dead end because it lacks some necessary probability information. In this study, the nonprobabilistic reliability model with fuzzy failure criterion is established, which involves two different evaluation indices in terms of the limit state surface. Based on this, a corresponding calculation method is proposed to deal with it, and the interval model and the ellipsoid model are shown for instance. In addition, the HRHL-RF method owning strong robustness is utilized to calculate the index of the ellipsoid model. Eventually, an established algorithm frame can achieve the calculation of the unified fuzzy reliability index, and three examples with the classical fuzzy membership functions are computed to show its feasibility and efficiency.