Safety analysis for the posfust reliability model under possibilistic input and fuzzy state

The structural input can be simply classified as probabilistic one and possibilistic one, and the structural state can be divided into binary state and fuzzy state. Combining different kinds of structural input and state, the reliability analysis model can be sorted into four types, i.e., the one based on probabilistic input and binary state (probist), the one based on probabilistic input and fuzzy state (profust), the one based on possibilistic input and binary state (posbist) and the one based on possibilistic input and fuzzy state (posfust). Various researches about the former three reliability models have been developed, whereas the study on the posfust reliability model is rare. Due to this fact, the fuzzy failure credibility is established to measure the safety degree of the posfust model, and it is a fuzzy safety index defined by the definite integral of the failure membership function. Then, to estimate the defined fuzzy failure credibility efficiently, two adaptive Kriging based methods are proposed. The first one is based on the definition of the fuzzy failure credibility, in which the lower and upper bounds of performance function are mainly concerned by the strategy of constructing the Kriging model. The second one combines the adaptive Kriging and fuzzy simulation algorithm, and it is based on the relationship between the defined fuzzy failure credibility and the failure credibility in the posbist reliability model. Several examples are provided to verify the rationality of the established fuzzy failure credibility, and the efficiency and accuracy of the proposed methods.