Universal Reliability Method for Structural Models with Both Random and Fuzzy Variables

The conventional probabilistic reliability model for structures is based on the "probability assumption" and "binary-state assumption". These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the "mixed probability and possibility assumption" and "fuzzy state assumption". The presented universal structural reliability model can be regarded as the unification of probability reliability theory and possibility reliability theory. The universal reliability model can degenerate into probabilistic reliability model or possibility reliability model spontaneously for pure random basic variables or fuzzy basic variables. The Monte-Carlo simulation combing with optimization method is applied to calculate the failure probability of the structures. Numerical examples revealed the feasibility of the proposed reliability model for structures.