Abstract
The fuzzy safety index (FSI) is put forward in this article under the assumption that the fuzzy inputs are independently and identically distributed. Then, the failure possibility-based constraints in original possibility-based design optimization (PBDO) are equivalently converted to the FSI-based constraints, and the fuzzy safety index approach (FSIA) is presented for solving PBDO. Based on the definition of FSI and the relationship between FSI and the fuzzy most possible failure point (F-MPP), the analytical expression is derived for the local sensitivity of FSI (LS-FSI) with respect to the design parameters, and it is used to provide the exact gradient for FSIA. An efficient iterative method is proposed for solving the FSI, which can estimate LS-FSI as a by-product of analysing the FSI without any additional computational cost. Finally, five numerical examples are demonstrated to show the feasibility of the derived analytical expression of LS-FSI and the proposed FSIA for PBDO.
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