Possibility-Based Design Optimization Method for Design Problems with both Statistical and Fuzzy Input Data

The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with the statistical random and fuzzy input variables simultaneously. For the design problem with both statistical random and fuzzy input variables, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. For fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For statistical random variable, the membership function that yields least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input variables is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.