An efficient approach for the design optimization of dual uncertain structures involving fuzzy random variables

Abstract In engineering practice, the parameters of uncertain structures are often quantified as random variables, but their distribution parameters are appropriately modeled as fuzzy variables rather than deterministic values in some special engineering cases. To address such dual uncertain cases, an efficient approach is proposed for the possibility-based robust design optimization (PBRDO) of dual uncertain structures with fuzzy random variables (FRVs), in which the so-called dual robust design and the failure possibility are taken into account simultaneously. In the proposed approach, FRVs are firstly used to describe dual uncertainties and a design optimization model with FRVs is constructed. The structural responses involving FRVs are calculated and expressed in the forms of fuzzy means and fuzzy variances. To perform dual robust design, the weighted sum of the expectations and entropies of the fuzzy means and fuzzy variances of interested response is taken as optimization objective. The constraints involving dual uncertainties are established in the possibility context based on the concept of failure possibility. The established PBRDO model is a complicated nested problem. Secondly, the random moment-interval perturbation center difference method (RM-IPCDM) is derived to calculate the optimization objective efficiently. Next, the target performance approach (TPA) is employed to simplify the possibilistic constraints, and the obtained equivalent constraints can also be efficiently solved by RM-IPCDM. The nested PBRDO model with FRVs is finally simplified into a single-loop one with the aid of RM-IPCDM and TPA. Three dual uncertain numerical examples involving FRVs are given to demonstrate the feasibility of the proposed approach.