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Abstract Most of the existing methods of brake squeal instability analysis are merely available to handle single type of uncertain case. In this study, an improved unified method is developed for uncertainty quantification, which is capable of handling two types of fuzzy–interval cases. In the first fuzzy–interval case, uncertain parameters of engineering structures are assumed as either fuzzy variables or interval variables, which exist in structures simultaneously and independently. In the second fuzzy–interval case, all uncertain parameters are represented by interval variables, but their lower and upper bounds just can be expressed as fuzzy variables instead of deterministic values. In the proposed method, fuzzy–boundary interval variables are introduced to handle fuzzy–interval uncertainties, and based on which an improved response analysis model is established. In the improved model, the fuzzy–boundary interval variables are firstly converted into interval-boundary variables by level-cut technique. Then by temporarily neglecting boundary uncertainties, the initial interval responses can be approximated via conducting once Taylor series expansion and subinterval analysis. Next, Taylor series expansion and central difference method are combined twice to deal with boundary uncertainties, and the interval responses of the structures with interval-boundary variables are yielded. Finally, the fuzzy–interval responses of the structures are derived on the basis of interval union operation and fuzzy decomposition theorem. The improved method is subsequently extended to quantify the uncertainties in brake squeal instability analysis involving two types of fuzzy–interval uncertainties. The effectiveness of the proposed method on tackling fuzzy–interval problems is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

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. • The dual robust design is proposed. • The dual robust design and failure possibility are considered simultaneously. • The dual uncertain objective with fuzzy random variables is estimated fast. • The possibilistic constraints involving fuzzy randomness are equivalently addressed. • The approach presents good computational accuracy and efficiency. [ABSTRACT FROM AUTHOR]