An improved method for fuzzy–interval uncertainty analysis and its application in brake instability study

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.