Uncertainty quantification of squeal instability under two fuzzy-interval cases

Automotive brake systems are always subjected to various kinds of uncertain factors and the uncertainty analyses of brake squeal have been investigated for decades. However, most of the existing methods of squeal analysis are merely effective in tackling single uncertain case. In this study, a unified method is developed for the uncertainty quantification of disc brake squeal, which is able to handle two fuzzy-interval cases. Due to subjective opinions or limited data, in the first fuzzy-interval case, the uncertain brake parameters are expressed as either fuzzy variables or interval variables, which exist in brake systems simultaneously and independently; whereas, the uncertain brake parameters are all treated as interval variables, but their lower and upper bounds are expressed as fuzzy variables in the second fuzzy-interval case. In the developed method, the first fuzzy-interval case is equivalently treated as a special case of the second one. On the basis of fuzzy-boundary interval variables, an uncertainty quantification model under two fuzzy-interval cases is established, in which the unified uncertain response is computed with the aid of the combination of level-cut strategy, Taylor series expansion, subinterval analysis and Monte Carlo simulation. The unified method is then extended to quantify the uncertainty in disc brake squeal analysis. The studies of several numerical examples demonstrate that the proposed method is able to quantify the uncertainty of squeal instability effectively. In addition, the proposed method can also help to carry out reliability analysis and optimization to reduce the likelihood of squeal occurrence.