A new hybrid uncertainty analysis method and its application to squeal analysis with random and interval variables

A new hybrid uncertainty analysis method with random and interval variables is proposed in this paper. In the proposed method, the uncertain parameters with sufficient information are treated as random variables, while the uncertain parameters with limited information are modeled as interval variables. Both random variables and interval variables can be viewed as special evidence variables. From this special point of view, both random variables and interval variables are represented by equivalent evidence variables in this study, and a unified framework for hybrid uncertainty analysis is developed based on evidence theory and subinterval perturbation technique. The effects of the mixture of random and interval uncertainties on uncertain output are assessed by belief measure and plausibility measure. On the base of the proposed method, the squeal analysis model of automotive disc brakes involving both random and interval uncertainties can be developed. A numerical example of brake squeal analysis is provided to illustrate the effectiveness of the proposed method. The analysis results show that the equivalent evidence variables can be explored to represent random variables and interval variables reasonably and the proposed method has good accuracy and efficiency in the hybrid uncertainty analysis of squeal instability The proposed method gives a unified framework to tackle several types of uncertain cases, and it is quite general and not only limited to the uncertainty analysis of brake squeal. (C) 2017 Elsevier Ltd. All rights reserved.