A unified method and its application to brake instability analysis involving different types of epistemic uncertainties

The key idea of the proposed method is the use of the equivalent variables named as evidence-based fuzzy variables, which are special evidence variables with fuzzy focal elements. On the basis of the equivalent variables, an uncertainty quantification model is established, in which the unified probabilistic information related to the uncertain responses of engineering systems can be computed with the aid of the fuzziness discretization and reconstruction, the belief and plausibility measures analysis, and the interval response analysis. Monte Carlo simulation is presented as a reference method to validate the accuracy of the proposed method. The proposed method then is extended to perform squeal instability analysis involving different types of epistemic uncertainties. To illustrate the feasibility and effectiveness of the proposed method, seven numerical examples of disc brake instability analysis involving different epistemic uncertainties are provided and analyzed. By conducting appropriate comparisons with reference results, the high accuracy and efficiency of the proposed method on quantifying the effects of different epistemic uncertainties on brake instability are demonstrated.