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Shock and Vibration
Volume 2016 (2016), Article ID 3497468, 13 pages
Research Article

Stability Optimization of a Disc Brake System with Hybrid Uncertainties for Squeal Reduction

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China

Received 2 November 2015; Revised 28 January 2016; Accepted 28 January 2016

Academic Editor: Tai Thai

Copyright © 2016 Hui Lü and Dejie Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A hybrid uncertain model is introduced to deal with the uncertainties existing in a disc brake system in this paper. By the hybrid uncertain model, the uncertain parameters of the brake with enough sampling data are treated as probabilistic variables, while the uncertain parameters with limited data are treated as interval probabilistic variables whose distribution parameters are expressed as interval variables. Based on the hybrid uncertain model, the reliability-based design optimization (RBDO) of a disc brake with hybrid uncertainties is proposed to explore the optimal design for squeal reduction. In the optimization, the surrogate model of the real part of domain unstable eigenvalue of the brake system is established, and the upper bound of its expectation is adopted as the optimization objective. The lower bounds of the functions related to system stability, the mass, and the stiffness of design component are adopted as the optimization constraints. The combinational algorithm of Genetic Algorithm and Monte-Carlo method is employed to perform the optimization. The results of a numerical example demonstrate the effectiveness of the proposed optimization on improving system stability and reducing squeal propensity of a disc brake under hybrid uncertainties.