Optimization design of a disc brake system with hybrid uncertainties

• Uncertainties are taken into account for brake squeal reduction.
• Hybrid uncertain model is introduced to deal with the brake uncertainties.
• The optimization approach based on reliability and confidence interval is proposed.

Squeal reduction of disc brake systems have been extensively investigated for both academic and industrial purposes. However, most of the existing optimization designs of squeal reduction are based on deterministic approaches which have not considered the uncertainties of material properties, loading conditions, geometric dimensions, etc. In this paper, a hybrid probabilistic and interval model is introduced to deal with the uncertainties existing in a disc brake system for squeal reduction. The uncertain parameters of the brake system with enough information are treated as probabilistic variables, while the parameters with limited information are treated as interval variables. To improve computational efficiency, the response surface methodology (RSM) is introduced to replace the time-consuming finite element (FE) simulations. By the hybrid uncertain model, an optimization design based on reliability and confidence interval is proposed to explore the optimal design for squeal reduction. In the proposed optimization, both the design objective and the design constraint are interval probabilistic functions due to the effects of hybrid uncertainties. In this case, the maximum of the upper bound of confidence interval of design objective is selected as the objective function, while the minimal value of the probabilistic constraint is selected as the constraint function. 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 reducing squeal propensity of the disc brake systems with hybrid uncertainties.