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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. [ABSTRACT FROM AUTHOR]

This paper developed an effective optimization method, i.e., gradient-Hessian matrix-based method or second order method, of frame structures subjected to the transient loads. An algorithm of first and second derivatives of dynamic displacement and stress with respect to design variables is formulated based on the Newmark method. The inequality time-dependent constraint problem is converted into a sequence of appropriately formed time-independent unconstrained problems using the integral interior point penalty function method. The gradient and Hessian matrixes of the integral interior point penalty functions are also computed. Then the Marquardt's method is employed to solve unconstrained problems. The numerical results show that the optimal design method proposed in this paper can obtain the local optimum design of frame structures and sometimes is more efficient than the augmented Lagrange multiplier method. [ABSTRACT FROM AUTHOR]