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The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.

Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.

CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.

The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.