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• A sub-parallelepiped perturbation algorithm is designed to calculate the marginal intervals of output responses. • A second-order perturbation algorithm is used to calculate the correlation coefficients of output responses. • The uncertainty domains of responses are created based on the marginal intervals and correlation coefficients of responses. • The proposed algorithms present good computational accuracy and efficiency. The correlation analysis of the uncertain structures with multi-responses is carried out based on the multidimensional parallelepiped model in this research. Firstly, the multidimensional parallelepiped model is introduced to quantify the uncertainty and correlation of input parameters. Then, to deal with the large uncertainty of input parameters, the sub-parallelepiped perturbation analysis algorithm is designed to calculate the marginal intervals of output responses. Next, based on the Monte Carlo simulation and the second-order perturbation technique, the Monte Carlo correlation analysis algorithm and the second-order perturbation correlation analysis algorithm are respectively designed to obtain the correlation coefficients of output responses. Subsequently, two uncertainty domain analysis algorithms based on the marginal intervals analysis and the correlation coefficients analysis, are presented to establish the uncertainty domains of output responses. Finally, the effectiveness of proposed algorithms is verified by three numerical examples. [ABSTRACT FROM AUTHOR]

• The effective subinterval analysis is conducted to handle large uncertainty. • The positive and negative gradients are used simultaneously. • The method can avoid falling into the local optimal solution. • The method presents good computational accuracy and efficiency. An effective subinterval analysis method is proposed to predict the response boundaries of uncertain problems with large uncertainty based on the positive and negative gradients. In the proposed method, the uncertain parameters with large uncertainty are described as interval variables. The variation intervals of interval variables are firstly divided into a series of uniform subintervals, and the original uncertainty domain with large uncertainty is thereby transformed into a series of subdomains with small uncertainty. Then, based on the gradient information of response function, the positive and negative gradients are employed as the search directions to identify the potential uncertainty subdomains which may contribute to the response boundaries. Next, the first-order Taylor expansion is used to precisely calculate the response boundaries of the uncertain problem on the potential uncertainty subdomains. Subsequently, the response boundaries on the original large uncertainty domain are further obtained through comparing the responses obtained on the uncertainty subdomains. Finally, several numerical examples and application examples are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract Most of the existing methods of brake squeal instability analysis are merely available to handle single type of uncertain case. In this study, an improved unified method is developed for uncertainty quantification, which is capable of handling two types of fuzzy–interval cases. In the first fuzzy–interval case, uncertain parameters of engineering structures are assumed as either fuzzy variables or interval variables, which exist in structures simultaneously and independently. In the second fuzzy–interval case, all uncertain parameters are represented by interval variables, but their lower and upper bounds just can be expressed as fuzzy variables instead of deterministic values. In the proposed method, fuzzy–boundary interval variables are introduced to handle fuzzy–interval uncertainties, and based on which an improved response analysis model is established. In the improved model, the fuzzy–boundary interval variables are firstly converted into interval-boundary variables by level-cut technique. Then by temporarily neglecting boundary uncertainties, the initial interval responses can be approximated via conducting once Taylor series expansion and subinterval analysis. Next, Taylor series expansion and central difference method are combined twice to deal with boundary uncertainties, and the interval responses of the structures with interval-boundary variables are yielded. Finally, the fuzzy–interval responses of the structures are derived on the basis of interval union operation and fuzzy decomposition theorem. The improved method is subsequently extended to quantify the uncertainties in brake squeal instability analysis involving two types of fuzzy–interval uncertainties. The effectiveness of the proposed method on tackling fuzzy–interval problems is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

A new hybrid uncertainty analysis method with random and interval variables is proposed in this paper. In the proposed method, the uncertain parameters with sufficient information are treated as random variables, while the uncertain parameters with limited information are modeled as interval variables. Both random variables and interval variables can be viewed as special evidence variables. From this special point of view, both random variables and interval variables are represented by equivalent evidence variables in this study, and a unified framework for hybrid uncertainty analysis is developed based on evidence theory and subinterval perturbation technique. The effects of the mixture of random and interval uncertainties on uncertain output are assessed by belief measure and plausibility measure. On the base of the proposed method, the squeal analysis model of automotive disc brakes involving both random and interval uncertainties can be developed. A numerical example of brake squeal analysis is provided to illustrate the effectiveness of the proposed method. The analysis results show that the equivalent evidence variables can be explored to represent random variables and interval variables reasonably and the proposed method has good accuracy and efficiency in the hybrid uncertainty analysis of squeal instability The proposed method gives a unified framework to tackle several types of uncertain cases, and it is quite general and not only limited to the uncertainty analysis of brake squeal. [ABSTRACT FROM AUTHOR]

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively. [ABSTRACT FROM AUTHOR]