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In this study, a hybrid uncertainties-based analysis and optimization method is presented for the designs of the powertrain mounting system (PMS) involving mixed uncertainties. In the presented method, the PMS parameters with sufficient data are treated as random variables, while those with limited information are defined as interval variables. Then, an uncertainty-based analysis method called as hybrid interval-random perturbation-central difference method (HIRP-CDM), is proposed to compute the hybrid interval-random outputs of the inherent characteristics of the PMS in concerned directions. In addition, the hybrid interval-random-Monte Carlo method (HIR-MCM) is developed to verify the computational accuracy of HIRP-CDM. Next, an optimization model mixed uncertainties is built up for the PMS design based on HIRP-CDM, in which the hybrid intervalrandom outputs of the concerned inherent characteristics are adopted to construct the design objective and constrains. The complex optimization problem can be effectively settled by means of HIRP-CDM. The effectiveness of the presented method is verified by a numerical example.

In engineering practice, some uncertain parameters of structures are usually independent while others might be correlated in the design problems of automotive engineering. This study introduces the multidimensional parallelepiped (MP) model to handle the independent and correlated parameters of an uncertain automotive powertrain mounting system (PMS) in a unified framework. Two uncertainty analysis methods, including the multidimensional parallelepiped-Monte Carlo method (MP-MCM) and the multidimensional parallelepiped-regularization-perturbation method (MP-RPM), are developed for the uncertainty analysis of the dynamic responses of PMS, in which independent and correlated parameters coexist. In the proposed MP-MCM, the uncertainty domain of all uncertain parameters is firstly established based on the MP model. Then, the correlated parameters are treated as independent uncertain variables and the traditional Monte Carlo simulation is applied to obtain random samples. Among the obtained samples, the ones satisfying the matrix inequality of MP model are selected and finally used to calculate the interval responses of PMS. In the proposed MP-RPM, the regularization method is firstly introduced to transform the parametric uncertainty domain into a standard multidimensional cube domain, where all uncertain parameters become independent with each other. And then, the perturbation analysis and central difference strategy are combined to efficiently calculate the interval responses of PMS. A numerical application is provided to demonstrate the effectiveness of the proposed methods on uncertainty analysis of the PMS with independent and correlated parameters. The influence of different parametric correlation on system dynamic responses, and the effect of the parametric correlation of different mounts on system responses are discussed in detail.