In the traditional uncertainty-based analyses and optimizations of the automotive powertrain mounting system (PMS), uncertain parameters are usually treated as either random variables or interval variables. In this article, an efficient analysis and optimization method is proposed for PMS designs with hybrid random and interval uncertainties. An efficient analysis method, named the hybrid perturbation–finite difference method (HPFDM), is first derived to calculate the uncertain responses of the natural frequencies (NFs) and the decoupling ratios (DRs) of the PMS. Then, an optimization model of the PMS with hybrid uncertainties is established based on the HPFDM, where the uncertain responses of the relevant NFs and DRs are taken to create optimization constraints and optimization objectives. With the aid of the HPFDM, the nested optimization model can be solved efficiently. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

中文翻译：

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一种具有混合随机和区间不确定性的动力总成悬置系统的高效分析与优化方法

在传统的基于不确定性的汽车动力总成安装系统 (PMS) 分析和优化中，不确定参数通常被视为随机变量或区间变量。在本文中，针对具有混合随机和区间不确定性的 PMS 设计提出了一种有效的分析和优化方法。一种有效的分析方法，称为混合微扰-有限差分法（HPFDM），首先被推导出来计算 PMS 的固有频率（NFs）和去耦比（DRs）的不确定响应。然后，基于HPFDM建立具有混合不确定性的PMS优化模型，利用相关NF和DR的不确定响应来创建优化约束和优化目标。在 HPFDM 的帮助下，可以有效地求解嵌套优化模型。最后，给出了一个数值例子来证明所提出方法的有效性。