In engineering practice, the parametric uncertainty and correlation may coexist in the powertrain mounting system (PMS). An effective robust-based design optimization approach is proposed for uncertain PMS based on full vehicle model, where both the parametric uncertainty and correlation are considered. The uncertain parameters of PMS are firstly treated as probabilistic variables, and the Unscented Transformation Inspired (UTI) transformation is introduced to quantify the correlation of uncertain parameters. Then, to perform the uncertainty and correlation analysis, the UTI-Monte Carlo (UMC) method is developed based on UTI transformation and Monte Carlo sampling to estimate the means, standard deviations, variation ranges and correlation coefficients of PMS responses. Meanwhile, an efficient method named UTI-Arbitrary Polynomial Chaos Expansion (UAPCE) method is derived for the uncertainty and correlation analysis of PMS responses by combining UTI transformation and arbitrary polynomial chaos expansion. Next, an optimization model considering parametric uncertainty and correlation is formulated to perform the robust-based design of PMS, in which the weight coefficients of optimization components are calculated by principal component analysis. Finally, the numerical example is investigated to verify the effectiveness of the proposed methods.

The parametric uncertainty and correlation may coexist in the powertrain mounting system (PMS) in engineering practice. An effective approach is proposed for the multi-objective reliability-based robust design optimization of the PMS involving parametric uncertainty and correlation. In the proposed approach, the uncertain parameters of PMS with sufficient information are characterized as correlated random variables, whereas the uncertain parameters with discrete information are considered as discrete uncertain variables. Then, the Nataf-arbitrary polynomial chaos expansion (NAPCE) method is developed to estimate the means, standard deviations, and correlation coefficients of PMS responses. Meanwhile, the Nataf-Monte Carlo method is presented as a reference method to verify the NAPCE method. Next, the generalized maximum entropy principle and the correlation coefficient weighting method are respectively utilized to evaluate the reliabilities of PMS responses and the weight factors of optimization components. Afterwards, a multi-objective optimization model is established to explore the optimum design of the uncertain PMS considering both reliability and robustness simultaneously. Finally, the numerical application is provided to demonstrate the effectiveness of the proposed approach.

针对电动汽车动力总成悬置系统(Powertrain Mounting System,PMS)参数可能被处理为不同类型概率变量的情形,提出了一种基于任意多项式混沌(Arbitrary Polynomial Chaos,APC)展开和最大熵原理(Maximum Entropy Principle,MEP)的电动汽车PMS固有特性不确定性分析方法.采用概率模型描述任意概率不确定情形下的PMS参数,通过APC展开获得任意概率不确定情形下PMS固有特性不确定性响应的前几阶统计矩,通过MEP拟合不确定性响应的概率密度函数(Probability Density Function,PDF)和累积分布函数(Cumulative Distribution Function,CDF)等信息,通过算例分析了5种概率不确定情形下的电动汽车PMS固有特性响应.分析结果表明,以蒙特卡洛法作为参考,所提出的方法可有效地分析不同概率不确定情形下的PMS固有特性响应,分析具有较高的计算精度和计算效率,能进一步获得响应满足设计要求的可靠度.