针对纯电动汽车动力总成悬置系统(Powertrain Mounting System,PMS)参数同时存在不确定性和相关性的情形,开展了纯电动汽车PMS固有特性的不确定性和相关性传播分析研究.利用多维平行六面体模型量化系统参数不确定性和相关性;基于多维平行六面体模型,将正则化法、泰勒展开法及中心差分法相结合,提出了一种PMS固有特性响应不确定性传播分析的MP摄动法.结合系统固有特性响应数据,基于蒙特卡罗法和置信度,提出了一种系统固有特性响应的相关性传播分析方法.以某纯电动汽车PMS算例验证了方法的有效性.分析结果表明:系统参数的不确定性会使得系统响应具有不确定性,而系统参数的相关性会使得系统响应具有一定的相关性.

在实际工程中,受测量、制造、装配、疲劳老化、工程经验、认知程度和系统复杂性等主观和客观因素的影响,汽车动力总成悬置系统(Powertrain Mounting Systems,PMS)不可避免地存在着一定的不确定性因素.相关不确定性情形主要概括为PMS参数信息充足的概率情形、PMS参数信息匮乏的非概率情形、系统部分参数信息充足而部分参数信息匮乏的概率-非概率混合情形.针对三大类不确定性情形下的汽车PMS研究,围绕不确定性建模、不确定性分析和不确定性优化等3个方面的研究方法进行了系统性的分析和总结,并指出了相关分析模型和研究方法的分析特点和适用范围等.对汽车PMS不确定性分析与优化方法的未来研究方向进行了展望.

In engineering practice, uncertainty and correlation may coexist in both input parameters and output responses of the powertrain mounting system (PMS) of a vehicle. A methodology is developed for the uncertainty and correlation propagation analysis of the inherent characteristics of PMSs in this research. In the proposed methodology, the multi-ellipsoid convex model is introduced to quantify multiple groups of uncertain parameters with correlation, where dependent and independent uncertain parameters are considered simultaneously. In the uncertainty propagation analysis, it aims to calculate the interval bounds of system responses. To perform uncertainty propagation analysis, the Monte Carlo uncertainty analysis (MCUA) method is firstly presented based on Monte Carlo simulation, and the first-order perturbation-central differenceLagrange multiplier (FPCDLM) method and the second-order perturbation-central differenceLagrange multiplier (SPCDLM) method are then derived to promote the computational efficiency. In the correlation propagation analysis, it aims to compute the correlation between different system responses. To conduct the correlation propagation analysis, the Monte Carlo correlation analysis (MCCA) method is firstly proposed and the second-order perturbation correlation analysis (SPCA) method are then developed to enhance the computational efficiency. Next, the whole procedures for uncertainty and correlation propagation analysis of PMS are established by combining the above uncertainty analysis and correlation analysis methods, and the elliptical domain of any two system responses can be obtained. Finally, numerical examples of the PMS of an electric vehicle are provided to demonstrate the effectiveness of the proposed methodology.

In order to deal with the complex situation that parametric uncertainty and correlation coexist in the automotive powertrain mounting system (PMS),an uncertainty analysis method for calculating the natural frequency and decoupling rate of PMS was proposed.In the proposed method,the multi-dimensional parallelepiped model was firstly constructed to describe the PMS parameters with uncertainty and correlation.Then,the uncertain responses of the natural frequency and decoupling rate were calculated by integrating the regulation technique,Taylor series expansion and central difference method.Next,the analysis procedure of the proposed method was presented.Finally,the Monte Carlo method was used as a reference method for comparison and verification.The numerical analysis results show that the correlation of uncertain parameters of PMS has a certain influence on the inherent characteristics of the system.The method presents acceptable computational accuracy and higher computational efficiency in solving the uncertain response of PMS,which provides important reference for the calculation,evaluation and optimization design of the inherent characteristics of automotive PMS.

为研究悬置刚度参数的不确定性和相关性对系统固有特性的影响,提出了一种基于多椭球凸模型的动力总成悬置系统固有频率和解耦率分析方法.该方法采用多椭球凸模型描述系统各悬置的三向刚度参数,基于泰勒级数展开、拉格朗日乘子法及中心差分法,计算系统固有频率和解耦率的不确定变化范围,并以蒙特卡洛法作为参考验证分析结果的有效性.算例分析结果表明:在考虑不确定参数的相关性时,该方法可精确、高效地计算出固有频率和解耦率的变化范围.此外,与不考虑相关性的区间方法相比,此方法可求得更为合理的频率和解耦率响应范围.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

In engineering practice, the parameters of uncertain structures are often quantified as random variables, but their distribution parameters are appropriately modeled as fuzzy variables rather than deterministic values in some special engineering cases. To address such dual uncertain cases, an efficient approach is proposed for the possibility-based robust design optimization (PBRDO) of dual uncertain structures with fuzzy random variables (FRVs), in which the so-called dual robust design and the failure possibility are taken into account simultaneously. In the proposed approach, FRVs are firstly used to describe dual uncertainties and a design optimization model with FRVs is constructed. The structural responses involving FRVs are calculated and expressed in the forms of fuzzy means and fuzzy variances. To perform dual robust design, the weighted sum of the expectations and entropies of the fuzzy means and fuzzy variances of interested response is taken as optimization objective. The constraints involving dual uncertainties are established in the possibility context based on the concept of failure possibility. The established PBRDO model is a complicated nested problem. Secondly, the random moment-interval perturbation center difference method (RM-IPCDM) is derived to calculate the optimization objective efficiently. Next, the target performance approach (TPA) is employed to simplify the possibilistic constraints, and the obtained equivalent constraints can also be efficiently solved by RM-IPCDM. The nested PBRDO model with FRVs is finally simplified into a single-loop one with the aid of RM-IPCDM and TPA. Three dual uncertain numerical examples involving FRVs are given to demonstrate the feasibility of the proposed approach.

工程实际中,汽车动力总成悬置系统不可避免地存在着一定的参数不确定性,且不确定参数间往往同时存在一定的相关性与独立性.本文中引入多维平行六面体模型处理系统参数相关性和独立性并存的情形,结合蒙特卡洛法提出了一种悬置系统固有特性的不确定性分析方法,并给出了方法的分析步骤.对某悬置系统的数值分析结果表明:该方法能有效处理系统不确定参数的相关性和独立性,与未考虑参数相关性的区间方法相比,该方法能获得更为合理的固有频率和解耦率区间范围;对于给定的研究模型,其左右悬置点的刚度相关性对系统固有特性的影响比较明显,在设计和研究过程中应给予重点关注.

工程实际中,汽车动力总成悬置系统(Powertrain Mount System,PMS)不可避免地存在着各种不确定因素.针对PMS一部分参数信息充足而另一部分参数信息匮乏的情形:将样本信息充足的参数视为随机变量,而将信息匮乏的参数处理为区间变量;提出了一种求解PMS固有特性混合响应的混合蒙特卡洛法;进一步,结合泰勒展开、随机矩法和中心差分法提出了一种快速求解PMS固有特性混合响应的混合摄动-中心差分法;通过算例验证了方法的有效性,并分析了混合不确定性对PMS固有特性的影响.

工程实际中,汽车动力总成悬置系统(PMS)不可避免地存在着不确定因素.文中引入模糊变量描述PMS中具有模糊特性的不确定参数,首先推导了一种求解PMS固有特性的模糊-蒙特卡洛法;然后结合泰勒展开和中心差分法推导了一种快速求解PMS固有特性的模糊摄动-中心差分法(FPCDM);随后,基于FPCDM提出了PMS固有特性的模糊可靠性分析与优化方法;最后,通过数值算例验证了文中方法的有效性,并对系统进行了模糊可靠性分析与优化设计.

In some special engineering cases, the lower and upper bounds of uncertain parameters are appropriately quantified as fuzzy variables instead of deterministic values. To address such cases, a possibility-based robust design optimization (PBRDO) framework is suggested for the hybrid uncertain structures with fuzzy-boundary interval (FuBI) variables. Firstly, an optimization model with FuBI variables is established where FuBI uncertainties exist in both the objective and constraint functions. The so-called dual robust design is presented and it is adopted to create the optimization objective. The first robust design aims to handle fuzziness while the second one attends to tackle interval property. The failure possibility is employed to construct the optimization constraints in possibilitic context. Then, the fuzzy-boundary interval Taylor series-central difference method (FITS-CDM) is derived to manage FuBI uncertainties and calculate the optimization objective efficiently. Next, the target performance approach (TPA) is employed to process the possibilistic constraints and the simplified constraints can be easily solved by FITS-CDM. The nested-loop PBRDO with FuBI variables can be simplified to a single-loop one based on FITS-CDM and TPA. Finally, the effectiveness of the proposed optimization approach on dealing with FuBI uncertainties is demonstrated by three examples.

Through a push-over analysis,various limit states of coupled shear walls were disclosed,and the reduction factor K for the strength of coupling beams was put forward to reduce the shear overstrength of the coupling beams under an ideal limit state.The change of the axial forces of shear walls corresponding to different limit states can be obtained,and the overstrength of the whole coupled shear wall can be calculated,which offers a theory foundation to the capacity design of transfer structure in tall buildings with transfer stories.

The philosophy of capacity design is introduced into the design of transfer-storey structures in this paper. The theory of strong transfer and weak upper structure is put forward, and then the capacity design formulas of transfer structures are derived. Firstly, a series of nonlinear dynamic time-history analysis has been finished, which considers the influence of varied parameters such as the stiffness and mass of transfer structures, seismic fortification intensity and the position of transfer storey on the dynamic behavior of transfer structures under severe earthquake. And then, the simplified formulas and the detail procedure for capacity design of transfer structures are presented. Based on a tall building structural analysis, the results are compared among the three methods of the codes, the enlarged coefficient of horizontal earthquake action used in practical engineering design (G + βE) and the capacity design herein. At last, some design advices are given.

There exists the risk which producter and user face in the sampling inspection for product delivery. In conventional sampling inspection, the uncertainty of sampling is studied and the interaction of productor and user is ignored in research. In view of this problem, to mimimize the pay off of productor and user, the stategies of both sides are selected based on insufficient information. Static game model of insufficient information is applied to analyze the above selection. Using number example bayes equlibrium is given and the relative conclusions are presented.