汽车转向性能一致性分析关键问题的研究
|
摘要
随着汽车行业的发展，汽车品质变得越来越重要。生产一致性不好，无法体现汽车的品质；使用耐久性不好，无法实现汽车的保值。良好的一致性是高品质汽车的表现。目前，中国汽车工业与国外竞争，生产一致性和使用耐久性是最大问题之一。主要表现为同批次生产的汽车中，一部分汽车的性能与目标性能存在较大差异以及某辆汽车在使用一段时间之后，汽车性能与原性能相比会发生较大偏差。目前，全世界的汽车行业由于缺少设计参数容差对性能偏差影响的分析方法，难以实现在设计阶段对汽车性能一致性的分析与控制；同时，也使得尺寸工程分析难以实现设计参数容差与性能容差之间的优化组合。因此，汽车行业大多采用对制造过程的精确控制来提高汽车性能一致性，即选择高精度工装设备，严格控制汽车生产工艺，从而保证汽车性能的一致性，其结果导致了生产成本过高。
本文提出在汽车概念设计阶段，建立目标性能与设计参数之间的数学联系，实现设计参数容差与性能容差之间的分析方法，从而建立了建立一套一致性设计流程方法，可以在汽车概念设计阶段，通过将设计性能优化到同级别竞争车型性能之上，然后将性能适当下降，从而形成性能容差，再将性能容差分解到硬点、结构参数、总成特性和功能部件上，得到设计参数的容差范围，保证汽车性能一致性，同时也可以指导汽车尺寸工程设计，使汽车制造商和总成供应商选择合理工装设备，实现生产成本的控制。
为实现研究设想，本文在广泛调研了国内外相关理论的基础上，以汽车转向性能一致性为切入点，在以下几个方面做了相关探索性研究：
首先，对性能一致性设计方法做了相关研究。建立了一整套适用于汽车一致性分析的设计流程。在对目前已经公开发表的关于汽车一致性分析的文章做全面的理论调研的基础上，提出了汽车性能一致性设计流程的流程目标，分析了汽车性能一致性设计流程的关键环节，并针对一致性分析的流程目标与关键环节，尝试建立了汽车一致性分析的设计流程。针对汽车性能一致性流程中的参数的表达以及性能与参数度耦合度分析做了具体的理论研究，为一致性设计流程的下一步目标性能容差区间分解做好相关理论准备。
其次，对一致性分析设计流程中的关键环节：目标性能容差区间分解理论方法的做了相关理论研究，建立了目标性能容差区间向设计参数分解的相关理论方法。分析了目标性能容差区间分解的难点问题，并在此基础上，针对性的提出了目标性能容差分解的理论框架。研究了目标性能优化设计，性能容差区间的确定方法以及设计参数区间模型的表达问题，并结合下一步目标性能容差分解算法的研究性能了完整的目标性能容差区间分解理论，从而实现汽车性能一致性分析。
随后，针对一致性设计流程中目标性能容差区间分解理论的算法做了相关研究。针对容差区间的非对称性以及传统算法在工程求解过程中可能产生工程矛盾解或者难以求解的问题，引入了区间数学和广义逆矩阵理论，提出了目标性能容差分解的算法，得到设计参数的工程最小二乘解。
之后，建立的转向性能品质动力学模型，实现汽车性能一致性分析的理论基础。回顾了转向系统模型的历史发展，并在此基础上分析了汽车转向性能品质动力学模型的关键环节，提出了转向性能品质动力学的建模思路，在此基础上建立了具体的转向系统动力学模型和整车动力学模型，反映出汽车本身的包容性、稳定性和鲁棒性，解决了传统汽车动力学模型在性能一致性分析应用中表现出模型太敏感这一特点。并针对典型汽车转向性能，选择相应实验工况，通过实车实验数据与仿真数据的对比，验证了建立的汽车转向性能动力学模型的正确性。
最后，以汽车转向性能为例，选取汽车转向性能指标，对汽车转向性能做了一致性分析，从而验证了建立的一致性分析方法的可行性。
The quality of vehicle becomes much more important with the development of the automotive industry. A good consistency means a high quality of the vehicle. Consistency and durability are two main problems for Chinese automotive industry to compete with foreign companies. There are two aspects of the performance of consistency. One is that the characteristics of many vehicles are much more different to the design characteristics. The other is that the characteristics of one car may be very different from the design characteristics after some time. The traditional method is using the precision equipment to ensure the consistency which causes the high cost.
It attempts to establish a new process of consistency design during the concept design. Firstly, makes the vehicle performance indicators above the average level to get a tolerance. Then, deliver the tolerance to the design parameters of the vehicle. So the tolerance of design parameters can be received and the consistency can be guaranteed. With the tolerance of the design parameters, the manufacturers and suppliers can choose the equipment to make the cost under‐control.
After a detailed review on domestic and foreign thesis, some key issues on consistency design are addressed. From the view of difficult points of the research, the following works are researched.
A3‐step consistency design process is established after the analysis of its5key issues.
Relating and coupling degree analysis method between vehicle performance parameters and design parameters is researched based on the DOE thesis. First, make the parameters sensitivity analysis one by one system. Second, put all system parameters chosen together to make parameter sensitivity analysis again. Finally, put the performance parameters and design parameter chosen together to analysis the relating and coupling degree.
Parameter modeling expression method is established. It provides the mathematics expression models for the points, characters of plane curves and space surfaces. It also provides the model for the tolerance of all the parameters.
Target characters tolerance delivery theory is established by the interval Taylor and Generalized inverse matrix theory in the thesis.
The steering quality dynamics model is established. It can reflect the robustness andstability of the vehicle which is important to the consistency analysis.
Finally, the steering performance indicators are chosen as the starting point to validate the steering consistence analysis process.
本文提出在汽车概念设计阶段，建立目标性能与设计参数之间的数学联系，实现设计参数容差与性能容差之间的分析方法，从而建立了建立一套一致性设计流程方法，可以在汽车概念设计阶段，通过将设计性能优化到同级别竞争车型性能之上，然后将性能适当下降，从而形成性能容差，再将性能容差分解到硬点、结构参数、总成特性和功能部件上，得到设计参数的容差范围，保证汽车性能一致性，同时也可以指导汽车尺寸工程设计，使汽车制造商和总成供应商选择合理工装设备，实现生产成本的控制。
为实现研究设想，本文在广泛调研了国内外相关理论的基础上，以汽车转向性能一致性为切入点，在以下几个方面做了相关探索性研究：
首先，对性能一致性设计方法做了相关研究。建立了一整套适用于汽车一致性分析的设计流程。在对目前已经公开发表的关于汽车一致性分析的文章做全面的理论调研的基础上，提出了汽车性能一致性设计流程的流程目标，分析了汽车性能一致性设计流程的关键环节，并针对一致性分析的流程目标与关键环节，尝试建立了汽车一致性分析的设计流程。针对汽车性能一致性流程中的参数的表达以及性能与参数度耦合度分析做了具体的理论研究，为一致性设计流程的下一步目标性能容差区间分解做好相关理论准备。
其次，对一致性分析设计流程中的关键环节：目标性能容差区间分解理论方法的做了相关理论研究，建立了目标性能容差区间向设计参数分解的相关理论方法。分析了目标性能容差区间分解的难点问题，并在此基础上，针对性的提出了目标性能容差分解的理论框架。研究了目标性能优化设计，性能容差区间的确定方法以及设计参数区间模型的表达问题，并结合下一步目标性能容差分解算法的研究性能了完整的目标性能容差区间分解理论，从而实现汽车性能一致性分析。
随后，针对一致性设计流程中目标性能容差区间分解理论的算法做了相关研究。针对容差区间的非对称性以及传统算法在工程求解过程中可能产生工程矛盾解或者难以求解的问题，引入了区间数学和广义逆矩阵理论，提出了目标性能容差分解的算法，得到设计参数的工程最小二乘解。
之后，建立的转向性能品质动力学模型，实现汽车性能一致性分析的理论基础。回顾了转向系统模型的历史发展，并在此基础上分析了汽车转向性能品质动力学模型的关键环节，提出了转向性能品质动力学的建模思路，在此基础上建立了具体的转向系统动力学模型和整车动力学模型，反映出汽车本身的包容性、稳定性和鲁棒性，解决了传统汽车动力学模型在性能一致性分析应用中表现出模型太敏感这一特点。并针对典型汽车转向性能，选择相应实验工况，通过实车实验数据与仿真数据的对比，验证了建立的汽车转向性能动力学模型的正确性。
最后，以汽车转向性能为例，选取汽车转向性能指标，对汽车转向性能做了一致性分析，从而验证了建立的一致性分析方法的可行性。
The quality of vehicle becomes much more important with the development of the automotive industry. A good consistency means a high quality of the vehicle. Consistency and durability are two main problems for Chinese automotive industry to compete with foreign companies. There are two aspects of the performance of consistency. One is that the characteristics of many vehicles are much more different to the design characteristics. The other is that the characteristics of one car may be very different from the design characteristics after some time. The traditional method is using the precision equipment to ensure the consistency which causes the high cost.
It attempts to establish a new process of consistency design during the concept design. Firstly, makes the vehicle performance indicators above the average level to get a tolerance. Then, deliver the tolerance to the design parameters of the vehicle. So the tolerance of design parameters can be received and the consistency can be guaranteed. With the tolerance of the design parameters, the manufacturers and suppliers can choose the equipment to make the cost under‐control.
After a detailed review on domestic and foreign thesis, some key issues on consistency design are addressed. From the view of difficult points of the research, the following works are researched.
A3‐step consistency design process is established after the analysis of its5key issues.
Relating and coupling degree analysis method between vehicle performance parameters and design parameters is researched based on the DOE thesis. First, make the parameters sensitivity analysis one by one system. Second, put all system parameters chosen together to make parameter sensitivity analysis again. Finally, put the performance parameters and design parameter chosen together to analysis the relating and coupling degree.
Parameter modeling expression method is established. It provides the mathematics expression models for the points, characters of plane curves and space surfaces. It also provides the model for the tolerance of all the parameters.
Target characters tolerance delivery theory is established by the interval Taylor and Generalized inverse matrix theory in the thesis.
The steering quality dynamics model is established. It can reflect the robustness andstability of the vehicle which is important to the consistency analysis.
Finally, the steering performance indicators are chosen as the starting point to validate the steering consistence analysis process.
引文
[1]一汽丰田汽车销售有限公司.零售渠道的客户满意度[R].2007
[2] Greenwood W H． Transactions［J］．Transactions of the ASME，1987，109:112－116．
[3]王德伦，程周，罗劲松．移动公差在车身公差分配中的应用［J］．重庆理工大学学报:自然科学版，2011(2):1－7．
[4] Ceglarek D，Shi J，Zhou Z．Variation reduction for assembly methodologies andcase studies analysis，Technical Report of the“2mm”Program［Z］．Ann Arbor:University of Michigan，1994．
[5]一汽丰田汽车销售有限公司.零售渠道的客户满意度[R].2007
[6]张荣瑞．尺寸链原理及其应用［M］．北京:机械工业出版社，1986．
[7]李良，王德伦．车身公差分配工程应用［J］．重庆理工大学学报:自然科学版，2008(11):16－22．
[8]吕淑萍．位置度公差与尺寸公差的联合控制［J］．机械工程师，2011(4):106．
[9]林忠钦、胡敏等.轿车车体装配偏差研究方法综述［J］.机械设计与研究.1999(3).
[10]王德伦，宋华．基于新分配方法的蒙特卡洛公差模拟优化［J］．四川兵工学报，2011(1):73－75．
[11] Steven P. Fuja, Henry A. Schmid, Joseph P. Ryan．Synthesis of chassis parametersfor ride and handling on the1997Chevrolet Corvette[C]．SAE paper970097
[12] Joseph P. Ryan, Steven P. Fuja, Henry A. Schmid．Objective ride and handlinggoals for the1997Chevrolet Corvette[C]．SAE paper970091
[13] D. Geoff Rideout, Jeffrey L. Stein, John B. Ferris．Target cascading: a designprocess for achieving vehicle ride and handling targers[C]．New York,Proceedings of IMECE2001Symposium on Advanced Automotive Technologies,2001
[14]管欣．汽车动态模拟国家重点实验室车辆运动动力学建模与仿真的研究进展[R]．长春：吉林大学汽车动态模拟国家重点实验室学术报告，2009
[15]施普尔克劳舍著，宁汝新等译．虚拟产品开发技术[M]．北京：机械工业出版社，2002
[16]石晓明．汽车底盘创新研发与计算机模拟[R]．长春：吉林大学汽车动态模拟国家重点实验室学术报告，2006
[17]熊光楞，郭斌，陈晓波等．协同仿真与虚拟样机技术[M]．北京：清华大学出版社，2004
[18]中国汽车工程学会，中国汽车技术研究中心．我国汽车行业自主品牌培育与自主开发能力建设的措施研究[R]．2005.10
[19]曾迥立等.扭力梁式后悬架对不足转向性的影响分析[J].汽车科技,2009年7月第4期.
[20]廖芳等.概念设计阶段扭转梁式后悬架建模方法研究[J].汽车技术，2007年第11期.
[21]刘艳华.轿车扭力梁后悬架的开发研究[J].沈阳大学学报,第18卷第4期2006年8月.
[22]王蠡.扭力梁后桥总成参数对整车转向特性影响的分析[J].汽车工程，2011年(第33卷)第1期.
[23]柳江.基于虚拟样机技术悬架系统性能分析和优化设计[D].上海交通大学博士学位论文，2007
[24]景立新，郭孔辉，卢荡.麦弗逊悬架减震器侧向力优化[J].科学技术与工程.2011,1：76-80.
[25]景立新，郭孔辉.扭转梁式后悬架运动学及动力学特性[J].吉林大学学报(工学版)，2010，9，40：1-5.(EI：20104613383658).
[26]唐晓峰.拖曳臂式扭杆梁后桥的设计流程和方法[J].上海汽车，2009,4.
[27] Soon R，Gummadi L N B，Cao K．Robustness considerations in the design of astabilizer bar system[J]．SAE paper2005-01-1718
[28] Zhou J．Reliability and robustness mindset in automotive product developmentfor global markets[J]．SAE paper2005-01-212
[29] Narasimhan K，Sharma A K．Multistage process optimization for manufacturingautomotive component using finite element method[J]．SAE paper2005-26-332
[30] Ball D J，Zammit MG，Mitchell G C．Pgm optimization by robust design[J]．SAEpaper2005-01-3849
[31] An H，Chae S，Kim H．Optimum design of exhaust system using the robustdesign[J]．SAE paper2006-01-0082
[32] Leaphart E G．Application ofrobust engineering methods to improve ECUsoftware testing[J]．SAEpaper2006-01-1600
[33] Zutshi A，Avutapalli B，Stagner D，et a1．Applying six sigma tools to the reardriveline system forimproved vehicle level NVH performance[J]．SAE paper2007-01-2286
[34] Lee S，Ha W，Yeo T．Robust design for occupant protection system using taguchi’S method[J]．SAE paper2007-01-3724
[35]曾小华,王庆年,王伟华等．正交优化设计理论在混合动力汽车设计中的应用[J]．农业机械学报，2006，37(5)：26—28
[36]张云清.基于正交试验的虚拟样车平顺性分析及参数选择[J].汽车技术，2005,10
[37]姚明，王国林，周孔亢等．车辆鼓式制动器结构参数的稳健优化设计[J]．农业机械学报，2005，36(121：17-20)
[38]汪鸣琦.田口法在汽车车身骨架刚度优化中的应用[J].汽车技术,1998年第5期P5-7
[39]黄金陵，崔岸，陈晓华等．稳健设计方法用于车门系统设计[J]．汽车工程，2006，28(11)1012-1014
[40]邢天伟.基于田口方法的整车平顺性仿真及优化[D].吉林大学博士学位论文,2008.
[41]唐超勇.车辆动力学操稳特性稳健性优化设计[D].华中科技大学硕士学位论文,2007.
[42]董俊红.基于微型遗传算法的多目标优化方法及应用研究[D].湖南大学硕士学位论文,2010.
[43]龚璇韬.基于某微型客车的平顺性稳健优化设计[D].湖南大学硕士学位论文,2010.
[44]田口玄一.试验设计法（魏锡禄，王世芳译）.北京：机械工业出版社，1987.
[45] Box,G.E.P.,Signal-to-noise ratios,performance criteria,and transformations(withdiscussion),Technometrics,1988,30（1）：1~40.
[46] G.G.Vining,R.H.Myers.,Combining Taguchi and Response SurfacePhilosophies ADual Response Approach,Journal of Quality Technology,1990,22,38~45.
[47] Myers R H,Khuri A I,Vining G G.Response Surface Alternatives to the Taguchi’sRobust Parameter Design Approach.American Statistician,1992,46(2):131~139.
[48] J.A.Nelder,Y.Lee.Generalized Linear Models for Analysis of Taguchi-TypeExperiments,Communications in Statistics:Theory andMethods,1991,20,477~496.
[49]董恩国等.基于双响应面法的行星齿轮机构稳健设计研究[J].机械传动,2009年第2期35-38
[50]高世杰.双响应面鲁棒设计在乘用车传动系统参数匹配中的应用[J].上海汽车.2006.11.27-30
[51]常亮明.稳健性设计的双响应面法[J].中国机械工程.1998年第9卷第8期.
[52]王涛.考虑随机因素的汽车悬架参数多目标稳健优化[J].振动与冲击.第28卷第11期.
[53]刘仁云.基于多目标优化策略的结构可靠性稳健设计[J].应用力学学报.2007年3月.
[54]于繁华.钢筋混凝土简支梁的多目标可靠性稳健优化设计[J].公路交通科技.2007年8月.
[55]黄风立等.注塑成型工艺多目标稳健设计及优化算法[J].同济大学学报（自然科学版）,2011年2月
[56]孙光永.多目标稳健优化设计方法在车身设计制造中的应用研究[J].固体力学学报，2011年4月
[57]李玉强等.基于双响应面模型的6σ稳健设计[J].机械强度,2006,28(5)：690-694．
[58] Dr. Thomas Meitinger, BMW Group. Functional Virtual Prototyping in VehicleChassis Development. EF-80,80788München, Germany.
[59] Hyung Min Kim. Target Cascading in Optimal System Design[D]. The Univer-sity of Michigan,2001.
[60] H.M.Kim, Nestor F.Michelena, Panos Y.Papalambros, Tao Jiang. TargetCascading Optimal System Design[J]. Journal of Mechanical Design,2003,125:474-480.
[61] H.M.Kim, M.Kokkolaras, L.S.Louca, G.J.Delagrammatikas, N.F.Michelena,Z.S.Filipi, P.Y.Papalambros, J.L.Stein and D.N.Assanis. Target Cascading inVehicle redesign: a class VI truck study. Int. J. of Vehicle Design,2002,29(3):199-225.
[62]20SIM(2001) Pro User’s Manual, Version3.2. The University of Twente–Controllab Products B.V., Enschede, The Netherlands.
[63] H.M.Kim, M.Kokkolaras, L.S.Louca, G.J.Delagrammatikas, N.F.Michelena,Z.S.Filipi, P.Y.Papalambros, J.L.Stein and D.N.Assanis. Target Cascading inVehicle redesign: a class VI truck study. Int. J. of Vehicle Design,2002,29(3):199-225.
[64] HuibinLiu, Wei Chen, Michael Kokkolaras, Panos Y.Papalambros, HarrisonM.Kim. Probabilistic Target Cascading: A Moment Matching Formulation forMultilevel Optimization Under Uncertainty[J]. Journal of Mechanical Design,2006,128:991-1000.
[65] Kim H M, Chen W, Wiecek M M. Lagrangian coordination for enhancing theconver-gence of analytical target cascading[J]. AIAA journal,2006,44(10):2197-2207.
[66] S. Tosserams. Analytical Target Cascading: Convergence Improvement by Sub-problem Post-optimality Sensitivities[D]. Eindhoven University of TechnologyDepartment of Mechanical Engineering Systems Engineering Group SE420389,2004.6.
[67] Blouin V Y, Fadel G M, Haque I Q, et al. Continuously variable transmissiondesign for optimum vehicle performance by analytical target cascading[J].International Journal of Heavy Vehicle Systems,2004,11(3):327-348.
[68]陈潇凯，林逸.目标分流法理论及其关键技术[J].公路交通科技，2009，26(9)：125-130.
[69]赵迁，陈潇凯，林逸.解析目标分流在汽车多学科设计优化中的应用[J].汽车技术，2010，(6)：25-28
[70]陈潇凯，陈勇，林逸.目标分流法理论及其在汽车开发中的应用[J].北京理工大学学报，2009，29(6)：515-519.
[71]陈潇凯，陈勇，林逸.电动汽车设计方案优化及软件系统开发[J].吉林大学学报（工学版），2009，39：47-52.
[72]赵迁，陈潇凯，林逸.基于罚函数的解析目标分流法计算特性分析[J].计算机工程与设计，2010，31(11)：2564-2567.
[73]赵迁，陈潇凯，林逸.改进的解析目标分流法[J].计算机工程与设计，2010，31(21)：4701-4703
[74] Xiong F, Yin X, Chen W, et al. Enhanced probabilistic analytical target cascadingwith application to multi-scale design[J]. Engineering Optimization,2010,42(6):581-592.
[75] Harrison M. Kim. Target Exploration for Disconnected Feasible Regions inEnter-prise-Driven Multilevel Product Design[J]. AIAA JOURNAL,2006,44(1):67-77.
[76] Tosserams S, Kokkolaras M, Etman L F P, et al. Extension of analytical targetcascading using augmented Lagrangian coordination for multidisciplinary designoptimization[C].12th AIAA/ISSMO multidisciplinary analysis and optimizationconference, AIAA paper.2008(2008-5843).
[77] Kokkolaras M., Mourelatos Z.P., Papalambros P. Y.. Design Optimization ofHi-erarchically Decomposed Multilevel System under Uncertainty[J]. ASME,2006,128(2):503-508.
[78] R.E. Moore, Methods and Applications of Interval Analysis, Prentice-Hall Inc.,London,1979.
[79] Sobieszczanski-So bieski J. Sensitiv ity o f Complex,Internally Co upledSystems [J]. AIAA Journal,1990,28(1):153O160.
[80] B. Liu, K. Iwamura, Modelling stochastic decision systems usingdependentchance programming, Eur. J. Oper. Res.101(1)(1997)193 203.
[81] Cho Gyeong-Mi, Log-barrier method for two-stage quadratic stochasticprogramming, Appl. Math. Comput.164(1)(2005)45 69.
[82] Sobieszczanski-So bieski J. Sensitiv ity o f Complex, Internally Co upledSystems [J]. AIAA Journal,1990,28(1):153O160.
[83] Jiang C, Han X, Liu G R. A Nonlinear Inter val Number Pro gr amming Methodfor Uncer tain Opt-I mizat ion Pr oblems[J]. Euro pean Jo ur na l of OperationalResear ch,2008,188(1):1O13.
[84] Jiang C, H an X, Liu G R. The Opt imizatio n o f the Variable Binder Fo rce in U-shaped Fo rming w ith Uncer tain Fr ictio n Co efficient[J]. Journal of MaterialProcessing Technolo gy,2007,182(4):262O267.
[85] Y.G. Xu, G.R. Liu, Z.P. Wu, A novel hybrid genetic algorithm using localoptimizer based on heuristic pattern move, Appl. Artif. Intell.15(7)(2001)601 631.
[86] G.R. Liu, X. Han, Computational Inverse Techniques in NondestructiveEvaluation, CRC Press, Florida,2003.
[87]阿达姆.措莫托[著]，黄锡朋，解春阳[译].汽车行驶性能[M].北京:科学普及出版社,1992.9.
[88] Dixon J. C. Tires, Suspension and handling [J]. Cambridge University Press,1991.
[89]郭孔辉.汽车操纵动力学[M].长春；吉林科学技术出版社，1991.12
[90] Rieckert P and Schunk T E. Zur Fahrmechanik des GummibereiftenKraftfahrzeugs[J]. Ingenieur Archiv, Vol.11,1940.12.
[91] Milliken W F and Whitcomb D W. General Introduction to a Program ofDynamic Research[J]. Proceedings of ImechE. Automobile Division,1956:287-309.
[92] Segel L. Research in the Fundamentals of Automobile Control andStability[C].SAE,1956, Vol.65:527-540.
[93] Segel L. Theoretical Prediction and Experimental Substantiation of the Responseof the Automobile to Steering Control [J]. Proceedings of ImechE. AutomobileDivision,1956-1957, No.7:310-330.
[94] ADI Technical Staff. Seventeen-Degree-of-Freedom Motor VehicleSimulation[R]. Application Report.
[95] D J Segal. Highway Vehicle Object Simulation Model. Programmers Manual.1976.
[96] D J Segal. Highway Vehicle Object Simulation Model. Users Manual,1976
[97] D J Segal. Highway Vehicle Object Simulation Model. Validation,1976
[98] Michael W Sayers. A Generic Mutibody Vehicle Model for Simulating Handlingand Braking [J]. Vehicle System Dynamics.1996vol (25) Suppl:599-613.
[99] Michael W Sayers. Vehicle Model for RTS Applications[J]. Vehicle SystemDynamics.1999vol (32):421-438
[100]刘拥军.非水平路面上汽车动力学仿真[D].长春：吉林工业大学2000
[101]叶显峰.面向结构的悬架实时仿真模型的建立[D].长春：吉林工业大学2000
[102]张威.非水平路面汽车动力学实时仿真计算的研究[D].长春：吉林大学2004
[103]吴振昕.基于总成结构的汽车动力学实时仿真方法的研究[D].长春：吉林大学2007
[104]王鹏.汽车实时动力学仿真中转向回正特征建模方法研究[D].长春：吉林大学2008
[105] L.Segel (1966). On the Lateral Stability and Control of the Automobile asInfluences by the Dynamics of the Steering System. Transactions of the ASME:Journal of Engineering for Industry,1966.
[106] Jindra, F. Mathematical Model of Four-Wheeled Vehicle for Hybrid ComputerVehicle Handling Program. Deparment of Transportation-National HighwayTraffic Safety Administration, DOT HS-801-800, January1976
[107] Erik M. Lowndes. Development of an Intermediate DOF Vehicle DynamicsModel for Optimal Design Studies[D] North Carolina State University.1998.
[108] M.Kamel Salaani. Closed loop steering system model for the National AdvancedDriving Simulator. SAE:2004-01-0172,2004.
[109] Zbigniew Lozia. Friction and Stick-Slip Phenomena in Steering System–Modeling and Simulation Studies. SAE:2007-01-1153
[110] Zbigniew Lozia. Dynamics of steering system with freeplay and dry friction–compare investigation for2WS and4WS. SAE:2005-01-1261,2005.
[111]管欣，吴振昕，詹军.面向结构的汽车齿轮齿条式转向系统仿真模型[J].汽车技术，2007
[112]郝惟拓.转向特性方程建模与仿真[D].长春：吉林大学，2008.
[113] Fujii. The Influence of Elasticity of the Steering Mechanism on the Motion of theVehicle. Trans. Jpn. Soc. Mech. Eng. Vol.22No.119,1956.
[114] Subiman Das, P Ramamurthy. A Report on Improving the Ride and HandlingPerformance in the Roll and Pitch Modes of an Utility Vehicle.SAE:2005-26-329,2005.
[115] P. E. Pfeffera, M. Harrerb, D. N. Johnstonb. Interaction of vehicle and steeringsystem. IJVSD. Vol.46, No.5, May2008,413–428.
[116]2007_ASCL汽车动力学实时仿真模型理论手册.吉林大学汽车动态模拟国家重点实验室技术报告
[117]赵剑，管迪华.独立悬架汽车转向系统刚度测量[J].北京：汽车工程，2001(vol23)，No.5，2001
[118] SD Sewell. Overview of Matlab Curve Fitting Toolbox,2002.
[119] Mechanical Simulation Corporation. CarSim Reference Manual, Version6.03,July,2005
[120]夏传延.转向系统综合刚度知识模型的建立与应用[D].上海：同济大学，2005.
[121]王爽.悬架运动学及弹性运动学建模、分析与评价[D].长春：吉林大学硕士论文，2004.
[122]管欣，逄淑一，詹军，姬鹏.基于转向几何的主销轴线角度和位置的解算[J].科学技术与工程，2009(vol.9)，No.21：6593-6596
[123] ISO7401, Road vehicles--Lateral transient response test methods--Open-looptest methods,2003.
[124] Andrew Heather Shaw. Development in On-Center Steering Evaluation andTesting[C]. SAE:2006-01-0796,2002
[125] ISO4138, Passenger cars--Steady-state circular driving behavior--Open-looptest methods,2004.
[126] Z.Lozi. Vehicle Dynamics and Motion Simulation Versus Experiment. SAE PaperNo.980220. SAE Transactions1998, Passenger Cars, Section6, volume107,p344-360
[127]郭科，陈聆，魏友华.最优化及其应用[M].北京：高等教育出版社，2007.7.
[128]高媛.非支配排序遗传算法（NSGA）的研究与应用[D].浙江：浙江大学，2006.
[129] Srinivas,N., Deb,K.. Multi-objective Optimization Using Non-dominated Sortingin Genetic Algorithm[J]. Evolutionary Computation,1994,2(3):221-248
[130] Kaylynmoy Deb, Amrit Partap, Sameer Agarwal, et al. A Fast and ElitistMulti-objective Genetic Algorithm: NSGA-II[J]. IEEE Transactions onEvolutionary Computation,2002,6(22):182-197.
[131] Jeffery J. Leader著，张威，刘志军，李艳红等译，数值分析与科学计算[M]，北京：清华大学出版社,2008
[132]李庆阳编著，科学计算方法基础[M]，北京：清华大学出版社，2006
[133]李庆阳，王能超，易大义编，数值分析[M]，北京：清华大学出版社，2008
[134]郭文彬、魏木生著，奇异值分解及其在广义逆理论中的应用[M]，北京：科学出版社,2008
[135]方保镕，周继东，李医民编著，矩阵论[M]，北京：清华大学出版社，2004
[136]陈永林著，广义逆矩阵的理论与方法[M]，南京师范大学出版社，2005
[2] Greenwood W H． Transactions［J］．Transactions of the ASME，1987，109:112－116．
[3]王德伦，程周，罗劲松．移动公差在车身公差分配中的应用［J］．重庆理工大学学报:自然科学版，2011(2):1－7．
[4] Ceglarek D，Shi J，Zhou Z．Variation reduction for assembly methodologies andcase studies analysis，Technical Report of the“2mm”Program［Z］．Ann Arbor:University of Michigan，1994．
[5]一汽丰田汽车销售有限公司.零售渠道的客户满意度[R].2007
[6]张荣瑞．尺寸链原理及其应用［M］．北京:机械工业出版社，1986．
[7]李良，王德伦．车身公差分配工程应用［J］．重庆理工大学学报:自然科学版，2008(11):16－22．
[8]吕淑萍．位置度公差与尺寸公差的联合控制［J］．机械工程师，2011(4):106．
[9]林忠钦、胡敏等.轿车车体装配偏差研究方法综述［J］.机械设计与研究.1999(3).
[10]王德伦，宋华．基于新分配方法的蒙特卡洛公差模拟优化［J］．四川兵工学报，2011(1):73－75．
[11] Steven P. Fuja, Henry A. Schmid, Joseph P. Ryan．Synthesis of chassis parametersfor ride and handling on the1997Chevrolet Corvette[C]．SAE paper970097
[12] Joseph P. Ryan, Steven P. Fuja, Henry A. Schmid．Objective ride and handlinggoals for the1997Chevrolet Corvette[C]．SAE paper970091
[13] D. Geoff Rideout, Jeffrey L. Stein, John B. Ferris．Target cascading: a designprocess for achieving vehicle ride and handling targers[C]．New York,Proceedings of IMECE2001Symposium on Advanced Automotive Technologies,2001
[14]管欣．汽车动态模拟国家重点实验室车辆运动动力学建模与仿真的研究进展[R]．长春：吉林大学汽车动态模拟国家重点实验室学术报告，2009
[15]施普尔克劳舍著，宁汝新等译．虚拟产品开发技术[M]．北京：机械工业出版社，2002
[16]石晓明．汽车底盘创新研发与计算机模拟[R]．长春：吉林大学汽车动态模拟国家重点实验室学术报告，2006
[17]熊光楞，郭斌，陈晓波等．协同仿真与虚拟样机技术[M]．北京：清华大学出版社，2004
[18]中国汽车工程学会，中国汽车技术研究中心．我国汽车行业自主品牌培育与自主开发能力建设的措施研究[R]．2005.10
[19]曾迥立等.扭力梁式后悬架对不足转向性的影响分析[J].汽车科技,2009年7月第4期.
[20]廖芳等.概念设计阶段扭转梁式后悬架建模方法研究[J].汽车技术，2007年第11期.
[21]刘艳华.轿车扭力梁后悬架的开发研究[J].沈阳大学学报,第18卷第4期2006年8月.
[22]王蠡.扭力梁后桥总成参数对整车转向特性影响的分析[J].汽车工程，2011年(第33卷)第1期.
[23]柳江.基于虚拟样机技术悬架系统性能分析和优化设计[D].上海交通大学博士学位论文，2007
[24]景立新，郭孔辉，卢荡.麦弗逊悬架减震器侧向力优化[J].科学技术与工程.2011,1：76-80.
[25]景立新，郭孔辉.扭转梁式后悬架运动学及动力学特性[J].吉林大学学报(工学版)，2010，9，40：1-5.(EI：20104613383658).
[26]唐晓峰.拖曳臂式扭杆梁后桥的设计流程和方法[J].上海汽车，2009,4.
[27] Soon R，Gummadi L N B，Cao K．Robustness considerations in the design of astabilizer bar system[J]．SAE paper2005-01-1718
[28] Zhou J．Reliability and robustness mindset in automotive product developmentfor global markets[J]．SAE paper2005-01-212
[29] Narasimhan K，Sharma A K．Multistage process optimization for manufacturingautomotive component using finite element method[J]．SAE paper2005-26-332
[30] Ball D J，Zammit MG，Mitchell G C．Pgm optimization by robust design[J]．SAEpaper2005-01-3849
[31] An H，Chae S，Kim H．Optimum design of exhaust system using the robustdesign[J]．SAE paper2006-01-0082
[32] Leaphart E G．Application ofrobust engineering methods to improve ECUsoftware testing[J]．SAEpaper2006-01-1600
[33] Zutshi A，Avutapalli B，Stagner D，et a1．Applying six sigma tools to the reardriveline system forimproved vehicle level NVH performance[J]．SAE paper2007-01-2286
[34] Lee S，Ha W，Yeo T．Robust design for occupant protection system using taguchi’S method[J]．SAE paper2007-01-3724
[35]曾小华,王庆年,王伟华等．正交优化设计理论在混合动力汽车设计中的应用[J]．农业机械学报，2006，37(5)：26—28
[36]张云清.基于正交试验的虚拟样车平顺性分析及参数选择[J].汽车技术，2005,10
[37]姚明，王国林，周孔亢等．车辆鼓式制动器结构参数的稳健优化设计[J]．农业机械学报，2005，36(121：17-20)
[38]汪鸣琦.田口法在汽车车身骨架刚度优化中的应用[J].汽车技术,1998年第5期P5-7
[39]黄金陵，崔岸，陈晓华等．稳健设计方法用于车门系统设计[J]．汽车工程，2006，28(11)1012-1014
[40]邢天伟.基于田口方法的整车平顺性仿真及优化[D].吉林大学博士学位论文,2008.
[41]唐超勇.车辆动力学操稳特性稳健性优化设计[D].华中科技大学硕士学位论文,2007.
[42]董俊红.基于微型遗传算法的多目标优化方法及应用研究[D].湖南大学硕士学位论文,2010.
[43]龚璇韬.基于某微型客车的平顺性稳健优化设计[D].湖南大学硕士学位论文,2010.
[44]田口玄一.试验设计法（魏锡禄，王世芳译）.北京：机械工业出版社，1987.
[45] Box,G.E.P.,Signal-to-noise ratios,performance criteria,and transformations(withdiscussion),Technometrics,1988,30（1）：1~40.
[46] G.G.Vining,R.H.Myers.,Combining Taguchi and Response SurfacePhilosophies ADual Response Approach,Journal of Quality Technology,1990,22,38~45.
[47] Myers R H,Khuri A I,Vining G G.Response Surface Alternatives to the Taguchi’sRobust Parameter Design Approach.American Statistician,1992,46(2):131~139.
[48] J.A.Nelder,Y.Lee.Generalized Linear Models for Analysis of Taguchi-TypeExperiments,Communications in Statistics:Theory andMethods,1991,20,477~496.
[49]董恩国等.基于双响应面法的行星齿轮机构稳健设计研究[J].机械传动,2009年第2期35-38
[50]高世杰.双响应面鲁棒设计在乘用车传动系统参数匹配中的应用[J].上海汽车.2006.11.27-30
[51]常亮明.稳健性设计的双响应面法[J].中国机械工程.1998年第9卷第8期.
[52]王涛.考虑随机因素的汽车悬架参数多目标稳健优化[J].振动与冲击.第28卷第11期.
[53]刘仁云.基于多目标优化策略的结构可靠性稳健设计[J].应用力学学报.2007年3月.
[54]于繁华.钢筋混凝土简支梁的多目标可靠性稳健优化设计[J].公路交通科技.2007年8月.
[55]黄风立等.注塑成型工艺多目标稳健设计及优化算法[J].同济大学学报（自然科学版）,2011年2月
[56]孙光永.多目标稳健优化设计方法在车身设计制造中的应用研究[J].固体力学学报，2011年4月
[57]李玉强等.基于双响应面模型的6σ稳健设计[J].机械强度,2006,28(5)：690-694．
[58] Dr. Thomas Meitinger, BMW Group. Functional Virtual Prototyping in VehicleChassis Development. EF-80,80788München, Germany.
[59] Hyung Min Kim. Target Cascading in Optimal System Design[D]. The Univer-sity of Michigan,2001.
[60] H.M.Kim, Nestor F.Michelena, Panos Y.Papalambros, Tao Jiang. TargetCascading Optimal System Design[J]. Journal of Mechanical Design,2003,125:474-480.
[61] H.M.Kim, M.Kokkolaras, L.S.Louca, G.J.Delagrammatikas, N.F.Michelena,Z.S.Filipi, P.Y.Papalambros, J.L.Stein and D.N.Assanis. Target Cascading inVehicle redesign: a class VI truck study. Int. J. of Vehicle Design,2002,29(3):199-225.
[62]20SIM(2001) Pro User’s Manual, Version3.2. The University of Twente–Controllab Products B.V., Enschede, The Netherlands.
[63] H.M.Kim, M.Kokkolaras, L.S.Louca, G.J.Delagrammatikas, N.F.Michelena,Z.S.Filipi, P.Y.Papalambros, J.L.Stein and D.N.Assanis. Target Cascading inVehicle redesign: a class VI truck study. Int. J. of Vehicle Design,2002,29(3):199-225.
[64] HuibinLiu, Wei Chen, Michael Kokkolaras, Panos Y.Papalambros, HarrisonM.Kim. Probabilistic Target Cascading: A Moment Matching Formulation forMultilevel Optimization Under Uncertainty[J]. Journal of Mechanical Design,2006,128:991-1000.
[65] Kim H M, Chen W, Wiecek M M. Lagrangian coordination for enhancing theconver-gence of analytical target cascading[J]. AIAA journal,2006,44(10):2197-2207.
[66] S. Tosserams. Analytical Target Cascading: Convergence Improvement by Sub-problem Post-optimality Sensitivities[D]. Eindhoven University of TechnologyDepartment of Mechanical Engineering Systems Engineering Group SE420389,2004.6.
[67] Blouin V Y, Fadel G M, Haque I Q, et al. Continuously variable transmissiondesign for optimum vehicle performance by analytical target cascading[J].International Journal of Heavy Vehicle Systems,2004,11(3):327-348.
[68]陈潇凯，林逸.目标分流法理论及其关键技术[J].公路交通科技，2009，26(9)：125-130.
[69]赵迁，陈潇凯，林逸.解析目标分流在汽车多学科设计优化中的应用[J].汽车技术，2010，(6)：25-28
[70]陈潇凯，陈勇，林逸.目标分流法理论及其在汽车开发中的应用[J].北京理工大学学报，2009，29(6)：515-519.
[71]陈潇凯，陈勇，林逸.电动汽车设计方案优化及软件系统开发[J].吉林大学学报（工学版），2009，39：47-52.
[72]赵迁，陈潇凯，林逸.基于罚函数的解析目标分流法计算特性分析[J].计算机工程与设计，2010，31(11)：2564-2567.
[73]赵迁，陈潇凯，林逸.改进的解析目标分流法[J].计算机工程与设计，2010，31(21)：4701-4703
[74] Xiong F, Yin X, Chen W, et al. Enhanced probabilistic analytical target cascadingwith application to multi-scale design[J]. Engineering Optimization,2010,42(6):581-592.
[75] Harrison M. Kim. Target Exploration for Disconnected Feasible Regions inEnter-prise-Driven Multilevel Product Design[J]. AIAA JOURNAL,2006,44(1):67-77.
[76] Tosserams S, Kokkolaras M, Etman L F P, et al. Extension of analytical targetcascading using augmented Lagrangian coordination for multidisciplinary designoptimization[C].12th AIAA/ISSMO multidisciplinary analysis and optimizationconference, AIAA paper.2008(2008-5843).
[77] Kokkolaras M., Mourelatos Z.P., Papalambros P. Y.. Design Optimization ofHi-erarchically Decomposed Multilevel System under Uncertainty[J]. ASME,2006,128(2):503-508.
[78] R.E. Moore, Methods and Applications of Interval Analysis, Prentice-Hall Inc.,London,1979.
[79] Sobieszczanski-So bieski J. Sensitiv ity o f Complex,Internally Co upledSystems [J]. AIAA Journal,1990,28(1):153O160.
[80] B. Liu, K. Iwamura, Modelling stochastic decision systems usingdependentchance programming, Eur. J. Oper. Res.101(1)(1997)193 203.
[81] Cho Gyeong-Mi, Log-barrier method for two-stage quadratic stochasticprogramming, Appl. Math. Comput.164(1)(2005)45 69.
[82] Sobieszczanski-So bieski J. Sensitiv ity o f Complex, Internally Co upledSystems [J]. AIAA Journal,1990,28(1):153O160.
[83] Jiang C, Han X, Liu G R. A Nonlinear Inter val Number Pro gr amming Methodfor Uncer tain Opt-I mizat ion Pr oblems[J]. Euro pean Jo ur na l of OperationalResear ch,2008,188(1):1O13.
[84] Jiang C, H an X, Liu G R. The Opt imizatio n o f the Variable Binder Fo rce in U-shaped Fo rming w ith Uncer tain Fr ictio n Co efficient[J]. Journal of MaterialProcessing Technolo gy,2007,182(4):262O267.
[85] Y.G. Xu, G.R. Liu, Z.P. Wu, A novel hybrid genetic algorithm using localoptimizer based on heuristic pattern move, Appl. Artif. Intell.15(7)(2001)601 631.
[86] G.R. Liu, X. Han, Computational Inverse Techniques in NondestructiveEvaluation, CRC Press, Florida,2003.
[87]阿达姆.措莫托[著]，黄锡朋，解春阳[译].汽车行驶性能[M].北京:科学普及出版社,1992.9.
[88] Dixon J. C. Tires, Suspension and handling [J]. Cambridge University Press,1991.
[89]郭孔辉.汽车操纵动力学[M].长春；吉林科学技术出版社，1991.12
[90] Rieckert P and Schunk T E. Zur Fahrmechanik des GummibereiftenKraftfahrzeugs[J]. Ingenieur Archiv, Vol.11,1940.12.
[91] Milliken W F and Whitcomb D W. General Introduction to a Program ofDynamic Research[J]. Proceedings of ImechE. Automobile Division,1956:287-309.
[92] Segel L. Research in the Fundamentals of Automobile Control andStability[C].SAE,1956, Vol.65:527-540.
[93] Segel L. Theoretical Prediction and Experimental Substantiation of the Responseof the Automobile to Steering Control [J]. Proceedings of ImechE. AutomobileDivision,1956-1957, No.7:310-330.
[94] ADI Technical Staff. Seventeen-Degree-of-Freedom Motor VehicleSimulation[R]. Application Report.
[95] D J Segal. Highway Vehicle Object Simulation Model. Programmers Manual.1976.
[96] D J Segal. Highway Vehicle Object Simulation Model. Users Manual,1976
[97] D J Segal. Highway Vehicle Object Simulation Model. Validation,1976
[98] Michael W Sayers. A Generic Mutibody Vehicle Model for Simulating Handlingand Braking [J]. Vehicle System Dynamics.1996vol (25) Suppl:599-613.
[99] Michael W Sayers. Vehicle Model for RTS Applications[J]. Vehicle SystemDynamics.1999vol (32):421-438
[100]刘拥军.非水平路面上汽车动力学仿真[D].长春：吉林工业大学2000
[101]叶显峰.面向结构的悬架实时仿真模型的建立[D].长春：吉林工业大学2000
[102]张威.非水平路面汽车动力学实时仿真计算的研究[D].长春：吉林大学2004
[103]吴振昕.基于总成结构的汽车动力学实时仿真方法的研究[D].长春：吉林大学2007
[104]王鹏.汽车实时动力学仿真中转向回正特征建模方法研究[D].长春：吉林大学2008
[105] L.Segel (1966). On the Lateral Stability and Control of the Automobile asInfluences by the Dynamics of the Steering System. Transactions of the ASME:Journal of Engineering for Industry,1966.
[106] Jindra, F. Mathematical Model of Four-Wheeled Vehicle for Hybrid ComputerVehicle Handling Program. Deparment of Transportation-National HighwayTraffic Safety Administration, DOT HS-801-800, January1976
[107] Erik M. Lowndes. Development of an Intermediate DOF Vehicle DynamicsModel for Optimal Design Studies[D] North Carolina State University.1998.
[108] M.Kamel Salaani. Closed loop steering system model for the National AdvancedDriving Simulator. SAE:2004-01-0172,2004.
[109] Zbigniew Lozia. Friction and Stick-Slip Phenomena in Steering System–Modeling and Simulation Studies. SAE:2007-01-1153
[110] Zbigniew Lozia. Dynamics of steering system with freeplay and dry friction–compare investigation for2WS and4WS. SAE:2005-01-1261,2005.
[111]管欣，吴振昕，詹军.面向结构的汽车齿轮齿条式转向系统仿真模型[J].汽车技术，2007
[112]郝惟拓.转向特性方程建模与仿真[D].长春：吉林大学，2008.
[113] Fujii. The Influence of Elasticity of the Steering Mechanism on the Motion of theVehicle. Trans. Jpn. Soc. Mech. Eng. Vol.22No.119,1956.
[114] Subiman Das, P Ramamurthy. A Report on Improving the Ride and HandlingPerformance in the Roll and Pitch Modes of an Utility Vehicle.SAE:2005-26-329,2005.
[115] P. E. Pfeffera, M. Harrerb, D. N. Johnstonb. Interaction of vehicle and steeringsystem. IJVSD. Vol.46, No.5, May2008,413–428.
[116]2007_ASCL汽车动力学实时仿真模型理论手册.吉林大学汽车动态模拟国家重点实验室技术报告
[117]赵剑，管迪华.独立悬架汽车转向系统刚度测量[J].北京：汽车工程，2001(vol23)，No.5，2001
[118] SD Sewell. Overview of Matlab Curve Fitting Toolbox,2002.
[119] Mechanical Simulation Corporation. CarSim Reference Manual, Version6.03,July,2005
[120]夏传延.转向系统综合刚度知识模型的建立与应用[D].上海：同济大学，2005.
[121]王爽.悬架运动学及弹性运动学建模、分析与评价[D].长春：吉林大学硕士论文，2004.
[122]管欣，逄淑一，詹军，姬鹏.基于转向几何的主销轴线角度和位置的解算[J].科学技术与工程，2009(vol.9)，No.21：6593-6596
[123] ISO7401, Road vehicles--Lateral transient response test methods--Open-looptest methods,2003.
[124] Andrew Heather Shaw. Development in On-Center Steering Evaluation andTesting[C]. SAE:2006-01-0796,2002
[125] ISO4138, Passenger cars--Steady-state circular driving behavior--Open-looptest methods,2004.
[126] Z.Lozi. Vehicle Dynamics and Motion Simulation Versus Experiment. SAE PaperNo.980220. SAE Transactions1998, Passenger Cars, Section6, volume107,p344-360
[127]郭科，陈聆，魏友华.最优化及其应用[M].北京：高等教育出版社，2007.7.
[128]高媛.非支配排序遗传算法（NSGA）的研究与应用[D].浙江：浙江大学，2006.
[129] Srinivas,N., Deb,K.. Multi-objective Optimization Using Non-dominated Sortingin Genetic Algorithm[J]. Evolutionary Computation,1994,2(3):221-248
[130] Kaylynmoy Deb, Amrit Partap, Sameer Agarwal, et al. A Fast and ElitistMulti-objective Genetic Algorithm: NSGA-II[J]. IEEE Transactions onEvolutionary Computation,2002,6(22):182-197.
[131] Jeffery J. Leader著，张威，刘志军，李艳红等译，数值分析与科学计算[M]，北京：清华大学出版社,2008
[132]李庆阳编著，科学计算方法基础[M]，北京：清华大学出版社，2006
[133]李庆阳，王能超，易大义编，数值分析[M]，北京：清华大学出版社，2008
[134]郭文彬、魏木生著，奇异值分解及其在广义逆理论中的应用[M]，北京：科学出版社,2008
[135]方保镕，周继东，李医民编著，矩阵论[M]，北京：清华大学出版社，2004
[136]陈永林著，广义逆矩阵的理论与方法[M]，南京师范大学出版社，2005