随机参数平面机构运动设计若干关键问题研究
|
摘要
随机参数机构运动设计是指：在考虑结构件几何加工误差、弹性变形、运动副间隙误差以及随机载荷等随机因素的前提下,研究机构的运动规律,运用稳健(优化)设计、可靠性(优化)设计、可靠性稳健(优化)设计等新兴的设计方法,设计出能够同时满足机构性能和运动精度要求的优化机构。能够精确、及时地完成规定动作(运动)是机构设计的主要目的之一。机构设计参数的随机性是大多数工程实际问题所固有的,而机构所承受的荷载同样具有随机变化的性质,这样就必然导致具有随机结构参数的承受随机载荷的随机机构系统。因此研究这种随机机构系统的运动设计问题有着十分重要的意义。
可靠性设计和稳健设计是非常先进的设计思想’,由于它们对于提高产品质量和保持产品性能的稳定性方面具有非常重要的作用,因此具有广阔的应用前景。将它们应用到机构设计中,处理机构运动设计中设计参数的随机性问题必将有重大的理论意义和实用价值。可靠性设计利用可靠性理论处理随机性,而稳健设计是使所设计的机构对设计变量的变化不敏感。在考虑随机参数的情况下,上述方法都可以有效地提高工程设计水平。然而,这些设计方法总是被独立的应用在不同的设计阶段。因此,将可靠性优化设计理论、可靠性灵敏度分析技术和稳健设计方法有机地结合在一起,发展一种机构可靠性稳健设计方法是十分必要的。
本论文共分六章,主要研究内容包括：
第1章：绪论。明确了本文的工程背景及选题目的和意义,介绍了可靠性理论的兴起、概念及发展状况,简述了可靠性优化设计方法的研究进展及其发展趋势,阐明了研究稳健设计理论与方法的重大意义。
第2章：数学基础和可靠性基本理论。本章首先简要介绍了本文所用的数学理论与方法,然后详细地阐述了可靠性设计理论和可靠性优化设计方法。
第3章：平面连杆机构运动精度分析。本章综合考虑机构结构参数和由载荷的随机性引起的输入参数的不确定性,采用矩阵法建立平面连杆机构的运动精度模型
第4章：任意分布参数机构可靠性优化设计。本章提出了一种实用有效的具有任意分布参数的机构可靠性优化设计的数值方法。采用随机摄动法、Edgeworth级数、可靠性设计理论和优化设计方法讨论了随机参数服从任意分布参数的机构可靠性优化设计问题,建立了任意分布参数的机构可靠性优化设计的数学模型,发展了可靠性优化设计理论。
第5章：机构可靠性稳健设计。本章首先将可靠性设计理论与灵敏度分析方法相结合,提出了机构可靠性灵敏度设计的计算方法,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对机构可靠性的影响,为机构的可靠性设计提供了理论依据。然后在可靠性优化设计理论、可靠性灵敏度分析和稳健设计方法的基础上,讨论了机构可靠性稳健设计问题,提出了机构可靠性稳健设计的数值方法,建立了机构可靠性稳健设计的数学模型,把可靠性灵敏度溶入优化设计模型之中,将机构可靠性稳健设计归结为满足可靠性要求的多目标优化问题。
本章提出了机构可靠性稳健设计的分析方法,拓展了可靠性稳健设计方法的应用范围。在机构的设计中,正确地应用可靠性稳健设计的方法,可以使机构在经受各种因素的干扰下,都能保持其可靠性的稳定,以使机构可靠性对设计参数的变化不敏感,提高产品的安全可靠性和鲁棒稳健性。
第6章：结论与展望。总结了本文研究结论,展望了可靠性理论和稳健设计方法及其在机构运动设计的应用和发展前景。
Stochastic uncertainty analysis of mechanism is the art of formulating a mathematical model within which one can ask and get answer to the question:"What is the motion law that a mechanism complies with when given that one or more of its material properties or geometric dimensions and properties are of a random or incompletely known nature, and/or that the actions on the structure in some respects have random or incompletely known properties?". And stochastic uncertainty design is a decision problem added to the stochastic uncertainty analysis. Being capable of completing the prescriptive motion (movement) accurately and duly is one of the major objectives of mechanisms design. Parameter uncertainty of the mechanical structures that compose the mechanisms is inherent in most engineering problems, and loads that are applied to the mechanisms are also random. Thus, the random mechanism systems with random structural parameters subjected to random loads are appeared. Therefore, the research on the kinematic design of the mechanism systems with stochastic uncertainty parameters is of the highest importance for design purposes.
Reliability-based design and robust design are very advanced ideas. They have extensive application prospects on account of significance in improving product quality and making performance more stable. Therefore, these two theories can be applied to deal with stochastic uncertainty parameters in kinematic design of mechanisms. Reliability theory is used to deal with uncertainties in reliability-based design, and robust design attempts to make the structure abilities insensitive to variations of design variables. In practical engineering, the aforementioned methods are very effective to improve engineering design with the consideration of the uncertainties. Unfortunately, these methods usually have been used separately in different design stages for different purposes. Therefore, it is essential to combine the reliability-based optimization theory, the reliability sensitivity analysis technique and the robust design method and to develop a reliability-based robust design approach of mechanisms.
In this dissertation, based on summarizing the theory of kinematic design of planar mechanisms with stochastic parameters in the world, a brilliant concept for kinematic design of planar linkages is proposed. In this new system, the theory of robust design, reliability design and reliability-based robust design are widely used. The main productions obtained from this paper are following as:
This dissertation is divided into 6 Chapters and the main productions obtained from this paper are following as:
Chapter 1:Introduction. We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability-based design theory; narrate briefly advances in reliability-based optimization method and the tendency of the reliability-based optimization approach development, and set forth the significant meaning of the study on the theory & method of robust design.
Chapter 2:Mathematics background and basic theory of reliability. First, mathematics theories and methods used by this dissertation are briefly introduced, and then the details of reliability-based theory and reliability-based optimization methods are described in Chapter 2.
Chapter 3:Kinematic accuracy analysis for planar linkage mechanism. In Chapter 3, comprehensively considering the parameters uncertainty of the mechanical structures and input, the kinematic accuracy model is formed.
Chapter 4:Reliability-based optimization design of mechanisms with arbitrary distribution parameters. A practical and effective numerical method of reliability-based optimization design of mechanisms with arbitrary distribution parameters is proposed in Chapter 3. Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory and the optimization technique are employed to present an approach for the reliability-based optimization of mechanisms with arbitrary distribution parameters on the condition of first four moments of original random variables known. The theoretical formulae of reliability-based optimization method of mechanisms with arbitrary distribution parameters are obtained. The approach is applied to develop the reliability-based optimization design theory with arbitrary distribution parameters.
Chapter 5:Reliability-based robust design of mechanisms. In Chapter 5, firstly, by composing the reliability-based design theory and sensitivity analysis method, a useful and efficient approach of reliability sensitivity is presented, change laws of the reliability sensitivity are given, the influences of design parametric changes on reliability of mechanisms are studied and theoretic foundation are provided for reliability-based design of mechanisms. Secondly, on the basis of the reliability-based optimization design theory, the reliability sensitivity analysis technique and the robust design method, the reliability-based robust design is discussed and a practical and effective numerical approach of reliability-based robust design of mechanisms is presented. The theoretical formula for reliability-based robust design of mechanisms is obtained. The reliability sensitivity is added to the reliability-based optimization design model and the reliability-based robust design is described as a multi-objection optimization, in which the maximum of the capability of the mechanisms and the minimum of the reliability sensitivity with respect to the mean value of design variables are taken as objective functions, while including a series of reliability constrains and geometry constrains etc..
The reliability-based robust design method of mechanisms is proposed and the application field of reliability-based robust design is developed well in Chapter 5. The reliability-based robust design of mechanisms attempts to make the kinematic accuracy reliability variations of mechanisms are insensitive to variations in design variables in the stage of design, which can minimize the effect of variations without eliminating the causes. When the reliability-based robust design approach is applied to mechanisms design, which is very useful and effective to improve quality and reliability of mechanisms.
Chapter 6:Conclusions and prospects. We draw the main conclusions of this dissertation and discuss the outlooks of reliability theory and robust design method, and their applications in the kinematic design of mechanisms with stochastic parameters.
可靠性设计和稳健设计是非常先进的设计思想’,由于它们对于提高产品质量和保持产品性能的稳定性方面具有非常重要的作用,因此具有广阔的应用前景。将它们应用到机构设计中,处理机构运动设计中设计参数的随机性问题必将有重大的理论意义和实用价值。可靠性设计利用可靠性理论处理随机性,而稳健设计是使所设计的机构对设计变量的变化不敏感。在考虑随机参数的情况下,上述方法都可以有效地提高工程设计水平。然而,这些设计方法总是被独立的应用在不同的设计阶段。因此,将可靠性优化设计理论、可靠性灵敏度分析技术和稳健设计方法有机地结合在一起,发展一种机构可靠性稳健设计方法是十分必要的。
本论文共分六章,主要研究内容包括：
第1章：绪论。明确了本文的工程背景及选题目的和意义,介绍了可靠性理论的兴起、概念及发展状况,简述了可靠性优化设计方法的研究进展及其发展趋势,阐明了研究稳健设计理论与方法的重大意义。
第2章：数学基础和可靠性基本理论。本章首先简要介绍了本文所用的数学理论与方法,然后详细地阐述了可靠性设计理论和可靠性优化设计方法。
第3章：平面连杆机构运动精度分析。本章综合考虑机构结构参数和由载荷的随机性引起的输入参数的不确定性,采用矩阵法建立平面连杆机构的运动精度模型
第4章：任意分布参数机构可靠性优化设计。本章提出了一种实用有效的具有任意分布参数的机构可靠性优化设计的数值方法。采用随机摄动法、Edgeworth级数、可靠性设计理论和优化设计方法讨论了随机参数服从任意分布参数的机构可靠性优化设计问题,建立了任意分布参数的机构可靠性优化设计的数学模型,发展了可靠性优化设计理论。
第5章：机构可靠性稳健设计。本章首先将可靠性设计理论与灵敏度分析方法相结合,提出了机构可靠性灵敏度设计的计算方法,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对机构可靠性的影响,为机构的可靠性设计提供了理论依据。然后在可靠性优化设计理论、可靠性灵敏度分析和稳健设计方法的基础上,讨论了机构可靠性稳健设计问题,提出了机构可靠性稳健设计的数值方法,建立了机构可靠性稳健设计的数学模型,把可靠性灵敏度溶入优化设计模型之中,将机构可靠性稳健设计归结为满足可靠性要求的多目标优化问题。
本章提出了机构可靠性稳健设计的分析方法,拓展了可靠性稳健设计方法的应用范围。在机构的设计中,正确地应用可靠性稳健设计的方法,可以使机构在经受各种因素的干扰下,都能保持其可靠性的稳定,以使机构可靠性对设计参数的变化不敏感,提高产品的安全可靠性和鲁棒稳健性。
第6章：结论与展望。总结了本文研究结论,展望了可靠性理论和稳健设计方法及其在机构运动设计的应用和发展前景。
Stochastic uncertainty analysis of mechanism is the art of formulating a mathematical model within which one can ask and get answer to the question:"What is the motion law that a mechanism complies with when given that one or more of its material properties or geometric dimensions and properties are of a random or incompletely known nature, and/or that the actions on the structure in some respects have random or incompletely known properties?". And stochastic uncertainty design is a decision problem added to the stochastic uncertainty analysis. Being capable of completing the prescriptive motion (movement) accurately and duly is one of the major objectives of mechanisms design. Parameter uncertainty of the mechanical structures that compose the mechanisms is inherent in most engineering problems, and loads that are applied to the mechanisms are also random. Thus, the random mechanism systems with random structural parameters subjected to random loads are appeared. Therefore, the research on the kinematic design of the mechanism systems with stochastic uncertainty parameters is of the highest importance for design purposes.
Reliability-based design and robust design are very advanced ideas. They have extensive application prospects on account of significance in improving product quality and making performance more stable. Therefore, these two theories can be applied to deal with stochastic uncertainty parameters in kinematic design of mechanisms. Reliability theory is used to deal with uncertainties in reliability-based design, and robust design attempts to make the structure abilities insensitive to variations of design variables. In practical engineering, the aforementioned methods are very effective to improve engineering design with the consideration of the uncertainties. Unfortunately, these methods usually have been used separately in different design stages for different purposes. Therefore, it is essential to combine the reliability-based optimization theory, the reliability sensitivity analysis technique and the robust design method and to develop a reliability-based robust design approach of mechanisms.
In this dissertation, based on summarizing the theory of kinematic design of planar mechanisms with stochastic parameters in the world, a brilliant concept for kinematic design of planar linkages is proposed. In this new system, the theory of robust design, reliability design and reliability-based robust design are widely used. The main productions obtained from this paper are following as:
This dissertation is divided into 6 Chapters and the main productions obtained from this paper are following as:
Chapter 1:Introduction. We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability-based design theory; narrate briefly advances in reliability-based optimization method and the tendency of the reliability-based optimization approach development, and set forth the significant meaning of the study on the theory & method of robust design.
Chapter 2:Mathematics background and basic theory of reliability. First, mathematics theories and methods used by this dissertation are briefly introduced, and then the details of reliability-based theory and reliability-based optimization methods are described in Chapter 2.
Chapter 3:Kinematic accuracy analysis for planar linkage mechanism. In Chapter 3, comprehensively considering the parameters uncertainty of the mechanical structures and input, the kinematic accuracy model is formed.
Chapter 4:Reliability-based optimization design of mechanisms with arbitrary distribution parameters. A practical and effective numerical method of reliability-based optimization design of mechanisms with arbitrary distribution parameters is proposed in Chapter 3. Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory and the optimization technique are employed to present an approach for the reliability-based optimization of mechanisms with arbitrary distribution parameters on the condition of first four moments of original random variables known. The theoretical formulae of reliability-based optimization method of mechanisms with arbitrary distribution parameters are obtained. The approach is applied to develop the reliability-based optimization design theory with arbitrary distribution parameters.
Chapter 5:Reliability-based robust design of mechanisms. In Chapter 5, firstly, by composing the reliability-based design theory and sensitivity analysis method, a useful and efficient approach of reliability sensitivity is presented, change laws of the reliability sensitivity are given, the influences of design parametric changes on reliability of mechanisms are studied and theoretic foundation are provided for reliability-based design of mechanisms. Secondly, on the basis of the reliability-based optimization design theory, the reliability sensitivity analysis technique and the robust design method, the reliability-based robust design is discussed and a practical and effective numerical approach of reliability-based robust design of mechanisms is presented. The theoretical formula for reliability-based robust design of mechanisms is obtained. The reliability sensitivity is added to the reliability-based optimization design model and the reliability-based robust design is described as a multi-objection optimization, in which the maximum of the capability of the mechanisms and the minimum of the reliability sensitivity with respect to the mean value of design variables are taken as objective functions, while including a series of reliability constrains and geometry constrains etc..
The reliability-based robust design method of mechanisms is proposed and the application field of reliability-based robust design is developed well in Chapter 5. The reliability-based robust design of mechanisms attempts to make the kinematic accuracy reliability variations of mechanisms are insensitive to variations in design variables in the stage of design, which can minimize the effect of variations without eliminating the causes. When the reliability-based robust design approach is applied to mechanisms design, which is very useful and effective to improve quality and reliability of mechanisms.
Chapter 6:Conclusions and prospects. We draw the main conclusions of this dissertation and discuss the outlooks of reliability theory and robust design method, and their applications in the kinematic design of mechanisms with stochastic parameters.
引文
1. (美)Robert L. Norton陈立周,韩建友,李威等译.机械设计[M],北京：机械工业出版社,2002：1-190
2. 曹惟庆等.连杆机构的分析与综合[M],北京：科学出版社,2001：126-170
3. 赵均.机构数值分析与综合[M],北京：机械工业出版社,2005：1-40
4. 张义民.静、动态随机结构系统振动理论的研究[D],长春：吉林工业大学,1995
5. 张义民.非线性随机结构系统振动理论的研究[D],沈阳：东北大学,1998
6. 张义民.汽车零部件可靠性设计[M],北京：北京理工大学出版社,2000：1-156
7. 贺向东.机械结构可靠性稳健设计若干关键问题的研究[D],长春：吉林大学,2005
8. 孙志礼,陈良玉.实用机械可靠性设计理论与方法[M],北京：科学出版社,2003：1-268
9. Freuenthal A M. The safety of structures[J],ASCE Trans.,1947:112,125-129
10.黄克中,毛善培.随机方法与模糊数学应用[M],上海：同济大学出版社,1987：1-261
11. Hasofer A M, Lind N C. Exact and invariant second-moment code format[J], J. Eng. Mech. Div., ASCE,1974,100(EM1):111-121
12. Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J], Comput. Struct.,1978,9(5):489-494
13. Shinozuka M. Basic analysis of structural safety[J], J. Struct. Eng., ASCE,1983,109(3):721-740
14. Der Kiureghian A, Lin H-Z, Hwang S-J. Second-order reliability approximations[J], J. Eng. Mech., ASCE,1987,113(8):1208-1225
15. Hurtado J.E, Alvarez D A. Neural-network-based reliability analysis:a comparative study[J], Comput. Meth.Appl. Mech. Eng.,2001,191(1-2):113-132
16. Raizer V. Theory of reliability in structural design[J], Appl. Mech. Rev.,2004,57(1):1-21
17.李云贵,赵国藩.结构可靠度的四阶矩分析法[J],大连理工大学学报,1992,32(4)：455-459
18. Zhao Y G, Ono T. Moment method for structural reliability[J], Struct. Saf.,2001,23(6):47-45
19. Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis[J], Struct. Saf.,1993,12(3):205-220
20. Zheng Y, Das P K. Improved response surface method and its application to stiffened plate reliability analysis[J], Eng. Struct,2000,22(5):544-551
21. Gomes H M, Awruch A M. Comparison of response surface and neural network with other methods for structural reliability analysis[J], Struct. Saf.,2004,26(1):49-67
22. Der Kiureghian A, Ke J-B. The stochastic finite element method in structural reliability[J], Prob. Eng. Mech.,1988,3(2):83-91
23. Ghanem R G, Spanos P D. Spectral stochastic finite-element formulation for reliability analysis[J], J. Eng. Mech., ASCE,1991,117(10):2351-2372
24. Zhang Yimin, Liu Eruo, Liu Qiaoling. Uncertain eigenvalue analysis by stochastic finite order method[J], Proceedings of ICDVC, Beijing, P. R. China, July,1990,1030-1036
25.张义民,刘巧伶.多随机参数结构可靠性分析的随机有限元法[J],东北工学院学报,1992,13(增刊)：97-99
26.张义民,陈塑寰,周振平等.静力分析的一般随机摄动法[J],应用数学与力学,1995,16(8)：709-714
27. Zhang Y M, Chen S H, Liu Q L, et al. Stochastic perturbation finite elements[J], Comput. Struct., 1996,59(3):425-429
28. Zhang Y M, Wen B C, Chen S H. PFEM formalism in Kronecker notation[J], Mathematics and Mechanics of Solids,1996,1(4):445-461
29. Wen B C, Zhang Y M, Liu Q L. Response of uncertain nonlinear vibration systems with 2D matrix functions[J], Nonlinear Dynamics,1998,15(2):179-190
30.张义民,刘巧伶,闻邦椿.多自由度非线性随机参数振动系统响应分析的概率摄动有限元法[J],计算力学学报,2003,20(1)：8-11
31. Hurtado J E, Alvarez D A. Classification approach for reliability analysis with stochastic finite-element modeling[J]. J. Struct. Eng., ASCE,2003,129(8):1141-1149
32.黄洪钟.对常规可靠性的批判评述[J],机械设计,1994,11(3)：1-5
33.王光远,张鹏,陈艳艳,等.工程结构的系统的模糊可靠性分析[M],南京：东南大学出版社,2001：1-102
34.黄洪钟.机械模糊可靠性原理与方法[M],大连：大连理工大学出版社,2002：1-58
35.王光远,王文泉.抗震结构的模糊可靠性分析[J],力学学报,1986,18(5)：448-455
36.王光远,王文泉,段明珠.具有多种失效模式的抗震结构的模糊可靠性分析[J],力学学报,1988,20(3)：278-282
37.吕震宙,冯元生.元件强度可靠性的模糊概率计算模型[J],航空学报,1996,17(6)：752-754
38.赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京：中国建筑工业出版社,2000：1-52
39.冯元生.机构可靠性理论的研究[J],中国机械工程,1992,3(3)：1-3
40.羊妗,冯元生.机构可靠性破坏模式研究[J],机械科学与技术,1991,10(2)：62-65
41.Н.Г.勃鲁也维奇,浙江大学机械原理及零件教研室译.机构精确度[M],上海：上海科学技术出版社,1966：1-165
42.B.Z.Sandler著,马培荪,马烈译.机构概率设计[M],北京：科学出版社,1991：1-80
43. S. J. Lee, B. J. Gilmore, The Determination of the Probabilistic properties of Velocities & Accelerations in Kinematic Chains with Uncertainty, Transactions of the ASME,1991,113(3):84-90
44.徐卫良,张启先.空间机构运动误差的概率分析和蒙特卡罗模拟[J],机械工程学报,1988,24(3)：97-104
45.石则昌,刘深厚.机构精确度[M],北京：高等教育出版社,1995：1-251
46.史天录,苏俊华,冯元生.铰链四杆机构运动精度和可靠性分析[J],西北建筑工程学院学报,1995,(1)：42-48
47.师忠秀,王峰.机构运动精度可靠性分析方法的研究[J],机械科学与技术,1997,16(1)：115-121
48. Shi Z X, Li F Q. Reliability-based Analysis and Synthesis of Mechanical Error for Path Generating Linkages[J], Chinese Journal of Mechanical Engineering,1997,10(2):130-135
49.张建国,白广臣.机构运动功能可靠性分析方法[J],机械工程师,1999,(1)：45-46
50.孟宪举,张策,詹敏晶,等.机构运动与动力精度概率分析模型[J],机械科学与技术,2004,23(1)：66-70
51.孙颉,吕震宙.考虑基本变量模糊随机性的弹性连杆机构广义可靠性分析[J],机械强度,2005,27(6)：851-854
52.纪玉杰,孙志礼,李良巧.一种机构运动可靠性的研究方法[J],机械与电子,2006,(5)：57-60
53.冯元生.机构磨损可靠性[J],航空学报,1993,14(12)：643-644
54.赵英美,冯元生.机构磨损可靠性高精度算法[J],机械强度,1998,20(1)：49-52
55.江新瑜,孙晓云.直动滚子从动盘形凸轮传动系统磨损的数值仿真[J],机械工程学报,2000,36(10)：86-90
56.罗继曼,孙志礼.对曲柄滑块机构运动精度可靠性模型的研究[J],机械科学与技术,2002,21(6)：959-962
57.贺东斌,宋占成.机构变形卡住可靠性分析[J],中国机械工程.1994,5(2)：3-5
58. Charnes A, Cooper W W. Chance constrained programming[J], Management Science,1959,6(1), 73-79
59. Frangopol D M. Sensitivity of reliability-based optimum design[J], J. Struct. Eng., ASCE,1985, 111(8):1703-1721
60. Lee T W, Kwak B M. A reliability-based optimal design using advanced first order second moment method[J], Mech. Struct. Mach.,1987,15(4):523-542
61. Nikolaidis E, Burdisso R. Reliability based optimization-a safety index approach[J], Comput. Struct., 1988,28(6):781-788
62. Reddy M V, Grandhi R V, Hopkins D A. Reliability based structural optimization:a simplified safety index approach[J], Comput. Struct.,1994,53(6):1407-1418
63.陈立周,翁海珊.概率优化设计的一种新计算方法[J],机械工程学报,1998,34(5)：8-12
64. Youn B D, Choi K K. A new response surface methodology for reliability-based design optimization[J], Comput. Struct.,2004,82(2-3):241-256
65.陈塑寰,宋大同,韩万芝.多自由度振动结构的随机优化方法[J],力学学报,1994,26(4)：432-439
66. Chen J J, Duan B Y. Structural optimization by displaying the reliability constraints[J], Comput. Struct.,1994,50(6):777-783
67.王光远,谭东耀.结构随机模糊优化设计方法及其对抗震结构的应用[J],地震工程与工程振动,1989,9(1)：1-9
68.李兴斯,钱令希.基于概率极限状态的结构优化设计[J],计算结构力学及其应用,1996,13(4)：379-384
69. Madan S R, et al. Synthesis of Slider-Crank Mechanism Using the Reliability Concept[J], J. inst. Eng. Indian. Part ME,1988,68(6):187-190
70. J. H. Rhyu, B. M. Kwak. Optimal Stochastic Design of Four-Bar Mechanisms for Tolerance and Clearance[J], Transactions of ASME,1988,110(9):225-262
71.师忠秀.函数再现机构的可靠性综合[J],华中理工大学学报,1994,22(7)：117-120
72.杜小平.机构的运动可靠性综合[J],机械,1995,22(4)：16-18
73. Shi Zhongxiu, Li Fengqiang. Analysis and Synthesis of Mechanical Error in Path Gene-rating Linkages Based on Reliability[C], IEEE. Proceedings of the 1997 Annual Reliabili-ty and Maintainability Symposium, USA,303-306
74.陈建军,陈勇,崔明涛,等.连杆机构稳健性优化设计[J].机械科学与技术,2002,21(6)：31-33
75. Howell L L, Rao S S, Midha A. Reliability-based optimal-design of bistable complaint mechanism[J], Journal of Mechanical Design,1994,116(4):1115-1121
76. Taguchi G. Introduction to Quality Engineering[M], Tokyo:Asian Productivity Organization,1986, 1-152
77.韩之俊.三次设计[M],北京：机械工业出版社,1992：1-98
78.陈立周.稳健设计[M],北京：机械工业出版社,2000：1-21
79.闻邦椿,周知承等.现代机械产品设计在新产品开发中的重要作用—兼论面向产品总体质量的“动态优化智能化和可视化”三化综合设计法[J],机械工程学报,2003,39(10)：43-52
80.陈立周.工程稳健设计发展现状与趋势[J],中国机械工程,1998,9(6)：5-62
81. Belegundu A D, Zhang S H. Robustness of design through minimum sensitivity[J], ASME J. Mech. Des.,1992,114(6):213-217
82. Parkinson A, Sorensen C, Pourhassan N. A general approach for robust optimal design[J], ASME J. Mech. Des.,1993,115(1):74-79
83. Emch G, Parkinson A. Robust optimal design for worst-case tolerances[J], ASME J. Mech. Des.,1994, 116(4):1019-1025
84.陈立周,于晓红,翁海珊.基于随机优化的工程稳健设计[J],北京科技大学学报,1999,21(1)：57-59
85. Lee K H, Park G J. Robust optimization considering tolerances of design variables[J], Comput. Struct., 2001,79(1):77-86
86.朱学军,王安麟,张惠侨.非稳态罚函数遗传算法及其用于机械／结构系统的健壮性设计[J],机械科学与技术,2000,19(1)：49-51
87.谭晓兰,韩建友,陈立周.基于随机模型的轨迹发生机构稳健设计研究[J],燕山大学学报,2004,28(5)：395-399
88.孟宪举,张策,师忠秀,等.连杆机构稳健优化设计[J],机械设计,2004,21(6)：31-33
89.孟宪举,张策,詹梅晶.基于成本的连杆机构的稳健性设计[J],河北理工学院学报,2004,26(4)：8-11
90.孟宪举,张策,师忠秀,等.基于成本的弹性连杆机构的稳健性设计[J],河北理工学院学报,2004,26(3)：18-21
91. Vetter W J. Matrix calculus operations and Taylor expansions[J], SIAM Review,1973,15(2):352-369
92. Brewer J W. Kronecker products and matrix calculus in system theory[J], IEEE Tran, Circuits and Systems,1978, CAS-25(9):772-781
93. Ma F. Extension of second moment analysis to vector-valued and matrix-valued func-tions[J], Int. J. Non-linear Mechanics,1987,22(3):251-260
94. Cramer H. Mathematical Methods of Statistics[M], N J:Princeton University Press,1964,1-115
95. Johnson N L, Kotz S. Distributions in Statistics[M]. New York:John Wiley & Sons, Inc.,1972,1-153
96.刘善维.机械零件的可靠性优化设计.北京：中国科学技术出版社[J],1993：233-349
97.宋笔锋,李为吉,吉国明等.大型结构可靠性优化设计的大系统方法[J],力学进展,2000,30(1)： 29-36
98.李良巧.机械可靠性设计与分析.北京：国防工业出版社[M],1998：58-275
99. Zhang Y M, Wen B C, Liu Q L. First passage of uncertain single degree-of-freedom nonlinear oscillators[J], Comput. Meth. Appl. Mech. Eng.,1998,165(4):23-231
100.Zhang Yimin, Liu Qiaoling. Reliability-based design of automobile components. Proc. Instn Mech. Engrs, Part D:J. Automobile Engineering,2002,216(D6),455-471
101.Zhang Yimin, Liu Qiaoling. Practical reliability-based analysis of coil tube-spring. Proc. Instn Mech. Engrs, Part C:J. Mechanical Engineering Science,2002,216(C2),179-182
102.Zhang Yimin, Liu Qiaoling, Wen Bangchun. Practical reliability-based design of gear pairs. Mech. Mach. Theory,2003,38(12),1363-1370
103.Zhang Yimin, He Xiangdong, Liu Qiaoling, Wen Bangchun. Reliability-based optimization of front-axle with non-normal distribution parameters[J], Transactions of the Chinese Society of Agricultural Engineering,2003,19(5):60-63
104.张义民,贺向东.钳式盘形制动器的多目标可靠性优化设计[J],中国机械工程,2004,15(2)：175-177
105.张义民,贺向东,刘巧伶,闻邦椿.不完全概率信息的连杆的可靠性优化设计[J],内燃机学报,2004,22(1)：86-90
106.贺向东,张义民,刘巧伶,闻邦椿.任意分布参数的后桥的可靠性优化设计[J],农业机械学报,2005,36(2)：22-26
107.Zhang Y M, Wen B C, Liu Q L. Reliability sensitivity for rotor-stator systems with rubbing. J. Sound Vib.,2003,259(5),1095-1107
108.张义民.任意分布参数的机械零件的可靠性灵敏度设计[J],机械工程学报,2004,40(8)：100-105
109.Zhang Y M, He X D, Liu Q L, Wen B C, et al. Reliability sensitivity of automobile components with arbitrary distribution parameters[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering,2005,219(2):165-182
110.Zhang Y M, He X D, Liu Q L, Wen B C. An approach of robust reliability design for mechanical components[J]. Proceedings of the Institution of Mechanical Engineers, Part E:Journal of Process Mechanical Engineering,2005,219(11):275-283
111.张义民,贺向东,刘巧伶,闻邦椿.汽车零部件的可靠性稳健优化设计：理论部分[J],中国工程科学,2004,6(3)：75-79
112.张义民,贺向东,刘巧伶,闻邦椿.任意分布参数的机械零件的可靠性稳健设计(一)：理论部分 [J],工程设计学报,2004,11(5)：233-237
113.贺向东,张义民,刘巧伶.整体法兰的可靠性稳健优化设计[J],机械强度,2004,26(6)：666-669
2. 曹惟庆等.连杆机构的分析与综合[M],北京：科学出版社,2001：126-170
3. 赵均.机构数值分析与综合[M],北京：机械工业出版社,2005：1-40
4. 张义民.静、动态随机结构系统振动理论的研究[D],长春：吉林工业大学,1995
5. 张义民.非线性随机结构系统振动理论的研究[D],沈阳：东北大学,1998
6. 张义民.汽车零部件可靠性设计[M],北京：北京理工大学出版社,2000：1-156
7. 贺向东.机械结构可靠性稳健设计若干关键问题的研究[D],长春：吉林大学,2005
8. 孙志礼,陈良玉.实用机械可靠性设计理论与方法[M],北京：科学出版社,2003：1-268
9. Freuenthal A M. The safety of structures[J],ASCE Trans.,1947:112,125-129
10.黄克中,毛善培.随机方法与模糊数学应用[M],上海：同济大学出版社,1987：1-261
11. Hasofer A M, Lind N C. Exact and invariant second-moment code format[J], J. Eng. Mech. Div., ASCE,1974,100(EM1):111-121
12. Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J], Comput. Struct.,1978,9(5):489-494
13. Shinozuka M. Basic analysis of structural safety[J], J. Struct. Eng., ASCE,1983,109(3):721-740
14. Der Kiureghian A, Lin H-Z, Hwang S-J. Second-order reliability approximations[J], J. Eng. Mech., ASCE,1987,113(8):1208-1225
15. Hurtado J.E, Alvarez D A. Neural-network-based reliability analysis:a comparative study[J], Comput. Meth.Appl. Mech. Eng.,2001,191(1-2):113-132
16. Raizer V. Theory of reliability in structural design[J], Appl. Mech. Rev.,2004,57(1):1-21
17.李云贵,赵国藩.结构可靠度的四阶矩分析法[J],大连理工大学学报,1992,32(4)：455-459
18. Zhao Y G, Ono T. Moment method for structural reliability[J], Struct. Saf.,2001,23(6):47-45
19. Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis[J], Struct. Saf.,1993,12(3):205-220
20. Zheng Y, Das P K. Improved response surface method and its application to stiffened plate reliability analysis[J], Eng. Struct,2000,22(5):544-551
21. Gomes H M, Awruch A M. Comparison of response surface and neural network with other methods for structural reliability analysis[J], Struct. Saf.,2004,26(1):49-67
22. Der Kiureghian A, Ke J-B. The stochastic finite element method in structural reliability[J], Prob. Eng. Mech.,1988,3(2):83-91
23. Ghanem R G, Spanos P D. Spectral stochastic finite-element formulation for reliability analysis[J], J. Eng. Mech., ASCE,1991,117(10):2351-2372
24. Zhang Yimin, Liu Eruo, Liu Qiaoling. Uncertain eigenvalue analysis by stochastic finite order method[J], Proceedings of ICDVC, Beijing, P. R. China, July,1990,1030-1036
25.张义民,刘巧伶.多随机参数结构可靠性分析的随机有限元法[J],东北工学院学报,1992,13(增刊)：97-99
26.张义民,陈塑寰,周振平等.静力分析的一般随机摄动法[J],应用数学与力学,1995,16(8)：709-714
27. Zhang Y M, Chen S H, Liu Q L, et al. Stochastic perturbation finite elements[J], Comput. Struct., 1996,59(3):425-429
28. Zhang Y M, Wen B C, Chen S H. PFEM formalism in Kronecker notation[J], Mathematics and Mechanics of Solids,1996,1(4):445-461
29. Wen B C, Zhang Y M, Liu Q L. Response of uncertain nonlinear vibration systems with 2D matrix functions[J], Nonlinear Dynamics,1998,15(2):179-190
30.张义民,刘巧伶,闻邦椿.多自由度非线性随机参数振动系统响应分析的概率摄动有限元法[J],计算力学学报,2003,20(1)：8-11
31. Hurtado J E, Alvarez D A. Classification approach for reliability analysis with stochastic finite-element modeling[J]. J. Struct. Eng., ASCE,2003,129(8):1141-1149
32.黄洪钟.对常规可靠性的批判评述[J],机械设计,1994,11(3)：1-5
33.王光远,张鹏,陈艳艳,等.工程结构的系统的模糊可靠性分析[M],南京：东南大学出版社,2001：1-102
34.黄洪钟.机械模糊可靠性原理与方法[M],大连：大连理工大学出版社,2002：1-58
35.王光远,王文泉.抗震结构的模糊可靠性分析[J],力学学报,1986,18(5)：448-455
36.王光远,王文泉,段明珠.具有多种失效模式的抗震结构的模糊可靠性分析[J],力学学报,1988,20(3)：278-282
37.吕震宙,冯元生.元件强度可靠性的模糊概率计算模型[J],航空学报,1996,17(6)：752-754
38.赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京：中国建筑工业出版社,2000：1-52
39.冯元生.机构可靠性理论的研究[J],中国机械工程,1992,3(3)：1-3
40.羊妗,冯元生.机构可靠性破坏模式研究[J],机械科学与技术,1991,10(2)：62-65
41.Н.Г.勃鲁也维奇,浙江大学机械原理及零件教研室译.机构精确度[M],上海：上海科学技术出版社,1966：1-165
42.B.Z.Sandler著,马培荪,马烈译.机构概率设计[M],北京：科学出版社,1991：1-80
43. S. J. Lee, B. J. Gilmore, The Determination of the Probabilistic properties of Velocities & Accelerations in Kinematic Chains with Uncertainty, Transactions of the ASME,1991,113(3):84-90
44.徐卫良,张启先.空间机构运动误差的概率分析和蒙特卡罗模拟[J],机械工程学报,1988,24(3)：97-104
45.石则昌,刘深厚.机构精确度[M],北京：高等教育出版社,1995：1-251
46.史天录,苏俊华,冯元生.铰链四杆机构运动精度和可靠性分析[J],西北建筑工程学院学报,1995,(1)：42-48
47.师忠秀,王峰.机构运动精度可靠性分析方法的研究[J],机械科学与技术,1997,16(1)：115-121
48. Shi Z X, Li F Q. Reliability-based Analysis and Synthesis of Mechanical Error for Path Generating Linkages[J], Chinese Journal of Mechanical Engineering,1997,10(2):130-135
49.张建国,白广臣.机构运动功能可靠性分析方法[J],机械工程师,1999,(1)：45-46
50.孟宪举,张策,詹敏晶,等.机构运动与动力精度概率分析模型[J],机械科学与技术,2004,23(1)：66-70
51.孙颉,吕震宙.考虑基本变量模糊随机性的弹性连杆机构广义可靠性分析[J],机械强度,2005,27(6)：851-854
52.纪玉杰,孙志礼,李良巧.一种机构运动可靠性的研究方法[J],机械与电子,2006,(5)：57-60
53.冯元生.机构磨损可靠性[J],航空学报,1993,14(12)：643-644
54.赵英美,冯元生.机构磨损可靠性高精度算法[J],机械强度,1998,20(1)：49-52
55.江新瑜,孙晓云.直动滚子从动盘形凸轮传动系统磨损的数值仿真[J],机械工程学报,2000,36(10)：86-90
56.罗继曼,孙志礼.对曲柄滑块机构运动精度可靠性模型的研究[J],机械科学与技术,2002,21(6)：959-962
57.贺东斌,宋占成.机构变形卡住可靠性分析[J],中国机械工程.1994,5(2)：3-5
58. Charnes A, Cooper W W. Chance constrained programming[J], Management Science,1959,6(1), 73-79
59. Frangopol D M. Sensitivity of reliability-based optimum design[J], J. Struct. Eng., ASCE,1985, 111(8):1703-1721
60. Lee T W, Kwak B M. A reliability-based optimal design using advanced first order second moment method[J], Mech. Struct. Mach.,1987,15(4):523-542
61. Nikolaidis E, Burdisso R. Reliability based optimization-a safety index approach[J], Comput. Struct., 1988,28(6):781-788
62. Reddy M V, Grandhi R V, Hopkins D A. Reliability based structural optimization:a simplified safety index approach[J], Comput. Struct.,1994,53(6):1407-1418
63.陈立周,翁海珊.概率优化设计的一种新计算方法[J],机械工程学报,1998,34(5)：8-12
64. Youn B D, Choi K K. A new response surface methodology for reliability-based design optimization[J], Comput. Struct.,2004,82(2-3):241-256
65.陈塑寰,宋大同,韩万芝.多自由度振动结构的随机优化方法[J],力学学报,1994,26(4)：432-439
66. Chen J J, Duan B Y. Structural optimization by displaying the reliability constraints[J], Comput. Struct.,1994,50(6):777-783
67.王光远,谭东耀.结构随机模糊优化设计方法及其对抗震结构的应用[J],地震工程与工程振动,1989,9(1)：1-9
68.李兴斯,钱令希.基于概率极限状态的结构优化设计[J],计算结构力学及其应用,1996,13(4)：379-384
69. Madan S R, et al. Synthesis of Slider-Crank Mechanism Using the Reliability Concept[J], J. inst. Eng. Indian. Part ME,1988,68(6):187-190
70. J. H. Rhyu, B. M. Kwak. Optimal Stochastic Design of Four-Bar Mechanisms for Tolerance and Clearance[J], Transactions of ASME,1988,110(9):225-262
71.师忠秀.函数再现机构的可靠性综合[J],华中理工大学学报,1994,22(7)：117-120
72.杜小平.机构的运动可靠性综合[J],机械,1995,22(4)：16-18
73. Shi Zhongxiu, Li Fengqiang. Analysis and Synthesis of Mechanical Error in Path Gene-rating Linkages Based on Reliability[C], IEEE. Proceedings of the 1997 Annual Reliabili-ty and Maintainability Symposium, USA,303-306
74.陈建军,陈勇,崔明涛,等.连杆机构稳健性优化设计[J].机械科学与技术,2002,21(6)：31-33
75. Howell L L, Rao S S, Midha A. Reliability-based optimal-design of bistable complaint mechanism[J], Journal of Mechanical Design,1994,116(4):1115-1121
76. Taguchi G. Introduction to Quality Engineering[M], Tokyo:Asian Productivity Organization,1986, 1-152
77.韩之俊.三次设计[M],北京：机械工业出版社,1992：1-98
78.陈立周.稳健设计[M],北京：机械工业出版社,2000：1-21
79.闻邦椿,周知承等.现代机械产品设计在新产品开发中的重要作用—兼论面向产品总体质量的“动态优化智能化和可视化”三化综合设计法[J],机械工程学报,2003,39(10)：43-52
80.陈立周.工程稳健设计发展现状与趋势[J],中国机械工程,1998,9(6)：5-62
81. Belegundu A D, Zhang S H. Robustness of design through minimum sensitivity[J], ASME J. Mech. Des.,1992,114(6):213-217
82. Parkinson A, Sorensen C, Pourhassan N. A general approach for robust optimal design[J], ASME J. Mech. Des.,1993,115(1):74-79
83. Emch G, Parkinson A. Robust optimal design for worst-case tolerances[J], ASME J. Mech. Des.,1994, 116(4):1019-1025
84.陈立周,于晓红,翁海珊.基于随机优化的工程稳健设计[J],北京科技大学学报,1999,21(1)：57-59
85. Lee K H, Park G J. Robust optimization considering tolerances of design variables[J], Comput. Struct., 2001,79(1):77-86
86.朱学军,王安麟,张惠侨.非稳态罚函数遗传算法及其用于机械／结构系统的健壮性设计[J],机械科学与技术,2000,19(1)：49-51
87.谭晓兰,韩建友,陈立周.基于随机模型的轨迹发生机构稳健设计研究[J],燕山大学学报,2004,28(5)：395-399
88.孟宪举,张策,师忠秀,等.连杆机构稳健优化设计[J],机械设计,2004,21(6)：31-33
89.孟宪举,张策,詹梅晶.基于成本的连杆机构的稳健性设计[J],河北理工学院学报,2004,26(4)：8-11
90.孟宪举,张策,师忠秀,等.基于成本的弹性连杆机构的稳健性设计[J],河北理工学院学报,2004,26(3)：18-21
91. Vetter W J. Matrix calculus operations and Taylor expansions[J], SIAM Review,1973,15(2):352-369
92. Brewer J W. Kronecker products and matrix calculus in system theory[J], IEEE Tran, Circuits and Systems,1978, CAS-25(9):772-781
93. Ma F. Extension of second moment analysis to vector-valued and matrix-valued func-tions[J], Int. J. Non-linear Mechanics,1987,22(3):251-260
94. Cramer H. Mathematical Methods of Statistics[M], N J:Princeton University Press,1964,1-115
95. Johnson N L, Kotz S. Distributions in Statistics[M]. New York:John Wiley & Sons, Inc.,1972,1-153
96.刘善维.机械零件的可靠性优化设计.北京：中国科学技术出版社[J],1993：233-349
97.宋笔锋,李为吉,吉国明等.大型结构可靠性优化设计的大系统方法[J],力学进展,2000,30(1)： 29-36
98.李良巧.机械可靠性设计与分析.北京：国防工业出版社[M],1998：58-275
99. Zhang Y M, Wen B C, Liu Q L. First passage of uncertain single degree-of-freedom nonlinear oscillators[J], Comput. Meth. Appl. Mech. Eng.,1998,165(4):23-231
100.Zhang Yimin, Liu Qiaoling. Reliability-based design of automobile components. Proc. Instn Mech. Engrs, Part D:J. Automobile Engineering,2002,216(D6),455-471
101.Zhang Yimin, Liu Qiaoling. Practical reliability-based analysis of coil tube-spring. Proc. Instn Mech. Engrs, Part C:J. Mechanical Engineering Science,2002,216(C2),179-182
102.Zhang Yimin, Liu Qiaoling, Wen Bangchun. Practical reliability-based design of gear pairs. Mech. Mach. Theory,2003,38(12),1363-1370
103.Zhang Yimin, He Xiangdong, Liu Qiaoling, Wen Bangchun. Reliability-based optimization of front-axle with non-normal distribution parameters[J], Transactions of the Chinese Society of Agricultural Engineering,2003,19(5):60-63
104.张义民,贺向东.钳式盘形制动器的多目标可靠性优化设计[J],中国机械工程,2004,15(2)：175-177
105.张义民,贺向东,刘巧伶,闻邦椿.不完全概率信息的连杆的可靠性优化设计[J],内燃机学报,2004,22(1)：86-90
106.贺向东,张义民,刘巧伶,闻邦椿.任意分布参数的后桥的可靠性优化设计[J],农业机械学报,2005,36(2)：22-26
107.Zhang Y M, Wen B C, Liu Q L. Reliability sensitivity for rotor-stator systems with rubbing. J. Sound Vib.,2003,259(5),1095-1107
108.张义民.任意分布参数的机械零件的可靠性灵敏度设计[J],机械工程学报,2004,40(8)：100-105
109.Zhang Y M, He X D, Liu Q L, Wen B C, et al. Reliability sensitivity of automobile components with arbitrary distribution parameters[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering,2005,219(2):165-182
110.Zhang Y M, He X D, Liu Q L, Wen B C. An approach of robust reliability design for mechanical components[J]. Proceedings of the Institution of Mechanical Engineers, Part E:Journal of Process Mechanical Engineering,2005,219(11):275-283
111.张义民,贺向东,刘巧伶,闻邦椿.汽车零部件的可靠性稳健优化设计：理论部分[J],中国工程科学,2004,6(3)：75-79
112.张义民,贺向东,刘巧伶,闻邦椿.任意分布参数的机械零件的可靠性稳健设计(一)：理论部分 [J],工程设计学报,2004,11(5)：233-237
113.贺向东,张义民,刘巧伶.整体法兰的可靠性稳健优化设计[J],机械强度,2004,26(6)：666-669