摘要
混沌分形作为非线性科学研究的核心内容,近二十年来引起了人们的广泛关注,并在混沌分形理论的探讨和混沌分形工程应用等方面均取得了可喜的研究成果。本文对混沌分形理论进行了系统深入的研究,在此研究成果的基础上,对机构学、机器人及全局优化设计主要问题中的混沌分形现象做出了详细的分析,并针对混沌分形在计算运动学、全局优化技术、进化计算等方面的应用做了深入而富有创造性的研究和试验验证,研究面向机构学及全局优化设计中一些一直比较困难的课题。本文的主要内容与创新成果包括以下几个方面:
第一章(绪论)系统回顾了混沌分形的研究历史和发展趋势,详细介绍了混沌分形在机构学及优化设计中的研究进展。在仔细研究了计算运动学、全局优化技术以及进化计算的发展现状的基础上,阐明了课题研究的意义和本文的研究内容。
第二章(混沌分形理论与方法的研究)系统阐述了混沌分形动力学的相关定义和定理,证明了Li-Yorke混沌定义与Devaney混沌定义之间关系和有关命题,研究了Julia点集的混沌特性,证明有关Julia集的关键命题,为混沌分形技术的应用奠定了坚实的理论基础。提出了确定动力系统倍周期分叉点的一种基于遗传算法的计算方法及提出了寻找迭代函数Julia点的方法,为混沌在机构学及优化设计中的应用提供了有效的方法。研究了离散动力系统和连续动力系统的Lyapunov指数,提出了定量识别混沌的新方法:计算最大Lvapunov指数的变分法,为判定混沌是否存在提供了有效方法。
第三章(混沌分形在机构学中的应用研究)将混沌分形技术作为机构学综合问题数值求解的新工具,系统分析了计算运动学各种理论方法的优缺点,研究了计算运动学中的混沌分形现象,通过理论证明和数值试验验证了Newton-Raphson迭代法具有混沌分形特性,提出了求解NR迭代函数Julia点的优化模型及进化规划求解方法,利用非线性离散动力系统在其Julia集出现混沌分形现象的特点,提出了一种基于NR搜索技术的求解机构综合问题全部/部分解的混沌分形方法。并在刚体导引和轨迹再现两大平面机构综合问题上进行了应用研究,比同伦方法找到了更多的有意义的实解。
第四章(混沌分形在无约束全局优化设计中的应用研究)系统地提出了基于混沌分形的无约束全局优化新方法,分析了机械优化设计中各种无约束全局优化方法的优缺点,对牛顿优化方法所构成的非线性离散动力系统的混动分形动力行为进行了深入研究,利用混沌分形理论研究牛顿优化方法对初始
第日页
西南交通大学博士研究生学位论文
点敏感的原因,提出了一种求解牛顿优化迭代函数的Julia点的反函数迭代
方法,发现J。lia集一般具有分形结构,而产生此动力系统的迭代函数在其
Julia集上呈混沌现象,利用牛顿优化方法的混沌分形敏感区域,提出了一种
全局优化的新方法,求解非线性优化问题的全部和/或全局最优解。给出了基
于混沌分形的全局优化新方法的计算步骤,并在函数发生优化综合问题和刚
体导引优化综合问题上进行了应用研究和数值试验,证明了该方法的有效性。
第五章(混沌在约束全局优化设计中的应用研究)提出了基于连续时间
变量的混沌全局优化新方法,证明子贯吐连续系统具有一定的优化能力,同
时证明了通过调整适当的受迫力,惯性耗散系统产生的混沌运动能得到控制,
系统通过混沌运动的方式在众多局部极小点之间迁移,随着受迫力的逐渐消
失,系统最终能收敛到全局最优解,在此理论基础上提出了具有全局优化能
力的基于连续时间变量的混沌优化算法。并研究了应用于冗余度机器人在有
障碍的环境中逆运动学问题优化求解,首次提出了一种避开任意多边形的避
障算法,通过构造避障势函数使该混沌全局优化算法能够处理该约束优化问
题。对平面7自由度操作手的多个仿真试验表明,该优化算法不仅能进行避
障运动而且位置误差非常小。
第六章(混沌进化计算及其在机构学及优化设计中的应用)建立了混沌进
化计算的理论框架,提出了求解复杂工程优化问题的全部/部分极小点的全局
优化算法—混沌进化计算方法。论述了进化计算的理论基础,建立了进化
计算的统一模型;研究了混沌发生器的随机性、遍历性和规律性以及混沌与
进化计算相结合的三种方式。设计了相应的混沌进化算子以及混沌群体嵌入
算子,提出了基于混沌吸引域概念的种群保护策略,适应了极值点分布不均
匀的情况,达到求解全部/大部分极小点的目的。针对机械优化设计中普遍存
在的混合离散变量问题,完整地阐明了利用线性表技术实现离散变量的编码
方法,连续变量按加工精度离散化编码方法,多余码的处理技术的混合个体
表示方法,并用于机械工程优化设计实例求解。并将混沌进化计算应用于机
构运动链同构识别中,建立了机构运动链同构识别全新的优化模型,提出了
用有序编码来描述机构运动链的变换矩阵,设计了有效的混沌有序进化算子,
实例研究及计算机仿真,显示该方法是成功的。
最后,结论部分对本文工作进行了总结,指出了进一步研究的方向。
关键词:混沌;分形;计算运动学;全局优化设计;进化计算
Chaos and Fractals, as the important fields of nonlinear system science, have been paid great attention in recent years, and a great deal of achievements has been made both in the theory and application in engineering. In this dissertation Chaotic and Fractal theory have been studied thoroughly and systematically, and the chaotic and fractal phenomenas of problems in mechanisms, robotics and design optimization have been detailed analyzed, and the application for computational kinematics, design optimization and evolution computation have been investigated in a creative way. The researches are all oriented to the difficulty problems in mechanisms and global optimization. The main researches and contributions of this dissertation are as follows:Definitions and theorems pertaining to the chaotic and fractal dynamics are investigated systematically. The relation between Li-Yorke chaotic and Devaney chaotic definitions and the related propositions are demonstrated and proved, and the chaotic characteristics of Julia set are studied and key propositions of Julia set are proved. Two new methods toward the chaos are proposed which provides an effective tool for the application of chaos to mechanisms and design optimization: method of computing the bifurcation accurately based on genetic algorithms and method of finding the Julia set point of iteration function. Lyapunov exponent for discrete and continuous dynamic systems are investigated, and an effective criteria for determining chaos based on computing the largest Lyapunov exponent using variation method is proposed.Chaotic and fractal technique is used as a tool for solving problems of mechanism synthesis for the first time, and the advantages and disadvantages of several computational kinematics theories are analyzed. The phenomena of chaos and fractals in computational kinematics are investigated, and the phenomena that chaos and fractal does exist in Newton-Raphson iterative method are proved both in theory and numerical simulation. The optimization model for finding Julia set point of Newton-Raphson iteration function is proposed and solved by evolutionary programming. Based on that Julia set is the boundaries of basins of attractions(roots) a novel method for obtaining all solutions of system of nonlinear equations arising from mechanism synthesis problem by utilizing sensitive fractal areas to locate the Julia set point is proposed, and planar rigid body guidance with five precision positions and planar path generation with nine precision points are solved by the method, and more meaningful solutions have been found compared with that by Homotopy method.An unconstrained optimization method for global solution based on chaos and fractal is proposed for the first time. The chaotic and fractal dynamic characteristics of discrete nonlinear system in Newton technique optimization are studied deeply, and reasons that sensitivity of Newton technique optimization heavily dependents on the initial guess point are investigated by means of chaos
and fractal theory. Based on that Julia set is the boundaries of basins of attractions (optimal) a new global optimization method of finding all local optima in nonlinear optimization problem is proposed by utilizing sensitive fractal areas to locate the Julia set point. The developed technique uses an important feature of fractals to preserve shape of basins of attraction(optima) on infinitely small scales. The method has been applied to the approximate synthesis of planar function generation and planar rigid body guidance effectively.The chaotic global optimization method based on continuous time variables is also proposed for the first time. That the continuous inertial system has optimization ability is proved. By adjusting compelling force adequately the chaos motion generated by inertial dissipative system is controlled to let the system migrating among the local minima and finally converging to global minimum. The proposed method is aplicated to the problem of point-to-point motion of redundant robot manipulators working in the
引文
[1] 卢侃,孙建华,欧阳容百等编译.混动动力学.上海:上海远东出版社,1990.
[2] 谢和平,张永平,宋晓秋等编译.分形几何——数学基础与应用.重庆:重庆大学出版社,1991.
[3] Raghavan M. , Roth B. Sovling Polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulator. 50~(th) Anniversary Design Issue, ASME Journal of Mechanical Design, Vol. 117, 1995. 71~79
[4] 吴祥兴,陈忠等编著.混沌学导论.上海:上海科学技术文献出版社,1996.
[5] 席德勋.非线性物理学.南京:南京大学出版社,2000.
[6] 李浙生.倏忽之间—混沌与认识.北京:冶金工业出版社,2002.
[7] Arnold V. I. Mathematical Methods of Classical Mechanics, Pringer-Verlag, New York, Heidelberg, Berlin, 1978.
[8] Arnold V. I. Instability of dynamical systems with several degrees of freedom, Soviet Mathematics Doklady, Vol. 5, 1964.
[9] Lorenz E. N. Deterministic nonperiodic flow, J. Atomos. Sci. , 1963, 20(1).
[10] Lorenz E.N.混沌的本质.北京:气象出版社,1997.
[11] Li T. Y. , Yorke J. A. Period three implies chaos, Amer. Math. Monthly, Vol. 82, 1975. 985-992
[12] May R. M. Simple Mathematical Models with Very Complicated Dynamics. Nature, Vol. 261, 1976.
[13] Feigenbaum M. Quantitative universality for a class of non-linear transformations, J. Stat. Phys. , Vol. 21, 1978.
[14] Feigenbaum M. Universality behavior in nonlinear system. Los Alamos: Los Alamos Science, 1980.
[15] 苗东升,刘华杰.混沌学纵横论.北京:中国人民大学出版社,1994.
[16] Mandelbrot. B. B. Fractal: Form, Chance and Dimension. San Francisco, W. H. Freeman and Co. 1975.
[17] Mandelbrot. B. B. The Fractal Geometry of Nature. San Francisco, W. H. Freeman and Co. , 1982.
[18] Falconer K. J. Fractal Geometry: Mathematical Foundation and Application, Wiley, New York, 1990.
[19] 谢利平等编译.分形几何——数学基础与应用.重庆:重庆大学出版社,1991.
[20] 吴敏.一类递归集的Hausdorff维数及Bouligand维数,数学学报,1995,38(2).
[21] 吴敏.关于自相似集的一个维数定理,数学学报,1995,38(2).
[22] 谢和平.分形力学的数学基础,力学进展,1995,24(9).
[23] Pentland A. P. Fractal-based Decription of Nature Scenes, IEEE Trans on PAMI, 1984, 6(6): 661-674.
[24] 李后强.分形研究的若干问题及动向,分形理论及其应用(三),合肥:中国科学 技术大学出版社,1993,1~4.
[2
[25] 张济忠.分形,北京:清华大学出版社,1995.
[26] 谢和平,薛秀谦.分形应用中的数学基础和方法,北京:科学技术出版社,1997.
[27] 李水根,吴纪桃.分形与小波,北京:科学出版社,2002.
[28] Seneviratne L. D. , Earles S. W. E. Chaotic behaviour exhibited during contact loss in a clearance joint of a four-bar mechanism. Mechanism & Machine Theory, 1992, 27(3), 307~321.
[29] Seneviratne L. D. , Earles S. W. E. , Fenner D. N. Analysis of a four-bar mechanism with a radially compliant clearance joint. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1996. 210 (3). 215~223.
[30] 常宗瑜,王玉新,张策,邱明旭.含间隙机构中的混沌现象.机械科学与技术,1998,17(3):345~350.
[31] 常宗瑜,张策,王玉新.含间隙连杆机构的分叉和混沌现象.机械强度,2001,23(1):77~79.
[32] Farahanchi F. , Shaw S. W. Chaotic and periodic dynamics of a slider-crank mechanism with slider clearance. Journal of Sound and Vibration, 1994, 177(3): 307~324.
[33] Jalali M. A. , Mehri B. Periodicity and chaos in a flexible crank-rocker mechanism. International J. of Non-Linear Mechanics, 1999, 34(6): 1103~1111.
[34] 史绍熙,刘双喜,宁智.带间隙副的曲柄-连杆机构中的混沌现象.内燃机学报,2000.18(2):184~186.
[35] Marghitu D. B. , Stoenescu, Eleonor D. Dynamics of mechanisms with slider joints and clearance. Proceedings of the ASME Design Engineering Technical Conference, 2001, 1755~1760
[36] 李哲.一种浑沌振动筛机构.北京工业大学学报,1994,20(1):1~4.
[37] Zhe Li. Chaotic vibration sieve. Mechanism Machine Theory, 1995, 30(4): 613~618.
[38] 龙运佳等.强非线性水平混沌振动台.农业工程学报,中国农业工程学会.1996,1:109~113
[39] Raghothama A. , Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method. Journal of Sound and Vibration, 1999, 226(3): 469~492.
[40] 张锁怀,沈允文,丘大谋.齿轮耦合的转子轴承系统的不平衡响应.机械工程学报,2002,38(6):51~55.
[41] Sato Keijin, Yamamoto Sumio, etc. Chaotic behavior in gear system. JSME International Journal, Series C, 1998, 41(3): 577~582.
[42] Li Yinong, Mi Lin, Zheng Ling, Zhu Caichao. Bifurcation and chaos in gear-pairs system with piecewise linearity. Proceedings of the International Conference on Mechanical Transmissions (ICMT 2001), 2001, 239~242.
[43] 王三民,沈允文,董海军.含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究,机械工程学报,2003,39(2):28~32.
[44] 孙智民,沈允文,王三民,李华.星型齿轮传动系统分岔与混沌的研究,机械工程学报,2001,37(12):11~15.
[45] 孙智民,沈允文,李华,董海军.星型齿轮传动系统定常与奇怪吸引子的共存现象,振动工程学报,2003,16(2):243~246.
[46] 孙智民,季林红,沈允文.2K-H行星齿轮传动非线性动力学,清华大学学报(自然科学版),2003,43(5):637~639.
[47] Cveticanin, L. Dynamic behavior of the lifting crane mechanism, Mechanism and Machine Theory, 1995, 30(1): 141~151.
[48] Ge, Zheng-Ming, Lee, Ching-I, Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring, Journal of Sound and Vibration, 2003, 262(4): 845~864.
[49] Jovanovic V T, Kazerounian K. Using Chaos to Obtain Global Solutions in Computational Kinematis. Transactions of the ASME, Journal of Mechanical Design, 1998, 120(7): 299~304.
[50] 谢进,陈永.混沌理论和平面连杆机构综合.机械科学与技术,2000,19(4):524~526.
[51] 谢进,陈永.计算运动学中牛顿迭代法的混沌现象.机械传动,2000,24(1):4~6.
[52] 谢进,陈永.基于混沌的刚体导引 Burmester点的求解方法.中国机械工程,2002.13(7):608~610
[53] 关立文,王知行,庄乾兴.分形论在平面机构位置分析中的应用.机械设计,1999,16(7):13~16
[54] 肖人彬,周济,王雪.分形设计:复杂产品设计的新途径.高技术通讯,1997,7(1):22~26
[55] Motoyoshi Hasegawa, et al. Calculation of the Fractal Dimensions of Machied Surface Profiles. Wear, 1996, 192: 40~45
[56] Xiong F, Jiang X Q. , Gao, Y, Li, Z, Evaluation of Engineering Surfaces Using a Combined Fractal Modeling and Wavelet Analysis Method. International J. of Machine Tools and Manufacture, 2001, 41(13-14): 2187~2193
[57] Zhou G Y, et al. Fractal Geometry Model for Wear Prediction. Wear, 1996, 170: 1~14
[58] 赵国堂.钢轨波磨的分形描述.铁道学报,1998,20(2):106~109
[59] 谢和平等.分形裂纹扩展对材料疲劳行为的影响.机械强度,1996,18(1):1~5
[60] 蒋东翔等.分形几何及其在旋转机械故障诊断中的应用.哈尔滨工业大学学报,1996,28(2):27~31
[61] Ryu K, Son Y, Jung M. Modeling and Specifications of Dynamic Agents in Fractal Manufacturing Systems. Computers in Industry 2003, 52(2): 161~182
[62] Tharumarajah A. A Self-organising View of Manufacturing Enterprises. Computers in Industry 2003, 51(2): 185~196
[63] Pedrycz W, Bargiela A. Fuzzy Fractal Dimensions and Fuzzy Modeling. Information Sciences 2003, 153(July): 199~216
[64] 李兵,蒋慰孙.混沌优化方法及其应用[J].控制理论与应用,1997,14(3):285~288
[65] Li B, Jiang W. Optmizing Complex functions by chaos search. Cybernetics and Systems, 1998, 29(4): 409~419
[66] 欧阳红兵,汪希萱.电磁式在线自动平衡头结构参数的混沌优化[J].中国机械工程,2000,11(5):557~559
[67] 张彤,王宏伟,王子才.变尺度混沌优化方法及其应用[J].控制与决策,1999,14(3):285~288
[68] 李昊,胡云昌,曹宏铎.加速混沌优化方法及其应用[J].系统工程学报,2002,17(1):41~44
[69] 王子才,张彤,王宏伟.基于混沌变量的模拟退火优化方法[J].1997,14(4):381~384
[70] Choi C, Lee J. Chaotic local search algorithm[J], Artificial Life & Robotics, 1998, 2(1): 41~47
[71] 梁瑞鑫,郑德玲.基于区间套混沌搜索的混合优化方法.北京科技大学学报,2002,24(3):342~344
[72] 张春慨.徐立云.邵惠鹤.改进混沌优化及其在非线性约束优化问题中的应用.上海交通大学学报 2000,34(5):593~595
[73] 骆晨钟.邵惠鹤.用混沌搜索求解非线性约束优化问题.系统工程理论与实践 2000.20(8):54~57
[74] Liu S, Hou Z, Wang M. A hybrid algorithm for optimal power flow using the chaos optimization and the linear interior point algorithm. Power System Technology, 2002. Proceedings. PowerCon 2002. International Conference on, 2002 2: 793~797
[75] 徐宁,周尚波,张红民,虞厥邦.一种混合混沌优化方法及其应用.系统工程与电子技术,2003,25(2):226~227
[76] Hopfield J J, Tank D W. 'Neural' computation od decisions in optimization problems, Biol. Cybern. , 1985, 52: 141~152
[77] Kirkpatrick S, Gellatt C, Vecchi C. Optimization by simulated annealing. Science, 1983, 220(4598): 671~680
[78] Chen L, Aihara L. Chaotic simulated annealing by aneural network model with transient chaos, Neural Networks, 1995, 8(6): 915~930
[79] Wang L, Smith K. On chaotic simulated annealing. IEEE Trans. Neural Networks, 1998, 9(4): 716~718
[80] Tokuda I, Aihara R, Nagashima T. Adaptive annealing for chaotic optimization. Physical Review E, 1998, 58(4): 5157~5160
[81] Zhou C, Chen T. Chaotic neural networks and chaotic annealing. Neurocomputing, 2000, 30: 293~300
[82] Yuyao He. Chaotic simulated annealing with decaying chaotic noise. IEEE Transactions on Neural Networks, 2002, 13(6): 1526~1531
[83] Ikeguchi T, Sato K, Hasegawa M, Aihara K. Chaotic optimization for quadratic assignment problems. IEEE International Symposium on Circuits and Systems, 2003, 3: Ⅲ-469~Ⅲ-472
[84] 张强,马润年,许进.一种混沌神经网络模型及其在优化中的应用.系统工程与电子技术,2002,24(2):48~50
[85] 张强,马润年,王超,许进.具有暂态混沌动力学的神经网络及其在函数优化计算中的应用.自然科学进展,2003,13(1):104~107
[86] 徐耀群,孙尧,郝燕玲.一种混沌Hopfield网络及其在优化计算中的应用,计算机工程与应用,2002,38(6):41~42
[87] Chen L, Aihara L. Global Searching Ability of Chaotic Neural Networks. IEEE Trans. On Circuit & System-Ⅰ: Fundament Theory & Applications, 1999, 46(8): 974~993.
[88] Chen L, Aihara L. Strange attractors in chaotic neural networks. IEEE Transactions on Circuits and Systems Ⅰ: Fundamental Theory and Applications, 2000, 47(10): 1455~1468
[89] Tanaka T, Hiura E. Computational abilities of a chaotic neural network. Physics Letters A, 2003, 315(3-4): 225~230
[90] Zhou C, Chen T. Chaotic annealing for optimization. Physical review E, 1997, 55(3): 2580~2587
[91] Suykens J A K, Yalcin M E, Vandewalle J. Coupled chaotic simulated annealing processes. Proceedings of the 2003 International Symposium on Circuits and Systems, 2003, 3: Ⅲ-582~Ⅲ-585
[92] Reuleaux F. Theoretische kinematik, Grundz u ge einer Theoriedes Maschinenwesens. Vol. 1 Braunschweig: Verlag Fredrich Vieweg & Sohn, 1875
[93] Burmester L. Lehrbuch der kinematik. Leipzig: Verlag von Arthur Felix, 1886
[94] Grashof F. Theoretische maschinenlehre. Vol. 2. Leipzig: verlag von L Voss, 1883
[95] Bricard R. Lecons de cinématique. Paris: Gauthier-Villars, 1927
[96] Goldberg M. New five-bar and six-bar linkages in three dimensions. Trans ASME, 1943, 65: 649~661
[97] Freudenstein F. An analytical approach to the design of four-link mechanism. Transactions of the ASME, 1954, 76: 483~492
[98] Levitskii N L, Shakvzian K K. Synthesis of spatial four-link mechanisms with lower pairs. Trudy Seminara Po Teorii Mshin I Mekhanizmov. Moscow: Akademiia Nauk SSSR, 1954.
[99] Denavit J, Hartenberg R S. A kinematic notation for lower pair mechanisms based on matrices. ASME J. Applied mechanics, 1955, 22: 215~221
[100] Hartenberg R S, Denavit J. Kinematic synthesis of linkages. New York: McGraw-Hill Book Co, 1964.
[101] Uicker Jr J J, Denavit J, Hartenberg R S. An Method for the displacement analysis of spatial mechnism. ASME J. Applied Mechanics, 1964, 309~314
[1
[102] Freudenstein F. Approximate synthesis of Four-bar linkage. Transaction of ASME, 1955, 77(6)
[103] Sub C. H. , Radcliffe C. W. Synthesis of plane linkage with use of the Displacement Matrix. ASME: Journal of Engineering for Industry, 1967, 89(2)
[104] Erdman A. G. The first forty years of modern kinematics. Atribute to ferdinand freudenstein. New York: John Wiley and Sons Inc, 1992
[105] Bottema O. , Roth B. Theoretical kinematic. Mineola N Y: Dover Publications, 1990
[106] 姚进,Jorge Angeles.论计算运动学在机构理论中的作用.四川大学学报(工程科学版),2003,35(3):1~8
[107] 李立,导师陈永.机构学及优化设计基于新算法的理论与方法的研究.西南交通大学博士论文,1998
[108] 王东明著.消去法及其应用.北京:科学出版社,2002
[109] Duffy J. , Gane C. Displacement analysis of the General spatial 7-link 7R Mechanism. MMT, vol. 15, 1980, 153~169
[110] Lee H. Y. , Liang C. G. Displacement analysis of the General spatial 7-link 7R Mechanism. MMT, vol. 23, 1988, 219~226
[111] Raghavan M. , Roth g. Inverse kinematics of the general 6R manipulator and related linkages. ASME J. of Mechanical Design, 1993, 115(3): 502~508
[112] Almadi A. N. , Dhingra A. K. , Kohli D. Framework for closed-form displacement analysis of planar mechanisms. ASME J. Mechanical Design, 1999, 121(3): 392~401
[113] Alici G. An inverse position analysis of five-bar planar parallel manipulators. Robotica, 2002, 20(2): 195~201
[114] Kim Jinwook, Park F. C. Direct kinematic analysis of 3-RS parallel mechanisms. Mechanism and Machine Theory. 2001, 36(10): 1121~1134
[115] Lee Tae-Young, Shim Jae-Kyung. Improved dialytic elimination algorithm for the forward kinematics of the general Stewart-Cough platform. Mechanism and Machine Theory. 2003, 38(6): 563-577
[116] 吴文俊著.数学机械化,北京:科学出版社,2003
[117] 林光春,徐礼钜.平面四杆机构刚体导引综合问题的符号解法.机械设计,1998(92)
[118] 殷成刚,丁洪生,张同庄.应有吴方法求解平面四杆机构四点轨迹综合的探讨.机械设计与制造,2002,6:76~77
[119] 韩林,张昱,梁崇高.吴方法在平面并联机构位置正解中的应用.北京航空航天大学学报,1998,24(1):116~119
[120] 林光春.机器人机构位置分析的符号法及力学解析模型.博士学位论文,四川联合大学,1998.5
[121] Lazard D. On the Representation of rigid-body motion and its applications to generalized platform manipulators. Comptational Kinematics, 1999, 175~ 181
[1
[122] Kalker-Kalkman C. M. An implementation of Buchberger's algorithm with application to Robotics. Mechanism and Machine Theory, 1993, 28(4): 523~537
[123] 李立,陈永.用Groebner基法求机构学问题的符号形式的解.机械科学与技术,1998.17(1):5~7
[124] 李立,陈永.用Groebner基方法求平面刚体导引综合问题的封闭形式的解.机械设计与研究,1998(1):25~27
[125] 李立,刘朝晖,陈永.基于Groebner基的空间Burmester问题的求解方法.机械科学与技术,2002,21(3):397~399
[126] Dhingra A. K, klmadi A. N, Kohli D. Closed-form displacement and coupler curve analysis of planar multi-loop mechanisms using Grbner bases. Mechanism and Machine Theory, 2001, 36(2): 273~298
[127] Wampler C. , Morgan A. , Sommese A. Numerical continuation methods for solving polynomial systems arising in kinematic, ASME J. of Mech. Des. 1990, 112: 59~68
[128] Li T. Y. , Saver T. , Yorke J. A. The Random product homotopy and deficient polynomial systems. Numerische Mathematik, 1987, 51: 481~500
[129] Li T. Y. , Saver T. , Yorke J. A. Numerical Solution of a class of deficient polynomial systems, SIAM J. of Numerical Analysis, 1988, 18(2): 173~177
[130] Morgan A. P. , Sommese A. J. Coefficient parameters polynomial continuation. Appl. Math. Comput, 1989, 29: 123~160
[131] Tsai L. W. , Morgan A. Solving the kinematics of the most general six-and five-degree-of-freedom manipulators by continuation methods. ASME J. of Mechanism, Transmissions and Automation in Design, 1985, 107: 189~200
[132] Wampler C. , Morgan A. , Sommese A. Complete Solution of the nine-point path synthesis problem for four-bar linkages. ASME J. of Mech. Des. 1992, 153~159
[133] 刘安心.机构运动综合与位置分析的理论与实用方法.博士学位论文,东南大学,1994
[134] 严静,导师陈永.概率同伦方法及其应用于机构学.硕士学位论文,西南交通大学,1996
[135] 张剑,导师陈永.改进的同伦方法及其在机构学中的应用.硕士学位论文,西南交通大学,1997
[136] 陈永,李立,张剑,严静.一种基于同伦函数的迭代法——同伦迭代法.数值计算与计算机应用,2001,(2):149~155
[137] 黄红选译.全局优化引论.北京:清华大学出版社,2003
[138] Horst R. , Pardalos P. M. , Thoai N. V. Introduction to Global Optimization, 2~(nd) Edition. Kluwer Academic Publisher, Dordrecht, The Netherlands, 2000
[139] 李柏林,导师陈永.基于单调性分析与符号处理技术的智能优化.西南交通大学博士学位论文,1995
[140] Horst R. , Pardalos P. M. Handbook of Global Optimization. Kluwer Academic Publisher, Dordrecht, The Netherlands, 1995
[141] Levy A, Montalvo A. The tunneling algorithm for the global minimization of functions. SIAM J. Scientifc and Stastical Computing, 1985, 6(1): 15~29
[142] Ge R, Qin Y. A class of filled function for finding global minimizer of a function of several variables. Journal of Optimization Theory and Application, 1987, 54: 241~52
[143] Xian L, Wilsun X. A new filled function applied to global optimiztion. Computers & Operations Research, 2004, 31: 61~80
[144] Casado L G, Martinez J A, Garcia I. Experiments with a new selection criterion in a fast interval optimization algorithm. Journal of Global Optimization, 2001, 19: 247~264
[145] Bezedek J C. On the relationship between Neural Network, Pattern Recognition and Intelligence. International Journal of Approximate Reasoning, 1992, 6: 85~107
[146] Kirkpatrick S. Optimization by simulated annealing: quantitative studied. Journal of Statistical physics, 1984, 34: 975~986
[147] Romeijin H E, Smith R L. Simulated annealing for constrained global optimiztion. J. Global Optimization. 1994, 5: 101~126
[148] Lin CY, Jiang JF. Nonconvex and discrete optimal design via multiple state simulated annealing. Structures Optimization. 1998, 14: 121~128
[149] Lin C-Y, Chen W-T. Stochastic multistage algorithms for multimodal structural optimization. Computers and Structures. 2000, 74: 233~241
[150] Glover F, M. Laguna. Tabu Search, Optimization, and Machine Learning. Addisiom-Wesley, San Marco, CA, Netherlands, 1995
[151] Siarry P, Berthiau G. Fitting of tabu search to optimize functions of continuous variables. International Journal for Numerical methods in Engineering, 1997, 40: 2449~2457
[152] Chelouah R, Siarry P. Tabu search applied to global optimization. European Journal of Operational Research, 2000, 123: 256~270
[153] 冯春,黄洪钟,谢泗淮.遗传算法住机械工程全局优化设计中的应用.机械设计,1997.5:18~10
[154] 冯春,黄洪钟,谢泗淮.机械工程全局优化中的遗传算法.机械科学与技术,1997,16(1):21~24
[155] 冯春,李柏林.解TSP的有序遗传算法.西南交通大学学报,1997,32(5):528~533
[156] 冯春,谢泗淮,张怡.遗传算法作为两层决策的一个新方法.西南交通大学学报,1996年,31(百年校庆增刊):388~391
[157] 冯春,卢存光,谢泗淮.基于遗传算法的轨迹发生机构最优解综合.机械传动,1996年增刊,21~24
[158] 冯春,陈永.遗传算法在一类组合优化中的应用.计算机工程与应用,2001, 37(5):44~46
[1
[159] 冯春,陈永.基于遗传算法的机构运动链同构识别.机械工程学报,2001,37(10):27~30
[160] 冯春,陈永.确定Logistic映射倍周期分叉点的遗传算法.西南交通大学学报,2003.38(3):290~293
[161] 冯春,李柏林,陈永.进化规划原理及其在机械工程中的展望.机械,2003,30(2):1~3
[162] 冯春,陈永.进化规划在控制混沌中的应用.机械设计.2002,19(8):10~12
[163] 张怡,冯春,胡鹏飞.基于进化规划的时间最优控制问题求解.西南交通大学学报.2002,(37)5:553~556
[164] 冯春,黄洪钟.一种新的优化搜索算法:进化策略.机械科学与技术,1997,16(3):398~410
[165] Beasley D. , Bull D. R. , Martin R. R. A sequential niche technique for muitimodal function optimization. Evolutionary Computation, 1993, 1(2): 101~125
[166] De Jong K. A. Genetic algorithms: A 25year perspective. In: Proceedings of the fifth international conference on genetic algorithms, Los Altos, CA: Morgan Kaufman Publishers, 1993
[167] Mahfoun S. W. Crowding and pre-selection revisited. In: Parallel Problem Solving from Nature, Manner R, Manderick B(eds). Berlin: Springer, 1992. 67~76
[168] Mengshoel O. J. , Goldberg D. E. Probability crowding: deterministic crowding with probabilistic replacement. In: Proceedings of the Genetic and Evolutionary Computation Conference 1999, Banzhaf W. et al(eds). San Francisco, CA: Morgan Kaufman, 1999, 409~416
[169] Goldberg D. E. , Richardson J. Genetic algorithms with sharing for multimodal function. In Grenfenstette J. J. editor, Genetic Algorithms and their Applictions: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Earlbaum, Hillsdale, New Jersey. 1987. 41~49
[170] Petrowski A. A clearing procedure as a niching method for genetic algorithms. In: Proceedings of the 3rd IEEE Conference on Evolutionary Computation, Piscataway, NJ: IEEE Press, 1996, 798~803
[171] Yin X, Germay N. A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization. In: Albrecht R F, Reeves C R, Steele N C, eds. Proc Int Conf Artificial Neural Nets and Genetic Algorithms, New York: Springer-Verlag, 1993, 450~457
[172] Miller B L, Shaw M J. Genetic algorithm with dynamic niche sharing for multimodal function optimization. In: Proceedings of the 3rd IEEE Conference on Evolutionary Computation, Piscataway, NJ: IEEE Press, 1996, 786~791
[173] Goldberg D E, Wang L. Adaptive niching via coevolutionary sharing. IlliGAl Report 97007, 1997
[174] Holland J. H. Adaptation in Natural and Artificial System. 2nd ed. Cambridge. Ma: MIT Press. 1992
[175] Deb K, Goldberg D E. An Investigation of niche and species formation in genetic function optimization. In: Schaffer J D, eds Proc. 3rd Int. Conf. Genetic Algorithms, San Mateo, CA: Morgan Kaufmann, 1989, 42~50
[176] Spears W M. Simple subpopulation schemes. In: Sebald A. V. and Fogel L. J. editors, Proceedings of the Third Annual Conference on Evolutionary Programming, World Scientific, Singapore, 1994, 296~307
[177] Gupta K C. Copmutational Kinematic. In: The First 40 Years of Modern Kinematics, A. Erdman, ed. , J. Wiley
[178] Baillieul J. Kinematic programming alternatives for redundant manipulators. Proc. Of IEEE International Conference on Robotics and Automation, Raleigh, N. Carolina, 1988
[179] Baker D R, Wampler C W. On the Inverse kinematics of redundant manipulators. International J. of Robotics Research, Vol. 7~2, 1988
[180] 耿祥义 Li-Yorke混沌的充要条件,数学学报,2001,44(5):929~932
[181] Devaney R. L. , AN Introduction to Chaotic Dynamical Systems, The Benjamin/Cummings Publishing, Co. , Inc. , 1986.
[182] 郭会,赵新.对混沌定义的一些研究,华北工学院学报,2001,22(5):395~396.
[183] 吴敏金.分形信息导伦,上海科学技术文献出版社,1993
[184] 姜万录,张淑清,王益群.混沌运动特征的数值试验分析.机械工程学报,2000.36(10):13~17.
[185] 郝柏林.从抛物线谈起—混沌动力学引论.上海:上海教科技教育出版社,1993:36~40
[186] 石博强,申焱华.机械故障诊断的分形方法——理论与实践.北京:冶金工业出版社,2001:104~121.
[187] Moon F. C. Chaotic Vibrations[M], Wiley, New York, 1985.
[188] Parker T. S. , Chua L. O. Practical Numerical Algorithms for Chaotic Systems [M], New York: Springer-Verlag, 1989
[189] 克鲁E著,非线性动力学系统的数值研究.凌复华译.上海:上海交通大学出版社,1989:75~81
[190] 王东生,曹磊.混沌、分形及其应用.中国科技大学出版社,合肥:1995
[191] Gao J, Zheng Z. Local exponential divergence plot and optimal embedding of a chaotic time series. Physics Letter A. 1993, 181(3): 153~158
[192] Wolf A, Swift J B, Swinney H L, Vastano J. A. Determining Lyapunov exponents from a time series. Physics D, 1985, 16(2): 285~317
[193] Benettin G, Galgani L. , Strelcyn J M. Lyapunov characteristic exponents for smooth dynamical system: a method for computing all of them, Meccanica 15: Part 1: Theory. 9-20; Part 2: Numerical applications, 21~30, 1980
[194] Casaleggio A, Braiotta S, Corana A. Study of the Lyapunov exponents of ECG signals from MIT-BIH database, Computers in Cardiology, 1995, 10-13 Sep: 697~700
[195] Rosenstein MT. et al. Apractical method for calculating largest Lyapunov exponents from small data sets. Physics D, 1993, 65: 117~134
[196] Becker K H, Drfler M. Dynamical systems and fractals. Cambridge University Press, 1989.
[197] Benzinger H E, Burns S A, Palmore J I. Chaotic complex dynamics and Newton's method. Physics Lett. A 1987, 119(9): 441
[198] Kyle Kneis. Julia sets for the super-Newton method, Cauchy's method, and Halley' s method. Choas. 2001, 11(2): 359~370
[199] Fogel G B, Fogel D B. Continuous evolutionary programming: analysis and experiments. Cybernetics and Systems, 1995, 26(1): 79~90
[200] X. Yao, Y. Liu and G. Lin, Evolutionary programming made faster. IEEE Transactions on evolutionary computation, Vol. 3, No. 2, July 1999, 82~102
[201] 付金元,陈永.刚体导引的平面四杆机构综合的新方法.机械工程学报,1996,32(2):40~45
[202] Zhang Jian, Chen Yong. Improved Homotopy Iteration Method and Applied to the Nine-point Path Synthesis Problem for Four-bar Linkages. Chinese J. of Mech. Eng. 2000, 13(1): 10~16
[203] Michalewicz Z. Genetic algorithms + data structures = evolution programs. New York: Springer-Verlag, 1996
[204] 孟兆明,常德功.机械最优化设计技术,北京:化学工业出版社,2002
[205] 刘安心,杨廷力.机械系统运动学设计.北京:中国石化出版社,1999
[206] Michalewicz Z, Fogel D B. How to solve it: Morden Heuristics. Spring-Verlag Berlin Heidelberg, 2000
[207] Himmelblau D. Applied nonlinear programming. McGraw-Hill, NY, 1992
[208] 赵华敏,陈开周.全局优化的神经网络方法.控制理论与应用,2002,19(6):824~828
[209] 黄润生.混沌及其应用.武汉:武汉大学出版社,2000
[210] Ravishankar A S, Ashitava Ghosal. Nonlinear Dynamics and Chaotic Motions in Feedback-Controlled Two- and Three-Degree-of-Freedom Robots. The International Journal of Robots Research, 1999; 18(1): 93~108
[211] Khosla P. K. , Real-Time Control and Identification of Direct-Drive Manipulators, [ Ph. D. Thesis] USA: Dept. of Electrical and Computer Eng. Carnegie Mellon University, 1986.
[212] Fujita T, Watanabe T, Yasuda K, Yokoyama R. Golbal Optimization Method using Intermittency chaos. Proceedings of the 36th Conference on Decision & Control, San Diego, California USA, 1997, 1508~1509
[213] Jovanovic, V. T. , and Kazerounian, K. , Optimal Design Using Chaotic Descent Method, ASME J. Mech. Des. 122(3): 265~270.
[2
[214] Griewank A O. Generalized descent for global optimization. J. of Optimization Therory and Application. Vol. 34, No 1, 1981.
[215] Whitney E. Resolved Motion Rate Control of Manipulators and Human Prostheses. IEEE Transaction on Man Machine System, 1969, 10(2): 47~53.
[216] Yoshikawa T. Analysis and Control of Robot Manipulators with Redundancy. The International Journal of Robots Research, 1984, 735~747.
[217] YoshikawaT. Manipulability and Redundancy Control of Robotics Mechanism. Proceeding of the IEEE International Conference on Robotics and Automation, 1985, 1: 1004~1009.
[218] Kireanski M V and Petrovic T M. Combined Analytical Pseudoinverse Inverse Kinematic Solution for Simpie Redundant Manipulators and Singularity Avoidance. The International Journal of Robots Research, 1993, 12(2): 188~196.
[219] Khatib O. Real-time obstacle avoidance for manipulator and mobile robots. The International Journal of Robots Research, 1986, 5(1): 90~98.
[220] Volpe R, Khosla P. Manipulator control with superquadric artificial potential function. IEEE Transaction on Systems Man and Cybernetics, 1990, 20(6): 379~386.
[221] Mohri A, Marushima S, Yamamoto M. Collision free trajectory planning for manipulator using potential funtion. IEEE International Conference on Robot and Automation, 1995, 3069~3074.
[222] Maciejewski A, Klein C. Obstacle avoidance for kinematiclly redundant manipilators in Dynamically varying enviromrnts. International Journal of Robotics Research, 1985, 4(3): 109~117
[223] Chein R T. Planning collision-free paths for robotic arm among obstacles. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1986, 6(1): 229~238.
[224] Lozano P T. Spatial planning: a configuration space approach. IEE Transaction on Computer, 1983(2): 162~169.
[225] Dermatas E, Aspragathos N. Collision-free motion planning for redundant robots rsing neural-network. Processing Engineering Applications of Artificial Intelligence. 1997, 10(2): 179~188
[226] Khoogar A R, Parker J K. Obstacle avoidance of redundant manipulators using genetic algorithms. Conference Proceedings-IEEE SOUTHEASTCON, v 1, 1991, 317~320
[227] Holland J H. Adaptation in Natural & Artificial Systems(M). Ann Arbrr. MI: Univ. of Michigan Press, 1975
[228] Goldberg D E. genetic Algorithms in Search, Optimization and Machine Learning(M). Reading: Addison-Wesley, 1989
[229] 张涛.热力系统在线进化优化体系研究[博十学位论文],北京:清华大学,2000
[230] 王鑫鑫.热力系统模拟进化新技术研究[博士学位论文],北京:清华大学,2003
[231] Fogel D E. Asymptotic convergence properties of genetic algorithms and evolutionary programming: Analysis and experiment. Cybernetics and Systems, 1994, 25(3): 389~407
[232] Wesson, Robert G. Beyond natural selection. Cambridge, Massachusetts: The MIT Press, 1981
[233] 陈式刚.混沌与映射.北京:国防科技出版社,1992
[234] Golinski J. Optimum synthesis problems solved by means of nonlinear programming and random methods. J. of Mechanism, 1970, 5: 287~309
[235] Mohame B T, Xiao B L. A fuzzy adaprive simplex search optimization algorithm. Tran. of ASME, J. of Mechanical Design, 2001, 123(6): 216~225
[236] 吴兆汉,万耀青.机械优化设计.北京:机械工业出版社,1986.256~262
[237] 孔凡国,邹慧君.一种机构运动链同构识别的新方法研究.中国机械工程,1997, 8(2):30~32
[238] Kong F G, Q. Li, Zhang W J. An artificial neural network approach to mechanism kinematics chain isomorphism identification. Mech. and Mach. Theory, 1999, 34: 271~283
[239] Ambekar A G, Agrawal V P. Canonical numbering of kinematics chains and isomorphism problem: min code, Mech. and Mach. Theory, 1987, 22: 453~461.
[240] Tang C S, Liu T. The degree code-a new mechanism identifier. ASME J of Mech. Design, 1993, 115: 627~630
[241] Shin J K, Krishnamurthy S. On identification and canonical numbering of pin jointed kinematic chains. ASME J of Mech. Design, 1994, 116: 182~188
[242] Yan H S, Hwang W M. Linkage path code. Mech. and Mach. Theory, 1984, 119: 425~429
[243] Chu J K, Wei-Quing, Cao. Identification of isomorphism among kinematics chains and inversions using link's adjacent Chain Table. Mech. and Mach. Theory, 1994, 29: 53~58