转子碰摩非线性行为与故障辨识的研究
|
摘要
20世纪下半叶兴起的混沌理论为非线性动力学系统的研究开创了新途径。对复杂机械
系统中可能出现的强非线性行为(如混沌）展开研究并探讨混沌理论在机械故障诊断中的
应用，对于复杂机械系统的设计、使用、诊断与维修具有重要意义。
随着机械运转速度的日益提高以及各种新型材料在高速机械中的广泛应用，机械系
统的非线性将更加突出，可能直接（或间接）导致机械系统的故障。从理论和实验上对
这个问题进行研究意义重大，而对非线性行为特别是混沌行为的预测与运行状态早期检
测，以及利用基于混沌理论的信号／信息处理方法的研究显得尤为突出。本文正是在这样
的背景下，提出对转子系统中存在的复杂非线性行为展开研究，并对非线性行为的辨识方
法以及基于混沌理论的转子故障早期诊断新方法进行了深入研究与探讨。
本论文主要完成两个方面的研究工作：从碰摩转子实验系统中观测混沌现象并进行辨
识与分析；基于非线性科学理论与技术对转子系统的行为进行分析、预测与早期辨识。概
述地说，围绕上述问题所开展的具体研究内容包括：
1．深入系统地研究了碰摩转子的非线性行为与特征规律。
(1）采用并改进了已有的转子尖锐碰摩模型，通过定量和定性的理论分析，获得了尖
锐碰摩转子振动响应形式；设计了尖锐碰摩转子试验台并开展了细致的实验研究，获得了
不同碰摩情况下的振动响应特征规律；通过理论和实验分析，得出在尖锐碰摩情况下，早
期碰摩在一定条件下会出现1／3X、2／3X的分频成分的结果（X表示工频）。
（2） 建立了基于局部碰摩力变化且具有转、定于偏心的Jeffcott非线性转子的动力学
模型，大量的数值仿真表明局部碰摩转子存在分频现象和一定的分叉规律，获得了大不平
衡、小阻尼、高转速条件下，局部碰摩容易产生拟周期或混沌振动的结果；基于数值分析
结果，设计并建立了局部碰摩转子系统试验台，在大范围的转速里进行了细致的实验研究，
观察到了包括周期、拟周期、次谐波与超谐波以及混沌振动在内的丰富的振动现象。观测
与仿真结果定性一致。
（3）采用基于观测时间序列的重构相空间分析方法对转子系统的非线性行为进行辨识
与分析，获得了系统出现强非线性行为的统计意义上的证据。
研究表明早期碰摩时产生的分频现象这一结果对这类故障的早期诊断提供了依据。理
论与实验分析获得的碰摩转子振动响应的特征规律对于碰摩的预测具有一定的参考价值。
2．提出了具有工程化前景的相空间重构技术和统计特征指数算法，以评判碰摩转子
观测数据所隐含的动力学行为。
（1）在短数据集情况下，为了快速、合理地选择嵌入空间参数，提出了延迟时间选择
的交叉位移改进法和嵌入维数选择的伪近邻距离统计增长法，其特点是速度快、重复性好。
（2）对影响关联维数计算的各种因素进行了深入分析，提出了在短数据集约束下估计
关联维数的具体方法。
国防科学技术大学研究生院学位论文
一
o）提出了在短数据集条件下，通过最大瞬时Lyapunov指数来估计最大LyaPunov指
数的方法，并指出Lyapunov指数之和与系统的能量耗散机制相关联。从理论上分析并提
出了Lyapunov指数之和的变化规律可用来监测强非线性系统的阻尼变化，从而可以监测
系统状态变化的新策略和新方法。
研究表明关联维数和最大Lyapunov指数对非线性动力学行为的辨识是行之有效的，其
有效性在转子碰摩的各种状态的分类与辨识中获得了证实。
3．提出了通过观测数据的不可长期预测性并结合特征指数 分析对信号的混油特性
进行综合判别的新方法。
O）改进了局部线性拟合的非线性预测方法。
c）提出了非线性时间序列预测的相轨迹方法。
＊）提出了利用观测数据的短期、长期可预测性可对动力学行为进行辨识的新方法。
研究表明，上述预测方法结合特征指数分析，可以对非线性行为进行综合分类与辨识，
通过多指数、多角度地对观测数据进行分析，使获得的辨识结果更为可信。该预测方法在
转子碰摩非线性行为的分类与辨识中的应用表明是行之有效的。
4．以理论和实验分析所获得的碰摩故障特征规律为基础，提出采用Duffing振子微弱
信号检测方法对转子系统碰摩故障特征进行早期检测的新方法。
＊）理论分析了Duffing方程的全局解和全局分叉规律并讨论了分叉值随阻尼、外部
激励幅值的变化规律，发现Duffing方程外轨解的最大轨道所对应的分叉阈值特性可用来
进行微弱信号检测。
O）提出了利用Duffing振子进行早期故障特征微弱信号检测的实现模型
Chaos theory developed in the late half of 20th century gives a new approach for the research on nonlinear dynamical system. The researches on strong nonlinear behavior such as chaos in complex mechanical system and application of chaos theory in machinery fault diagnosis are of significance to design, operation, diagnosis and maintenance of complex mechanical system.
With the increase of machinery operating speed and wide application of various new-style material in high-speed machinery, nonlinear problem of mechanical system which may cause abnormal state even fault directly or indirectly becomes more and more obvious. Theoretical and experimental studies focusing on this problem are very important. Particularly, it is more important to study the prediction of nonlinear behavior and chaotic behavior, early detection of operating state and signal/information processing method based on chaos theory. Under this circumstance, this dissertation suggests two research aspects, namely experimental study on complex nonlinear behavior underlying rotor system with stator-rotor rub and deep study on identification method and early diagnosis of rotor fault based on chaos theory.
Subsequently, this dissertation mainly includes, observation and identification of chaotic phenomena from rub-impact rotor rig, analysis and prediction for nonlinear behavior of rotor rub-impact based on nonlinear signal processing, early detection and recognition of rub-impact fault based on nonlinear theory and chaos theory. The detailed contents and innovative work include,
1. Nonlinear behavior and characteristic rule of rub-impact rotor are deeply and systematically studied.
(1) Combined with quantitative and qualitative analysis, solutions of vibration response of sharp rub-impact rotor are obtained by the improved sharp rub-impact model of rotor. Test rig of sharp rub-impact rotor is designed and meticulous experiment has been accomplished. Characteristic Rile of vibration response is obtained in various cases of rub-impact. The result that the 1/3X,2/3X sub-harmonic components (X denotes operating frequency component) occur in inception of rub-impact in the case of sharp rub-impact under certain condition, is obtained via theoretical and experimental analysis.
(2) Dynamics model of Jeffcott nonlinear rotor with eccentric between stator and rotor is built based on rub-impact force. Numerical simulation demonstrates that local rub-impact has sub-harmonic phenomena and bifurcation phenomena. The rub-impact rotor response includes quasi-periodic or chaotic vibration when severe unbalance, small damping and high rotating speed. Based on the result of numerical analysis, rotor test rig about local rub-impact is designed
and built. Experimental research has been done within broad range of rotating speed. A very rich and complicated vibration phenomenon including not only periodic (synchronous and non-synchronous) components but also quasiperiodic and chaotic motions, is observed. The observed result is qualitatively consistent with that of simulation.
(3) Phase space reconstruction analysis method based on observed time series is used to analyze and identify nonlinear dynamics of rotor system. The evidence with statistical meaning representing strong nonlinear behavior is obtained.
The results show that sub-harmonic phenomena produced by local rub-impact provide mechanism and evidence for the early diagnosis of this fault. Vibration response characteristics of rub-impact rotor obtained by theoretical and experimental analysis are of significance to prediction of rub-impact.
2. Phase space reconstruction technology and characteristic indices algorithms, which show the wide prospects of engineering application, are presented to In order to distinguish dynamical behavior underlying observed time series from rub-impact rotor.
(1) In the case of short data set, to select embedding space parameters as fast and exact as possible, the improved across displacement method for selecting time delay and the relative gain ratio of fal
系统中可能出现的强非线性行为(如混沌）展开研究并探讨混沌理论在机械故障诊断中的
应用，对于复杂机械系统的设计、使用、诊断与维修具有重要意义。
随着机械运转速度的日益提高以及各种新型材料在高速机械中的广泛应用，机械系
统的非线性将更加突出，可能直接（或间接）导致机械系统的故障。从理论和实验上对
这个问题进行研究意义重大，而对非线性行为特别是混沌行为的预测与运行状态早期检
测，以及利用基于混沌理论的信号／信息处理方法的研究显得尤为突出。本文正是在这样
的背景下，提出对转子系统中存在的复杂非线性行为展开研究，并对非线性行为的辨识方
法以及基于混沌理论的转子故障早期诊断新方法进行了深入研究与探讨。
本论文主要完成两个方面的研究工作：从碰摩转子实验系统中观测混沌现象并进行辨
识与分析；基于非线性科学理论与技术对转子系统的行为进行分析、预测与早期辨识。概
述地说，围绕上述问题所开展的具体研究内容包括：
1．深入系统地研究了碰摩转子的非线性行为与特征规律。
(1）采用并改进了已有的转子尖锐碰摩模型，通过定量和定性的理论分析，获得了尖
锐碰摩转子振动响应形式；设计了尖锐碰摩转子试验台并开展了细致的实验研究，获得了
不同碰摩情况下的振动响应特征规律；通过理论和实验分析，得出在尖锐碰摩情况下，早
期碰摩在一定条件下会出现1／3X、2／3X的分频成分的结果（X表示工频）。
（2） 建立了基于局部碰摩力变化且具有转、定于偏心的Jeffcott非线性转子的动力学
模型，大量的数值仿真表明局部碰摩转子存在分频现象和一定的分叉规律，获得了大不平
衡、小阻尼、高转速条件下，局部碰摩容易产生拟周期或混沌振动的结果；基于数值分析
结果，设计并建立了局部碰摩转子系统试验台，在大范围的转速里进行了细致的实验研究，
观察到了包括周期、拟周期、次谐波与超谐波以及混沌振动在内的丰富的振动现象。观测
与仿真结果定性一致。
（3）采用基于观测时间序列的重构相空间分析方法对转子系统的非线性行为进行辨识
与分析，获得了系统出现强非线性行为的统计意义上的证据。
研究表明早期碰摩时产生的分频现象这一结果对这类故障的早期诊断提供了依据。理
论与实验分析获得的碰摩转子振动响应的特征规律对于碰摩的预测具有一定的参考价值。
2．提出了具有工程化前景的相空间重构技术和统计特征指数算法，以评判碰摩转子
观测数据所隐含的动力学行为。
（1）在短数据集情况下，为了快速、合理地选择嵌入空间参数，提出了延迟时间选择
的交叉位移改进法和嵌入维数选择的伪近邻距离统计增长法，其特点是速度快、重复性好。
（2）对影响关联维数计算的各种因素进行了深入分析，提出了在短数据集约束下估计
关联维数的具体方法。
国防科学技术大学研究生院学位论文
一
o）提出了在短数据集条件下，通过最大瞬时Lyapunov指数来估计最大LyaPunov指
数的方法，并指出Lyapunov指数之和与系统的能量耗散机制相关联。从理论上分析并提
出了Lyapunov指数之和的变化规律可用来监测强非线性系统的阻尼变化，从而可以监测
系统状态变化的新策略和新方法。
研究表明关联维数和最大Lyapunov指数对非线性动力学行为的辨识是行之有效的，其
有效性在转子碰摩的各种状态的分类与辨识中获得了证实。
3．提出了通过观测数据的不可长期预测性并结合特征指数 分析对信号的混油特性
进行综合判别的新方法。
O）改进了局部线性拟合的非线性预测方法。
c）提出了非线性时间序列预测的相轨迹方法。
＊）提出了利用观测数据的短期、长期可预测性可对动力学行为进行辨识的新方法。
研究表明，上述预测方法结合特征指数分析，可以对非线性行为进行综合分类与辨识，
通过多指数、多角度地对观测数据进行分析，使获得的辨识结果更为可信。该预测方法在
转子碰摩非线性行为的分类与辨识中的应用表明是行之有效的。
4．以理论和实验分析所获得的碰摩故障特征规律为基础，提出采用Duffing振子微弱
信号检测方法对转子系统碰摩故障特征进行早期检测的新方法。
＊）理论分析了Duffing方程的全局解和全局分叉规律并讨论了分叉值随阻尼、外部
激励幅值的变化规律，发现Duffing方程外轨解的最大轨道所对应的分叉阈值特性可用来
进行微弱信号检测。
O）提出了利用Duffing振子进行早期故障特征微弱信号检测的实现模型
Chaos theory developed in the late half of 20th century gives a new approach for the research on nonlinear dynamical system. The researches on strong nonlinear behavior such as chaos in complex mechanical system and application of chaos theory in machinery fault diagnosis are of significance to design, operation, diagnosis and maintenance of complex mechanical system.
With the increase of machinery operating speed and wide application of various new-style material in high-speed machinery, nonlinear problem of mechanical system which may cause abnormal state even fault directly or indirectly becomes more and more obvious. Theoretical and experimental studies focusing on this problem are very important. Particularly, it is more important to study the prediction of nonlinear behavior and chaotic behavior, early detection of operating state and signal/information processing method based on chaos theory. Under this circumstance, this dissertation suggests two research aspects, namely experimental study on complex nonlinear behavior underlying rotor system with stator-rotor rub and deep study on identification method and early diagnosis of rotor fault based on chaos theory.
Subsequently, this dissertation mainly includes, observation and identification of chaotic phenomena from rub-impact rotor rig, analysis and prediction for nonlinear behavior of rotor rub-impact based on nonlinear signal processing, early detection and recognition of rub-impact fault based on nonlinear theory and chaos theory. The detailed contents and innovative work include,
1. Nonlinear behavior and characteristic rule of rub-impact rotor are deeply and systematically studied.
(1) Combined with quantitative and qualitative analysis, solutions of vibration response of sharp rub-impact rotor are obtained by the improved sharp rub-impact model of rotor. Test rig of sharp rub-impact rotor is designed and meticulous experiment has been accomplished. Characteristic Rile of vibration response is obtained in various cases of rub-impact. The result that the 1/3X,2/3X sub-harmonic components (X denotes operating frequency component) occur in inception of rub-impact in the case of sharp rub-impact under certain condition, is obtained via theoretical and experimental analysis.
(2) Dynamics model of Jeffcott nonlinear rotor with eccentric between stator and rotor is built based on rub-impact force. Numerical simulation demonstrates that local rub-impact has sub-harmonic phenomena and bifurcation phenomena. The rub-impact rotor response includes quasi-periodic or chaotic vibration when severe unbalance, small damping and high rotating speed. Based on the result of numerical analysis, rotor test rig about local rub-impact is designed
and built. Experimental research has been done within broad range of rotating speed. A very rich and complicated vibration phenomenon including not only periodic (synchronous and non-synchronous) components but also quasiperiodic and chaotic motions, is observed. The observed result is qualitatively consistent with that of simulation.
(3) Phase space reconstruction analysis method based on observed time series is used to analyze and identify nonlinear dynamics of rotor system. The evidence with statistical meaning representing strong nonlinear behavior is obtained.
The results show that sub-harmonic phenomena produced by local rub-impact provide mechanism and evidence for the early diagnosis of this fault. Vibration response characteristics of rub-impact rotor obtained by theoretical and experimental analysis are of significance to prediction of rub-impact.
2. Phase space reconstruction technology and characteristic indices algorithms, which show the wide prospects of engineering application, are presented to In order to distinguish dynamical behavior underlying observed time series from rub-impact rotor.
(1) In the case of short data set, to select embedding space parameters as fast and exact as possible, the improved across displacement method for selecting time delay and the relative gain ratio of fal
引文
[1] 钟掘，陈安华．关于机械系统非线性故障诊断的若干思考，第五届全国机械设备故障诊断学术会议论文集．1996：1-5．
[2] Moon F C. Chaotic Vibrations, John Wiley&Sons, Inc. 1987.
[3] Moon F C. Chaotic and Fractal Dynamics - An Introduction for Applied Scientists and Engineers, John Wiley &Sons, INC, 1992.
[4] Kapitaniak T. Chaotic Oscillations in Mechanical Systems, Nonlinear Science-Theory and Applications, Manchester and New York, 1991.
[5] Kapitaniak T, et. al. Specific Issue on dynamics of Impact Systems, Chaos, Solitions and Fractals, 2000, 11(15):2411-2578.
[6] 冯奇，沈荣瀛编著．工程中的浑沌振动，上海：上海交通大学出版社，1998．
[7] 王聪玲，龙运佳．关于混沌振动的研究．中国农业大学学报，1997，2(6)：23-27．
[8] 黄进，叶尚辉．摩擦振子的混沌振荡研究．机械科学与技术，1999，18(2)：176-179．
[9] 鲁宏伟，杨叔子．基于非线性模型的切削过程的混沌研究，1996，9(2)：169-172．
[10] Karagiannis K, Pfeiffer F. Theoretical and Experimental Investigations of Gear-Rattling, Nonlinear Dynamics, 1991,2:267-387.
[11] Singh R, Xie H, Comparin R J. Analysis of Automotive Neutral Gear Rattle, Journal of Sound and Vibration, 1989,131(2):177-196.
[12] Pfeiffer F, Kunert A. Rattling Models from Deterministic to Stochastic Processes, Nonlinear Dynamics, 1990, 1:63-74.
[13] Comparin R J, Singh R. An Analytical Study of Automotive Neutral Gear Rattle, Journal of Mechanical Design, 1990, 112:237-245.
[14] Kunert A, Pfeiffer F. Description of Chaotic Motion by an Invariant Distribution at the Example of the Driven Duffing Oscillator, Int. Series Num. Math.,1991,97:225-230.
[15] Ted Frison, Chaos in a High Speed Gearbox, AD-A283 940, 1993.
[16] Theodossiades S, Natsiavas S. Periodic and Chaotic Dynamics of Motor-driven Gear-pair Systems with Backlash. Chaos, Solitions and Fractals, 2001, 12(13):2427-2440.
[17] 郑吉兵，孟光．考虑非线性涡动时的裂纹转子的分叉与混沌特性．振动工程学报，1997，10(2)：190-197．
[18] 曾复，吴昭同，严拱标．裂纹转子的分岔与混沌特性分析．振动与冲击，2000，19(1)：40-42．
[19] 郑吉兵，谢建华，孟光．非线性裂纹转子系统环面分叉的数值研究．铁道学报，1998，20(增刊)：152-155．
[20] 张伟，陈予恕．含有参数激励非线性动力系统的现代理论的发展．力学进展，1998，28(1)：1-16．
[21] 张伟，陈予恕．机械系统中的非线性动力学问题及其研究进展．中国机械工程，1998，
9(7)：64-69．
[22] 陈予恕，王德石，余俊．参外激励作用下非线性振动系统的混沌．振动工程学报，1996，9(1)：54-59．
[23] Cvitanovic P. Invariant Measurement of Strange Sets in terms of Cycles, Physics Review Letters, 1988,61:2729-2732.
[24] Lathrop D P, Kostelich E J. Characterization of an Experimental Strange Attractor by Periodic Orbits, Physics Review A, 1989,40:4028-4031.
[25] Oppenheim A V, Wornell G W. Signal Analysis, Synthesis and Processing Using Fractal and Wavelets, ADA305490.
[26] Staszewski W J and Worden K. Wavelet Analysis of Time-series: Coherent Structures, Chaos and Noise, International Journal of Bifurcation and Chaos, 1999, 9(3):455-471.
[27] Stright J R. Embedded Chaotic Time Series: Applications in Prediction and Spatio-Temporal Classification, ADA280690.
[28] Farmer J D, Sidorowich J J. Predicting Chaotic Time Series, Physical Review Letters, 1987,59(8):845-848.
[29] Bookhart J R. The Development of Methods and Techniques to Detect and Model the Underlying Structure of Chaotic Systems, ADA292435.
[30] Grassberger P, Procaccia I. Measuring the Strangeness of Strange Attractors, Physica D, 1983,9:189-208.
[31] Barnett K D. Estimation of the Correlation Dimension and Its Application to Radar Reflector Discrimination, N94-23304.
[32] Katayama R, et al. Developing Tools and Methods for Applications Incorporating Neuro, Fuzzy and Chaos Technology, Computers ind. Engng., 1993,24(4):579-592.
[33] Logan D B, Mathew J. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearings- Ⅰ.Basic Concepts, Mechanical Systems and Signal Processing, 1996,10(3):241-250.
[34] Logan D B, Mathew J. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearings- Ⅱ. Selection of Experimental Parameters, Mechanical Systems and Signal Processing, 1996,10(3):251-264.
[35] 陈安华，朱萍玉，钟掘．对基于振动分析的机械故障诊断方法的讨论．湘潭矿业学院学报，1997，12(4)：41-47．
[36] 陈怡然，周轶尘，白烨，郑伟涛．发动机振动诊断中的多重分形法，内燃机学报，1997，15(1)：114-119．
[37] 姜建东，屈梁生．相关维数在大机组故障诊断中的应用，西安交通大学学报，1998，32(4)：27-31．
[38] Jiang J D, Chen J, Qu L S. The Application of Correlation Dimension in Gearbox Condition Monitoring. Journal of Sound and Vibration, 1999, 223(4):529-541.
[39]姜建东 屈梁生．大机组振动信号复杂性的定量描述，西安交通大学学报，1998，32(6)：31-35．
[40]杨世锡，汪慰军．柯尔莫哥洛夫熵及其在故障诊断中的应用．机械科学与技术，2000，19(1)：6-8．
[41]胡茑庆，温熙森．分形维数特征在设备运行状态分类中的应用研究，第五届全国机械设备故障诊断学术会议论文集，1996，174-178．
[42]Hu Niaoqing, Wen Xisen. A New Method of Feature Extracting Techniques Using Fractal Information for Machine Condition Monitoring, 6th COMADEM'97, Xi'an, China.
[43]温熙森，胡茑庆，邱静编著．模式识别与状态监控，长沙：国防科技大学出版社，1997．
[44]尹承丽．关联维数在机械系统状态监测中应用．硕士论文，1998．
[45]杨光．转子系统混沌现象的产生与分析方法研究．硕士论文，1999．
[46]胡茑庆，温熙森，唐丙阳．机械状态监测特征提取方法研究．机械动力学及其在工程中的应用，1997．4：212-215．
[47]Simard P, Tavernier E L. Fractal Approach for Signal Processing and Application to the Diagnosis of Cavitation. MSSSP, 2000,14(3):459-469.
[48]徐章遂，房立清，王希武，左宪章．故障信息诊断原理及应用．北京：国防工业出版社，2000．
[49]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，2001．3．
[50]焦映厚等．非线性转子动力学的研究现状与展望．哈尔滨工业大学学报，1999，31(3)：1-4．
[51]汪慰军，吴昭同，严拱标，杨世锡．转子——轴承系统的稳定性、分岔与混沌行为研究．振动、测试与诊断，1999，19(1)：44-47．
[52]张雨，刘耀宗，胡茑庆，温熙森．轴系非对中时轴承振动的数值模拟与物理模拟研究．中国造船，1999，147(4)：64-70．
[53]褚福磊，方泽南，张正松．带有支座松动故障的转子——轴承系统的混沌特性．清华大学学报(自然科学版)，1998，38(4)：60-63．
[54]Adams M L, Abu-Mahfouz I A. Exploratory Research on Chaos Concepts as Diagnostic Tools for Assessing Rotating Machinery Vibration Signatures, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September 1994, pp. 29-39.
[55]Muszynska A. Partial Lateral Rotor to Stator Rubs, Proceedings of Third International Conference on Vibrations in Rotating Machinery, C281/84, IMechE, York, UK, 1984:327-335.
[56]Nikolajsen J I, Holmes R. Investigation of Squeeze-film Isolators for the Vibration Control of a Flexible Rotor, ASME Journal of Mechanical Science, 1979,21(4):247-252.
[57] Li X H, Taylor D L. Nonsynchronous Motion of Squeeze-film Damper Systems, ASME Journal of Tribology,1987,109:169-176．
[58] Ehrich F F. High Order Subharmanic Response of High Speed Rotor in Bearing Clearance, ASME Journal of Vibration , Acoustics, Stress and Reliability in Design, 1988,110:9-16．
[59] Holmes A G, Ettles C M, Mayes I W. Aperiodic Behavior of a Rigid Shaft in Short Journal Bearings, International Journal for Numerical Method in Engineering, 1978,12:695-702．
[60] Ehrich F F. Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics, Transactions of ASME, J. of Vib. and Acous., 1991,113:50-57．
[61] Ehrich F F. Nonlinear Phenomena in Dynamic Response of Rotors in Anisotropic Mounting Systems, Transactions of the ASME, J. of Vib. and Acous., 1995,117:154-161．
[62] Zhao J Y, Linnett I W, Mclean L J. Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor, Transactions of ASME, Journal of Vibration and Acoustics, 1994,116:357-363．
[63] Brown R D, Addison P, Chan A H C. Chaos in the Unbalance Response of Journal Bearings, Nonlinear dynamics, 1994, (5) :421-432．
[64] Chieh-Li Chen, Her-terng Yau. Chaos in the Inbalance Response of a Flexible Rotor Supported by Oil Film Bearings with Non-linear Suspension, Nonlinear Dynamics 1988,16:71-90．
[65] Gonsalves D H, Neilson R D, Barr A D S. A Study of the Response of a Discontinuously Nonlinear Rotor system. Nonlinear Dynamics, 1995, 7:451-470．
[66] Kraker D, et. al. The Dynamics of a Rotor with Rubbing. C284/88, IMechE, 1988．
[67] Guido A R, Adiletta G. Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part I theoretical Analysis. Nonlinear Dynamics, 1999, 19 (4) : 359-385．
[68] Guido A R, Adiletta G. Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part II Experimental Analysis. Nonlinear Dynamics, 1999, 19 (4) 1387-397．
[69] Muszynska A, et al. Influence of Rubbing on Rotor Dynamics. NASA Contract No. Nas8-36719, Final Report. Bently Nevada Corporation, March 1989．
[70] Ehrich F F. Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics, Journal of Vibration and Acoustics, 1992,114:93-100．
[71] Beatty R F. Differentiation on Rotor Response Due to Radial Rubbing, Trans. ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1985, (107) :151-160．
[72] Choy F K, Padovan J. Non-linear Transient Analysis of Rotor-Casing Rub Events, Journal of Sound and Vibration, 1987, 113(3) :529-545．
[73] Shaw S W, Radovan P J. A Periodically Forced Piecewise Linear Oscillator, Journal of Sound and Vibration, 1983, 90:129-155．
[74] Thompson J M T, Stewart H B. Geometrical Methods for Engineers and Scientists, Nonlinear Dynamics and Chaos, Chichester:Wiley.
[75] Choi S K, Noah S T. Mode-locking and Chaos in a Jeffcott Rotor with Bearing Clearances, Transactions of the ASME .Journal of Applied Mechanics, 1994, 61:131-138．
[76] Kim Y B, Noah S T. Bifurcation Analysis for a Modified Jeffcott Rotor with Bearing Clearances. Nonlinear Dynamics, 1990,1 (3) :221-243．
[77] Choi Y. S, Noah S T. Nonlinear Steady-state Response of A Rotor-support System, Transactions of the ASME, Journal of Vibration, Acoustics, Stress and Reliability in Design, 1987, 109:255-261．
[78] Chon K H, et. al. Modeling Nonlinear Determinism in Short Time Series from Noise Driven Discrete and Continuous Systems, International Journal of Bifurcation and Chaos, 2000, 10(20) :2745-2766．
[79] Ehrich F F. Rotordynamic Response in Nonlinear Anisotropic Mounting Systems, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September, 1994, 1-6．
[80] Isaksson J L. Dynamics of a Rotor with Annular Rub, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September, 1994, 85-90．
[81] Chu F, Zhang Z. Periodic Quasi-periodic and Chaotic Vibrations of a Rub-impact Rotor System Supported on Oil Film Bearings, International Journal of Engineering Science, 1997,35:963-973．
[82] Chu F, Zhang Z. Bifurcation and Chaos in A Rrub-impact Jeffcott Rotor System, Journal of Sound and vibration, 1998, 210(1) :1-18．
[83] Li G X, Paidoussis M P. Impact Phenomena of Rotor-casing Dynamical Systems, Nonlinear Dynamics, 1994, 5:53-70．
[84] Piccoli H C, Weber H I. Experimental Observation of Chaotic Motion in a Rotor with Rubbing, Nonlinear Dynamics, 1998, 16:55-70．
[85] 褚福磊等。碰摩转子系统中的阵发性及混沌,航空动力学报,1996, 11(3) : 261-264．
[86] 陈安华,朱萍玉,钟 掘。转子系统动静件径向摩擦的振动特征,湘潭矿业学院学报,1998,13(1) : 33-38 (55) .
[87] 陈安华,刘德顺,朱萍玉。转子系统非线性振动研究进展。湘潭矿业学院学报,14(2) : 59-65．
[88] Yang Wei,et.al. Nonlinear Response of Rotor to Stator Rubs. N19970024786, p269-p278．
[89] Chancellor R S, Alexander R M, Noah S T. Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos, Transactions of the ASME, Journal
of Vibration and Acoustics,1996,118:375-383.
[90]褚福磊，张正松，冯冠平．碰摩转子系统的混沌特性．清华大学学报(自然科学版)，1996，36(7)：52—57．
[91]褚福磊，张正松．带故障转子系统中的复杂运动现象，第五届全国机械设备故障诊断学术会议论文集，科学技术文献出版社，1996，229-233．
[92]刘献栋，李其汉．转静件碰摩模型及不对中转子局部碰摩的混沌特性，航空动力学报，1998，13(14)：361-364(456)．
[93]刘献栋 李其汉．质量偏心旋转机械碰摩故障特征及全息谱分析，航空动力学报，1998，13(4)：428-430(462)．
[94]季进臣 虞烈．高速对称刚性转子碰摩运动的稳定性分析，航空动力学报，1998，14(1)：65-68(109)．
[95]褚福磊，张正松．转子-轴承系统发生动静件碰摩时的混沌路径，应用力学学报，1998，15(2)：81-86(v)．
[96]张思进，陆启韶，王琪．转子与定子几何不对中引起的碰摩分析，振动工程学报，1998，11(4)：492-496．
[97]刘献栋 李其汉 杨绍普．质量偏心旋转机械整圈碰摩的稳定性及其Hopf分叉，振动工程学报，1999，12(1)：40-46．
[98]戴兴建，张小章，金兆熊．大幅度进动转子与位移限制器碰摩动力行为，清华大学学报(自然科学版)，1998，38(8)：104-106．
[99]晏砺堂，王德友，航空双转子发动机动静件碰摩振动特征研究，航空动力学报，1998，13(2)：173-176(220，221)．
[100]吴建，梁家惠，李淮凌．大型转动机械碰摩故障分析的声发射检测系统，北京航空航天大学学报，1998，24(1)：104-107．
[101]闻邦椿，顾家柳，夏松波，王正主编．高等转子动力学——理论、技术与应用，北京：机械工业出版社，2000．
[102]龙运佳．混沌振动研究—方法与实践，北京：清华大学出版社，1997．
[103]龙运佳．混沌工程学进展，振动与波利用技术学术会议论文集——振动与波利用技术的新进展，东北大学出版社，2000．9，439-446．
[104]胡汉平，李德华，吴晓刚，陈丹．创造性思维中可能性构造空间理论的动力学模型，高技术通讯，1998，5：20-23．
[105]伍言真，丘水生．非线性系统理论及混沌研究的动态和评述，电路与系统学报，1997，2(3)：62-66．
[106]董军，胡上序．混沌神经网络研究进展与展望，信息与控制，1997，26(5)：360-368(378)．
[107]陈德钊，董军，胡上序．混沌动力学在智能信息处理中应用研究．计算机科学，1998，25(3)：85-88．
[108]王东生，曹磊．混沌、分形及其应用．合肥：中国科学技术大学出版社，1995．
[109]唐巍，李殿璞，陈学允．混沌理论及其应用研究，电力系统自动化，2000，24(7)：67-70．
[110]王保云，董恒．基于混沌的信息记忆，南京邮电学院学报，1998，18(1)：102-105．
[111]张毅锋，何振亚．混沌系统在信息处理中的应用，数据采集与处理，1998，13(2)：101-106．
[112]刘孝贤．利用同步混沌系统和对称混沌信号实现保密通信，山东工业大学学报，1997，27(2)：101-106．
[113]Pecora L M, Carroll T L, Johnson G A, Mar D J. Fundamentals of Synchronization in Chaotic Systems, Concepts, and Applications, Chaos, 1997,7(4):520-543.
[114]Cuomo K M, Oppenheim A V. Circuit Implementation of Synchronized Chaos with Applications to Communications. Physical Review Letters, 1993,71(1):65-68.
[115]Cuomo K M, Oppenheim A V, Strogatz S H. Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications. IEEE Transactions on Circuits and systems, 1993,40(10):626-633.
[116]裴留庆，匡锦瑜，邵媛．混沌同步系统的频率特性和微弱信号检测．中国科学(E辑)，1997，27(3)：237-242．
[117]赵永龙，丁晶，邓育仁．混沌分析在水文预测中的应用和展望，水科学进展，1998，9(2)：181-186．
[118]吴耿锋等．基于相空间重构的预测方法及其在天气预报中的应用．自然杂志，1999，21(2)：107-110．
[119]徐晓红，谢正祥，陈良迟，何伟．心动周期信号的混沌特征分析及应用，中国生物医学工程学报，1999，18(1)：74-81(88)．
[120]贺太纲．基于混沌理论的脑电图(EEG)分析与预测研究，西安交通大学博士学位论文，1997．
[121]Pecora L, Carroll T. Synchronization Chaotic Systems. Physical Review Letters, 1990, 64(8):821-824.
[122]王光瑞，于熙龄，陈式刚．混沌的控制、同步与利用．北京：国防工业出版社，2001．
[123]陈立群，刘延柱．混沌的抑制研究进展综述．力学进展，1998，28(3)：299-309．
[124]戴冠中，刘华强，郑会永．非线性科学中的一些问题及其应用．电子科技导报，1996，4：5-8．
[125]Haykin S, Li X B. Detection of Signals in Chaos, Proceedings of the IEEE, 1995,83(1):95-122.
[126]Donald LB. Chaotic Oscillators and CMFFNS for Signal Detection in Noise Environment, IEEE International Joint Conference on Neural Networks, 1992,2:881-888.
[127]姜万录、王益群、孔祥东、李久彤．液压系统故障检测与诊断技术的新进展，中国机械工程，1998，9(9)：58-62．
[128]王冠宇，陶国良，陈行，林建亚．混沌振子在强噪声背景信号检测中的应用．仪器仪表学报，1997：18(2)：209-212．
[129]姜万录、王益群、孔祥东．齿轮故障的混沌诊断识别方法，机械工程学报，1999，35(6)：44-47．
[130]吕志民，徐金梧，翟绪圣．基于混沌振子的微弱特征信号检测原理及方法，河北工业大学学报，1998，27(4)：13-17．
[131]聂春燕．微弱正弦信号的时域处理方法研究，计量技术，2000，5：3-5．
[132]陈敏，胡茑庆，温熙森．混沌振子在转子系统早期碰摩故障检测中的应用，国防科技大学学报，2001，23(1)：36-39．
[133]陈敏，混沌振子在转子系统早期碰摩故障检测中的应用．硕士论文，2001．
[134]姜万录，王益群．混沌振子在液压泵故障诊断中的应用．机床与液压，1999，(5)：52-53．
[135]王林翔．扭转弯管中的混沌混合机理及其可视化研究，杭州：浙江大学博士学位论文，1999．
[136]熊峻江，武哲，高镇同．混沌疲劳初探．北京航空航天大学学报，1998，24(6)：667-670．
[137]Leonardi M L. Prediction and Geometry of Chaotic Time Series. 1997, ADA333449.
[138]Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from Time Series, Phys. Rev. Lett., 1980, 47: 712-716.
[139]Barenblatt G L, Looss G, Joseph D D, Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983.
[140]Barenblatt G L, Looss G, Joseph D D, Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983.
[141]马军海，陈予恕，刘曾荣．动力系统实测数据的非线性混沌特性的判定．应用数学和力学，1998，19(6)：481-488．
[142]马军海，盛昭瀚，唐文雄．不同相位随机化对时序混沌特征影响的研究．1999，29(2)：93-99．
[143]刘耀宗．碰摩转子混沌振动分析与控制，长沙：国防科学技术大学博士学位论文，2001．
[144]胡晓棠．转子系统中的非线性时间序列预测方法研究，国防科技大学硕士论文，2000．
[145]Stam C J, Pi jn J P M, Pritchard W S. Reliable Detection of Nonlinearity in Experimental Time Series with Strong Periodic Components, Physica D 112(1998):361-380.
[146]Ma Junhai, Zheng Wanming, Wang Liqin. Testing Value for Nonlinear Chaotic Nature of the Data Obtained in Dynamic Analysis. Journal of Tianjin University of Commerce, 1997,3:23-27.
[147]吴振奎．混沌平话，数学通讯，1999，2：42-43．
[148]郑会永，肖田元，王新龙，韩向利．混沌及混沌保密通讯技术，中国图象图形学报，1998，3(12)：1042-1050．
[149]Holmes J P. Averaging and Chaotic Motions in Forced Oscillations, SIAM Appl. Math, 1980, 38(1): 65～92, 1981, 40(1): 167-168.
[150]Holmes J P, Marsden J E. Horseshoes in Perturbations of Hamiltonians with Two
Degree of Freedom. Commun. Math. Phys., 1982, 82: 523-544.
[151]Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, springwer-Verlag, New York, N. T. 1983.
[152]凌复华．混沌、随机、信息流和其他，力学与实践，1985，7(5)：17-20．
[153]Haken H. At Least One Lyapunov Exponent Vanishes if the Trajectory of an Attractor does not Contain a Fixed Point, Phys. Lett. 1983, 94A(2): 71-72.
[154]Devaney R L. An Introduction to Chaotic Dynamical Systems, Menlo Park, CA: Benjam in uCummings, 1986.
[155]程极泰．混沌的理论与应用，上海：上海科学技术文献出版社，1991．
[156]汪秉宏．非线性科学选讲．合肥：中国科学技术大学出版社，1994：35-102．
[157]Thomas S Parker, Leon O Chua. Practical Numerical Algorithms for Chaotic Systems. Springer—Verlag, New York Inc., 1989.
[158]林鸿溢，李映雪．分形论——奇异性探索，北京：北京理工大学出版社，1992．
[159]Marek Milos. Chaotic Behavior of Deterministic Dissipative Systems, Cambridge Univ. Press, 1991.
[160]陈式刚．映象与混沌．北京：国防工业出版社，1992．
[161]陆启韶，黄克累．非线性动力学、分叉和混沌．一般力学(动力学、振动与控制)最新进展．北京：科学出版社，1994．
[162]Neil R S. Chaotic Dynamic of Nonlinear Systems, John Wiley&Sons Inc., 1990.
[163]Wiggins S. Global Bifurcations and Chaos, Analytical Methods. Springer-Verlag,1988.
[164]郑伟谋，郝柏林．实用符号动力学．上海：上海科技教育出版社，1995．
[165]郝柏林．非线性科学丛书．上海：上海科技教育出版社，1995．
[166]陈予恕，唐云等．非线性动力学中的现代分析方法，北京：科学出版社，1992．
[167]Blazejczyk-Okolewska B, Czolczynski K, Kapitaniak T, Wojewoda J. Chaotic Mechanics in Systems with Impacts and Friction, World Scientific Series on Nonlinear Science, World Scientific Publishing Co. Pte. Ltd, 1999.
[168]李继彬，冯贝叶．稳定性、分支与混沌，昆明：云南科技出版社，1995．
[169]胡茑庆，张雨，刘耀宗，胡晓棠，温熙森．转子系统动静件间尖锐碰摩时的振动特征实验研究．中国机械工程，拟发表于2002年第八期．
[170]刘耀宗，胡茑庆．系统参数对碰摩转子稳态响应的影响．非线性动力学学报，1999，6(4)：332-337．
[171]刘耀宗，胡茑庆，温熙森．不平衡激励对碰摩转了振动特性的影响．机械科学与技术，2000，19(4)：536-538．
[172]胡茑庆，刘耀宗，杨光．非线性碰摩转子系统响应的数值分析．将发表于中国振动工程学会机械动力学学会第九届年会上，2001．
[173]张雨，徐小林，张建华．设备状态监测与故障诊断的理论与实践．长沙：国防科技大学出版社，2000．
[174]徐敏等主编．设备故障诊断手册——机械设备状态监测和故障诊断．西安：西安交
通大学出版社，1998．
[175]王善永 陆颂元 马元奎 瞿红春．汽轮发电机组转子动静碰摩故障检测的小波分析方法研究，中国电机工程学报，1999，19(3)：1-5(70)．
[176]刘献栋，李其汉．小波变换在转子系统动静件早期碰摩故障诊断中的应用，航空学报，1999，20(3)：220-223．
[177]Choy F K, Padovan J, Baturc. Rub Interactions of Flexible Casing Rotor Systems. Journal of Engineering for Gas Turbine and Power, 1989,111:652-658.
[178]Goldman P, Muszynska A. Chaotic Behavior of Rotor-stator Systems with Rubs. Journal of Engineering for Gas Turbine and Power, 1994,116: 692-701.
[179]Kellenberger W. Spiral Vibration Due to the Seal Rings in Turbogenerator Thermally Induced Interaction between Rotor and Stator. Journal of Mechanical Design, Trans. Of ASME, 1980,102(1):178-184.
[180]Lee H P, Tan T H. Dynamics Stability of Spinnig Timoshenko Shaft with a Time-dependent Spin Rate. Journal of Sound and Vibration, 1997, 199(3): 401-415.
[181]Kim Y B, Noah S T. Stability and bifurcation Analysis of Oscillators with Piecewise Linear Characteristics: a General Approach. ASME J of Applied Mechanics, 1991,58(6):545-554.
[182]Muszynska A, Franklin W D, Hayashida R D. Rotor to Stator Partial Rubbing and its Effects on Rotor Dynamic Response. 1992, N92214367.
[183]Smalley A J. The Dynamic Response of Rotors to Rubs during Start up, J. of Vibration, Acoustics and Reliability in Design, 1989,111(3):226-233.
[184]Zhang W. Dynamic in Stability of Multi-degree-of-freedom Flexible Rotor Systems due to Full Annular Rub. Fourth International Conference on vibration in Rotating Machinery, Edinburgh, UK, 1988, ImechE: 305-310.
[185]胡茑庆，陈敏，刘耀宗，杨光，温熙森．非线性转子系统碰摩现象的动力学仿真，国防科技大学学报，2000，22(6)：101-104．
[186]岳国金等．转子碰摩的振动特征分析．航空学报，1990，11(10)：499-502．
[187]武新华等．旋转机械碰摩故障特性分析．汽轮技术，1996，38(1)：31-34．
[188]傅行军，杨建刚．摩擦对大型汽轮发电机组振动的影响分析，振动工程学报，1998，11(2)：215-219．
[189]刘耀宗，胡茑庆．Jeffcott转子碰摩故障试验研究．振动工程学报，2001，14(1)：96-99．
[190]王善永，陆颂元，童小忠．汽轮发电机组动静碰摩的奇异谱理论与小波分析诊断方法研究．动力工程，1999，19(6)：498-503．
[191]刘占生等．小波分析和分形几何在转子动静碰摩故障诊断中的应用．哈尔滨工业大学学报，1999，31(1)：55-56(92)．
[192]Integrated Diagnostics, ADA324130.
[193]周劲松等．工程随机信号的确定性混沌理论与分析方法．浙江大学学报，1997，
31(2)：245-252．
[194]洪时中．非线性时间序列分析的最新进展及其在地球科学中的应用前景．地球科学进展，1999，14(6)：559-565．
[195]黄文虎，夏松波，刘瑞岩等编著．设备故障诊断原理、技术及应用．北京科学出版社，1997．
[196]尹承丽，胡茑庆，温熙森．关联分形维数在转子系统状态监测中应用的实验研究，非线性动力学学报，1997，4(3)：264-268．
[197]尹承丽，胡茑庆，温熙森．关联维数在转子系统状态监测应用时参数选择的实验研究，火力与指挥控制，1998，23(3)：75-80．
[198]胡晓棠，胡茑庆，陈敏．一种改进的选择相空间重构参数的方法．振动工程学报，2001，14(2)：242-244．
[199]胡茑庆，杨光，尹承丽，温熙森．转子系统状态监测的关联维数方法实验研究，第六届全国机械设备故障诊断学术会议论文集，1998．10，pp．43-47，振动工程学报，1998，11(增刊)．
[200]汪慰军等．基于伪相图的大机组非线性故障诊断技术．上海交通大学学报，2000，34(9)．
[201]Kugiumtzis D. State Space Reconstruction Parameters in the Analysis of Chaotic Time Series. Physica D, 1996, (95):13-28.
[202]Abarbanel H D I. Analysis of Observed Chaotic Data, Springer-Verlag New York, Inc. 1996.
[203]Rosenstein M T, Collins J J, Luca C. Reconstruction Expansion as a Geometry-based Framework for Choosing Proper Delay Time. Physica D, 1994,73:82-89.
[204]Kember G, Fowler A C. A Correlation Function for Choosing Time Delays in Phase Portrait Reconstructions. Phy Lett A, 1993,179:72-80.
[205]Vautard R, et al. Singular Spectrum Analysis: a Toolkit for Short, Noisy Chaotic Singals. Physica D, 1992,58:95-126.
[206]Palus M, Dvorak I. Singular Value Decomposition in Attractor Reconstruction: Pitfalls and Precautions. Physica D, 1992,55:221-234.
[207]Buzug T, Pfister G. Comparison of Algorithms Calculating Optimal Embedding Parameters for Delay Time Coordinates. Physica D, 1992, (58):127-137.
[208]Buzug T, Pfister G. Optimal Delay Time and Embedding Dimension for Delay-time Coordinates by Analysis of the Global Static and Local Dynamical Behavior of Strange Attractors. Phy. Rev. A, 1992,45:7073-7084.
[209]Liebert W, et al. Optimal Embedding of Chaotic Attractors from Topological Considerations. Europhys Lett, 1991,14:521.
[210]Casdagli M, Sauer T, Yorke J A. Embedology, J. Stat. Phys, 1991,65:579-616.
[211]Callager R G. Information Theory and Reliable Communication, John Wiley and Sons, New York, 1968.
[212]Fraser A M, Swinney H L. Independent Coordinates for Strange Attractors from
Mutual Information. Phys. Rev. A, 1986,33:1134-1140.
[213]Broomhead D S, King G P. Extracting Qualitative Dynamics from Experimental Data. Physical D, 1987, (20):217-236.
[214]袁坚，肖先赐．低信噪比下的状态空间重构．物理学报，1997，46(7)：1290-1299．
[215]Kennel M B, Brown R, Abarbanel H D I. Determining Minimum Embedding Dimension Using a Geometrical Construction. Physical Review A, 1992,45:3403-3411.
[216]Aleksic Z. Estimating the Embedding Dimension, Physica D, 1991, (52):362-368.
[217]Mees A I, Rapp P E. Singular Value Decomposition and Embedding Dimension. Phys Rev A, 1987,36(1):340-346.
[218]Fraser A M. Information and Entropy in Strange Attractors. IEEE TR on IT, Mar 1989,35(2):245-262.
[219]Hong Pi, Peterson C. Finding the Embedding Dimension and Variable Dependencies in Time Series. Neu Comput, 1994,6:509-518.
[220]Liangyue Cao. Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series. Physica D, 1997,110:43-50.
[221]Nayfeh A H, Balachandran B. Applied Nonlinear Dynamics, Wiley, New York, 1995.
[222]Farmer J D, Ott E, Yorke J A. The Dimension of Chaotic Attractors, Physica D, 1983,7:153-180.
[223]Holger Kantz,Thomas Schreiber.Nonlinear Time Series Analysis(非线性时间序列分析)，清华大学出版社，2000(影印本)．
[224]张作生，彭虎，公佩祥．时间序列分维数提取算法的研究．中国科学技术大学学报，1997，27(2)：220-224．
[225]李擎，郑德玲，赵星浩，刘东方．一种新的混沌识别方法(Ⅰ)．北京科技大学学报，1999，21(2)：198-201．
[226]胡海岩编著．应用非线性动力学．北京：航空工业出版社，2000．
[227]Stefanski A. Estimation of the Largest Lyapunov Exponent in Systems with Impacts. Chaos, Solitions and Fractals, 2000,11(15):2443-2451.
[228]Wolf A, Swift J, Swinney H L, Vastano J A. Determining Lyapunov Exponents from a Time Series. Physica D, 1985,16: 285-317.
[229]Sano M, Sawada Y. Measurement of the Lyapunov Spectrum from a Chaotic Time Series. Phys. Rev. Lett.,1985,55(1O):1082-1085.
[230]Abarbanel H D I, Rrown R and Kennel M B. Vibration of Lyapunov Exponents on a Strange Attractor. Journal of Nonlinear Science, 1991, (1):175-199.
[231]Eckman L P, Ruelle D, Ciliberto S. Lyapunov Exponents from Time Series. Physical Review A, 1986, 34:4971-4979.
[232]Kruel T M, Eiswirth M, Schneider F W. Computation of Lyapunov Spectra: Effect of Interactive Noise and Application to a Chemical Oscillator. Physica D, 1993,63:117-137.
[233]Briggs K. An Improved Method for Estimating Lyapunov Exponents of Chaotic Time
Series. 1990 Physics Letters A, 1990,151:27-32.
[234]Brown R, Bryant P, Abarbanel H D I. Computing the Lyapunov Spectrum of A Dynamical System from An Observed Time Series. Physical Review A, 1991,(43):2787-2806.
[235]Darbyshire A G. Calculating Lyapunov Exponents from a time Series. Exploiting Chaos in Signal Processing, IEE Colloquium on Published: 1994,2:1-6.
[236]Banbrook M, Ushaw G, McLaughlin S. How to Extract Lyapunov Exponents from Short and Noisy Time Series. Signal Processing, IEEE Transactions on Published, 1997, 45(5): 1378-1382.
[237]Sato S, Sano M, Sawada Y. Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems. Prog. Theor. Phys.,1987,77(1):1-5.
[238]Rosenstein M T, Collins J J, Luca C J D.A practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Physica D, 1993, 65:117-134.
[239]Shin K, Hammond J K. The Instantaneous Lyapunov Exponent and Its Application to Chaotic Dynamical Systems. Journal of Sound and Vibration, 1998, 218(3): 389-403.
[240]Chon K H, Kanters J K, Iyengar N, Cohen R J, Holstein-Rathlou N H. Detection of Chaotic Determinism in Stochastic Short Time Series. Engineering in Medicine and Biology Society, 1997. Proceedings of the 19th Annual International Conference of the IEEE Published: 1997, 1: 275-277.
[241]Chatfield C. The Analysis of Time Series, Chapman and Hall,1989.
[242]Tong, Howell, Nonlinear Time Series: A Dynamical Systems Approach, Clarendon Press, 1990.
[243]Weigend A S, Gershenfeld N A. Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley Publishing Company, 1994.
[244]Kennel M B. Method to Distinguish Possible Chaos from Colored Noise and to Determine Embedding Parameters. Physical Review A, 1992, 46(6):3111-3118.
[245]刘洪．预测的混沌范式及动力学方法．系统工程与电子技术，1998，2：1-5．
[246]贺太纲，郑崇勋．混沌序列的非线性预测．自然杂志，1997，19(1)：10-13．
[247]马军海，盛昭瀚．低维混沌时序的预测方法及其应用研究．东南大学学报，1999，29(5)：65-69．
[248]任晓林，胡光锐，徐雄．混沌时间序列局域线性预测方法．上海交通大学学报，1999，33(1)：19-21．
[249]王永忠，曾昭磐．混沌时间序列的局域线性回归预测方法．厦门大学学报(自然科学版)，1999，38(4)：636-640．
[250]Casdagli M. Nonlinear Prediction of Chaotic Time Series. Physica D, 1989, 35: 335-356.
[251]Casdagli M, Stephen E, Farmer J D, Gibson J F. An Analytic Approach to Practical
State Space Reconstruction. Physica D, 1992, 57(1/2): 1-30.
[252]龙运佳．混沌工程学．中国工程科学，2001，3(2)：8-13．
[253]Jun Zhang, Man K F, Ke J Y. Time Series Prediction Using Lyapunov Exponents in Embedding Phase Space. Systems, Man, and Cybernetics, 1998, 2: 1744-1749.
[254]Sugihara G, May R M. Nonlinear Forecasting as a Way of Distinguishing Chaos From Measurement Error in Time Series. Nature, 1990,344(6268): 734-741.
[255]刘洪，李必强．基于混沌吸引子的时间序列预测．系统工程与电子技术，1997(2)：23-28．
[256]Martin J K, Nandi A K. Noise Reduction in Chaotic Time Series. IEE Colloquium on Exploiting Chaos in Signal Processing, 1994,4: 1-6.
[257]Mulgrew B, Strauch P. Nonlinear Dynamics and Noise Cancellation. IEE Colloquium on Signals Systems and Chaos, 1997,2:1-6.
[258]Heald J. Noise Reduction: Multiple Solutions. IEE Colloquium on Signals systems and Chaos, 1997,3:1-6.
[259]余建祖，苏南．混沌时序的噪声降低技术研究．航空学报，1999，20(6)：498-502．
[260]刘秉正．非线性动力学与混沌基础．沈阳：东北师范大学出版社，1994．
[261]Benzi R, Sutera A, Vulpiani A.The Mechanism of Stochastic Resonance. Journal of Physics A: Mathematical and General, 1981,14:453-457.
[262]McNamara B, Wiesenfeld K, Roy R. Observation of Stochastic Resonance in a Ring Laser. Phys. Rev. Lett., 1988,60:2626-2629.
[263]De-chun G, Gang H, Xiao-dong W. Chun-yan Y, Guang-rong Q, Rong L, Da-fu D. Experimental Study of Signal-to-noise Ratio of Stochastic Resonance Systems. Phys. Rev.A,1992,46:3243-3249.
[264]Spano M L, Wun-Fogle M, Ditto W L. Experimental Observation of Stochastic Resonance in a Magnetoelastic Ribbon. Phys. Rev.A, 1992,46:5253-5256.
[265]Melnikov V I. Schmitt trigger. A solvable Model of Stochastic Resonance. Phys. Rev.E, 1993,48:2481-2489.
[266]Liangsheng Qu, Jing Lin. A difference Resonator for Detecting Weak Signals, J. Measurement, 1999,26:69-77.
[267]Guanyu Wang, Dajun Chen, Jianya Lin, Xing Chen. The Application of Chaotic Oscillators to Weak Signal detection, Industrial Electronics. IEEE Transactions, 1999,46(2):440-444.
[268]李久彤，姜万录，王益群．齿轮早期故障的间歇混沌诊断方法．燕山大学学报，1999，23(3)：219-222．
[269]胡茑庆，陈敏．混沌振子在定频微弱信号检测中应用．振动工程学报，2000．10，13(增刊)：93-96．
[270]陈佳圭．微弱信号检测．北京：中央广播电视大学出版社，1987．
[271]戴逸松．微弱信号检测方法及仪器．北京：国防工业出版社，1994．
[272]Glenn C M, Hayes S. Weak Signal Detection by Small-perturbation Control of
Chaotic Orbits. Microwave Symposium Digest, 1996,3:1883-1886．
[273] Hock K M, Narrowband Weak Signal Detection by Higher Order Spectrum Signal Processing, IEEE Transactions on Published, 1996, 44(4) :874-879．
[274] Spooner C M, Gardner W A. Exploitation of Higher-order Cyclostationarity for Weak-signal Detection and Time-delay Estimation Statistical Signal and Array Processing, Conference Proceedings., IEEE Sixth SP Workshop, 1992,197-201．
[275] [SG94] Spooner C M, Gardner W A. The Cumulant Theory of Cyclostationary Time-series. II. Development and applications Signal Processing, IEEE Transactions,1994, 42(12) :3409-3429．
[276] Taek Sang Oh, lickho Song, Sun Yong Kim. Weak Signal Detection Using Suboptimum Quantization Communications, Computers and Signal Processing, IEEE Pacific Rim Conference, 1991, 1:154-157．
[277] Ehara N, Sasase I, Mori S. Weak Radar Signal Detection Based on Wavelet Transform, ICASSP-94． ,1994, ii(2) :377-380．
[278] 方晖,徐静娟,陈洪渊。一种有效提取微弱信号的新方法。化学学报,1998,56:990-993．
[279] Greenspan B D, Holmes P J. Homoclinic orbits, subharmonics, and global bifurcations in forced oscillators, Nonlinear Dynamics and Turbulence, Pitman:London, 1983, 172-214．
[280] Greenspan B D, Holmes P J. Repeated Resonance and Homoclinic Bifurcations in a Periodically Forced Family of Oscillators, SIAM J. Math.Anal., 1984, 15:69-97．
[281] 李骊。强非线性振动系统的定性理论与定量方法。北京:科学出版社,1997
[282] 高本庆。椭圆函数及其应用。北京:国防工业出版社,1991。
[283] Devaney R L. Chaotic Dynamical Systems, 2~(nd) ed, Add i son-Wesley, New York, 1989．
[284] Jackson E A. Perspectives of Nonlinear Dynamics, Cambridge University Press, Cambridge, England, 1989．
[285] Crutchfield J P, Packard N H. Symbolic Dynamics of Noisy Chaos, Physica D , 1983,7:201-223．
[286] Rechester A, White R B. Symbolic Kinetic Equation for a Chaotic Attractor, Physics Letters A, 1991, 156:419-424．
[287] Rechester A, White R B. Symbolic Kinetic Analysis of Two-dimensional Maps, Physics Letters A, 1991,158:51-56．
[288] Kurths J, Voss A, Saparin P, Witt A, Kleiner HJ, WesselN. Quantitative Analysis of Heart Rate Variability, Chaos, 1995, 5(1) : 88-94．
[289] Schwarz U, Benz A 0, Kurths J, Witt A. Analysis of Solar Spike Events by Means of Symbolic Dynamics Methods, Astronomy and Astrophysics, 1993,277:215-224．
[290] Lehrman M, Rechester A B, White R B. Symbolic Analysis of Chaotic Signals and Turbulent Fluctuations, Physical Review Letters, 1997, 78(1) :54-57．
[291] Tang X Z, Tracy E R, Brown R. Symbol Statistics and Spatio-temporal Systems, Physica D, 1997, 102:253-261．
[292] Tang X Z, Tracy E R, Boozer A D, deBrauw A, Brown R. Symbol Sequence Statistics in noisy Chaotic Signal Reconstruction, Physical Review E, 1995,51(5) : 3871-3889．
[293] Tang X Z, Tracy E R, Boozer A D, deBrauw A, Brown R. Reconstruction of Chaotic Signals Using symbolic Data, Physics Letters A, 1994,190:393-398．
[294] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA332494．
[295] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA332543．
[296] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA340951．
[297] Daw C S, Kennel M B, Finney C E A. Application of Symbolic Dynamics to Modeling and Control of an Internal Combustion Engine, SIAM DS97, Snowbird, 1997．
[298] Symbolic dynamics in mathematics, physics, and engineering, submitted by Warren Weckesser based on a talk presented by Dr. Nicholas Tufillaro of Hewlett-Packard Research Labs at the IMA Industrial Problems Seminar on September 26, 1997．
[299] Finney C E A, Green J B Jr, Daw C S. Symbolic Time-Series Analysis of Engine Combustion Measurements, 1998, SAE Paper No. 980624．
[300] Daw C S, Finney C E A, Kennel M B, Connolly F T. Cycle-by-cycle Combustion Variations in Spark-ignited Engines, Proceedings of the Fourth Experimental Chaos Conference, Boca Raton, Florida USA, 1997 .August 6-8．
[301] Daw C S, Finney C E A, Kennel M B. Measuring Time Irreversibility Using Symbolization, Fifth Experimental Chaos Conference Orlando, Florida, 1999 June 28-July 01．
[302] Finney C E A, Nguyen K, Daw C S, Halow J S. Symbol Statistics for Monitoring Fluidization, 1998 International Mechanical Engineering Congress & Exposition (ASME) (Anaheim, California USA; 1998 November 15-20) .
[303] Feng Lin, Use of Symbolic Time Series Analysis for Stall Precursor Detection, AIAA 98-3310．
[304] 朱剑英。面向21世纪的生产工程--第49届CIPP年会综述,中国机械工程, 1999,10 (11) : 1299-1301．
[305] Edwards K D, Finney C E A, Nguyen K, Daw C S. Use of symbol Statistics to Characterize Combustion in a Pulse combustor Operating near the Fuel-lean Limit, Proceedings of the 1998 Spring Technical Meeting of the Central States Section of the Combustion Institute (Lexington KY, 1998 May 31-June 2) , 385-390．
[306] Tang X Z, Tracy E R. Data Compression and Information Retrieval via
Symbolization, Chaos ,1998,8(3) :688-696．
[307] Gamraaitoni L. Stochastic Resonance, Reviews of Modern Physics, 1998,70(1) : 223-287．
[308] Wlesefeld K, Moss F. Stochastic Resonance and the Benefits of Noise:from Ice Ages to Crayfish and SQUIDs. Nature, 1995, 373(5) :33-36．
[309] Hanggi P, Talkner P, Borkovec M. Reaction-rate Theory: Fifty Years After Kramers, Rev. Mod.Phys., 1990, 62(2) : 251-341．
[310] Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S. Stochastic Resonance in Bistable Systems, Physical Review Letters, 1989,62(4) :349-352．
[311] Benzi R, Parisi G, Sutera A, Vulpiani A. A Theory of Stochastic Resonance in Climatic Change, SIAM Journal on Applied Mathematics, 1983, 43(3) :565-578．
[312] Nicolis C. Long-Term Climatic Transitions and Stochastic Resonance, Journal of Statistical Physics, 1993,70(1/2) :4-14．
[313] Imbrie J, Mix A C, Martinson D G. Milankovitch Theory Viewed from Devils Holes, Nature, 1993, (London)363(6429) : 531-533．
[314] Fauve S, Heslot F. Stochastic Resonance in a Bistable System, Physics Letters A, 1983, 97 (1,2) : 5-7．
[315] Mitaim S, Kosko B. Adaptive Stochastic Resonance, Proceedings of the IEEE, 1998, 86(11) :2152-2183．
[316] Jung P. Threshold Devices: Fractal Noise and Neural Talk, Physical Review E, 1994, 50 (4) : 2513-2522．
[317] Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F, Stochastic Resonance on a Circle, Physical Review Letters, 1994, 72:2125-2129．
[318] Gammaitoni L. Stochastic Resonance and the Dithering Effect in Threshold Physical Systems, Phys. Rev. E, 1995, 52(5) : 4691-4698．
[319] Jung P. Stochastic Resonance and Optimal Design of Threshold Detectors, Physics Letters A, 1995,207:93-104．
[320] Petrachi D, et. al. Specific Issue on Stochastic Resonance in Biological Systems, Chaos, Solitions and Fractals, 2000, 11 (12) :1819-1944．
[321] 胡岗。随机力与非线性系统。上海:上海科技教育出版社,1994。
[322] Moss F. Stochastic Resonance: a Signal+noise in aTwo State System. Proceedings of the 45th Annual Symposium on Frequency Control, 1991: 649-658．
[323] Albert T R, Bulsara A R, Schmera G, Inchiosa M. An Evaluation of the Stochastic Resonance Phenomenon as A Potential Tool for Signal Processing. Signals, Systems and Computers, Conference Record of The Twenty-Seventh Asilomar Conference, 1993, (1) : 583-587．
[324] Asdi A S.Tewfik A H. Detection of Weak Signals Using Adaptive Stochastic Resonance, Acoustics, Speech, and Signal Processing, 1995, (2) :1332-1335．
[325] Anishchenko V S, Neiman A B, Moss F, Schimansky-Geier L. Stochastic Resonance:
Noise-enhanced Order, Physics-Uspekhi, 1999, 42(1): 7-36.
[326]Zozor S, Amblard P-O. Stochastic Resonance in a Discrete Time Nonlinear SETAR (1,2,0,0) model, Higher-Order Statistics, Proceedings of the IEEE Signal Processing Workshop, 1997,166-170.
[327]Zozor S, Amblard P-O. Stochastic Resonance in Discrete Time Nonlinear AR(1) models, Signal Processing, IEEE Transactions, 1999,47(1):108-122.
[328]王利亚等．强噪声背景中微弱信号检测的初步研究．分析化学，1999，27(12)：1391-1396．
[329]王利亚等．一种有效提取弱信号的新方法．高等学校化学学报，2000，21(1)：53-55．
[330]王利亚等．随机共振应用初步研究．计算机与应用化学，2000，17(1)：79-80．
[331]McNamara B, Wiesenfeld K. Theory of Stochastic Resonance, Physical Review A, 1989,39(9):4854—4869.
[332]Presilla C, Marchesoni F, Gammaitoni L. Periodically Time-modulated Bistable Systems:Nonstationary Statistical Properties, Phys. Rev. A, 1989, 40(4): 2105-2113.
[333]Hu G, Nicolis G, Nicolis N. Periodically Forced Fokker-Planck Equation and Stochastic Resonance, Physical Review A, 1990,42(4):2030-2041.
[334]Fox R F, Lu Y N. Analytic and Numerical Study of Stochastic Resonance, Physical Review E, 1993,48(5):3390-3398.
[335]Jung P, Hanggi P. Amplification of Small Signals via Stochastic Resonance, Physical Review A, 1991,44(12):8032-8042.
[336]Debnath G, Zhou T, Moss F. Remarks on Stochastic Resonance, Physical Review A, 1989,39(8):4323-4326.
[337]Zhou T, Moss F. Analog Simulations of Stochastic Resonance, Physical Review A, 1990,41(8):4255-4264.
[338]Vemuri G, Roy R. Stochastic Resonance in a Bistable Ring Laser, Physical Review A, 1989,39(9):4668-4674.
[339]Gong D C, Hu G, Wen X D, Yang C Y, Qin G R, Li R, Ding D F. Experimental Study of the Signal-to-Noise Ratio of Stochastic Resonance Systems, Physical Review A, 1992,46(6):3243--3249.
[340]Gong D, Qin G R, Hu G, Weng X D. Experimental Study of Stochastic Resonance, Phys. Lett. A ,1991,159: 147-152.
[341]方崇智，萧德云．系统辨识．北京：清华大学出版社，1988．
[342]刘耀宗，温熙森，胡茑庆．非最小相位线性非高斯序列的替代数据检验．物理学报，2001，50(4)：633-637．
[343]刘耀宗，温熙森，胡茑庆．线性非高斯序列的替代数据检验新方法．物理学报，2001，50(7)：1241-1247．
[2] Moon F C. Chaotic Vibrations, John Wiley&Sons, Inc. 1987.
[3] Moon F C. Chaotic and Fractal Dynamics - An Introduction for Applied Scientists and Engineers, John Wiley &Sons, INC, 1992.
[4] Kapitaniak T. Chaotic Oscillations in Mechanical Systems, Nonlinear Science-Theory and Applications, Manchester and New York, 1991.
[5] Kapitaniak T, et. al. Specific Issue on dynamics of Impact Systems, Chaos, Solitions and Fractals, 2000, 11(15):2411-2578.
[6] 冯奇，沈荣瀛编著．工程中的浑沌振动，上海：上海交通大学出版社，1998．
[7] 王聪玲，龙运佳．关于混沌振动的研究．中国农业大学学报，1997，2(6)：23-27．
[8] 黄进，叶尚辉．摩擦振子的混沌振荡研究．机械科学与技术，1999，18(2)：176-179．
[9] 鲁宏伟，杨叔子．基于非线性模型的切削过程的混沌研究，1996，9(2)：169-172．
[10] Karagiannis K, Pfeiffer F. Theoretical and Experimental Investigations of Gear-Rattling, Nonlinear Dynamics, 1991,2:267-387.
[11] Singh R, Xie H, Comparin R J. Analysis of Automotive Neutral Gear Rattle, Journal of Sound and Vibration, 1989,131(2):177-196.
[12] Pfeiffer F, Kunert A. Rattling Models from Deterministic to Stochastic Processes, Nonlinear Dynamics, 1990, 1:63-74.
[13] Comparin R J, Singh R. An Analytical Study of Automotive Neutral Gear Rattle, Journal of Mechanical Design, 1990, 112:237-245.
[14] Kunert A, Pfeiffer F. Description of Chaotic Motion by an Invariant Distribution at the Example of the Driven Duffing Oscillator, Int. Series Num. Math.,1991,97:225-230.
[15] Ted Frison, Chaos in a High Speed Gearbox, AD-A283 940, 1993.
[16] Theodossiades S, Natsiavas S. Periodic and Chaotic Dynamics of Motor-driven Gear-pair Systems with Backlash. Chaos, Solitions and Fractals, 2001, 12(13):2427-2440.
[17] 郑吉兵，孟光．考虑非线性涡动时的裂纹转子的分叉与混沌特性．振动工程学报，1997，10(2)：190-197．
[18] 曾复，吴昭同，严拱标．裂纹转子的分岔与混沌特性分析．振动与冲击，2000，19(1)：40-42．
[19] 郑吉兵，谢建华，孟光．非线性裂纹转子系统环面分叉的数值研究．铁道学报，1998，20(增刊)：152-155．
[20] 张伟，陈予恕．含有参数激励非线性动力系统的现代理论的发展．力学进展，1998，28(1)：1-16．
[21] 张伟，陈予恕．机械系统中的非线性动力学问题及其研究进展．中国机械工程，1998，
9(7)：64-69．
[22] 陈予恕，王德石，余俊．参外激励作用下非线性振动系统的混沌．振动工程学报，1996，9(1)：54-59．
[23] Cvitanovic P. Invariant Measurement of Strange Sets in terms of Cycles, Physics Review Letters, 1988,61:2729-2732.
[24] Lathrop D P, Kostelich E J. Characterization of an Experimental Strange Attractor by Periodic Orbits, Physics Review A, 1989,40:4028-4031.
[25] Oppenheim A V, Wornell G W. Signal Analysis, Synthesis and Processing Using Fractal and Wavelets, ADA305490.
[26] Staszewski W J and Worden K. Wavelet Analysis of Time-series: Coherent Structures, Chaos and Noise, International Journal of Bifurcation and Chaos, 1999, 9(3):455-471.
[27] Stright J R. Embedded Chaotic Time Series: Applications in Prediction and Spatio-Temporal Classification, ADA280690.
[28] Farmer J D, Sidorowich J J. Predicting Chaotic Time Series, Physical Review Letters, 1987,59(8):845-848.
[29] Bookhart J R. The Development of Methods and Techniques to Detect and Model the Underlying Structure of Chaotic Systems, ADA292435.
[30] Grassberger P, Procaccia I. Measuring the Strangeness of Strange Attractors, Physica D, 1983,9:189-208.
[31] Barnett K D. Estimation of the Correlation Dimension and Its Application to Radar Reflector Discrimination, N94-23304.
[32] Katayama R, et al. Developing Tools and Methods for Applications Incorporating Neuro, Fuzzy and Chaos Technology, Computers ind. Engng., 1993,24(4):579-592.
[33] Logan D B, Mathew J. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearings- Ⅰ.Basic Concepts, Mechanical Systems and Signal Processing, 1996,10(3):241-250.
[34] Logan D B, Mathew J. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearings- Ⅱ. Selection of Experimental Parameters, Mechanical Systems and Signal Processing, 1996,10(3):251-264.
[35] 陈安华，朱萍玉，钟掘．对基于振动分析的机械故障诊断方法的讨论．湘潭矿业学院学报，1997，12(4)：41-47．
[36] 陈怡然，周轶尘，白烨，郑伟涛．发动机振动诊断中的多重分形法，内燃机学报，1997，15(1)：114-119．
[37] 姜建东，屈梁生．相关维数在大机组故障诊断中的应用，西安交通大学学报，1998，32(4)：27-31．
[38] Jiang J D, Chen J, Qu L S. The Application of Correlation Dimension in Gearbox Condition Monitoring. Journal of Sound and Vibration, 1999, 223(4):529-541.
[39]姜建东 屈梁生．大机组振动信号复杂性的定量描述，西安交通大学学报，1998，32(6)：31-35．
[40]杨世锡，汪慰军．柯尔莫哥洛夫熵及其在故障诊断中的应用．机械科学与技术，2000，19(1)：6-8．
[41]胡茑庆，温熙森．分形维数特征在设备运行状态分类中的应用研究，第五届全国机械设备故障诊断学术会议论文集，1996，174-178．
[42]Hu Niaoqing, Wen Xisen. A New Method of Feature Extracting Techniques Using Fractal Information for Machine Condition Monitoring, 6th COMADEM'97, Xi'an, China.
[43]温熙森，胡茑庆，邱静编著．模式识别与状态监控，长沙：国防科技大学出版社，1997．
[44]尹承丽．关联维数在机械系统状态监测中应用．硕士论文，1998．
[45]杨光．转子系统混沌现象的产生与分析方法研究．硕士论文，1999．
[46]胡茑庆，温熙森，唐丙阳．机械状态监测特征提取方法研究．机械动力学及其在工程中的应用，1997．4：212-215．
[47]Simard P, Tavernier E L. Fractal Approach for Signal Processing and Application to the Diagnosis of Cavitation. MSSSP, 2000,14(3):459-469.
[48]徐章遂，房立清，王希武，左宪章．故障信息诊断原理及应用．北京：国防工业出版社，2000．
[49]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，2001．3．
[50]焦映厚等．非线性转子动力学的研究现状与展望．哈尔滨工业大学学报，1999，31(3)：1-4．
[51]汪慰军，吴昭同，严拱标，杨世锡．转子——轴承系统的稳定性、分岔与混沌行为研究．振动、测试与诊断，1999，19(1)：44-47．
[52]张雨，刘耀宗，胡茑庆，温熙森．轴系非对中时轴承振动的数值模拟与物理模拟研究．中国造船，1999，147(4)：64-70．
[53]褚福磊，方泽南，张正松．带有支座松动故障的转子——轴承系统的混沌特性．清华大学学报(自然科学版)，1998，38(4)：60-63．
[54]Adams M L, Abu-Mahfouz I A. Exploratory Research on Chaos Concepts as Diagnostic Tools for Assessing Rotating Machinery Vibration Signatures, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September 1994, pp. 29-39.
[55]Muszynska A. Partial Lateral Rotor to Stator Rubs, Proceedings of Third International Conference on Vibrations in Rotating Machinery, C281/84, IMechE, York, UK, 1984:327-335.
[56]Nikolajsen J I, Holmes R. Investigation of Squeeze-film Isolators for the Vibration Control of a Flexible Rotor, ASME Journal of Mechanical Science, 1979,21(4):247-252.
[57] Li X H, Taylor D L. Nonsynchronous Motion of Squeeze-film Damper Systems, ASME Journal of Tribology,1987,109:169-176．
[58] Ehrich F F. High Order Subharmanic Response of High Speed Rotor in Bearing Clearance, ASME Journal of Vibration , Acoustics, Stress and Reliability in Design, 1988,110:9-16．
[59] Holmes A G, Ettles C M, Mayes I W. Aperiodic Behavior of a Rigid Shaft in Short Journal Bearings, International Journal for Numerical Method in Engineering, 1978,12:695-702．
[60] Ehrich F F. Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics, Transactions of ASME, J. of Vib. and Acous., 1991,113:50-57．
[61] Ehrich F F. Nonlinear Phenomena in Dynamic Response of Rotors in Anisotropic Mounting Systems, Transactions of the ASME, J. of Vib. and Acous., 1995,117:154-161．
[62] Zhao J Y, Linnett I W, Mclean L J. Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor, Transactions of ASME, Journal of Vibration and Acoustics, 1994,116:357-363．
[63] Brown R D, Addison P, Chan A H C. Chaos in the Unbalance Response of Journal Bearings, Nonlinear dynamics, 1994, (5) :421-432．
[64] Chieh-Li Chen, Her-terng Yau. Chaos in the Inbalance Response of a Flexible Rotor Supported by Oil Film Bearings with Non-linear Suspension, Nonlinear Dynamics 1988,16:71-90．
[65] Gonsalves D H, Neilson R D, Barr A D S. A Study of the Response of a Discontinuously Nonlinear Rotor system. Nonlinear Dynamics, 1995, 7:451-470．
[66] Kraker D, et. al. The Dynamics of a Rotor with Rubbing. C284/88, IMechE, 1988．
[67] Guido A R, Adiletta G. Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part I theoretical Analysis. Nonlinear Dynamics, 1999, 19 (4) : 359-385．
[68] Guido A R, Adiletta G. Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part II Experimental Analysis. Nonlinear Dynamics, 1999, 19 (4) 1387-397．
[69] Muszynska A, et al. Influence of Rubbing on Rotor Dynamics. NASA Contract No. Nas8-36719, Final Report. Bently Nevada Corporation, March 1989．
[70] Ehrich F F. Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics, Journal of Vibration and Acoustics, 1992,114:93-100．
[71] Beatty R F. Differentiation on Rotor Response Due to Radial Rubbing, Trans. ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1985, (107) :151-160．
[72] Choy F K, Padovan J. Non-linear Transient Analysis of Rotor-Casing Rub Events, Journal of Sound and Vibration, 1987, 113(3) :529-545．
[73] Shaw S W, Radovan P J. A Periodically Forced Piecewise Linear Oscillator, Journal of Sound and Vibration, 1983, 90:129-155．
[74] Thompson J M T, Stewart H B. Geometrical Methods for Engineers and Scientists, Nonlinear Dynamics and Chaos, Chichester:Wiley.
[75] Choi S K, Noah S T. Mode-locking and Chaos in a Jeffcott Rotor with Bearing Clearances, Transactions of the ASME .Journal of Applied Mechanics, 1994, 61:131-138．
[76] Kim Y B, Noah S T. Bifurcation Analysis for a Modified Jeffcott Rotor with Bearing Clearances. Nonlinear Dynamics, 1990,1 (3) :221-243．
[77] Choi Y. S, Noah S T. Nonlinear Steady-state Response of A Rotor-support System, Transactions of the ASME, Journal of Vibration, Acoustics, Stress and Reliability in Design, 1987, 109:255-261．
[78] Chon K H, et. al. Modeling Nonlinear Determinism in Short Time Series from Noise Driven Discrete and Continuous Systems, International Journal of Bifurcation and Chaos, 2000, 10(20) :2745-2766．
[79] Ehrich F F. Rotordynamic Response in Nonlinear Anisotropic Mounting Systems, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September, 1994, 1-6．
[80] Isaksson J L. Dynamics of a Rotor with Annular Rub, Proceedings of IFTOMM Fourth International Conference on Rotor Dynamics, Chicago, USA, September, 1994, 85-90．
[81] Chu F, Zhang Z. Periodic Quasi-periodic and Chaotic Vibrations of a Rub-impact Rotor System Supported on Oil Film Bearings, International Journal of Engineering Science, 1997,35:963-973．
[82] Chu F, Zhang Z. Bifurcation and Chaos in A Rrub-impact Jeffcott Rotor System, Journal of Sound and vibration, 1998, 210(1) :1-18．
[83] Li G X, Paidoussis M P. Impact Phenomena of Rotor-casing Dynamical Systems, Nonlinear Dynamics, 1994, 5:53-70．
[84] Piccoli H C, Weber H I. Experimental Observation of Chaotic Motion in a Rotor with Rubbing, Nonlinear Dynamics, 1998, 16:55-70．
[85] 褚福磊等。碰摩转子系统中的阵发性及混沌,航空动力学报,1996, 11(3) : 261-264．
[86] 陈安华,朱萍玉,钟 掘。转子系统动静件径向摩擦的振动特征,湘潭矿业学院学报,1998,13(1) : 33-38 (55) .
[87] 陈安华,刘德顺,朱萍玉。转子系统非线性振动研究进展。湘潭矿业学院学报,14(2) : 59-65．
[88] Yang Wei,et.al. Nonlinear Response of Rotor to Stator Rubs. N19970024786, p269-p278．
[89] Chancellor R S, Alexander R M, Noah S T. Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos, Transactions of the ASME, Journal
of Vibration and Acoustics,1996,118:375-383.
[90]褚福磊，张正松，冯冠平．碰摩转子系统的混沌特性．清华大学学报(自然科学版)，1996，36(7)：52—57．
[91]褚福磊，张正松．带故障转子系统中的复杂运动现象，第五届全国机械设备故障诊断学术会议论文集，科学技术文献出版社，1996，229-233．
[92]刘献栋，李其汉．转静件碰摩模型及不对中转子局部碰摩的混沌特性，航空动力学报，1998，13(14)：361-364(456)．
[93]刘献栋 李其汉．质量偏心旋转机械碰摩故障特征及全息谱分析，航空动力学报，1998，13(4)：428-430(462)．
[94]季进臣 虞烈．高速对称刚性转子碰摩运动的稳定性分析，航空动力学报，1998，14(1)：65-68(109)．
[95]褚福磊，张正松．转子-轴承系统发生动静件碰摩时的混沌路径，应用力学学报，1998，15(2)：81-86(v)．
[96]张思进，陆启韶，王琪．转子与定子几何不对中引起的碰摩分析，振动工程学报，1998，11(4)：492-496．
[97]刘献栋 李其汉 杨绍普．质量偏心旋转机械整圈碰摩的稳定性及其Hopf分叉，振动工程学报，1999，12(1)：40-46．
[98]戴兴建，张小章，金兆熊．大幅度进动转子与位移限制器碰摩动力行为，清华大学学报(自然科学版)，1998，38(8)：104-106．
[99]晏砺堂，王德友，航空双转子发动机动静件碰摩振动特征研究，航空动力学报，1998，13(2)：173-176(220，221)．
[100]吴建，梁家惠，李淮凌．大型转动机械碰摩故障分析的声发射检测系统，北京航空航天大学学报，1998，24(1)：104-107．
[101]闻邦椿，顾家柳，夏松波，王正主编．高等转子动力学——理论、技术与应用，北京：机械工业出版社，2000．
[102]龙运佳．混沌振动研究—方法与实践，北京：清华大学出版社，1997．
[103]龙运佳．混沌工程学进展，振动与波利用技术学术会议论文集——振动与波利用技术的新进展，东北大学出版社，2000．9，439-446．
[104]胡汉平，李德华，吴晓刚，陈丹．创造性思维中可能性构造空间理论的动力学模型，高技术通讯，1998，5：20-23．
[105]伍言真，丘水生．非线性系统理论及混沌研究的动态和评述，电路与系统学报，1997，2(3)：62-66．
[106]董军，胡上序．混沌神经网络研究进展与展望，信息与控制，1997，26(5)：360-368(378)．
[107]陈德钊，董军，胡上序．混沌动力学在智能信息处理中应用研究．计算机科学，1998，25(3)：85-88．
[108]王东生，曹磊．混沌、分形及其应用．合肥：中国科学技术大学出版社，1995．
[109]唐巍，李殿璞，陈学允．混沌理论及其应用研究，电力系统自动化，2000，24(7)：67-70．
[110]王保云，董恒．基于混沌的信息记忆，南京邮电学院学报，1998，18(1)：102-105．
[111]张毅锋，何振亚．混沌系统在信息处理中的应用，数据采集与处理，1998，13(2)：101-106．
[112]刘孝贤．利用同步混沌系统和对称混沌信号实现保密通信，山东工业大学学报，1997，27(2)：101-106．
[113]Pecora L M, Carroll T L, Johnson G A, Mar D J. Fundamentals of Synchronization in Chaotic Systems, Concepts, and Applications, Chaos, 1997,7(4):520-543.
[114]Cuomo K M, Oppenheim A V. Circuit Implementation of Synchronized Chaos with Applications to Communications. Physical Review Letters, 1993,71(1):65-68.
[115]Cuomo K M, Oppenheim A V, Strogatz S H. Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications. IEEE Transactions on Circuits and systems, 1993,40(10):626-633.
[116]裴留庆，匡锦瑜，邵媛．混沌同步系统的频率特性和微弱信号检测．中国科学(E辑)，1997，27(3)：237-242．
[117]赵永龙，丁晶，邓育仁．混沌分析在水文预测中的应用和展望，水科学进展，1998，9(2)：181-186．
[118]吴耿锋等．基于相空间重构的预测方法及其在天气预报中的应用．自然杂志，1999，21(2)：107-110．
[119]徐晓红，谢正祥，陈良迟，何伟．心动周期信号的混沌特征分析及应用，中国生物医学工程学报，1999，18(1)：74-81(88)．
[120]贺太纲．基于混沌理论的脑电图(EEG)分析与预测研究，西安交通大学博士学位论文，1997．
[121]Pecora L, Carroll T. Synchronization Chaotic Systems. Physical Review Letters, 1990, 64(8):821-824.
[122]王光瑞，于熙龄，陈式刚．混沌的控制、同步与利用．北京：国防工业出版社，2001．
[123]陈立群，刘延柱．混沌的抑制研究进展综述．力学进展，1998，28(3)：299-309．
[124]戴冠中，刘华强，郑会永．非线性科学中的一些问题及其应用．电子科技导报，1996，4：5-8．
[125]Haykin S, Li X B. Detection of Signals in Chaos, Proceedings of the IEEE, 1995,83(1):95-122.
[126]Donald LB. Chaotic Oscillators and CMFFNS for Signal Detection in Noise Environment, IEEE International Joint Conference on Neural Networks, 1992,2:881-888.
[127]姜万录、王益群、孔祥东、李久彤．液压系统故障检测与诊断技术的新进展，中国机械工程，1998，9(9)：58-62．
[128]王冠宇，陶国良，陈行，林建亚．混沌振子在强噪声背景信号检测中的应用．仪器仪表学报，1997：18(2)：209-212．
[129]姜万录、王益群、孔祥东．齿轮故障的混沌诊断识别方法，机械工程学报，1999，35(6)：44-47．
[130]吕志民，徐金梧，翟绪圣．基于混沌振子的微弱特征信号检测原理及方法，河北工业大学学报，1998，27(4)：13-17．
[131]聂春燕．微弱正弦信号的时域处理方法研究，计量技术，2000，5：3-5．
[132]陈敏，胡茑庆，温熙森．混沌振子在转子系统早期碰摩故障检测中的应用，国防科技大学学报，2001，23(1)：36-39．
[133]陈敏，混沌振子在转子系统早期碰摩故障检测中的应用．硕士论文，2001．
[134]姜万录，王益群．混沌振子在液压泵故障诊断中的应用．机床与液压，1999，(5)：52-53．
[135]王林翔．扭转弯管中的混沌混合机理及其可视化研究，杭州：浙江大学博士学位论文，1999．
[136]熊峻江，武哲，高镇同．混沌疲劳初探．北京航空航天大学学报，1998，24(6)：667-670．
[137]Leonardi M L. Prediction and Geometry of Chaotic Time Series. 1997, ADA333449.
[138]Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from Time Series, Phys. Rev. Lett., 1980, 47: 712-716.
[139]Barenblatt G L, Looss G, Joseph D D, Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983.
[140]Barenblatt G L, Looss G, Joseph D D, Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983.
[141]马军海，陈予恕，刘曾荣．动力系统实测数据的非线性混沌特性的判定．应用数学和力学，1998，19(6)：481-488．
[142]马军海，盛昭瀚，唐文雄．不同相位随机化对时序混沌特征影响的研究．1999，29(2)：93-99．
[143]刘耀宗．碰摩转子混沌振动分析与控制，长沙：国防科学技术大学博士学位论文，2001．
[144]胡晓棠．转子系统中的非线性时间序列预测方法研究，国防科技大学硕士论文，2000．
[145]Stam C J, Pi jn J P M, Pritchard W S. Reliable Detection of Nonlinearity in Experimental Time Series with Strong Periodic Components, Physica D 112(1998):361-380.
[146]Ma Junhai, Zheng Wanming, Wang Liqin. Testing Value for Nonlinear Chaotic Nature of the Data Obtained in Dynamic Analysis. Journal of Tianjin University of Commerce, 1997,3:23-27.
[147]吴振奎．混沌平话，数学通讯，1999，2：42-43．
[148]郑会永，肖田元，王新龙，韩向利．混沌及混沌保密通讯技术，中国图象图形学报，1998，3(12)：1042-1050．
[149]Holmes J P. Averaging and Chaotic Motions in Forced Oscillations, SIAM Appl. Math, 1980, 38(1): 65～92, 1981, 40(1): 167-168.
[150]Holmes J P, Marsden J E. Horseshoes in Perturbations of Hamiltonians with Two
Degree of Freedom. Commun. Math. Phys., 1982, 82: 523-544.
[151]Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, springwer-Verlag, New York, N. T. 1983.
[152]凌复华．混沌、随机、信息流和其他，力学与实践，1985，7(5)：17-20．
[153]Haken H. At Least One Lyapunov Exponent Vanishes if the Trajectory of an Attractor does not Contain a Fixed Point, Phys. Lett. 1983, 94A(2): 71-72.
[154]Devaney R L. An Introduction to Chaotic Dynamical Systems, Menlo Park, CA: Benjam in uCummings, 1986.
[155]程极泰．混沌的理论与应用，上海：上海科学技术文献出版社，1991．
[156]汪秉宏．非线性科学选讲．合肥：中国科学技术大学出版社，1994：35-102．
[157]Thomas S Parker, Leon O Chua. Practical Numerical Algorithms for Chaotic Systems. Springer—Verlag, New York Inc., 1989.
[158]林鸿溢，李映雪．分形论——奇异性探索，北京：北京理工大学出版社，1992．
[159]Marek Milos. Chaotic Behavior of Deterministic Dissipative Systems, Cambridge Univ. Press, 1991.
[160]陈式刚．映象与混沌．北京：国防工业出版社，1992．
[161]陆启韶，黄克累．非线性动力学、分叉和混沌．一般力学(动力学、振动与控制)最新进展．北京：科学出版社，1994．
[162]Neil R S. Chaotic Dynamic of Nonlinear Systems, John Wiley&Sons Inc., 1990.
[163]Wiggins S. Global Bifurcations and Chaos, Analytical Methods. Springer-Verlag,1988.
[164]郑伟谋，郝柏林．实用符号动力学．上海：上海科技教育出版社，1995．
[165]郝柏林．非线性科学丛书．上海：上海科技教育出版社，1995．
[166]陈予恕，唐云等．非线性动力学中的现代分析方法，北京：科学出版社，1992．
[167]Blazejczyk-Okolewska B, Czolczynski K, Kapitaniak T, Wojewoda J. Chaotic Mechanics in Systems with Impacts and Friction, World Scientific Series on Nonlinear Science, World Scientific Publishing Co. Pte. Ltd, 1999.
[168]李继彬，冯贝叶．稳定性、分支与混沌，昆明：云南科技出版社，1995．
[169]胡茑庆，张雨，刘耀宗，胡晓棠，温熙森．转子系统动静件间尖锐碰摩时的振动特征实验研究．中国机械工程，拟发表于2002年第八期．
[170]刘耀宗，胡茑庆．系统参数对碰摩转子稳态响应的影响．非线性动力学学报，1999，6(4)：332-337．
[171]刘耀宗，胡茑庆，温熙森．不平衡激励对碰摩转了振动特性的影响．机械科学与技术，2000，19(4)：536-538．
[172]胡茑庆，刘耀宗，杨光．非线性碰摩转子系统响应的数值分析．将发表于中国振动工程学会机械动力学学会第九届年会上，2001．
[173]张雨，徐小林，张建华．设备状态监测与故障诊断的理论与实践．长沙：国防科技大学出版社，2000．
[174]徐敏等主编．设备故障诊断手册——机械设备状态监测和故障诊断．西安：西安交
通大学出版社，1998．
[175]王善永 陆颂元 马元奎 瞿红春．汽轮发电机组转子动静碰摩故障检测的小波分析方法研究，中国电机工程学报，1999，19(3)：1-5(70)．
[176]刘献栋，李其汉．小波变换在转子系统动静件早期碰摩故障诊断中的应用，航空学报，1999，20(3)：220-223．
[177]Choy F K, Padovan J, Baturc. Rub Interactions of Flexible Casing Rotor Systems. Journal of Engineering for Gas Turbine and Power, 1989,111:652-658.
[178]Goldman P, Muszynska A. Chaotic Behavior of Rotor-stator Systems with Rubs. Journal of Engineering for Gas Turbine and Power, 1994,116: 692-701.
[179]Kellenberger W. Spiral Vibration Due to the Seal Rings in Turbogenerator Thermally Induced Interaction between Rotor and Stator. Journal of Mechanical Design, Trans. Of ASME, 1980,102(1):178-184.
[180]Lee H P, Tan T H. Dynamics Stability of Spinnig Timoshenko Shaft with a Time-dependent Spin Rate. Journal of Sound and Vibration, 1997, 199(3): 401-415.
[181]Kim Y B, Noah S T. Stability and bifurcation Analysis of Oscillators with Piecewise Linear Characteristics: a General Approach. ASME J of Applied Mechanics, 1991,58(6):545-554.
[182]Muszynska A, Franklin W D, Hayashida R D. Rotor to Stator Partial Rubbing and its Effects on Rotor Dynamic Response. 1992, N92214367.
[183]Smalley A J. The Dynamic Response of Rotors to Rubs during Start up, J. of Vibration, Acoustics and Reliability in Design, 1989,111(3):226-233.
[184]Zhang W. Dynamic in Stability of Multi-degree-of-freedom Flexible Rotor Systems due to Full Annular Rub. Fourth International Conference on vibration in Rotating Machinery, Edinburgh, UK, 1988, ImechE: 305-310.
[185]胡茑庆，陈敏，刘耀宗，杨光，温熙森．非线性转子系统碰摩现象的动力学仿真，国防科技大学学报，2000，22(6)：101-104．
[186]岳国金等．转子碰摩的振动特征分析．航空学报，1990，11(10)：499-502．
[187]武新华等．旋转机械碰摩故障特性分析．汽轮技术，1996，38(1)：31-34．
[188]傅行军，杨建刚．摩擦对大型汽轮发电机组振动的影响分析，振动工程学报，1998，11(2)：215-219．
[189]刘耀宗，胡茑庆．Jeffcott转子碰摩故障试验研究．振动工程学报，2001，14(1)：96-99．
[190]王善永，陆颂元，童小忠．汽轮发电机组动静碰摩的奇异谱理论与小波分析诊断方法研究．动力工程，1999，19(6)：498-503．
[191]刘占生等．小波分析和分形几何在转子动静碰摩故障诊断中的应用．哈尔滨工业大学学报，1999，31(1)：55-56(92)．
[192]Integrated Diagnostics, ADA324130.
[193]周劲松等．工程随机信号的确定性混沌理论与分析方法．浙江大学学报，1997，
31(2)：245-252．
[194]洪时中．非线性时间序列分析的最新进展及其在地球科学中的应用前景．地球科学进展，1999，14(6)：559-565．
[195]黄文虎，夏松波，刘瑞岩等编著．设备故障诊断原理、技术及应用．北京科学出版社，1997．
[196]尹承丽，胡茑庆，温熙森．关联分形维数在转子系统状态监测中应用的实验研究，非线性动力学学报，1997，4(3)：264-268．
[197]尹承丽，胡茑庆，温熙森．关联维数在转子系统状态监测应用时参数选择的实验研究，火力与指挥控制，1998，23(3)：75-80．
[198]胡晓棠，胡茑庆，陈敏．一种改进的选择相空间重构参数的方法．振动工程学报，2001，14(2)：242-244．
[199]胡茑庆，杨光，尹承丽，温熙森．转子系统状态监测的关联维数方法实验研究，第六届全国机械设备故障诊断学术会议论文集，1998．10，pp．43-47，振动工程学报，1998，11(增刊)．
[200]汪慰军等．基于伪相图的大机组非线性故障诊断技术．上海交通大学学报，2000，34(9)．
[201]Kugiumtzis D. State Space Reconstruction Parameters in the Analysis of Chaotic Time Series. Physica D, 1996, (95):13-28.
[202]Abarbanel H D I. Analysis of Observed Chaotic Data, Springer-Verlag New York, Inc. 1996.
[203]Rosenstein M T, Collins J J, Luca C. Reconstruction Expansion as a Geometry-based Framework for Choosing Proper Delay Time. Physica D, 1994,73:82-89.
[204]Kember G, Fowler A C. A Correlation Function for Choosing Time Delays in Phase Portrait Reconstructions. Phy Lett A, 1993,179:72-80.
[205]Vautard R, et al. Singular Spectrum Analysis: a Toolkit for Short, Noisy Chaotic Singals. Physica D, 1992,58:95-126.
[206]Palus M, Dvorak I. Singular Value Decomposition in Attractor Reconstruction: Pitfalls and Precautions. Physica D, 1992,55:221-234.
[207]Buzug T, Pfister G. Comparison of Algorithms Calculating Optimal Embedding Parameters for Delay Time Coordinates. Physica D, 1992, (58):127-137.
[208]Buzug T, Pfister G. Optimal Delay Time and Embedding Dimension for Delay-time Coordinates by Analysis of the Global Static and Local Dynamical Behavior of Strange Attractors. Phy. Rev. A, 1992,45:7073-7084.
[209]Liebert W, et al. Optimal Embedding of Chaotic Attractors from Topological Considerations. Europhys Lett, 1991,14:521.
[210]Casdagli M, Sauer T, Yorke J A. Embedology, J. Stat. Phys, 1991,65:579-616.
[211]Callager R G. Information Theory and Reliable Communication, John Wiley and Sons, New York, 1968.
[212]Fraser A M, Swinney H L. Independent Coordinates for Strange Attractors from
Mutual Information. Phys. Rev. A, 1986,33:1134-1140.
[213]Broomhead D S, King G P. Extracting Qualitative Dynamics from Experimental Data. Physical D, 1987, (20):217-236.
[214]袁坚，肖先赐．低信噪比下的状态空间重构．物理学报，1997，46(7)：1290-1299．
[215]Kennel M B, Brown R, Abarbanel H D I. Determining Minimum Embedding Dimension Using a Geometrical Construction. Physical Review A, 1992,45:3403-3411.
[216]Aleksic Z. Estimating the Embedding Dimension, Physica D, 1991, (52):362-368.
[217]Mees A I, Rapp P E. Singular Value Decomposition and Embedding Dimension. Phys Rev A, 1987,36(1):340-346.
[218]Fraser A M. Information and Entropy in Strange Attractors. IEEE TR on IT, Mar 1989,35(2):245-262.
[219]Hong Pi, Peterson C. Finding the Embedding Dimension and Variable Dependencies in Time Series. Neu Comput, 1994,6:509-518.
[220]Liangyue Cao. Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series. Physica D, 1997,110:43-50.
[221]Nayfeh A H, Balachandran B. Applied Nonlinear Dynamics, Wiley, New York, 1995.
[222]Farmer J D, Ott E, Yorke J A. The Dimension of Chaotic Attractors, Physica D, 1983,7:153-180.
[223]Holger Kantz,Thomas Schreiber.Nonlinear Time Series Analysis(非线性时间序列分析)，清华大学出版社，2000(影印本)．
[224]张作生，彭虎，公佩祥．时间序列分维数提取算法的研究．中国科学技术大学学报，1997，27(2)：220-224．
[225]李擎，郑德玲，赵星浩，刘东方．一种新的混沌识别方法(Ⅰ)．北京科技大学学报，1999，21(2)：198-201．
[226]胡海岩编著．应用非线性动力学．北京：航空工业出版社，2000．
[227]Stefanski A. Estimation of the Largest Lyapunov Exponent in Systems with Impacts. Chaos, Solitions and Fractals, 2000,11(15):2443-2451.
[228]Wolf A, Swift J, Swinney H L, Vastano J A. Determining Lyapunov Exponents from a Time Series. Physica D, 1985,16: 285-317.
[229]Sano M, Sawada Y. Measurement of the Lyapunov Spectrum from a Chaotic Time Series. Phys. Rev. Lett.,1985,55(1O):1082-1085.
[230]Abarbanel H D I, Rrown R and Kennel M B. Vibration of Lyapunov Exponents on a Strange Attractor. Journal of Nonlinear Science, 1991, (1):175-199.
[231]Eckman L P, Ruelle D, Ciliberto S. Lyapunov Exponents from Time Series. Physical Review A, 1986, 34:4971-4979.
[232]Kruel T M, Eiswirth M, Schneider F W. Computation of Lyapunov Spectra: Effect of Interactive Noise and Application to a Chemical Oscillator. Physica D, 1993,63:117-137.
[233]Briggs K. An Improved Method for Estimating Lyapunov Exponents of Chaotic Time
Series. 1990 Physics Letters A, 1990,151:27-32.
[234]Brown R, Bryant P, Abarbanel H D I. Computing the Lyapunov Spectrum of A Dynamical System from An Observed Time Series. Physical Review A, 1991,(43):2787-2806.
[235]Darbyshire A G. Calculating Lyapunov Exponents from a time Series. Exploiting Chaos in Signal Processing, IEE Colloquium on Published: 1994,2:1-6.
[236]Banbrook M, Ushaw G, McLaughlin S. How to Extract Lyapunov Exponents from Short and Noisy Time Series. Signal Processing, IEEE Transactions on Published, 1997, 45(5): 1378-1382.
[237]Sato S, Sano M, Sawada Y. Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems. Prog. Theor. Phys.,1987,77(1):1-5.
[238]Rosenstein M T, Collins J J, Luca C J D.A practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Physica D, 1993, 65:117-134.
[239]Shin K, Hammond J K. The Instantaneous Lyapunov Exponent and Its Application to Chaotic Dynamical Systems. Journal of Sound and Vibration, 1998, 218(3): 389-403.
[240]Chon K H, Kanters J K, Iyengar N, Cohen R J, Holstein-Rathlou N H. Detection of Chaotic Determinism in Stochastic Short Time Series. Engineering in Medicine and Biology Society, 1997. Proceedings of the 19th Annual International Conference of the IEEE Published: 1997, 1: 275-277.
[241]Chatfield C. The Analysis of Time Series, Chapman and Hall,1989.
[242]Tong, Howell, Nonlinear Time Series: A Dynamical Systems Approach, Clarendon Press, 1990.
[243]Weigend A S, Gershenfeld N A. Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley Publishing Company, 1994.
[244]Kennel M B. Method to Distinguish Possible Chaos from Colored Noise and to Determine Embedding Parameters. Physical Review A, 1992, 46(6):3111-3118.
[245]刘洪．预测的混沌范式及动力学方法．系统工程与电子技术，1998，2：1-5．
[246]贺太纲，郑崇勋．混沌序列的非线性预测．自然杂志，1997，19(1)：10-13．
[247]马军海，盛昭瀚．低维混沌时序的预测方法及其应用研究．东南大学学报，1999，29(5)：65-69．
[248]任晓林，胡光锐，徐雄．混沌时间序列局域线性预测方法．上海交通大学学报，1999，33(1)：19-21．
[249]王永忠，曾昭磐．混沌时间序列的局域线性回归预测方法．厦门大学学报(自然科学版)，1999，38(4)：636-640．
[250]Casdagli M. Nonlinear Prediction of Chaotic Time Series. Physica D, 1989, 35: 335-356.
[251]Casdagli M, Stephen E, Farmer J D, Gibson J F. An Analytic Approach to Practical
State Space Reconstruction. Physica D, 1992, 57(1/2): 1-30.
[252]龙运佳．混沌工程学．中国工程科学，2001，3(2)：8-13．
[253]Jun Zhang, Man K F, Ke J Y. Time Series Prediction Using Lyapunov Exponents in Embedding Phase Space. Systems, Man, and Cybernetics, 1998, 2: 1744-1749.
[254]Sugihara G, May R M. Nonlinear Forecasting as a Way of Distinguishing Chaos From Measurement Error in Time Series. Nature, 1990,344(6268): 734-741.
[255]刘洪，李必强．基于混沌吸引子的时间序列预测．系统工程与电子技术，1997(2)：23-28．
[256]Martin J K, Nandi A K. Noise Reduction in Chaotic Time Series. IEE Colloquium on Exploiting Chaos in Signal Processing, 1994,4: 1-6.
[257]Mulgrew B, Strauch P. Nonlinear Dynamics and Noise Cancellation. IEE Colloquium on Signals Systems and Chaos, 1997,2:1-6.
[258]Heald J. Noise Reduction: Multiple Solutions. IEE Colloquium on Signals systems and Chaos, 1997,3:1-6.
[259]余建祖，苏南．混沌时序的噪声降低技术研究．航空学报，1999，20(6)：498-502．
[260]刘秉正．非线性动力学与混沌基础．沈阳：东北师范大学出版社，1994．
[261]Benzi R, Sutera A, Vulpiani A.The Mechanism of Stochastic Resonance. Journal of Physics A: Mathematical and General, 1981,14:453-457.
[262]McNamara B, Wiesenfeld K, Roy R. Observation of Stochastic Resonance in a Ring Laser. Phys. Rev. Lett., 1988,60:2626-2629.
[263]De-chun G, Gang H, Xiao-dong W. Chun-yan Y, Guang-rong Q, Rong L, Da-fu D. Experimental Study of Signal-to-noise Ratio of Stochastic Resonance Systems. Phys. Rev.A,1992,46:3243-3249.
[264]Spano M L, Wun-Fogle M, Ditto W L. Experimental Observation of Stochastic Resonance in a Magnetoelastic Ribbon. Phys. Rev.A, 1992,46:5253-5256.
[265]Melnikov V I. Schmitt trigger. A solvable Model of Stochastic Resonance. Phys. Rev.E, 1993,48:2481-2489.
[266]Liangsheng Qu, Jing Lin. A difference Resonator for Detecting Weak Signals, J. Measurement, 1999,26:69-77.
[267]Guanyu Wang, Dajun Chen, Jianya Lin, Xing Chen. The Application of Chaotic Oscillators to Weak Signal detection, Industrial Electronics. IEEE Transactions, 1999,46(2):440-444.
[268]李久彤，姜万录，王益群．齿轮早期故障的间歇混沌诊断方法．燕山大学学报，1999，23(3)：219-222．
[269]胡茑庆，陈敏．混沌振子在定频微弱信号检测中应用．振动工程学报，2000．10，13(增刊)：93-96．
[270]陈佳圭．微弱信号检测．北京：中央广播电视大学出版社，1987．
[271]戴逸松．微弱信号检测方法及仪器．北京：国防工业出版社，1994．
[272]Glenn C M, Hayes S. Weak Signal Detection by Small-perturbation Control of
Chaotic Orbits. Microwave Symposium Digest, 1996,3:1883-1886．
[273] Hock K M, Narrowband Weak Signal Detection by Higher Order Spectrum Signal Processing, IEEE Transactions on Published, 1996, 44(4) :874-879．
[274] Spooner C M, Gardner W A. Exploitation of Higher-order Cyclostationarity for Weak-signal Detection and Time-delay Estimation Statistical Signal and Array Processing, Conference Proceedings., IEEE Sixth SP Workshop, 1992,197-201．
[275] [SG94] Spooner C M, Gardner W A. The Cumulant Theory of Cyclostationary Time-series. II. Development and applications Signal Processing, IEEE Transactions,1994, 42(12) :3409-3429．
[276] Taek Sang Oh, lickho Song, Sun Yong Kim. Weak Signal Detection Using Suboptimum Quantization Communications, Computers and Signal Processing, IEEE Pacific Rim Conference, 1991, 1:154-157．
[277] Ehara N, Sasase I, Mori S. Weak Radar Signal Detection Based on Wavelet Transform, ICASSP-94． ,1994, ii(2) :377-380．
[278] 方晖,徐静娟,陈洪渊。一种有效提取微弱信号的新方法。化学学报,1998,56:990-993．
[279] Greenspan B D, Holmes P J. Homoclinic orbits, subharmonics, and global bifurcations in forced oscillators, Nonlinear Dynamics and Turbulence, Pitman:London, 1983, 172-214．
[280] Greenspan B D, Holmes P J. Repeated Resonance and Homoclinic Bifurcations in a Periodically Forced Family of Oscillators, SIAM J. Math.Anal., 1984, 15:69-97．
[281] 李骊。强非线性振动系统的定性理论与定量方法。北京:科学出版社,1997
[282] 高本庆。椭圆函数及其应用。北京:国防工业出版社,1991。
[283] Devaney R L. Chaotic Dynamical Systems, 2~(nd) ed, Add i son-Wesley, New York, 1989．
[284] Jackson E A. Perspectives of Nonlinear Dynamics, Cambridge University Press, Cambridge, England, 1989．
[285] Crutchfield J P, Packard N H. Symbolic Dynamics of Noisy Chaos, Physica D , 1983,7:201-223．
[286] Rechester A, White R B. Symbolic Kinetic Equation for a Chaotic Attractor, Physics Letters A, 1991, 156:419-424．
[287] Rechester A, White R B. Symbolic Kinetic Analysis of Two-dimensional Maps, Physics Letters A, 1991,158:51-56．
[288] Kurths J, Voss A, Saparin P, Witt A, Kleiner HJ, WesselN. Quantitative Analysis of Heart Rate Variability, Chaos, 1995, 5(1) : 88-94．
[289] Schwarz U, Benz A 0, Kurths J, Witt A. Analysis of Solar Spike Events by Means of Symbolic Dynamics Methods, Astronomy and Astrophysics, 1993,277:215-224．
[290] Lehrman M, Rechester A B, White R B. Symbolic Analysis of Chaotic Signals and Turbulent Fluctuations, Physical Review Letters, 1997, 78(1) :54-57．
[291] Tang X Z, Tracy E R, Brown R. Symbol Statistics and Spatio-temporal Systems, Physica D, 1997, 102:253-261．
[292] Tang X Z, Tracy E R, Boozer A D, deBrauw A, Brown R. Symbol Sequence Statistics in noisy Chaotic Signal Reconstruction, Physical Review E, 1995,51(5) : 3871-3889．
[293] Tang X Z, Tracy E R, Boozer A D, deBrauw A, Brown R. Reconstruction of Chaotic Signals Using symbolic Data, Physics Letters A, 1994,190:393-398．
[294] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA332494．
[295] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA332543．
[296] Improved Techniques for Modeling and Controlling Nonlinear Systems with Few Degrees of Freedom, ADA340951．
[297] Daw C S, Kennel M B, Finney C E A. Application of Symbolic Dynamics to Modeling and Control of an Internal Combustion Engine, SIAM DS97, Snowbird, 1997．
[298] Symbolic dynamics in mathematics, physics, and engineering, submitted by Warren Weckesser based on a talk presented by Dr. Nicholas Tufillaro of Hewlett-Packard Research Labs at the IMA Industrial Problems Seminar on September 26, 1997．
[299] Finney C E A, Green J B Jr, Daw C S. Symbolic Time-Series Analysis of Engine Combustion Measurements, 1998, SAE Paper No. 980624．
[300] Daw C S, Finney C E A, Kennel M B, Connolly F T. Cycle-by-cycle Combustion Variations in Spark-ignited Engines, Proceedings of the Fourth Experimental Chaos Conference, Boca Raton, Florida USA, 1997 .August 6-8．
[301] Daw C S, Finney C E A, Kennel M B. Measuring Time Irreversibility Using Symbolization, Fifth Experimental Chaos Conference Orlando, Florida, 1999 June 28-July 01．
[302] Finney C E A, Nguyen K, Daw C S, Halow J S. Symbol Statistics for Monitoring Fluidization, 1998 International Mechanical Engineering Congress & Exposition (ASME) (Anaheim, California USA; 1998 November 15-20) .
[303] Feng Lin, Use of Symbolic Time Series Analysis for Stall Precursor Detection, AIAA 98-3310．
[304] 朱剑英。面向21世纪的生产工程--第49届CIPP年会综述,中国机械工程, 1999,10 (11) : 1299-1301．
[305] Edwards K D, Finney C E A, Nguyen K, Daw C S. Use of symbol Statistics to Characterize Combustion in a Pulse combustor Operating near the Fuel-lean Limit, Proceedings of the 1998 Spring Technical Meeting of the Central States Section of the Combustion Institute (Lexington KY, 1998 May 31-June 2) , 385-390．
[306] Tang X Z, Tracy E R. Data Compression and Information Retrieval via
Symbolization, Chaos ,1998,8(3) :688-696．
[307] Gamraaitoni L. Stochastic Resonance, Reviews of Modern Physics, 1998,70(1) : 223-287．
[308] Wlesefeld K, Moss F. Stochastic Resonance and the Benefits of Noise:from Ice Ages to Crayfish and SQUIDs. Nature, 1995, 373(5) :33-36．
[309] Hanggi P, Talkner P, Borkovec M. Reaction-rate Theory: Fifty Years After Kramers, Rev. Mod.Phys., 1990, 62(2) : 251-341．
[310] Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S. Stochastic Resonance in Bistable Systems, Physical Review Letters, 1989,62(4) :349-352．
[311] Benzi R, Parisi G, Sutera A, Vulpiani A. A Theory of Stochastic Resonance in Climatic Change, SIAM Journal on Applied Mathematics, 1983, 43(3) :565-578．
[312] Nicolis C. Long-Term Climatic Transitions and Stochastic Resonance, Journal of Statistical Physics, 1993,70(1/2) :4-14．
[313] Imbrie J, Mix A C, Martinson D G. Milankovitch Theory Viewed from Devils Holes, Nature, 1993, (London)363(6429) : 531-533．
[314] Fauve S, Heslot F. Stochastic Resonance in a Bistable System, Physics Letters A, 1983, 97 (1,2) : 5-7．
[315] Mitaim S, Kosko B. Adaptive Stochastic Resonance, Proceedings of the IEEE, 1998, 86(11) :2152-2183．
[316] Jung P. Threshold Devices: Fractal Noise and Neural Talk, Physical Review E, 1994, 50 (4) : 2513-2522．
[317] Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F, Stochastic Resonance on a Circle, Physical Review Letters, 1994, 72:2125-2129．
[318] Gammaitoni L. Stochastic Resonance and the Dithering Effect in Threshold Physical Systems, Phys. Rev. E, 1995, 52(5) : 4691-4698．
[319] Jung P. Stochastic Resonance and Optimal Design of Threshold Detectors, Physics Letters A, 1995,207:93-104．
[320] Petrachi D, et. al. Specific Issue on Stochastic Resonance in Biological Systems, Chaos, Solitions and Fractals, 2000, 11 (12) :1819-1944．
[321] 胡岗。随机力与非线性系统。上海:上海科技教育出版社,1994。
[322] Moss F. Stochastic Resonance: a Signal+noise in aTwo State System. Proceedings of the 45th Annual Symposium on Frequency Control, 1991: 649-658．
[323] Albert T R, Bulsara A R, Schmera G, Inchiosa M. An Evaluation of the Stochastic Resonance Phenomenon as A Potential Tool for Signal Processing. Signals, Systems and Computers, Conference Record of The Twenty-Seventh Asilomar Conference, 1993, (1) : 583-587．
[324] Asdi A S.Tewfik A H. Detection of Weak Signals Using Adaptive Stochastic Resonance, Acoustics, Speech, and Signal Processing, 1995, (2) :1332-1335．
[325] Anishchenko V S, Neiman A B, Moss F, Schimansky-Geier L. Stochastic Resonance:
Noise-enhanced Order, Physics-Uspekhi, 1999, 42(1): 7-36.
[326]Zozor S, Amblard P-O. Stochastic Resonance in a Discrete Time Nonlinear SETAR (1,2,0,0) model, Higher-Order Statistics, Proceedings of the IEEE Signal Processing Workshop, 1997,166-170.
[327]Zozor S, Amblard P-O. Stochastic Resonance in Discrete Time Nonlinear AR(1) models, Signal Processing, IEEE Transactions, 1999,47(1):108-122.
[328]王利亚等．强噪声背景中微弱信号检测的初步研究．分析化学，1999，27(12)：1391-1396．
[329]王利亚等．一种有效提取弱信号的新方法．高等学校化学学报，2000，21(1)：53-55．
[330]王利亚等．随机共振应用初步研究．计算机与应用化学，2000，17(1)：79-80．
[331]McNamara B, Wiesenfeld K. Theory of Stochastic Resonance, Physical Review A, 1989,39(9):4854—4869.
[332]Presilla C, Marchesoni F, Gammaitoni L. Periodically Time-modulated Bistable Systems:Nonstationary Statistical Properties, Phys. Rev. A, 1989, 40(4): 2105-2113.
[333]Hu G, Nicolis G, Nicolis N. Periodically Forced Fokker-Planck Equation and Stochastic Resonance, Physical Review A, 1990,42(4):2030-2041.
[334]Fox R F, Lu Y N. Analytic and Numerical Study of Stochastic Resonance, Physical Review E, 1993,48(5):3390-3398.
[335]Jung P, Hanggi P. Amplification of Small Signals via Stochastic Resonance, Physical Review A, 1991,44(12):8032-8042.
[336]Debnath G, Zhou T, Moss F. Remarks on Stochastic Resonance, Physical Review A, 1989,39(8):4323-4326.
[337]Zhou T, Moss F. Analog Simulations of Stochastic Resonance, Physical Review A, 1990,41(8):4255-4264.
[338]Vemuri G, Roy R. Stochastic Resonance in a Bistable Ring Laser, Physical Review A, 1989,39(9):4668-4674.
[339]Gong D C, Hu G, Wen X D, Yang C Y, Qin G R, Li R, Ding D F. Experimental Study of the Signal-to-Noise Ratio of Stochastic Resonance Systems, Physical Review A, 1992,46(6):3243--3249.
[340]Gong D, Qin G R, Hu G, Weng X D. Experimental Study of Stochastic Resonance, Phys. Lett. A ,1991,159: 147-152.
[341]方崇智，萧德云．系统辨识．北京：清华大学出版社，1988．
[342]刘耀宗，温熙森，胡茑庆．非最小相位线性非高斯序列的替代数据检验．物理学报，2001，50(4)：633-637．
[343]刘耀宗，温熙森，胡茑庆．线性非高斯序列的替代数据检验新方法．物理学报，2001，50(7)：1241-1247．