基于时—频分析的虚拟式旋转机械特征分析仪系统的研究
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摘要
旋转机械在机械装备中占有举足轻重的地位，它们大多为生产企业中的关键设备，因此，保证旋转机械的安全可靠运行对企业和国民经济有重要的意义。旋转机械特征分析是旋转机械故障诊断和状态监测的重要组成部分，其中的振动测试方法又是特征分析的主要手段，而特征信息提取技术的高低主要取决于相应测试仪器的分析功能。目前的测试仪器对平稳振动信号有比较成熟和完善的测试和分析手段，但在对以升、降速过程为代表的旋转机械非平稳振动信号的特征提取方面还缺乏完善而有效的分析功能，这也意味着现有测试仪器在旋转机械非平稳振动信号的分析上还不能很好地适应旋转机械的高速化、精密化和自动化的发展需要。因此迫切需要对现有技术的进行补充和完善，并增加新的分析功能。
本文在对旋转机械典型故障特征、传统特征分析方法和非平稳信号的时频分析技术进行了详细介绍的基础上，将时频分析技术引入旋转机械特征分析领域；同时，对旋转机械特征分析的主要手段——阶比分析技术进行了深入研究，利用信号的瞬时频率与旋转机械转速的对应关系提出了实现阶比分析的崭新途径，并在工程实践中证明了这一途径的正确性。
在课题研究中提出了基于瞬时频率估计的旋转机械阶比跟踪方法，该方法用时频分析技术中的峰值搜索方法直接从原始振动信号中获得旋转机械多分量振动信号中与转速相对应的瞬时频率估计，并通过曲线拟合的方法获得瞬时转速曲线，最后实现了阶比分析中的阶比跟踪采样，成功解决了原来阶比跟踪方法中存在的需要转速计、鉴相装置等专门辅助硬件设备和由此产生的复杂安装要求等问题，使阶比分析实现途径得以简化，并降低了阶比分析的使用成本。
通过对阶比跟踪滤波方法进行了深入研究，针对原有硬件方法中存在的需要转速计、跟踪滤波器等专门硬件辅助设备和计算阶比跟踪滤波中使用分块数字滤波会产生的边沿效应问题，提出了基瞬时频率估计和零相位数字滤波的阶比跟踪滤波方法。该方法是对现有方法的发展和补充。
研究并实现了基于时频滤波的阶比分量提取。该技术采用了时频分析中的Gabor变换，可有效地对旋转机械振动信号中的阶比分量信号进行重构提取，使对选定的阶比分量进行单独分析提供了可能。
基于以上研究成果，在实现了无需转速计的旋转机械阶比分析，包括：阶比谱分析、阶比谱阵、跟踪阶比谱和阶比分量提取等。这些分析功能的简化实现为旋转机械特征分析仪器的成功开发奠定了基础。
开发出虚拟式旋转机械特征分析仪。该特征分析仪具有时频分析功能和基于
研究成果的阶比分析功能，可实现对旋转机械非平稳信号特征信息的有效提取和分析，弥补了传统仪器在非平稳信号分析方面的不足，显示了虚拟仪器这一全新仪器设计理念的强大优势。
研究中用开发的虚拟式旋转机械特征分析仪对不同的测试对象进行了实测分析，试验结果表明所研究和提出的方法的有效性，同时也展示了所开发的虚拟仪器具有强大的非平稳信号分析功能。
本项目系国家自然科学基金重点资助项目“面向机械测试的控件化虚拟仪器系统的研究”（批准号: 50135050）之子项目。
Rotating machinery takes up the major part in all machinery equipments and plays an important role in industry enterprises. It is very important to ensure the running safety of rotating machinery for both enterprises and our society. Characteristics analysis plays an important role in faults find and diagnosis of rotating machinery. Vibration measurement and test is a popular method in all characteristics analysis methods. The level for getting information depends on the analysis functions associated with the measurement instruments. Up to now, most measurement instruments often used are very good to analysis stationary vibration of rotating machinery, but is lacking in non-stationary vibration characteristics analysis to some extend, for example, the vibration caused by rotating machinery during run-up or coast down. This means the non-stationary vibration analysis functions current used in measurement instruments are not satisfied the requirement by the advanced development of rotating machinery which with high speed and high precision. So, it is urgent to continue perfect the techniques current used and add new analysis functions.
In this dissertation, time-frequency analysis methods were introduced in the characteristics analysis of rotating machinery. While a good study to classic faults characteristics of rotating machinery, traditional methods for characteristics analysis and the time-frequency analysis for non-stationary signals, an important research were carried on order analysis, a very powerful tool for characteristics analysis of rotating machinery. Some new methods to perform order analysis were proposed and successful done based on the relationship between the instantaneous frequency of vibration signal and the rotating speed of machinery.
Order tracking of rotating machinery based on instantaneous frequency estimation was proposed in our research. In this method, the speed corresponding instantaneous frequency estimation was attained from multi-components vibration signals by peak searching on time-frequency plane, curve fitting was employed to obtain the instantaneous frequency law, and order tracking sampling was done for order analysis. By this method, some special hardware, such as speed counter, keyphasor device, etc. are avoid, and the corresponding installation limited required by traditional order tracking methods is not exist too. It makes the order analysis simplified and can be performed at a low cost.
By deep study and advanced research on traditional order tracking filtering method, a new order tracking filtering method based on instantaneous frequency estimation and zero-phase distortion digital filtering was proposed. It overcomes the problems of hardware requirement for speed counting and analog tracking filter to do tracking filtering in past time. It is an effective adding to traditional order tracking filtering methods.
Order component extraction based on time-frequency filtering was also researched. Gabor transform, a popular time-frequency analysis method, is employed to do the order component extraction by signal synthesis. So, the order component selected can by treat alone by further analysis.
The tacholess order analysis, such as order spectrum, order matrix and tracking order spectrum, order component extraction etc., was programmed based on these mentioned above. All of these functions provided a good foundation for the developing of virtual characteristics analyzer of rotating machinery.
A virtual instrument, rotating machinery characteristics analyzer, was programmed with some powerful time-frequency analysis functions and all order analysis functions introduced above. So, it is enabled the abilities to analysis non-stationary vibration of rotating machinery and eliminate the weak points of current used measurement and test instruments. The advantage of instruments developing by the new virtual instruments developing concept is also well showed by it.
Many actual tests for different test objects were done with the virtual characteristics analyzer
本文在对旋转机械典型故障特征、传统特征分析方法和非平稳信号的时频分析技术进行了详细介绍的基础上，将时频分析技术引入旋转机械特征分析领域；同时，对旋转机械特征分析的主要手段——阶比分析技术进行了深入研究，利用信号的瞬时频率与旋转机械转速的对应关系提出了实现阶比分析的崭新途径，并在工程实践中证明了这一途径的正确性。
在课题研究中提出了基于瞬时频率估计的旋转机械阶比跟踪方法，该方法用时频分析技术中的峰值搜索方法直接从原始振动信号中获得旋转机械多分量振动信号中与转速相对应的瞬时频率估计，并通过曲线拟合的方法获得瞬时转速曲线，最后实现了阶比分析中的阶比跟踪采样，成功解决了原来阶比跟踪方法中存在的需要转速计、鉴相装置等专门辅助硬件设备和由此产生的复杂安装要求等问题，使阶比分析实现途径得以简化，并降低了阶比分析的使用成本。
通过对阶比跟踪滤波方法进行了深入研究，针对原有硬件方法中存在的需要转速计、跟踪滤波器等专门硬件辅助设备和计算阶比跟踪滤波中使用分块数字滤波会产生的边沿效应问题，提出了基瞬时频率估计和零相位数字滤波的阶比跟踪滤波方法。该方法是对现有方法的发展和补充。
研究并实现了基于时频滤波的阶比分量提取。该技术采用了时频分析中的Gabor变换，可有效地对旋转机械振动信号中的阶比分量信号进行重构提取，使对选定的阶比分量进行单独分析提供了可能。
基于以上研究成果，在实现了无需转速计的旋转机械阶比分析，包括：阶比谱分析、阶比谱阵、跟踪阶比谱和阶比分量提取等。这些分析功能的简化实现为旋转机械特征分析仪器的成功开发奠定了基础。
开发出虚拟式旋转机械特征分析仪。该特征分析仪具有时频分析功能和基于
研究成果的阶比分析功能，可实现对旋转机械非平稳信号特征信息的有效提取和分析，弥补了传统仪器在非平稳信号分析方面的不足，显示了虚拟仪器这一全新仪器设计理念的强大优势。
研究中用开发的虚拟式旋转机械特征分析仪对不同的测试对象进行了实测分析，试验结果表明所研究和提出的方法的有效性，同时也展示了所开发的虚拟仪器具有强大的非平稳信号分析功能。
本项目系国家自然科学基金重点资助项目“面向机械测试的控件化虚拟仪器系统的研究”（批准号: 50135050）之子项目。
Rotating machinery takes up the major part in all machinery equipments and plays an important role in industry enterprises. It is very important to ensure the running safety of rotating machinery for both enterprises and our society. Characteristics analysis plays an important role in faults find and diagnosis of rotating machinery. Vibration measurement and test is a popular method in all characteristics analysis methods. The level for getting information depends on the analysis functions associated with the measurement instruments. Up to now, most measurement instruments often used are very good to analysis stationary vibration of rotating machinery, but is lacking in non-stationary vibration characteristics analysis to some extend, for example, the vibration caused by rotating machinery during run-up or coast down. This means the non-stationary vibration analysis functions current used in measurement instruments are not satisfied the requirement by the advanced development of rotating machinery which with high speed and high precision. So, it is urgent to continue perfect the techniques current used and add new analysis functions.
In this dissertation, time-frequency analysis methods were introduced in the characteristics analysis of rotating machinery. While a good study to classic faults characteristics of rotating machinery, traditional methods for characteristics analysis and the time-frequency analysis for non-stationary signals, an important research were carried on order analysis, a very powerful tool for characteristics analysis of rotating machinery. Some new methods to perform order analysis were proposed and successful done based on the relationship between the instantaneous frequency of vibration signal and the rotating speed of machinery.
Order tracking of rotating machinery based on instantaneous frequency estimation was proposed in our research. In this method, the speed corresponding instantaneous frequency estimation was attained from multi-components vibration signals by peak searching on time-frequency plane, curve fitting was employed to obtain the instantaneous frequency law, and order tracking sampling was done for order analysis. By this method, some special hardware, such as speed counter, keyphasor device, etc. are avoid, and the corresponding installation limited required by traditional order tracking methods is not exist too. It makes the order analysis simplified and can be performed at a low cost.
By deep study and advanced research on traditional order tracking filtering method, a new order tracking filtering method based on instantaneous frequency estimation and zero-phase distortion digital filtering was proposed. It overcomes the problems of hardware requirement for speed counting and analog tracking filter to do tracking filtering in past time. It is an effective adding to traditional order tracking filtering methods.
Order component extraction based on time-frequency filtering was also researched. Gabor transform, a popular time-frequency analysis method, is employed to do the order component extraction by signal synthesis. So, the order component selected can by treat alone by further analysis.
The tacholess order analysis, such as order spectrum, order matrix and tracking order spectrum, order component extraction etc., was programmed based on these mentioned above. All of these functions provided a good foundation for the developing of virtual characteristics analyzer of rotating machinery.
A virtual instrument, rotating machinery characteristics analyzer, was programmed with some powerful time-frequency analysis functions and all order analysis functions introduced above. So, it is enabled the abilities to analysis non-stationary vibration of rotating machinery and eliminate the weak points of current used measurement and test instruments. The advantage of instruments developing by the new virtual instruments developing concept is also well showed by it.
Many actual tests for different test objects were done with the virtual characteristics analyzer
引文
[1] 屈梁生, 何正嘉.《机械故障诊断学》, 上海: 上海科学技术出版社, 1986.
[2] Effective Machinery Measurements using Dynamic Signal Analyzers. Application Note 243-1, Hewlett Packard, 2002.
[3] Qin Shuren. Intelligent virtual controls new concept of virtual instrument. In: Tan Jiubin ed. Proceedings of ISIST'2002, 2nd International symposium on instrumentation science and technology, Jinan, 2002, Harbin: Harbin institute of technology press, 2002: 75~79.
[4] Cyril M.Harris, Shock and vibration handbook (Third Edition), New York: McGRAW-HILL BOOK COMPANY, 1988.
[5] 徐敏. 机械设备状态监测与故障诊断技术的现状与发展动向, 第二届全国机械设备故障诊断学术会议论文集, 1988.
[6] Cooley, J. W. and J. W. Tukey, "An Algorithm for the Machine Computation of the Complex Fourier Series," Mathematics of Computation, 1965, 19:297-301.
[7] Oppenheim, A. V. and R. W. Schafer, Discrete-Time Signal Processing, NJ:Prentice-Hall, 1989.
[8] 张贤达, 保铮. 非平稳信号分析与处理. 北京: 国防工业出版社, 1998.
[9] 杨福生. 小波变换的工程应用. 北京：科学出版社, 1999.
[10] Oppenheim A. V. and Willsky A. S., Signals and Systems Prentice Hall, 1997
[11] 邹红星, 周小波, 李延达. 时频分析: 回溯与前瞻, 电子学报, 2000, 28(9):78-84
[12] 秦前清, 杨宗凯. 实用小波分析，西安: 西安电子科学出版社, 1994.
[13] Conforto S. and D'Alessio T., Spectral analysis for non-stationary signals from mechanical measurements: A parametric approach. Mechanical Systems and Signal Processing, 1999, 13(3):395-411.
[14] 郭瑜, 秦树人, 梁玉前. 时频分析阶比跟踪技术, 重庆大学, 2002, 25(5):17-24.
[15] Carson J. and Fry T., Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency Modulation, J.Bell System Tech., 1937, 16:514-540.
[16] L.科恩 著, 白宪居 译. 时-频分析: 理论与应用. 西安:西安交通大学出版社，Prentice Hall, 1998.
[17] Aikawa K.; Singer H.; Kawahara H.; Tohkura, Y., A dynamic cepstrum incorporating time-frequency masking and its application to continuous speech recognition, Acoustics, Speech, and Signal Processing, Minneapolis, MN, USA, 1993. ICASSP-93, IEEE International Conference, 2, 1993:27-30.
[18] Zhang B. and Sato S., A new time-frequency distribution and its application to speech signal
processing, Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, IEEE-SP, 1992:417-420.
[19] Celebi S.; Principe J.C.; Magnitude spectral estimation via Poisson moments with application to speech recognition, ICASSP-95, Vol. 1, 1995:393-396.
[20] Celebi S.; Principe J.C.; Magnitude spectral estimation via Poisson moments with application to speech recognition, Acoustics, Speech, and Signal Processing, Detroit, MI, USA, 1995, ICASSP-95, IEEE International Conference, 1, 1995:393-396.
[21] Pitton J.W.; Atlas L.E.; Loughlin P.J.; Applications of positive time-frequency distributions to speech processing, Speech and Audio Processing, IEEE Transactions, 1994, 2:554-566.
[22] Zhang B.; Sato S.; A time-frequency distribution of Cohen's class with a compound kernel and its application to speech signal processing, Signal Processing, IEEE Transactions, 1994, 42:54 -64.
[23] Gaunaurd G.C., Strifors H.C.; Signal analysis by means of time-frequency (Wigner-type) distributions-applications to sonar and radar echoes; Proceedings of the IEEE, 1996, 84: 1231-1248.
[24] Marple S.L., Jr.; Large dynamic range time-frequency signal analysis with application to helicopter Doppler radar data, Signal Processing and its Appications, Sixth International, Symposium, Kuala Lumpur, Malaysia, 2001, 1, 2001:260-263.
[25] Shu X.and Shen F., The application of time-frequency analysis for extracting radar target in chaff-interference, CIE International Conference of Radar Proceedings, Beijing, China, 2001, Chinese Institute of Electronics (CIE), 2001:571-575.
[26] Matz G.; Hlawatsch F., Time-frequency methods for signal detection with application to the detection of knock in car engines, Statistical Signal and Array Processing, Portland, OR, USA, 1998, Ninth IEEE SP Workshop, 1998:196-199.
[27] Konig, D. and Bohme J.F., Application of cyclostationary and time-frequency signal analysis to car engine diagnosis, Acoustics, Speech, and Signal Processing, Adelaide, SA, Australia 1994. ICASSP-94, IEEE International Conference, 4, 1994:149-152.
[28] Rohrbaugh R.A.; Application of time-frequency analysis to machinery condition assessment, Signals, Systems and Computers, Pacific Grove, CA , USA, 1993, Conference Record of The Twenty-Seventh Asilomar Conference, 2, 1993:1455-1458.
[29] Kim Y.W.; Rizzoni G.; Samimy B.; Wang, Y.Y.; Analysis and processing of shaft angular velocity signals in rotating machinery for diagnostic applications, Detroit, MI, USA, 1995, ICASSP-95, IEEE International Conference, 5, 1995:2971-2974.
[30] Atlas L.E.; Bernard G.D.; Narayanan S.B.; Applications of time-frequency analysis to signals
from manufacturing and machine monitoring sensors, Proceedings of the IEEE, 1996, 84:1319-1329
[31] 王吉军, 张冰焰, 朱泓等. 时频分析方法在机器故障诊断中的应用, 大连理工大学学报, 1996, 36(3):301-305.
[32] Wang Z.S.,Chen J.D.Z., Robust ECG R-R wave detection using evolutionary programming based fuzzy inference system (EPFIS), and application to assessing brain-gut interaction, Measurement and Technology , IEE Proceedings: Science, 2000:351-356.
[33] Chen D., Durand L.-G., Lee H.C. etc. Time-frequency analysis of the first heart sound: Part 3: Application to dogs with varying cardiac contractility and to patients with mitral mechanical prosthetic heart valves, Medical & Biological Engineering & Computing, 1997, 35(5):455-461.
[34] Cohen L. Time- frequence distributions a rewiew. Proceedings of the IEEE, 1987, 77(7):941-978.
[35] 钟佑明, 博士学位论文, 重庆大学, 2001.
[36] Wigner E.P., On the Quantum Correction for Thermodynamic Equilibrium, Physical Review, 1932, 40:749-759.
[37] Gabor D., Theory of Communication, J. Inst. Elec. Eng., 1946, 93:429-457.
[38] Potter R.K., etal, Visible Speech, New York: Van Nostrand, 1947.
[39] Ville J., Theorie et Applications de La notion de Signal Analytique, Cables et Transmission, 1948, 2A: 61-74.
[40] Page C.H., Instantaneous Power Spectra, J., Appl.Phys., 1952, 23:103-106.
[41] Cohen L., Generalized Phase-space Distribution Functions, J. Math. Phys., 1966, 7:781-786.
[42] Jones D.L. and Baraniuk R.G., A simple scheme for adapting time-frequency representations, Signal Processing, IEEE Transactions, 1994, 42(12):3530-3535.
[43] Jones D.L. and Bariniuk R.G.; An adaptive optimal-kernel time-frequency representation, Signal Processing, IEEE Transactions, 1995, 43(10):2361-2371.
[44] Jones D.L. and Baraniuk R.G.A simple scheme for adapting time-frequency representations, Signal Processing, IEEE Transactions, 1994, 42(12):3530-3535.
[45] Jones D.L. and Baraniuk, R.G.;An adaptive optimal-kernel time-frequency representation, Signal Processing, IEEE Transactions, 1995, 43(10):2361-2371
[46] Mallat S. and Zhang Z., Adaptive time-frequency decomposition with matching pursuits, Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, 1992, IEEE-SP, 1992:7-10.
[47] Mallat S. and Zhang Z., Adaptive time-frequency transform, Acoustics, Speech, and Signal Processing, Minneapolis, MN ,USA, 1993, ICASSP-93, 3, 1993:241-244.
[48] Davis G. and Mallat S., Wavelet vector quantization with matching pursuit, Information Theory and Statistics, 1994, Proceedings, Alexandria, VA, USA, 1994, IEEE-IMS Workshop, 1994:55.
[49] Mallat S. and Zhang Z. Matching pursuits with time-frequency dictionaries, Signal Processing, IEEE Transactions, 1993, 41(12):3397 -3415.
[50] Qian S. and Chen D., Decomposition of the Wigner-Ville distribution and time-frequency distribution series,Signal Processing, IEEE Transactions, 1994, 42(10):2836-2842.
[51] Qian S. and Chen D., Optimal biorthogonal analysis window function for discrete Gabor transform, Signal Processing, IEEE Transactions , 1994, 42(3): 694 -697.
[52] Li S. and Qian S., A complement to a derivation of discrete Gabor expansions, IEEE Signal Processing Letters, 1995, 2(2):31-33.
[53] Victor G., Adrian C., Paulette G., REVIEW OF VIBRATION-BASED HELICOPTERS HEALTH AND USAGE MONITORING METHODS, 55th Meeting of the Society for Machinery Failure Prevention Technology, 2001. (from Internet)
[54] Samimy B, Rizzoni G. Mechanical Signature Analysis,Using Time- Frequency Signal Processing:Application to Internal Combustion Engine Knock Detection.Proceeding of the IEEE, 1996, 84(9):1330-1343.
[55] Williams W.J. and Zalubas, E.J., "Helicopter transmission fault detection via time-frequency, scale and spectral methods", Mechanical Systems and Signal Processing, 2000, 14(4):545-559
[56] 郑海波, 李志远, 陈心昭, 贾继德. 基于时频分布的发动机异响特征分析及故障诊断研究,内燃机学报, 2002, 20（3）：267-272
[57] Haar A., Zur yheorie der orthogonalen funktionensysteme, Math., Ann.,69, 1910:331-371.
[58] Stromberg J.O., A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces, Conference in Harmonic Analysis in honor of A. Zygmund, Vol. II (W.Beckner etal., eds.),Wadsworth Math. Series, 1981:475-493.
[59] Morlet J., Arens G., Fourgeau E., and Giard D., Wave Propagation and Sampling Theory——Part Ⅱ: Sampling Theory and Complex Waves, Geophysics, 1982, 2:222-236.
[60] Meyer Y., Principle d incertitude bases hilbertiennes et algebras d operateurs., Bourbaki Seminar, 662(27), 1985~1986:1271-1283.
[61] Lemarie P.G. and Ondelettes a localization exponentiells. J., Math. Pure. Appl. 1988:227-236.
[62] Battle G. A block spin construction of undulates, Part I: Lemarie Function. Comm. Math. Phys., 1987(110):601-615.
[63] Mallat S.G., A theory for multiresolution signal decomposition: the wavelet representation, Pattern Analysis and Machine Intelligence, IEEE Transaction, 1989, 11:674-693.
[64] Mallat S.G., Multiresolution approximation and wavelet orthonormal bases of L2, Transaction
of the American Mathematical Society, 1989, 315:69-87
[65] Mallat S.G., Multifrequency channel decompositions of images and wavelet models, Acoustic Speech and Signal Processing, IEEE Transaction, 1989, 37:2091-2110.
[66] 刘贵忠. 小波分析及应用, 西安: 西安电子科技大学出版社, 1992.
[67] Daubechies I., Orthonormal bases of compactly supported wavelets, Communication on Pure and Applied Mathematics, 1988, XII:9009-996.
[68] Daubechies I., The wavelet transform, time-frequency localization and signal analysis, Information Theory, IEEE Transactions, 1990, 36(5):961-1006.
[69] Adewusi S.A. and Al-Bedoor B.O., Wavelet analysis of vibration signals of an overhang rotor with a propagating transverse crack, Journal of Sound and Vibration, 2001, 246(5):777-793.
[70] 何岭松, 吴波, 康宜华等. 小波分析及其在设备诊断中的应用. 华中理工大学学报, 1993, 21(1):17-21.
[71] 林京, 刘红星, 屈梁生. 信号包络特征识别在故障诊断中的应用. 振动、测试与诊断, 1998, 18(1):34-39.
[72] Newland D E., Wavelet analysis of vibration, Journal of Vibration and Acoustics, Transaction of the ASME, 1994, 116(10): 409-416 and 417-425.
[73] Newland D E., An introduction to random vibration, spectral and wavelet analysis. Longman Scientific and Technical,1993.
[74] Pryor A. H., Mosher M., Lewicki D.G. The Application of Time-Frequency Methods to HUMS. NASA Ames Research Center, 2001.
[75] 林京, 屈梁生, 基于连续小波变换的奇异性检测与故障诊断, 振动工程学报, 2000, 13(4):523-530.
[76] 何晓霞, 沈玉娣, 张西宁. 连续小波变换在滚动轴承故障诊断中的应用.机械科学与技术, 2001, 20(4):571-574.
[78] 陈进. 机械设备振动监测与故障诊断. 上海: 上海交通大学出版社, 1999.
[79] 韩捷, 张瑞林. 旋转机械故障机理及诊断技术. 北京: 机械工业出版社, 1997.
[80] 晏砺堂, 朱梓根, 李其汉等. 高速旋转机械振动. 北京: 国防工业出版社, 1994.
[81] 周祖德, 陈幼平. 现代机械制造系统的监控与故障诊断. 武汉: 华中理工大学出版社, 1999.
[82] 张正松, 傅尚新, 冯冠平等. 旋转机械振动监测及故障诊断. 北京: 机械工业出版社, 1991.
[83] 中国电子仪器仪表学会信号处理学会《振动数字信号处理程序库》编委会. 振动数字信号处理程序库. 北京: 科学出版社, 1988.
[84] 何正嘉, 孟庆丰等. 机械设备非平稳信号的故障诊断呀及应用. 北京: 高等教育出版社,
2001.
[85] 陈进, 机械设备故障诊断与现代信号处理技术. 振动工程学报, 1998, 11(Sup):6-10.
[86] Agilent 35670A Operator's Guide. Agilent Part Number 35670-90053, Agilent Technologies Inc, 2000.
[87] Brüel&Kj?r, Order Analysis-Type 7702, Product Data, BP 1634.
[88] 郭瑜, 秦树人. 旋转机械非稳定信号的伪转速跟踪阶比分析. 振动与冲击, 已录用, 待发表.
[89] Boggess A. and Narcowich F.J., 小波与傅里叶分析基础（A First Course in Wavelet with Fourier Analysis）（英文引进版）. 北京: 电子工业出版社, 2002.
[90] Qian S. and Chen D., Joint time-frequency analysis, IEEE Signal Processing Magazine, 1999, 16(2):52-67.
[91] Daubechies I., The wavelet transform, time-frequency localization and signal analysis. Information Theory, IEEE Transactions, 1990, 36(5):961-1005.
[92] Battle G., Heisenberg proof of the Ballian-low theorem, Lett. Math. Phys., 1988, 15(7):175-177.
[93] Jones, D.L.; Parks, T.W., A high resolution data-adaptive time-frequency representation. Acoustics, Speech, and Signal Processing, IEEE Transactions, 1990, 38(12):2127 -2135.
[94] Kwok, H.K.C. and Jones, D.L., Instantaneous frequency estimation using an adaptive short-time Fourier transform. Signals, Systems and Computers, Pacific Grove, CA, USA, 1995, Conference Record of the Twenty-Ninth silomar Conference, 1, 1995:543 -547.
[95] 郭瑜, 汤宝平, 纪跃波, 秦树人. 基于解析信号和带通滤波的频率细化分析. 重庆大学学报, 2001, 24(4):17-21.
[96] 朱华, 黄辉宁, 李永庆等. 随机信号分析. 北京：北京理工大学出版社,1990.
[97] 胡广书, 数字信号处理:理论、算法与实现. 北京：清华大学出版社,1997.
[98] 卢文祥, 杜润生, 机械工程测试.信息.信号分析. 武汉：华中理工大学出版社,1991.
[99] Boashash B. Interpreting and estimating the instantaneous frequency of a signal-Part 1: Fundamentals. Proc. IEEE, 1992, 80(4):520~538.
[100] Boashash B. Interpreting and estimating the instantaneous frequency of a signal-Part 2: Algorithms and Applications, Proc. IEEE, 1992, 80(4):540~568.
[101] Emresoy M K, El-Jaroudi A. Iterative instantaneous frequency estimation and adaptive matched spectrogram, Signal Processing, 1998, 64:157~165.
[102] Fyfe K.R., Munck E.D.S., ANALYSIS OF COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing. 1997, 11(2):187-205.
[103] Bossley K.M., Mckendrick R.J., Harris C.J., Mercer C., HYBRID COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing. 1999, 13(4):627-641.
[104] 郭瑜, 秦树人, 汤宝平, 纪跃波. 基于瞬时频率估计的旋转机械阶比跟踪. 机械工程学报, 第39卷第3期，2003：32-36.
[105] Guo Yu, Qin Shuren, Laing Yuqian. Order tracking of rotating machinery based on instantaneous frequency estimation, Proceeding of 2nd International Symposium on Instrumentation Science and Technology (ISIST 2002), JINAN, CHINA, AUG 18-22, Vol.3, 2002:547-552.
[106] 郭瑜, 秦树人. 旋转机械阶比分析中的零相位跟踪滤波法. 中国机械工程, 已录用, 待发表.
[107] E.Lopartinskaia, J..Zhu, J.Mathew, MONITORING VARYING SPEED MACHINERY VIBRATIONS-II, RECURSIVE FILTERS AND ANGLE DOMAIN, Mechanical Systems and Signal Processing , 1995, 9(6): 647-655.
[108] K.R. Fyfe, E.D.S. Munck, ANALYSIS OF COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing , 1997, 11(2):187-205.
[109] 陈循, 田江红, 温熙森, 唐丙阳. 阶比谱分析与汽车起动电机故障的实时诊断, 国防科技大学学报, 1996, 18(4):44-48.
[110] Gustafsson F., Determining the initial states in forward-backward filtering, IEEE Transactions on Signal Processing, 1996, 44(4):988-992.
[111] 纪跃波, 秦树人, 汤宝平. 零相位数字滤波器. 重庆大学学报, 2000, 23(6):4-7
[112] 郭瑜, 秦树人. 基于瞬时频率估计及时频滤波的阶比分量提取, 中国机械工程, 已录用, 待发表.
[113] Vold H., Leuridan J., Order Tracking at Extreme Slew Rates, Using Kalman Tracking Filters. SAE Paper, Number 931288, 1993
[114] Vold H., Deel J., Vold-Kalman Order Tracking: New Methods for Vehicle.Sound Quality and Drive Train NVH Applications. SAE Paper, Number 972033, 1997
[115] Vold, H., Mains, M., Blough, J., "Theoretical Foundations for High Performance Order Tracking with the Vold-Kalman Tracking Filter", SAE Paper, Number 972007, 1997
[116] Albright M.and Qian S., A Comparison of the Newly Proposed Gbaor Order Tracking Technique in vs. Other Order Tracking Methods. SAE Noise and Vibration Conference, 2001, from internet.
[117] Bastiaans M.J., Gabor 's expansion of a signal into Gaussian elementary signals. Proc. IEEE, 1981, 68:594-598.
[118] Wexler J. and Raz S., Discrete Gbaor Expansions. Signal Processing, 1990, 21:207-220.
[119] Bastiaans M.J., A sampling theorem for the complex spectrogram, and Gabor's expansion of a signal in Gaussian elementary signals, Optical Engineering, 1981, 20(4):594-598.
[120] Einziger P.D., Gabor expansion of an aperture field in exponential elementary beams. IEE Electron. Lett., 1988, 24:665-666.
[121] Shidong Li; Healy, D.M., Jr.; A parametric class of discrete Gabor expansions. Signal Processing, IEEE Transactions, 1996, 44(2):201 -211.
[122] Yao J., Complete Gabor transformation for signal representation, Image Processing, IEEE Trans., 1993, 2:152-159.
[123] Qian S. and Chen D., Discrete Gabor transform. Signal Processing, IEEE Trans., 1993, 41(7):2429-2439.
[124] Morris J.M. and Lu Y., Discrete Gabor expansion of discrete-time signals in L2(Z) via frame theory, IEEE Signal Processing Magazine, 1994, 40(2):155-181.
[125] Qian S. and Chen D., Joint Time-Frequency Analysis, Englewood Cliffs, NJ:Prentice-Hall, 1996.
[126] Qian S. and Chen D.; A general solution of biorthogonal analysis window functions for orthogonal-like discrete Gabor transform. Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, 1992, IEEE-SP, 1992:387 -389.
[127] Order Analysis Toolset for LabVIEW User Manual，National Insttruments, May 2001 Edition
[128] 秦树人, 张思复, 汤宝平. 何辉等, 集成测试技术与虚拟式仪器, 中国机械工程, 1999, 10(1):77-80.
[129] 秦树人, 汤宝平, 徐铭陶, 何辉等. 工程信号小波变换分析仪系统的研究, 中国机械工程, 1999, 10(4):443-446.
[130] 秦树人, 汤宝平, 面向21世纪的绿色仪器系统, 中国机械工程, 2000, 11(3):275-278.
[2] Effective Machinery Measurements using Dynamic Signal Analyzers. Application Note 243-1, Hewlett Packard, 2002.
[3] Qin Shuren. Intelligent virtual controls new concept of virtual instrument. In: Tan Jiubin ed. Proceedings of ISIST'2002, 2nd International symposium on instrumentation science and technology, Jinan, 2002, Harbin: Harbin institute of technology press, 2002: 75~79.
[4] Cyril M.Harris, Shock and vibration handbook (Third Edition), New York: McGRAW-HILL BOOK COMPANY, 1988.
[5] 徐敏. 机械设备状态监测与故障诊断技术的现状与发展动向, 第二届全国机械设备故障诊断学术会议论文集, 1988.
[6] Cooley, J. W. and J. W. Tukey, "An Algorithm for the Machine Computation of the Complex Fourier Series," Mathematics of Computation, 1965, 19:297-301.
[7] Oppenheim, A. V. and R. W. Schafer, Discrete-Time Signal Processing, NJ:Prentice-Hall, 1989.
[8] 张贤达, 保铮. 非平稳信号分析与处理. 北京: 国防工业出版社, 1998.
[9] 杨福生. 小波变换的工程应用. 北京：科学出版社, 1999.
[10] Oppenheim A. V. and Willsky A. S., Signals and Systems Prentice Hall, 1997
[11] 邹红星, 周小波, 李延达. 时频分析: 回溯与前瞻, 电子学报, 2000, 28(9):78-84
[12] 秦前清, 杨宗凯. 实用小波分析，西安: 西安电子科学出版社, 1994.
[13] Conforto S. and D'Alessio T., Spectral analysis for non-stationary signals from mechanical measurements: A parametric approach. Mechanical Systems and Signal Processing, 1999, 13(3):395-411.
[14] 郭瑜, 秦树人, 梁玉前. 时频分析阶比跟踪技术, 重庆大学, 2002, 25(5):17-24.
[15] Carson J. and Fry T., Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency Modulation, J.Bell System Tech., 1937, 16:514-540.
[16] L.科恩 著, 白宪居 译. 时-频分析: 理论与应用. 西安:西安交通大学出版社，Prentice Hall, 1998.
[17] Aikawa K.; Singer H.; Kawahara H.; Tohkura, Y., A dynamic cepstrum incorporating time-frequency masking and its application to continuous speech recognition, Acoustics, Speech, and Signal Processing, Minneapolis, MN, USA, 1993. ICASSP-93, IEEE International Conference, 2, 1993:27-30.
[18] Zhang B. and Sato S., A new time-frequency distribution and its application to speech signal
processing, Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, IEEE-SP, 1992:417-420.
[19] Celebi S.; Principe J.C.; Magnitude spectral estimation via Poisson moments with application to speech recognition, ICASSP-95, Vol. 1, 1995:393-396.
[20] Celebi S.; Principe J.C.; Magnitude spectral estimation via Poisson moments with application to speech recognition, Acoustics, Speech, and Signal Processing, Detroit, MI, USA, 1995, ICASSP-95, IEEE International Conference, 1, 1995:393-396.
[21] Pitton J.W.; Atlas L.E.; Loughlin P.J.; Applications of positive time-frequency distributions to speech processing, Speech and Audio Processing, IEEE Transactions, 1994, 2:554-566.
[22] Zhang B.; Sato S.; A time-frequency distribution of Cohen's class with a compound kernel and its application to speech signal processing, Signal Processing, IEEE Transactions, 1994, 42:54 -64.
[23] Gaunaurd G.C., Strifors H.C.; Signal analysis by means of time-frequency (Wigner-type) distributions-applications to sonar and radar echoes; Proceedings of the IEEE, 1996, 84: 1231-1248.
[24] Marple S.L., Jr.; Large dynamic range time-frequency signal analysis with application to helicopter Doppler radar data, Signal Processing and its Appications, Sixth International, Symposium, Kuala Lumpur, Malaysia, 2001, 1, 2001:260-263.
[25] Shu X.and Shen F., The application of time-frequency analysis for extracting radar target in chaff-interference, CIE International Conference of Radar Proceedings, Beijing, China, 2001, Chinese Institute of Electronics (CIE), 2001:571-575.
[26] Matz G.; Hlawatsch F., Time-frequency methods for signal detection with application to the detection of knock in car engines, Statistical Signal and Array Processing, Portland, OR, USA, 1998, Ninth IEEE SP Workshop, 1998:196-199.
[27] Konig, D. and Bohme J.F., Application of cyclostationary and time-frequency signal analysis to car engine diagnosis, Acoustics, Speech, and Signal Processing, Adelaide, SA, Australia 1994. ICASSP-94, IEEE International Conference, 4, 1994:149-152.
[28] Rohrbaugh R.A.; Application of time-frequency analysis to machinery condition assessment, Signals, Systems and Computers, Pacific Grove, CA , USA, 1993, Conference Record of The Twenty-Seventh Asilomar Conference, 2, 1993:1455-1458.
[29] Kim Y.W.; Rizzoni G.; Samimy B.; Wang, Y.Y.; Analysis and processing of shaft angular velocity signals in rotating machinery for diagnostic applications, Detroit, MI, USA, 1995, ICASSP-95, IEEE International Conference, 5, 1995:2971-2974.
[30] Atlas L.E.; Bernard G.D.; Narayanan S.B.; Applications of time-frequency analysis to signals
from manufacturing and machine monitoring sensors, Proceedings of the IEEE, 1996, 84:1319-1329
[31] 王吉军, 张冰焰, 朱泓等. 时频分析方法在机器故障诊断中的应用, 大连理工大学学报, 1996, 36(3):301-305.
[32] Wang Z.S.,Chen J.D.Z., Robust ECG R-R wave detection using evolutionary programming based fuzzy inference system (EPFIS), and application to assessing brain-gut interaction, Measurement and Technology , IEE Proceedings: Science, 2000:351-356.
[33] Chen D., Durand L.-G., Lee H.C. etc. Time-frequency analysis of the first heart sound: Part 3: Application to dogs with varying cardiac contractility and to patients with mitral mechanical prosthetic heart valves, Medical & Biological Engineering & Computing, 1997, 35(5):455-461.
[34] Cohen L. Time- frequence distributions a rewiew. Proceedings of the IEEE, 1987, 77(7):941-978.
[35] 钟佑明, 博士学位论文, 重庆大学, 2001.
[36] Wigner E.P., On the Quantum Correction for Thermodynamic Equilibrium, Physical Review, 1932, 40:749-759.
[37] Gabor D., Theory of Communication, J. Inst. Elec. Eng., 1946, 93:429-457.
[38] Potter R.K., etal, Visible Speech, New York: Van Nostrand, 1947.
[39] Ville J., Theorie et Applications de La notion de Signal Analytique, Cables et Transmission, 1948, 2A: 61-74.
[40] Page C.H., Instantaneous Power Spectra, J., Appl.Phys., 1952, 23:103-106.
[41] Cohen L., Generalized Phase-space Distribution Functions, J. Math. Phys., 1966, 7:781-786.
[42] Jones D.L. and Baraniuk R.G., A simple scheme for adapting time-frequency representations, Signal Processing, IEEE Transactions, 1994, 42(12):3530-3535.
[43] Jones D.L. and Bariniuk R.G.; An adaptive optimal-kernel time-frequency representation, Signal Processing, IEEE Transactions, 1995, 43(10):2361-2371.
[44] Jones D.L. and Baraniuk R.G.A simple scheme for adapting time-frequency representations, Signal Processing, IEEE Transactions, 1994, 42(12):3530-3535.
[45] Jones D.L. and Baraniuk, R.G.;An adaptive optimal-kernel time-frequency representation, Signal Processing, IEEE Transactions, 1995, 43(10):2361-2371
[46] Mallat S. and Zhang Z., Adaptive time-frequency decomposition with matching pursuits, Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, 1992, IEEE-SP, 1992:7-10.
[47] Mallat S. and Zhang Z., Adaptive time-frequency transform, Acoustics, Speech, and Signal Processing, Minneapolis, MN ,USA, 1993, ICASSP-93, 3, 1993:241-244.
[48] Davis G. and Mallat S., Wavelet vector quantization with matching pursuit, Information Theory and Statistics, 1994, Proceedings, Alexandria, VA, USA, 1994, IEEE-IMS Workshop, 1994:55.
[49] Mallat S. and Zhang Z. Matching pursuits with time-frequency dictionaries, Signal Processing, IEEE Transactions, 1993, 41(12):3397 -3415.
[50] Qian S. and Chen D., Decomposition of the Wigner-Ville distribution and time-frequency distribution series,Signal Processing, IEEE Transactions, 1994, 42(10):2836-2842.
[51] Qian S. and Chen D., Optimal biorthogonal analysis window function for discrete Gabor transform, Signal Processing, IEEE Transactions , 1994, 42(3): 694 -697.
[52] Li S. and Qian S., A complement to a derivation of discrete Gabor expansions, IEEE Signal Processing Letters, 1995, 2(2):31-33.
[53] Victor G., Adrian C., Paulette G., REVIEW OF VIBRATION-BASED HELICOPTERS HEALTH AND USAGE MONITORING METHODS, 55th Meeting of the Society for Machinery Failure Prevention Technology, 2001. (from Internet)
[54] Samimy B, Rizzoni G. Mechanical Signature Analysis,Using Time- Frequency Signal Processing:Application to Internal Combustion Engine Knock Detection.Proceeding of the IEEE, 1996, 84(9):1330-1343.
[55] Williams W.J. and Zalubas, E.J., "Helicopter transmission fault detection via time-frequency, scale and spectral methods", Mechanical Systems and Signal Processing, 2000, 14(4):545-559
[56] 郑海波, 李志远, 陈心昭, 贾继德. 基于时频分布的发动机异响特征分析及故障诊断研究,内燃机学报, 2002, 20（3）：267-272
[57] Haar A., Zur yheorie der orthogonalen funktionensysteme, Math., Ann.,69, 1910:331-371.
[58] Stromberg J.O., A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces, Conference in Harmonic Analysis in honor of A. Zygmund, Vol. II (W.Beckner etal., eds.),Wadsworth Math. Series, 1981:475-493.
[59] Morlet J., Arens G., Fourgeau E., and Giard D., Wave Propagation and Sampling Theory——Part Ⅱ: Sampling Theory and Complex Waves, Geophysics, 1982, 2:222-236.
[60] Meyer Y., Principle d incertitude bases hilbertiennes et algebras d operateurs., Bourbaki Seminar, 662(27), 1985~1986:1271-1283.
[61] Lemarie P.G. and Ondelettes a localization exponentiells. J., Math. Pure. Appl. 1988:227-236.
[62] Battle G. A block spin construction of undulates, Part I: Lemarie Function. Comm. Math. Phys., 1987(110):601-615.
[63] Mallat S.G., A theory for multiresolution signal decomposition: the wavelet representation, Pattern Analysis and Machine Intelligence, IEEE Transaction, 1989, 11:674-693.
[64] Mallat S.G., Multiresolution approximation and wavelet orthonormal bases of L2, Transaction
of the American Mathematical Society, 1989, 315:69-87
[65] Mallat S.G., Multifrequency channel decompositions of images and wavelet models, Acoustic Speech and Signal Processing, IEEE Transaction, 1989, 37:2091-2110.
[66] 刘贵忠. 小波分析及应用, 西安: 西安电子科技大学出版社, 1992.
[67] Daubechies I., Orthonormal bases of compactly supported wavelets, Communication on Pure and Applied Mathematics, 1988, XII:9009-996.
[68] Daubechies I., The wavelet transform, time-frequency localization and signal analysis, Information Theory, IEEE Transactions, 1990, 36(5):961-1006.
[69] Adewusi S.A. and Al-Bedoor B.O., Wavelet analysis of vibration signals of an overhang rotor with a propagating transverse crack, Journal of Sound and Vibration, 2001, 246(5):777-793.
[70] 何岭松, 吴波, 康宜华等. 小波分析及其在设备诊断中的应用. 华中理工大学学报, 1993, 21(1):17-21.
[71] 林京, 刘红星, 屈梁生. 信号包络特征识别在故障诊断中的应用. 振动、测试与诊断, 1998, 18(1):34-39.
[72] Newland D E., Wavelet analysis of vibration, Journal of Vibration and Acoustics, Transaction of the ASME, 1994, 116(10): 409-416 and 417-425.
[73] Newland D E., An introduction to random vibration, spectral and wavelet analysis. Longman Scientific and Technical,1993.
[74] Pryor A. H., Mosher M., Lewicki D.G. The Application of Time-Frequency Methods to HUMS.
[75] 林京, 屈梁生, 基于连续小波变换的奇异性检测与故障诊断, 振动工程学报, 2000, 13(4):523-530.
[76] 何晓霞, 沈玉娣, 张西宁. 连续小波变换在滚动轴承故障诊断中的应用.机械科学与技术, 2001, 20(4):571-574.
[78] 陈进. 机械设备振动监测与故障诊断. 上海: 上海交通大学出版社, 1999.
[79] 韩捷, 张瑞林. 旋转机械故障机理及诊断技术. 北京: 机械工业出版社, 1997.
[80] 晏砺堂, 朱梓根, 李其汉等. 高速旋转机械振动. 北京: 国防工业出版社, 1994.
[81] 周祖德, 陈幼平. 现代机械制造系统的监控与故障诊断. 武汉: 华中理工大学出版社, 1999.
[82] 张正松, 傅尚新, 冯冠平等. 旋转机械振动监测及故障诊断. 北京: 机械工业出版社, 1991.
[83] 中国电子仪器仪表学会信号处理学会《振动数字信号处理程序库》编委会. 振动数字信号处理程序库. 北京: 科学出版社, 1988.
[84] 何正嘉, 孟庆丰等. 机械设备非平稳信号的故障诊断呀及应用. 北京: 高等教育出版社,
2001.
[85] 陈进, 机械设备故障诊断与现代信号处理技术. 振动工程学报, 1998, 11(Sup):6-10.
[86] Agilent 35670A Operator's Guide. Agilent Part Number 35670-90053, Agilent Technologies Inc, 2000.
[87] Brüel&Kj?r, Order Analysis-Type 7702, Product Data, BP 1634.
[88] 郭瑜, 秦树人. 旋转机械非稳定信号的伪转速跟踪阶比分析. 振动与冲击, 已录用, 待发表.
[89] Boggess A. and Narcowich F.J., 小波与傅里叶分析基础（A First Course in Wavelet with Fourier Analysis）（英文引进版）. 北京: 电子工业出版社, 2002.
[90] Qian S. and Chen D., Joint time-frequency analysis, IEEE Signal Processing Magazine, 1999, 16(2):52-67.
[91] Daubechies I., The wavelet transform, time-frequency localization and signal analysis. Information Theory, IEEE Transactions, 1990, 36(5):961-1005.
[92] Battle G., Heisenberg proof of the Ballian-low theorem, Lett. Math. Phys., 1988, 15(7):175-177.
[93] Jones, D.L.; Parks, T.W., A high resolution data-adaptive time-frequency representation. Acoustics, Speech, and Signal Processing, IEEE Transactions, 1990, 38(12):2127 -2135.
[94] Kwok, H.K.C. and Jones, D.L., Instantaneous frequency estimation using an adaptive short-time Fourier transform. Signals, Systems and Computers, Pacific Grove, CA, USA, 1995, Conference Record of the Twenty-Ninth silomar Conference, 1, 1995:543 -547.
[95] 郭瑜, 汤宝平, 纪跃波, 秦树人. 基于解析信号和带通滤波的频率细化分析. 重庆大学学报, 2001, 24(4):17-21.
[96] 朱华, 黄辉宁, 李永庆等. 随机信号分析. 北京：北京理工大学出版社,1990.
[97] 胡广书, 数字信号处理:理论、算法与实现. 北京：清华大学出版社,1997.
[98] 卢文祥, 杜润生, 机械工程测试.信息.信号分析. 武汉：华中理工大学出版社,1991.
[99] Boashash B. Interpreting and estimating the instantaneous frequency of a signal-Part 1: Fundamentals. Proc. IEEE, 1992, 80(4):520~538.
[100] Boashash B. Interpreting and estimating the instantaneous frequency of a signal-Part 2: Algorithms and Applications, Proc. IEEE, 1992, 80(4):540~568.
[101] Emresoy M K, El-Jaroudi A. Iterative instantaneous frequency estimation and adaptive matched spectrogram, Signal Processing, 1998, 64:157~165.
[102] Fyfe K.R., Munck E.D.S., ANALYSIS OF COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing. 1997, 11(2):187-205.
[103] Bossley K.M., Mckendrick R.J., Harris C.J., Mercer C., HYBRID COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing. 1999, 13(4):627-641.
[104] 郭瑜, 秦树人, 汤宝平, 纪跃波. 基于瞬时频率估计的旋转机械阶比跟踪. 机械工程学报, 第39卷第3期，2003：32-36.
[105] Guo Yu, Qin Shuren, Laing Yuqian. Order tracking of rotating machinery based on instantaneous frequency estimation, Proceeding of 2nd International Symposium on Instrumentation Science and Technology (ISIST 2002), JINAN, CHINA, AUG 18-22, Vol.3, 2002:547-552.
[106] 郭瑜, 秦树人. 旋转机械阶比分析中的零相位跟踪滤波法. 中国机械工程, 已录用, 待发表.
[107] E.Lopartinskaia, J..Zhu, J.Mathew, MONITORING VARYING SPEED MACHINERY VIBRATIONS-II, RECURSIVE FILTERS AND ANGLE DOMAIN, Mechanical Systems and Signal Processing , 1995, 9(6): 647-655.
[108] K.R. Fyfe, E.D.S. Munck, ANALYSIS OF COMPUTED ORDER TRACKING, Mechanical Systems and Signal Processing , 1997, 11(2):187-205.
[109] 陈循, 田江红, 温熙森, 唐丙阳. 阶比谱分析与汽车起动电机故障的实时诊断, 国防科技大学学报, 1996, 18(4):44-48.
[110] Gustafsson F., Determining the initial states in forward-backward filtering, IEEE Transactions on Signal Processing, 1996, 44(4):988-992.
[111] 纪跃波, 秦树人, 汤宝平. 零相位数字滤波器. 重庆大学学报, 2000, 23(6):4-7
[112] 郭瑜, 秦树人. 基于瞬时频率估计及时频滤波的阶比分量提取, 中国机械工程, 已录用, 待发表.
[113] Vold H., Leuridan J., Order Tracking at Extreme Slew Rates, Using Kalman Tracking Filters. SAE Paper, Number 931288, 1993
[114] Vold H., Deel J., Vold-Kalman Order Tracking: New Methods for Vehicle.Sound Quality and Drive Train NVH Applications. SAE Paper, Number 972033, 1997
[115] Vold, H., Mains, M., Blough, J., "Theoretical Foundations for High Performance Order Tracking with the Vold-Kalman Tracking Filter", SAE Paper, Number 972007, 1997
[116] Albright M.and Qian S., A Comparison of the Newly Proposed Gbaor Order Tracking Technique in vs. Other Order Tracking Methods. SAE Noise and Vibration Conference, 2001, from internet.
[117] Bastiaans M.J., Gabor 's expansion of a signal into Gaussian elementary signals. Proc. IEEE, 1981, 68:594-598.
[118] Wexler J. and Raz S., Discrete Gbaor Expansions. Signal Processing, 1990, 21:207-220.
[119] Bastiaans M.J., A sampling theorem for the complex spectrogram, and Gabor's expansion of a signal in Gaussian elementary signals, Optical Engineering, 1981, 20(4):594-598.
[120] Einziger P.D., Gabor expansion of an aperture field in exponential elementary beams. IEE Electron. Lett., 1988, 24:665-666.
[121] Shidong Li; Healy, D.M., Jr.; A parametric class of discrete Gabor expansions. Signal Processing, IEEE Transactions, 1996, 44(2):201 -211.
[122] Yao J., Complete Gabor transformation for signal representation, Image Processing, IEEE Trans., 1993, 2:152-159.
[123] Qian S. and Chen D., Discrete Gabor transform. Signal Processing, IEEE Trans., 1993, 41(7):2429-2439.
[124] Morris J.M. and Lu Y., Discrete Gabor expansion of discrete-time signals in L2(Z) via frame theory, IEEE Signal Processing Magazine, 1994, 40(2):155-181.
[125] Qian S. and Chen D., Joint Time-Frequency Analysis, Englewood Cliffs, NJ:Prentice-Hall, 1996.
[126] Qian S. and Chen D.; A general solution of biorthogonal analysis window functions for orthogonal-like discrete Gabor transform. Proceedings of the IEEE-SP International Symposium, Victoria, BC, Canada, 1992, IEEE-SP, 1992:387 -389.
[127] Order Analysis Toolset for LabVIEW User Manual，National Insttruments, May 2001 Edition
[128] 秦树人, 张思复, 汤宝平. 何辉等, 集成测试技术与虚拟式仪器, 中国机械工程, 1999, 10(1):77-80.
[129] 秦树人, 汤宝平, 徐铭陶, 何辉等. 工程信号小波变换分析仪系统的研究, 中国机械工程, 1999, 10(4):443-446.
[130] 秦树人, 汤宝平, 面向21世纪的绿色仪器系统, 中国机械工程, 2000, 11(3):275-278.