发动机变速阶段振动信号阶比跟踪研究
|
摘要
由于车辆工业的发展和对乘用车舒适性的要求，提出了从内部结构方面进行设计优化来减小发动机振动和噪声的要求。发动机特征分析是对发动机进行优化设计、故障诊断和状态监测的重要组成部分，而振动测试方法又是特征分析的主要手段。如何通过对外部测量振动信号进行特征信息提取，从而建立起特征信息和机器内部结构的关系，是非常有意义的。
本课题是研究从复杂的发动机振动信号中提取和转速相关的信号，分离干扰噪声的阶比跟踪方法。工程师们可以利用所提取的阶比信号得到发动机的特征信息，更好地理解发动机内部结构，从减小发动机的运转振动和噪声方面对发动机的优化设计进行指导。
在阶比跟踪分析中，准确地获得基准转轴的转速是非常关键的。针对在实际应用中转速计脉冲信号测量不准的情况，直接计算脉冲到达时间得到的转速曲线误差较大。本论文提出了分段加权三次多项式曲线拟合方法，通过对转速曲线进行分段拟合，通过数据重叠和加权平均来保证各分段点处的连续及平滑，得到准确的转速曲线。
当前应用最为广泛的等角度重采样阶比跟踪方法一般是通过过采样插值实现等角度重采样的，最大信噪比只能达到65dB。本论文根据采样信号复原原理，提出了用插值滤波器来实现自适应数字重采样的方法。用一个预先设定好的具有很高过采样率的内插sin c(t)函数构成的滤波器实现了等角度自适应重采样，提高了自适应重采样的精度和阶比谱的信噪比。
采用等角度重采样加FFT进行阶比跟踪，只能得到三维瀑布图或二维阶比谱图和阶比跟踪谱，并不能得到阶比的时域提取。本论文研究了Gabor变换及满足信号时域重构的对偶函数双正交条件，实现了在时频域进行可变中心频率带通滤波来分离阶比和噪声，并采用相似对偶函数最小二乘法一次迭代实现了阶比成分的时域重构信号。成功地实现了阶比在时域的波形提取。
发动机结构复杂，是由许多轴的旋转和往复运动组成。不同转轴对应的阶比在频率上会有交叉，使阶比跟踪变得困难。等角度重采样加FFT方法只能以一个参考轴作为重采样的参照，提取的阶比波形就会受到相交叉阶比的干扰，产生失真。本文在Vold-Kalman自适应滤波器的基础上进行了改进，设计一个通带中心频率随着转速变化而变化的带通滤波器。用最小二乘法结合Kalman自适应滤波器同时提取多轴阶比，解决了多轴交叉阶比提取的耦合问题。
设计了几种不同幅值变化的仿真信号，对上述三种阶比跟踪方法进行了比较。设计了阶比跟踪实测实验方案，利用Visual C++和Matlab混合编程编制了实验测试软件，搭建了发动机测试平台和信号采集系统。通过气动发动机台架自测数据与美国提供实验数据相结合，分别采用不同的阶比跟踪算法对不同来源的发动机实测数据进行了阶比跟踪实验研究。
最后，对本文的研究工作做了简单的总结，提出了研究的不足之处和进一步研究的建议。
发动机变速阶段振动信号阶比跟踪研究
With the development of automobile industry and demand of riding comfort of car, design optimization from interior structure to lower engine vibration and noise is needed. How to extract characteristic information from exterior measurement vibration signal and get interior structure information is of vital meaning.
This project is to research the order tracking methods to extract rotation related signal and separate disturbed noise from complicated engine vibration signal. Engineers can better understand engine interior structure through extracted order signal, and instruct optimization design from depressing running vibration and noise aspect.
In order tracking analysis, it is very important to acquire rotating speed of reference shaft. In practical application, tachometer impulse measurement is not accurate. Therefore rotating speed curve through direct computing impulse arriving time may have big error. Aiming at this problem, a subsection weighing cubic spline curve fit method was proposed in this paper. This proposed method uses cubic spine curve fit rotating speed subsection, and through data overlap and weighing average to ensure continuuty and smooth of subsection point. Accurate rotating speed was achieved.
Wildly applied even-angle re-sampling order tracking method is commonly implemented by over sampling data and interpolation, and can only get 65dB signal noise ratio. Base on sampled signal recover theory, an interpolation filter adaptive numeric re-sampling method was proposed in this paper. Adaptive even-angle re-sampling is implemented by a filter which is constructed by pre-established over sampling rate interpolation sin c(t) function. Accuracy of re-sampling andsignal-noise-ratio of order spectrum were improved.
Even-angle re-sampling plus FFT order tracking method can get waterfall, order spectrum and order tracking spectrum result view, but it can not get order extraction in time domain. Gabor transform and dual function bi-orthogonal condition to fulfill time domain reconstruction were researched in this paper. Vary center frequency band pass filter in time-frequent domain was implemented to separate order and noise. And order component reconstruction in time domain was achieved by similar duel function least square method iteration. Order component was extracted in time domain by Gabor transform.
Engine is complicated in structure, and is consists of rotating and reciprocating movement of many shafts. Orders of different shafts crossing each other in frequency make order tracking difficult. Even-angle re-sampling plus FFT method can only take one shaft as re-sampling reference, extracted order waveform be interrupted by crossing order and cause distortion. A few changes was done on Vold-Kalman adaptive filter, and a band pass filter with center frequency vary with rotating speed was designed. Least square method combined with Kalman adaptive filter can extract orders of multi-shaft, solves crossing order decouple problem.
Several simulation signals with different amplitude change were designed. Comparison was done between three order tracking methods. A field experiment scheme was also designed. Test software was programmed by combining Visual C++ and Matlab. Engine test platform and signal collection system were constructed. Expermental data were collected form air powered engine platform and provided by Dactron corperation. Field expremet was carried out by different order tracking methods.
Final, a brief summarization of research job was done, and shortcoming and research proposal were put forward.
本课题是研究从复杂的发动机振动信号中提取和转速相关的信号，分离干扰噪声的阶比跟踪方法。工程师们可以利用所提取的阶比信号得到发动机的特征信息，更好地理解发动机内部结构，从减小发动机的运转振动和噪声方面对发动机的优化设计进行指导。
在阶比跟踪分析中，准确地获得基准转轴的转速是非常关键的。针对在实际应用中转速计脉冲信号测量不准的情况，直接计算脉冲到达时间得到的转速曲线误差较大。本论文提出了分段加权三次多项式曲线拟合方法，通过对转速曲线进行分段拟合，通过数据重叠和加权平均来保证各分段点处的连续及平滑，得到准确的转速曲线。
当前应用最为广泛的等角度重采样阶比跟踪方法一般是通过过采样插值实现等角度重采样的，最大信噪比只能达到65dB。本论文根据采样信号复原原理，提出了用插值滤波器来实现自适应数字重采样的方法。用一个预先设定好的具有很高过采样率的内插sin c(t)函数构成的滤波器实现了等角度自适应重采样，提高了自适应重采样的精度和阶比谱的信噪比。
采用等角度重采样加FFT进行阶比跟踪，只能得到三维瀑布图或二维阶比谱图和阶比跟踪谱，并不能得到阶比的时域提取。本论文研究了Gabor变换及满足信号时域重构的对偶函数双正交条件，实现了在时频域进行可变中心频率带通滤波来分离阶比和噪声，并采用相似对偶函数最小二乘法一次迭代实现了阶比成分的时域重构信号。成功地实现了阶比在时域的波形提取。
发动机结构复杂，是由许多轴的旋转和往复运动组成。不同转轴对应的阶比在频率上会有交叉，使阶比跟踪变得困难。等角度重采样加FFT方法只能以一个参考轴作为重采样的参照，提取的阶比波形就会受到相交叉阶比的干扰，产生失真。本文在Vold-Kalman自适应滤波器的基础上进行了改进，设计一个通带中心频率随着转速变化而变化的带通滤波器。用最小二乘法结合Kalman自适应滤波器同时提取多轴阶比，解决了多轴交叉阶比提取的耦合问题。
设计了几种不同幅值变化的仿真信号，对上述三种阶比跟踪方法进行了比较。设计了阶比跟踪实测实验方案，利用Visual C++和Matlab混合编程编制了实验测试软件，搭建了发动机测试平台和信号采集系统。通过气动发动机台架自测数据与美国提供实验数据相结合，分别采用不同的阶比跟踪算法对不同来源的发动机实测数据进行了阶比跟踪实验研究。
最后，对本文的研究工作做了简单的总结，提出了研究的不足之处和进一步研究的建议。
发动机变速阶段振动信号阶比跟踪研究
With the development of automobile industry and demand of riding comfort of car, design optimization from interior structure to lower engine vibration and noise is needed. How to extract characteristic information from exterior measurement vibration signal and get interior structure information is of vital meaning.
This project is to research the order tracking methods to extract rotation related signal and separate disturbed noise from complicated engine vibration signal. Engineers can better understand engine interior structure through extracted order signal, and instruct optimization design from depressing running vibration and noise aspect.
In order tracking analysis, it is very important to acquire rotating speed of reference shaft. In practical application, tachometer impulse measurement is not accurate. Therefore rotating speed curve through direct computing impulse arriving time may have big error. Aiming at this problem, a subsection weighing cubic spline curve fit method was proposed in this paper. This proposed method uses cubic spine curve fit rotating speed subsection, and through data overlap and weighing average to ensure continuuty and smooth of subsection point. Accurate rotating speed was achieved.
Wildly applied even-angle re-sampling order tracking method is commonly implemented by over sampling data and interpolation, and can only get 65dB signal noise ratio. Base on sampled signal recover theory, an interpolation filter adaptive numeric re-sampling method was proposed in this paper. Adaptive even-angle re-sampling is implemented by a filter which is constructed by pre-established over sampling rate interpolation sin c(t) function. Accuracy of re-sampling andsignal-noise-ratio of order spectrum were improved.
Even-angle re-sampling plus FFT order tracking method can get waterfall, order spectrum and order tracking spectrum result view, but it can not get order extraction in time domain. Gabor transform and dual function bi-orthogonal condition to fulfill time domain reconstruction were researched in this paper. Vary center frequency band pass filter in time-frequent domain was implemented to separate order and noise. And order component reconstruction in time domain was achieved by similar duel function least square method iteration. Order component was extracted in time domain by Gabor transform.
Engine is complicated in structure, and is consists of rotating and reciprocating movement of many shafts. Orders of different shafts crossing each other in frequency make order tracking difficult. Even-angle re-sampling plus FFT method can only take one shaft as re-sampling reference, extracted order waveform be interrupted by crossing order and cause distortion. A few changes was done on Vold-Kalman adaptive filter, and a band pass filter with center frequency vary with rotating speed was designed. Least square method combined with Kalman adaptive filter can extract orders of multi-shaft, solves crossing order decouple problem.
Several simulation signals with different amplitude change were designed. Comparison was done between three order tracking methods. A field experiment scheme was also designed. Test software was programmed by combining Visual C++ and Matlab. Engine test platform and signal collection system were constructed. Expermental data were collected form air powered engine platform and provided by Dactron corperation. Field expremet was carried out by different order tracking methods.
Final, a brief summarization of research job was done, and shortcoming and research proposal were put forward.
引文
[1] 杨寿藏，陈云彪．现代先进发动机技术平衡和振动．柴油机设计与制造，2002(4)：p．29-39．
[2] 孙学军等．摩托车发动机的振动分析与控制．内燃机工程，2005．26(2)：p．63-65
[3] S．Murakami，et al．Improvement in the noise and vibration performance for the new 1996 model V6 engine．JSAE Review,1998．19：p．129-135．
[4] 俞明，柳文斌．轿车车内振动噪声源的识别．机床与液压，2003(5)：p．117-119，189．
[5] 陈大禧，朱铁光．大型回转机械论断现场实用技术．2002，北京：机械工业出版社．
[6] 杨树莲，霍亮生．数控机床主轴在线故障诊断新方法的实现．机床与液压，2003，4．
[7] R.F.M. Marcal, et al. Detecting Faults in Rotating Machines, in IEEE Instrumentation & Measurement Magazine. 2000. p. 24-26.
[8] C. Sodsri, Time-Varying Autoregressive Modelling for Nonstationary Acoustic Signal and Its Frequency Analysis. Acoustic. 2003, Pennsylvania: The Pennsylvania State University. 118.
[9] Z.P. Mourelatos, A crankshaft system model for structural dynamic analysis of internal combustion engines. Computer and Structures, 2001, 79: p. 2009-2027.
[11] M．Albright，New tool for defining vehicle noise．Ee-Evaluation Engineering，2002．41(2)：62．
[12] 俞明，柳文斌，吴庆宏．汽车振动噪声测试的阶次跟踪方法．机床与液压，2003(6)：p．277-278,319．
[13] S. Qian. Gabor expansion for order tracking. Sound and Vibration, 2003.37(6):p. 18-22.
[14] G. Betta, A DSP-Based FFT-Analyzer for the Fault Diagnosis of Rotating Machine Based on Vibration Analysis. IEEE Transactions on Instrumentation and Measuremnet, 2002. 21(6): p. 1326-1322.
[15] M.C. Pan, Y.F. Lin, Further exploration of Vold-Kalman-filtering order tracking with shaft-speed informationI: Theoretical part, numerical implementation and parameter investigations. Mechanical Systems and Signal Processing. In Press,Corrected Proof.
[16] R. Potter, New order tracking method for rotating machinery. Sound and Vibration Magazine, 1990.24(9): p. 30-34.
[17] S. R. Qin, et al., The order tracking of rotating machinery based on instantaneous frequency estimation, in Fifth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E.P Tomasini, Editor. 2002. p.22-28.
[18] 陈循，唐丙阳．汽车起动电机异常噪声监测系统的设计原理．数据采集与处理，1995．10(1)：p．56-60．
[20] J.R. Blough, Improving the Analysis of Operating Data on Rotating Automotive Components. Mechanical, Industrial and Nuclear Engineering. 1998, Cincinati: University of Cincinati. 234.
[21] M.F. Albright, S. Qian, A Comparision of the newly Proposed Gabor Order Tracking Technique vs. Other Order Tracking Methods, in SAE Noise & Vibration Conference. 2001.
[22] 秦国军，陈循，温熙森．变速机械振动信号的伪同步重采样技术—Ⅱ滤波器设计与信号重采样．振动与冲击，1999．18(1)：p．26-29．
[23] 陈剑．旋转机械振动分析时进行外部采样的一种实现方法．合肥工业大学学报：自然科学版，1996．19(2)：p．112-116．
[24] H. Packard Appendix A - Computed synchronous resampling and order tracking.Effective machinery Measurements using Dynamic Signal Analyzers Volume, 64-69
[25] EW. Hall. Measuring instabilities and chaos in the real world: applications in rotating machinery. 1992.
[26] 周易．DSP技术在旋转机械振动监测与分析系统中的研究与应用控制理论与控制工程2002，上海：东华大学．75页．
[27] 郭瑜，秦树人，梁玉前．时频分析阶比跟踪技术．重庆大学学报(自然科学版)，2002,25(5)：p．17-20．
[28] 吕琛，宋希庚，邹积斌．基于DSP的振动信号阶比与时域同步平均分析．振动与冲击，2002，21(2)．
[29] Y. Guo, S. Qin, Pseudo-speed tracking order analysis for non-stationary vibration signals of rotating machinery. Zhendong yu Chongji/Journal of Vibration and Shock, 2004. 23(1): p. 61-64.
[30] R.B. Randall, B. Tech, eds. Frequency Analysis. 3th ed. 1987, Bruel & Kjaer:Denmark.
[31] D.K. Bandhopadhyay, D. Griffiths. Methods for Analyzing Order Spectra. in Proceedings of Society of Automotive Engineer 1995 Noise and Vibration Conference.1995: SAE paper.
[32] 仇越，刘向群，张洪钺．基于频谱法的航空起动发电机故障检测与诊断．北京航空航天大学学报，2004．30(5)．
[33] K.P Maynard, et al., Application of Double Resampling to Shaft Torsional Vibration Measurement for the Detection of Blade Natural Frequencies, in Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology. 2000: Virginia Beach.
[34] D. McDonald, M. Gribler. Digital Resampling - a viable alternative for order domain measurements of ratating machinery. Proceedings of International Modal Analysis Conference 9. 1991. Italy.
[36] R.T. Sokolov, J.C. Rogers. Removing harmonic signal nonstationarity by dynamic resampling. 1995.
[37] 陈循，田江红．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)：p．44-48．
[38] S. Qin, et al. The order tracking based on instantaneous frequency estimation in rotating machinery. 2002. Leuven, Belgium: Katholieke Universiteit Leuven,Heverlee, B-3001, Belgium.
[39] Y.-S. Han, C.-W. Lee, Directional Wigner Distribution for Order Analysis in Rotation/Reciprocating Machines. Mechanical System and Signal Processing, 1999.13(5): p. 723-737.
[40] 于德介，成琼，程军圣．基于复解析小波变换的瞬时频率分析方法．振动与冲击，2004．23(1)：p．108-109．
[41] D. Konig, C. Tork, J.E Bohme. Design of optimum periodic time varying filter for application in combustion diagnosis of car engines. IEEE, 1995: p. 1924-1927.
[42] H. Vold, J. Leuridan. High Resolution Order Tracking at Extreme Slew Rates Using Kalman Tracking Filters. in Proceedings of the SAE Noise and Vibration Conference. 1993. Traverse City, MI: SAE Paper no. 931288.
[43] H. Vold, J. Crowley, J. Nessler. Tracking sine waves in systems with high slew rates, in Proceedings of 6th International Modal Analysis Conference. 1988.Kissimmee.
[44] H. Vold, J. Crowley. Time variant spectral analysis using the maximum entropy method, in Proceedings of 6th International Modal Analysis Conference. 1988. Kissimmee.
[45] R Weber, Correlating oerating data with modal testing: an automotive application 1988, Cincinnati, Ohio: University of Cincinnati.
[46] J.R. Blough, D.L. Brown. Separating close and crossing orders with frequency domain order tracking. 1999. Kissimmee, FL, USA: SEM, Bethel, CT, USA.
[47] J.R. Blough. Multi-tachometer order tracking and operating shape extraction.2004. Leuven, Belgium: Katholieke Universiteit Leuven, Heverlee, B-3001, Belgium.
[48] 郭瑜，秦树人，汤宝平．基于分段重叠零相位滤波的阶比跟踪滤波法．振动工程学报，2003．16(4)．
[49] 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，2003．14(23)．
[50] M.R. Bai, J. Jeng, C. Chert. Adaptive Order Tracking Technique Using Recursive Least-Square Algorithm. Journal of Vibration and Acoustics-Transactions of the Asme, 2002. 124(4): p. 502-511.
[51] M.-S. Bai, et al., Fault diagnosis of rotating machinery using an intelligent order tracking system. Journal of Sound and Vibration, 2005.280(3-5): p. 699-718.
[52] 王新晴等．基于一种新的时频分布的机械故障诊断．机械工程学报，2003．39(7)：p．150-153．
[53] 贾继德等．基于阶比双谱分析的发动机故障特征提取．内燃机学报，2004,22(5)．
[54] 卢文祥，杜润生．机械工程测试、信息、信号分析．1990，武汉：华中理工大学出版社．481．
[55] 陈光化．瞬时频率估计及其应用研究．控制理论与控制工程，2001，上海：上海大学．104页．
[56] RM. Oliveira, V. Barroso. On the concept of instantaneous frequency. 1998.Seattle, WA, USA: IEEE, Piscataway, NJ, USA.
[57] W. Nho, RJ. Loughlin, When is instantaneous frequency the average frequency at each time. IEEE Signal Processing Letters, 1999.6(4): p. 78-80.
[58] 郭瑜，秦树人，梁玉前．时频分析阶比跟踪技术．重庆大学学报(自然科学版)，2002．25(5)：p．17-20．
[59] Y.Guo, S.R. Qin. Y.Q. Laing, Order tracking of rotating machinery based on instantaneous frequency estimation, in Proceedings of the Second International Symposium on Instrumentation Science and Technology, Vol 3, J.B. Tan and X.E Wen, Editors. 2002. p. 547-552.
[60] 郭瑜等．基于瞬时频率估计的旋转机械阶比跟踪．机械工程学报，2003．39(3)．
[61] 钟佑明，秦树，汤宝平．Hilbert-Huang 变换中的理论研究．振动与冲击．2002．21(4)：p．13-17．
[62] 谭善文．多分辨希尔伯特-黄 (Hilbert-Huang) 变换方法的研究．机械电子工程，2001，重庆：重庆大学．140页．
[63] 尉宇，孙德宝，郑继刚．基于FrFT优化窗的STFT及非线性调频信号瞬时频率估计．宇航学报，2005．26(2)．
[64] 程军圣，于德介，杨宇．一种基于 Hilbert-Huang 变换和 AR 模型的滚动轴承故障论断方法．系统工程理论与实践，2004(10)：p．92-98．
[65] 贾继德等 基于瞬时频率估计的内燃机信号阶比分析．内燃机工程，2005．26(3)：p．15-18，21．
[66] 梁玉前，秦树人，郭瑜．旋转机械升降速信号的瞬时频率估计．机械工程学报，2003．39(9)：p．75-79．
[67] 徐敏强，黄文虎，张嘉钟．旋转机械高速启动过程振动信号分析方法的研究．振动工程学报，2000,13(02)．
[68] 蔡毓．基于二进小波变换的实信号瞬时频率提取．信号与信息处理．2002，西安：西安交通大学．45页．
[69] W. Wang, et al. Study of automobile engine fault diagnosis based on wavelet neural networks, in Proceedings of the 5th World Congress on Intelligent Control and Automation 2004.
[70] 郭瑜，秦树人．无转速计旋转机械升降速振动信号零相位阶比跟踪滤波．机械工程学报，2004 40(3)．
[71] 吕琛，宋希庚，邹积斌．振动、噪声信号的阶比分析与DSP实现．数掘采集与处理，2001．16(4)．
[72] NI, Order Analysis Toolset for Labview User Manual. 2001，NI.
[73] 马扶南．用三次样条函数作通风机性能曲线拟合．风机技术，2002(3)：p．18-19．
[74] 王尊正．数值分析基本教程．1993，哈尔滨：哈尔滨工业大学出版社．
[75] H. Herlufsen, et al. Characteristics of the Vold-Kalman order tracking filter. 2000.Istanbul, Turkey: Institute of Electrical and Electronics Engineers Inc., Piscataway, NJ,USA.
[76] 霍亮生．采煤机故障检测关键技术的研究．机械制造及自动化．2002，北京：北京理工大学．112页．
[77] 田昊等．基于 LabVIEW 的重采样阶次分析技术．军械工程学院学报，2005．17(4)：p．41-43．
[78] 杨炯明，秦树人，季忠．旋转机械阶比分析技术中阶比采样实现方式的研究．中国机械工程，2005．16(3)．
[79] J.R. Blough, Development and analysis of time variant discrete Fourier transform order tracking. Mechanical Systems and Signal Processing, 2003. 17(6): p.1185-1199.
[80] 郭瑜，秦树人，汤宝平．基于分段重叠零相位滤波的阶比跟踪滤波法．振动工程学报，2003．16(4)．
[81] 杨炯明等．旋转机械虚拟式振动信号特征分析仪．中国机械工程，2005．16(5)．
[82] F. Lemvregts, J. Top, F Neyrinck, Off-line Synchronous Resampling of Vibration Measurements. IEEE, 1996: p. 748-755.
[83] K.R. Fyfe, E.D.S. Munck, Analysis of computed order tracking. Mechanical Systems & Signal Processing, 1997.11(2): p. 187-205.
[84] M. Rauter, K. Witrisal, eds. Multirate Signal Processing. 1.3 ed., ed. S.P.a.S.C.Laboratory. 2003, Graz University of Technology.
[85] 胡广书．数字信号处理—理论、算法与实现．1997，北京：清华大学出版社．
[86] K.M. Bossley, et al., Hybrid computed order tracking. Mechanical Systems and Signal Processing, 1999. 13(4): p. 627-641.
[87] R Jun-Yong, R. Chong-Yeon, Comparison error of signal interpolation methods for vibration signal analysis of revolution machine. Transactions of the Korean Institute of Electrical Engineers, D, 2004.53(12): p. 820-826.
[88] 周建川，李国红，信号的瀑布分析技术与实现．机电工程，2004. 21(12).
[89] 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，2004．23(1)．
[90] 李忆岚．时频分析理论及应用研究．信号与信息处理．2003，西安：西北工业大学．60页．
[91] 熊良才．自适应时频分析技术及其在故障诊断中应用的研究 机械制造及其自动化．2002，武汉：华中科技大学．107页．
[92] 杨国安，高金吉．多分量振动信号时频分析与应用研究．振动工程学报，2003．16(2)：p．133-136．
[93] 侯敬宏等．基于小波分析的放置机械振动信号定量特征研究．机械工程学报，2004．40(1)：p．131-135．
[94] S. Conforto, T. D'Alessio, Spectral Analysis for Non-stationary Signals from Mechanical Measurements:A Parametric Approach. Mechanical System and Signal Processing, 1999. 13(3): p. 395-411.
[95] D. Gabor, Theory of Communication. J. Inst. Elec. Eng.,, 1946.93: p. 429-453.
[96] J. Wexler, S. Raz, Discrete Gabor Expansions. Signal Process, 1990. 21(3): p.207-221.
[97] H. Shao, W. Jin, S. Qian, Order tracking by discrete Gabor expansion. IEEE Transactions on Instrumentation and Measurement, 2003.52(3): p. 754-761.
[98] S. Qian, D. Chen, Optimal Biorthogonal Analysis Window Function for Discre Gabor Transform. IEEE Transactions on Special Processing, 1994. 42(3): p.694-697.
[99] 张贤达．现代信号处理．1994，北京：清华大学出版社．
[100] X.-G. Xia, S. Qian, Convergence of an Iterative Time-Variant Filtering Based on Discrete Gabor Transform. IEEE REANSACTON OFN SIGNAL PROCESSING 1999.47(10): p. 2894-2899.
[101] S.-D. Li, S. Qian, A Complement t a Derivation of Discrete Gabor Expansions. IEEE SIGNAL PROCESSING LETTERS, 1995.2(2): p. 31-32.
[102] M.C. Pan, C.C. Chiu, Investigation on improved gabor order tracking technique, in Smart Structures and Materials 2004: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, S.C. Liu, Editor. 2004. p. 461-469.
[103] M.-C. Pan, C.-C. Chiu, Investigation on improved Gabor order tracking technique. Proceedings of the SPIE - The International Society for Optical Engineering, 2004. 5391.(1): p. 461-469.
[104] 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，2003．14(17)．
[105] S. Hui, J. Wei, Q. Shie, Order tracking by discrete Gabor expansion. IEEE Transactions on Instrumentation and Measurement, 2003.52(3): p. 754-761.
[106] S. Qian, D. Chen, Joint time-frequency analysis. IEEE Signal Processing Magazine, 1999(March): p. 52-67.
[107] J. Tuma. Sound Quality Assessment Using Vold-Kalman Filtering. in XXIX ASR 2004 Seminar. Instrument and Control. 2004. Ostrava,.
[108] H. Herlufsen, et al., Characteristics of the Vold-Kalman order tracking filter.S V Sound and Vibration, 1999. 33(4): p. 34-44.
[109] H. Vold, J. Deel, Vold-Kalman Order Tracking: New Method for Vehicle Sornd Quality and Drive-Train NVH Applications. SAE Paper Number 97NV161,1997.
[110] 杨国安，吴贞焕，高金吉．基于自适应滤波的机械故障诊断方法研究．振动与冲击，2003．22(4)：p．4-7．
[111] K. Kryniski, U. Carlsson, Order tracking of diesel engines with a Kalman filter. 1999. 105(2): p. 1284-1284.
[112] J. Tuma. Frequency Response of the Vold Order Tracking Filter. in XXVI ASR 2001 Seminar. Instrument and Control. 2001. Ostrava,.
[113] Lebold M, et al., Review of Vibration Analysis Methods for Gearbox Diagnostics and Prognostics, in Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology. 2000: Virginia Beach p. 623-634.
[114] C. Feldbauer, R. Holdrich. Realization of a Vold-Kalman Tracking Filter-a Least Square Problem. in Proceeding of the COST G-6 Conference on Digital Audio Effects (DAFX-00). 2000.
[115] S. Gade, et al., Filter characteristics of the Vold-Kalman order tracking filter.1999. 106(1): p. 1427-1432.
[116] H. Vold, J. Blough, Theoretical Foundations for High Performance Order Tracking with the Vold-Kalman Tracking Filter. SAE Paper Number 97NV164, 1997.
[117] J.D. Wu, C.W. Huang, R.W. Huang, An application of a recursive Kalman filtering algorithm in rotating machinery fault diagnosis. Ndt & E International, 2004. 37(5): p. 411-419.
[118] H. Vold, et al., Multi axle order tracking with the Vold-Kalman tracking filter. Sound and Vibration, 1997. 31(5): p. 30-34.
[119] S.-Gade, H. Herlufsen, H. Konstantin-Hansen, Order tracking using the Vold-Kalman tracking filter. 1999. 105(2): p. 1026-1026.
[120] S. Gade, et al. Order tracking using the vold-kalman order tracking filter.1998. Leuven, Belgium: Katholieke Universiteit Leuven, Heveflee, B-3001, Belgium.
[121] M.C. Pan, Y.E Lin, Further exploration of Vold-Kalman-filtering order tracking with shaft-speed information—II: Engineering applications. Mechanical Systems and Signal Processing. In Press, Corrected Proof.
[122] 薛定字．控制系统计算机辅助设计—Matlab 语言及应用．北京：清华大学出版社，1996．
[123] 卢新城等，用 VC++6．0和 Matlab 编制信号采集和处理程序的方法研究．机床与液压，2004(11)：p．155-157
[124] 李天昀，葛临东．综述 Matlab与VC++的交互编程．计算机仿真，2004．21(9)：p．193-195．
[125] 田成军，杨阳．VC与Matlab的混合编程方法研究．长春理工大学学报，2003．26(3)：p．57-62
[126] 丁洲，苏兰兰．VisualC++与 MatlabB 混合编程在数字信号处理中的应用．机电设备，2004．21(6)：p．17-21
[127] 亓慧，张艳丽．陈振生基于 Matlab 与VC混合编程的研究．现代电子技术，2004，27(19)：p．11-15．
[128] 刘昊等．压缩空气动力汽车集成技术．机电工程，2003，20(5)：p．95-97
[129] 张先刚等．某125型跨骑式摩托车结构的动态特性研究．机械设计与研究，2005,21(1)：p．72-75
[2] 孙学军等．摩托车发动机的振动分析与控制．内燃机工程，2005．26(2)：p．63-65
[3] S．Murakami，et al．Improvement in the noise and vibration performance for the new 1996 model V6 engine．JSAE Review,1998．19：p．129-135．
[4] 俞明，柳文斌．轿车车内振动噪声源的识别．机床与液压，2003(5)：p．117-119，189．
[5] 陈大禧，朱铁光．大型回转机械论断现场实用技术．2002，北京：机械工业出版社．
[6] 杨树莲，霍亮生．数控机床主轴在线故障诊断新方法的实现．机床与液压，2003，4．
[7] R.F.M. Marcal, et al. Detecting Faults in Rotating Machines, in IEEE Instrumentation & Measurement Magazine. 2000. p. 24-26.
[8] C. Sodsri, Time-Varying Autoregressive Modelling for Nonstationary Acoustic Signal and Its Frequency Analysis. Acoustic. 2003, Pennsylvania: The Pennsylvania State University. 118.
[9] Z.P. Mourelatos, A crankshaft system model for structural dynamic analysis of internal combustion engines. Computer and Structures, 2001, 79: p. 2009-2027.
[11] M．Albright，New tool for defining vehicle noise．Ee-Evaluation Engineering，2002．41(2)：62．
[12] 俞明，柳文斌，吴庆宏．汽车振动噪声测试的阶次跟踪方法．机床与液压，2003(6)：p．277-278,319．
[13] S. Qian. Gabor expansion for order tracking. Sound and Vibration, 2003.37(6):p. 18-22.
[14] G. Betta, A DSP-Based FFT-Analyzer for the Fault Diagnosis of Rotating Machine Based on Vibration Analysis. IEEE Transactions on Instrumentation and Measuremnet, 2002. 21(6): p. 1326-1322.
[15] M.C. Pan, Y.F. Lin, Further exploration of Vold-Kalman-filtering order tracking with shaft-speed informationI: Theoretical part, numerical implementation and parameter investigations. Mechanical Systems and Signal Processing. In Press,Corrected Proof.
[16] R. Potter, New order tracking method for rotating machinery. Sound and Vibration Magazine, 1990.24(9): p. 30-34.
[17] S. R. Qin, et al., The order tracking of rotating machinery based on instantaneous frequency estimation, in Fifth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E.P Tomasini, Editor. 2002. p.22-28.
[18] 陈循，唐丙阳．汽车起动电机异常噪声监测系统的设计原理．数据采集与处理，1995．10(1)：p．56-60．
[20] J.R. Blough, Improving the Analysis of Operating Data on Rotating Automotive Components. Mechanical, Industrial and Nuclear Engineering. 1998, Cincinati: University of Cincinati. 234.
[21] M.F. Albright, S. Qian, A Comparision of the newly Proposed Gabor Order Tracking Technique vs. Other Order Tracking Methods, in SAE Noise & Vibration Conference. 2001.
[22] 秦国军，陈循，温熙森．变速机械振动信号的伪同步重采样技术—Ⅱ滤波器设计与信号重采样．振动与冲击，1999．18(1)：p．26-29．
[23] 陈剑．旋转机械振动分析时进行外部采样的一种实现方法．合肥工业大学学报：自然科学版，1996．19(2)：p．112-116．
[24] H. Packard Appendix A - Computed synchronous resampling and order tracking.Effective machinery Measurements using Dynamic Signal Analyzers Volume, 64-69
[25] EW. Hall. Measuring instabilities and chaos in the real world: applications in rotating machinery. 1992.
[26] 周易．DSP技术在旋转机械振动监测与分析系统中的研究与应用控制理论与控制工程2002，上海：东华大学．75页．
[27] 郭瑜，秦树人，梁玉前．时频分析阶比跟踪技术．重庆大学学报(自然科学版)，2002,25(5)：p．17-20．
[28] 吕琛，宋希庚，邹积斌．基于DSP的振动信号阶比与时域同步平均分析．振动与冲击，2002，21(2)．
[29] Y. Guo, S. Qin, Pseudo-speed tracking order analysis for non-stationary vibration signals of rotating machinery. Zhendong yu Chongji/Journal of Vibration and Shock, 2004. 23(1): p. 61-64.
[30] R.B. Randall, B. Tech, eds. Frequency Analysis. 3th ed. 1987, Bruel & Kjaer:Denmark.
[31] D.K. Bandhopadhyay, D. Griffiths. Methods for Analyzing Order Spectra. in Proceedings of Society of Automotive Engineer 1995 Noise and Vibration Conference.1995: SAE paper.
[32] 仇越，刘向群，张洪钺．基于频谱法的航空起动发电机故障检测与诊断．北京航空航天大学学报，2004．30(5)．
[33] K.P Maynard, et al., Application of Double Resampling to Shaft Torsional Vibration Measurement for the Detection of Blade Natural Frequencies, in Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology. 2000: Virginia Beach.
[34] D. McDonald, M. Gribler. Digital Resampling - a viable alternative for order domain measurements of ratating machinery. Proceedings of International Modal Analysis Conference 9. 1991. Italy.
[36] R.T. Sokolov, J.C. Rogers. Removing harmonic signal nonstationarity by dynamic resampling. 1995.
[37] 陈循，田江红．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)：p．44-48．
[38] S. Qin, et al. The order tracking based on instantaneous frequency estimation in rotating machinery. 2002. Leuven, Belgium: Katholieke Universiteit Leuven,Heverlee, B-3001, Belgium.
[39] Y.-S. Han, C.-W. Lee, Directional Wigner Distribution for Order Analysis in Rotation/Reciprocating Machines. Mechanical System and Signal Processing, 1999.13(5): p. 723-737.
[40] 于德介，成琼，程军圣．基于复解析小波变换的瞬时频率分析方法．振动与冲击，2004．23(1)：p．108-109．
[41] D. Konig, C. Tork, J.E Bohme. Design of optimum periodic time varying filter for application in combustion diagnosis of car engines. IEEE, 1995: p. 1924-1927.
[42] H. Vold, J. Leuridan. High Resolution Order Tracking at Extreme Slew Rates Using Kalman Tracking Filters. in Proceedings of the SAE Noise and Vibration Conference. 1993. Traverse City, MI: SAE Paper no. 931288.
[43] H. Vold, J. Crowley, J. Nessler. Tracking sine waves in systems with high slew rates, in Proceedings of 6th International Modal Analysis Conference. 1988.Kissimmee.
[44] H. Vold, J. Crowley. Time variant spectral analysis using the maximum entropy method, in Proceedings of 6th International Modal Analysis Conference. 1988. Kissimmee.
[45] R Weber, Correlating oerating data with modal testing: an automotive application 1988, Cincinnati, Ohio: University of Cincinnati.
[46] J.R. Blough, D.L. Brown. Separating close and crossing orders with frequency domain order tracking. 1999. Kissimmee, FL, USA: SEM, Bethel, CT, USA.
[47] J.R. Blough. Multi-tachometer order tracking and operating shape extraction.2004. Leuven, Belgium: Katholieke Universiteit Leuven, Heverlee, B-3001, Belgium.
[48] 郭瑜，秦树人，汤宝平．基于分段重叠零相位滤波的阶比跟踪滤波法．振动工程学报，2003．16(4)．
[49] 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，2003．14(23)．
[50] M.R. Bai, J. Jeng, C. Chert. Adaptive Order Tracking Technique Using Recursive Least-Square Algorithm. Journal of Vibration and Acoustics-Transactions of the Asme, 2002. 124(4): p. 502-511.
[51] M.-S. Bai, et al., Fault diagnosis of rotating machinery using an intelligent order tracking system. Journal of Sound and Vibration, 2005.280(3-5): p. 699-718.
[52] 王新晴等．基于一种新的时频分布的机械故障诊断．机械工程学报，2003．39(7)：p．150-153．
[53] 贾继德等．基于阶比双谱分析的发动机故障特征提取．内燃机学报，2004,22(5)．
[54] 卢文祥，杜润生．机械工程测试、信息、信号分析．1990，武汉：华中理工大学出版社．481．
[55] 陈光化．瞬时频率估计及其应用研究．控制理论与控制工程，2001，上海：上海大学．104页．
[56] RM. Oliveira, V. Barroso. On the concept of instantaneous frequency. 1998.Seattle, WA, USA: IEEE, Piscataway, NJ, USA.
[57] W. Nho, RJ. Loughlin, When is instantaneous frequency the average frequency at each time. IEEE Signal Processing Letters, 1999.6(4): p. 78-80.
[58] 郭瑜，秦树人，梁玉前．时频分析阶比跟踪技术．重庆大学学报(自然科学版)，2002．25(5)：p．17-20．
[59] Y.Guo, S.R. Qin. Y.Q. Laing, Order tracking of rotating machinery based on instantaneous frequency estimation, in Proceedings of the Second International Symposium on Instrumentation Science and Technology, Vol 3, J.B. Tan and X.E Wen, Editors. 2002. p. 547-552.
[60] 郭瑜等．基于瞬时频率估计的旋转机械阶比跟踪．机械工程学报，2003．39(3)．
[61] 钟佑明，秦树，汤宝平．Hilbert-Huang 变换中的理论研究．振动与冲击．2002．21(4)：p．13-17．
[62] 谭善文．多分辨希尔伯特-黄 (Hilbert-Huang) 变换方法的研究．机械电子工程，2001，重庆：重庆大学．140页．
[63] 尉宇，孙德宝，郑继刚．基于FrFT优化窗的STFT及非线性调频信号瞬时频率估计．宇航学报，2005．26(2)．
[64] 程军圣，于德介，杨宇．一种基于 Hilbert-Huang 变换和 AR 模型的滚动轴承故障论断方法．系统工程理论与实践，2004(10)：p．92-98．
[65] 贾继德等 基于瞬时频率估计的内燃机信号阶比分析．内燃机工程，2005．26(3)：p．15-18，21．
[66] 梁玉前，秦树人，郭瑜．旋转机械升降速信号的瞬时频率估计．机械工程学报，2003．39(9)：p．75-79．
[67] 徐敏强，黄文虎，张嘉钟．旋转机械高速启动过程振动信号分析方法的研究．振动工程学报，2000,13(02)．
[68] 蔡毓．基于二进小波变换的实信号瞬时频率提取．信号与信息处理．2002，西安：西安交通大学．45页．
[69] W. Wang, et al. Study of automobile engine fault diagnosis based on wavelet neural networks, in Proceedings of the 5th World Congress on Intelligent Control and Automation 2004.
[70] 郭瑜，秦树人．无转速计旋转机械升降速振动信号零相位阶比跟踪滤波．机械工程学报，2004 40(3)．
[71] 吕琛，宋希庚，邹积斌．振动、噪声信号的阶比分析与DSP实现．数掘采集与处理，2001．16(4)．
[72] NI, Order Analysis Toolset for Labview User Manual. 2001，NI.
[73] 马扶南．用三次样条函数作通风机性能曲线拟合．风机技术，2002(3)：p．18-19．
[74] 王尊正．数值分析基本教程．1993，哈尔滨：哈尔滨工业大学出版社．
[75] H. Herlufsen, et al. Characteristics of the Vold-Kalman order tracking filter. 2000.Istanbul, Turkey: Institute of Electrical and Electronics Engineers Inc., Piscataway, NJ,USA.
[76] 霍亮生．采煤机故障检测关键技术的研究．机械制造及自动化．2002，北京：北京理工大学．112页．
[77] 田昊等．基于 LabVIEW 的重采样阶次分析技术．军械工程学院学报，2005．17(4)：p．41-43．
[78] 杨炯明，秦树人，季忠．旋转机械阶比分析技术中阶比采样实现方式的研究．中国机械工程，2005．16(3)．
[79] J.R. Blough, Development and analysis of time variant discrete Fourier transform order tracking. Mechanical Systems and Signal Processing, 2003. 17(6): p.1185-1199.
[80] 郭瑜，秦树人，汤宝平．基于分段重叠零相位滤波的阶比跟踪滤波法．振动工程学报，2003．16(4)．
[81] 杨炯明等．旋转机械虚拟式振动信号特征分析仪．中国机械工程，2005．16(5)．
[82] F. Lemvregts, J. Top, F Neyrinck, Off-line Synchronous Resampling of Vibration Measurements. IEEE, 1996: p. 748-755.
[83] K.R. Fyfe, E.D.S. Munck, Analysis of computed order tracking. Mechanical Systems & Signal Processing, 1997.11(2): p. 187-205.
[84] M. Rauter, K. Witrisal, eds. Multirate Signal Processing. 1.3 ed., ed. S.P.a.S.C.Laboratory. 2003, Graz University of Technology.
[85] 胡广书．数字信号处理—理论、算法与实现．1997，北京：清华大学出版社．
[86] K.M. Bossley, et al., Hybrid computed order tracking. Mechanical Systems and Signal Processing, 1999. 13(4): p. 627-641.
[87] R Jun-Yong, R. Chong-Yeon, Comparison error of signal interpolation methods for vibration signal analysis of revolution machine. Transactions of the Korean Institute of Electrical Engineers, D, 2004.53(12): p. 820-826.
[88] 周建川，李国红，信号的瀑布分析技术与实现．机电工程，2004. 21(12).
[89] 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，2004．23(1)．
[90] 李忆岚．时频分析理论及应用研究．信号与信息处理．2003，西安：西北工业大学．60页．
[91] 熊良才．自适应时频分析技术及其在故障诊断中应用的研究 机械制造及其自动化．2002，武汉：华中科技大学．107页．
[92] 杨国安，高金吉．多分量振动信号时频分析与应用研究．振动工程学报，2003．16(2)：p．133-136．
[93] 侯敬宏等．基于小波分析的放置机械振动信号定量特征研究．机械工程学报，2004．40(1)：p．131-135．
[94] S. Conforto, T. D'Alessio, Spectral Analysis for Non-stationary Signals from Mechanical Measurements:A Parametric Approach. Mechanical System and Signal Processing, 1999. 13(3): p. 395-411.
[95] D. Gabor, Theory of Communication. J. Inst. Elec. Eng.,, 1946.93: p. 429-453.
[96] J. Wexler, S. Raz, Discrete Gabor Expansions. Signal Process, 1990. 21(3): p.207-221.
[97] H. Shao, W. Jin, S. Qian, Order tracking by discrete Gabor expansion. IEEE Transactions on Instrumentation and Measurement, 2003.52(3): p. 754-761.
[98] S. Qian, D. Chen, Optimal Biorthogonal Analysis Window Function for Discre Gabor Transform. IEEE Transactions on Special Processing, 1994. 42(3): p.694-697.
[99] 张贤达．现代信号处理．1994，北京：清华大学出版社．
[100] X.-G. Xia, S. Qian, Convergence of an Iterative Time-Variant Filtering Based on Discrete Gabor Transform. IEEE REANSACTON OFN SIGNAL PROCESSING 1999.47(10): p. 2894-2899.
[101] S.-D. Li, S. Qian, A Complement t a Derivation of Discrete Gabor Expansions. IEEE SIGNAL PROCESSING LETTERS, 1995.2(2): p. 31-32.
[102] M.C. Pan, C.C. Chiu, Investigation on improved gabor order tracking technique, in Smart Structures and Materials 2004: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, S.C. Liu, Editor. 2004. p. 461-469.
[103] M.-C. Pan, C.-C. Chiu, Investigation on improved Gabor order tracking technique. Proceedings of the SPIE - The International Society for Optical Engineering, 2004. 5391.(1): p. 461-469.
[104] 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，2003．14(17)．
[105] S. Hui, J. Wei, Q. Shie, Order tracking by discrete Gabor expansion. IEEE Transactions on Instrumentation and Measurement, 2003.52(3): p. 754-761.
[106] S. Qian, D. Chen, Joint time-frequency analysis. IEEE Signal Processing Magazine, 1999(March): p. 52-67.
[107] J. Tuma. Sound Quality Assessment Using Vold-Kalman Filtering. in XXIX ASR 2004 Seminar. Instrument and Control. 2004. Ostrava,.
[108] H. Herlufsen, et al., Characteristics of the Vold-Kalman order tracking filter.S V Sound and Vibration, 1999. 33(4): p. 34-44.
[109] H. Vold, J. Deel, Vold-Kalman Order Tracking: New Method for Vehicle Sornd Quality and Drive-Train NVH Applications. SAE Paper Number 97NV161,1997.
[110] 杨国安，吴贞焕，高金吉．基于自适应滤波的机械故障诊断方法研究．振动与冲击，2003．22(4)：p．4-7．
[111] K. Kryniski, U. Carlsson, Order tracking of diesel engines with a Kalman filter. 1999. 105(2): p. 1284-1284.
[112] J. Tuma. Frequency Response of the Vold Order Tracking Filter. in XXVI ASR 2001 Seminar. Instrument and Control. 2001. Ostrava,.
[113] Lebold M, et al., Review of Vibration Analysis Methods for Gearbox Diagnostics and Prognostics, in Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology. 2000: Virginia Beach p. 623-634.
[114] C. Feldbauer, R. Holdrich. Realization of a Vold-Kalman Tracking Filter-a Least Square Problem. in Proceeding of the COST G-6 Conference on Digital Audio Effects (DAFX-00). 2000.
[115] S. Gade, et al., Filter characteristics of the Vold-Kalman order tracking filter.1999. 106(1): p. 1427-1432.
[116] H. Vold, J. Blough, Theoretical Foundations for High Performance Order Tracking with the Vold-Kalman Tracking Filter. SAE Paper Number 97NV164, 1997.
[117] J.D. Wu, C.W. Huang, R.W. Huang, An application of a recursive Kalman filtering algorithm in rotating machinery fault diagnosis. Ndt & E International, 2004. 37(5): p. 411-419.
[118] H. Vold, et al., Multi axle order tracking with the Vold-Kalman tracking filter. Sound and Vibration, 1997. 31(5): p. 30-34.
[119] S.-Gade, H. Herlufsen, H. Konstantin-Hansen, Order tracking using the Vold-Kalman tracking filter. 1999. 105(2): p. 1026-1026.
[120] S. Gade, et al. Order tracking using the vold-kalman order tracking filter.1998. Leuven, Belgium: Katholieke Universiteit Leuven, Heveflee, B-3001, Belgium.
[121] M.C. Pan, Y.E Lin, Further exploration of Vold-Kalman-filtering order tracking with shaft-speed information—II: Engineering applications. Mechanical Systems and Signal Processing. In Press, Corrected Proof.
[122] 薛定字．控制系统计算机辅助设计—Matlab 语言及应用．北京：清华大学出版社，1996．
[123] 卢新城等，用 VC++6．0和 Matlab 编制信号采集和处理程序的方法研究．机床与液压，2004(11)：p．155-157
[124] 李天昀，葛临东．综述 Matlab与VC++的交互编程．计算机仿真，2004．21(9)：p．193-195．
[125] 田成军，杨阳．VC与Matlab的混合编程方法研究．长春理工大学学报，2003．26(3)：p．57-62
[126] 丁洲，苏兰兰．VisualC++与 MatlabB 混合编程在数字信号处理中的应用．机电设备，2004．21(6)：p．17-21
[127] 亓慧，张艳丽．陈振生基于 Matlab 与VC混合编程的研究．现代电子技术，2004，27(19)：p．11-15．
[128] 刘昊等．压缩空气动力汽车集成技术．机电工程，2003，20(5)：p．95-97
[129] 张先刚等．某125型跨骑式摩托车结构的动态特性研究．机械设计与研究，2005,21(1)：p．72-75