基于循环平稳信号二维平面表示的滚动轴承早期故障诊断方法研究
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摘要
旋转机械结构复杂，对运转条件要求较高，滚动轴承的任何轻微故障都有可能改变其自身的运转状态，进而牵连到其它部件，引发一系列连锁反应，导致设备性能下降，甚至产生并发故障。如何提取滚动轴承的微弱故障特征，揭示其早期、微弱、潜在故障及其发生、发展和转移，是设备状态监测和故障诊断面临的巨大挑战。旋转机械在运转过程中，尤其是在故障状态下，其物理参数具有周期时变的特点，呈现循环平稳特征。从故障的物理本质入手，洞悉故障产生机理，是识别微弱故障特征的关键。
本文以实现滚动轴承早期故障特征提取为目的，针对旋转机械设备发生故障时具有循环平稳和非高斯的特点，通过研究基于二阶和三阶循环统计量的二维表示方法，有效实现旋转机械早期故障智能预示。研究内容如下：
(1)本文首先分析滚动轴承初期故障特点及类型，引入滚动轴承故障信号模型，将其分为确定性信号分量和随机信号分量，研究了其各自频谱特点：滚动轴承故障信号模型的确定性信号分量的频谱是离散频谱；而随机信号分量的功率谱密度函数是连续频谱。分析表明由于故障冲击周期的不严格确定（轴承转速的波动，滚动体接触角的改变等影响），滚动轴承故障信号频谱中的离散谱线会因此被连续频谱模糊，故障特征频率也就很难从信号的频谱中看到。
(2)根据滚动轴承等旋转机械设备关键部件的（正常/故障）振动信号具有明显的周期时变特征，采用二阶循环统计量理论（谱相关密度函数、谱相干函数）进行信号分析，做基于循环频率—频率二维表示的特征提取技术，在α f平面上有效提取噪声干扰下的早期微弱故障特征。
(3)由于时频分辨率、信号多分量导致的交叉项以及背景噪声的干扰等不利因素的影响，使时频二维表示得到的机械故障特征往往不够直观且对于故障早期诊断可靠性低。针对具有循环平稳特性的滚动轴承振动信号，本文研究了基于时间-频率二维信息的特征提取方法。尝试根据其谱相关密度函数与Wigner-Ville分布之间的函数关系，利用长数据序列计算得到循环谱密度重构Wigner-Ville分布。结果证明基于谱相关密度函数的Wigner-Ville分布可以极大削弱噪声对时频图的干扰，并且有很好的时频聚集性。
(4)在滚动轴承的早期故障监测过程中，由于微弱损伤激发的能量很小，易于淹没在背景噪声和较强的干扰之中，使得故障信息提取的难度加大，有时采用二阶循环统计量也不能有效地提取故障特征。因此采用的信号分析方法的抗噪性能显得尤为重要。理论上，在保证足够采样数据长度的情况下，高阶循环统计量对于任何高斯与非高斯噪声都是自然免疫的。
高阶循环统计量从实用的角度考虑，最常用的是三阶循环矩、三阶循环累积量、三阶循环矩谱、三阶循环累积量谱。本文重点研究了三阶循环累积量谱。三阶循环累积量谱，也称循环双谱，是含有三个参变量的多维函数。除了利用理论推导之外，用传统的谱分析表述方法很难将循环双谱表述清楚。若完整表述它则需要三根不同的频率轴——循环频率α轴、时延频率f1轴和时延频率f2轴，在传统的三维空间中无法完全表述其面貌。因此，我们研究了基于循环双谱的双频率二维表示的特征提取与智能诊断技术，将低阶循环平稳分析中的切片分析方法引入到高阶循环平稳分析之中。通过仿真和实验验证了，若选取合适的循环频率所得到的循环双谱的二维表示图谱更有特点。如当α=fn时，所得循环双谱切片图是一个关于中心频率f n成六边形的规则图谱。六边形的顶点与中心频率及故障特征频率之间有特定的关系。可以尝试由此处循环双谱切片进行故障信号特征提取，使高阶循环平稳分析结果更加直观。
由于循环双谱一次切片具有对称性，图谱上重复冗余信息比较多；另外，循环双谱特定频率下的一次切片谱是双频率轴的三维图谱，即便做成等高线图，对于故障特征的展示也不清晰和直接。在证明了循环双谱一次切片的有效性的基础上，本文尝试按照传统的双谱的分析方法，对特定循环频率α对应的循环双谱一次切片做进一步的切片，使其成为一个清晰的二维图谱。我们称最后得到的二维图谱为一个循环双谱的二次切片。
With the development of technology, rotating machinery possesses more and morecomplex structure, which asks for accurate operation situation to ensure long-term saferunning. As vital parts of rotating machinery, rolling element bearing plays a veryimportant role in the normal running of overall system. Their any deviation from thenormal situation that is caused by defects, no matter how light they are, will disturb therunning of connected components. Consequently, more components will be involved inand the performance of the system will deteriorate gradually together with a series of faults.Therefore, picking up fault characters of rolling element bearing as early as possibleguarantees the normal operation of overall system. But, it is not an easy task. Early faultsof them are weak, and fault information always buries under environment noise.Monitoring their occurrence and evolution is an arduous challenge. Parameters of rotatingmachinery are periodically time-varying, especially for those under failure situation.Periodical time-variance implies cyclostationarity. Therefore, studying the cyclostationarycharacters of rolling element bearing could clarify the fault essence and has easier access topicking up weak fault information.
To realize the early feature extraction of bearing faults, fault bearing signal model andcyclic statistics theories are investigated, the cyclostationary nature of bearing vibrationsignals is analyzed. Fault feature signal is separated from background noise and otherinterferences through the second order and third order cyclostationary analysis, thus theearly and weak fault signatures are identified objectively and effectively. The contents areas follows:
(1) The characteristics of incipient fault of rolling element bearing are analyzed, andits fault signal model is introduced. The signal model has two components, deterministicand random, whose frequency characteristics are studied: the deterministic part has discretespectrum while the random one has continuous spectrum. It is analyzed that the uncertaintyof impulse period, which is caused by variation of rotation speed or contact angle of rollingelements, can cause the decrease of discrete spectrum and make it very difficult tohighlight the fault characteristic frequency in power spectrum of rolling element bearings.
(2) Cyclostationary phenomena and basic concepts of cyclic statistics are brieflytalked about. Based on the theories of cyclic statistics, the second order cyclostationaryfeature is obtained for the rolling element bearing fault signal model. The methods basedon spectral correlation density function and cyclic autocorrelation function analysis forearly fault detecting of bearing is investigated. And both the methods are focus on thecyclic frequency-frequency plane or cyclic frequency-time lag plane.
(3) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. And statistical properties of the signals change periodically with time. Theaccurate analysis of time-varying signals is an essential pre-request for the fault diagnosisand hence safe operation of rolling element bearings. The Wigner distribution (WD) isprobably most widely used among the Cohen’s class in order to describe how the spectralcontent of a signal changes over time. However, the basic nature of such signals causessignificant interfering cross-terms, which do not permit a straightforward interpretation ofthe energy distribution. To overcome this difficulty, the Wigner-Ville distribution based onthe cyclic spectral density is discussed in this paper. It is shown that the improvedWigner-Ville distribution, which based on cyclic spectral density of a long time series, canrender the time-frequency distribution less susceptible to noise, and restrain the cross-termsin the time-frequency domain. Simulation and experiment of the rolling element bearingfault diagnosis are performed, and the results indicate the validity of the Wigner-Villedistribution based on cyclic spectral density in time-frequency analysis for bearing faultdetection.
(4) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. However, because the background noise is very heavy when the earlyfault occurs, it is difficult to disclose the latent periodic components successfully evenusing the second order cyclostationary analysis. To overcome this difficulty, the cyclicbispectrum (CBS), an alternative approach based on third-order cyclostationarity analysis,is discussed in this paper. Furthermore, the slice spectrum analysis of the CBS is proposed.
The CBS is a third-order cyclic statistical parameter, in the frequency domain. TheCBS gives full play to the advantage which is provided from the higher order cyclicstatistical methods. It can restrain noise and provide more information than classicalmethods such as amplitude spectrum analysis and envelope analysis when the fault at anearly stage. However, the CBS is four-dimensional. So, the Slices Spectrum Analysis of theCBS is introduced to fault diagnosis. According to the algorithm by C.T. Yiakopoulos andI.A. Antoniadis, the actual CBS analysis is a set of specific values for cyclic frequency α.And, each of them corresponds to a specific cyclic frequency α. We called each of them tothe once slice of the CBS. That is, the once slice of the CBS, which is3D structure, issliced along the cyclic frequency axis firstly. The CBS corresponding one cyclic frequencyis called the once slice of the CBS. Simulation and experiment of the rolling elementbearing fault diagnosis are performed, and the results indicate the feasibility and validity ofthe once slice of the CBS analysis in rolling element bearing early fault diagnosis.
However the information in the once slice is redundant and indirect for fault diagnosis.So the twice slice of the CBS, as the horizontal slice of the once slice (HSCBS), thevertical slice of the once slice (VSCBS) and the diagonal slice of the once slice (DSCBS), which is sliced along one frequency axis in the once slice is studied. By analysis, thehorizontal slice of the once slice of the CBS (HSCBS) which is at a special given cyclicfrequency is proposed to resolve the contradiction. Additionally, the less computation ofHSCBS is also appealing.
本文以实现滚动轴承早期故障特征提取为目的，针对旋转机械设备发生故障时具有循环平稳和非高斯的特点，通过研究基于二阶和三阶循环统计量的二维表示方法，有效实现旋转机械早期故障智能预示。研究内容如下：
(1)本文首先分析滚动轴承初期故障特点及类型，引入滚动轴承故障信号模型，将其分为确定性信号分量和随机信号分量，研究了其各自频谱特点：滚动轴承故障信号模型的确定性信号分量的频谱是离散频谱；而随机信号分量的功率谱密度函数是连续频谱。分析表明由于故障冲击周期的不严格确定（轴承转速的波动，滚动体接触角的改变等影响），滚动轴承故障信号频谱中的离散谱线会因此被连续频谱模糊，故障特征频率也就很难从信号的频谱中看到。
(2)根据滚动轴承等旋转机械设备关键部件的（正常/故障）振动信号具有明显的周期时变特征，采用二阶循环统计量理论（谱相关密度函数、谱相干函数）进行信号分析，做基于循环频率—频率二维表示的特征提取技术，在α f平面上有效提取噪声干扰下的早期微弱故障特征。
(3)由于时频分辨率、信号多分量导致的交叉项以及背景噪声的干扰等不利因素的影响，使时频二维表示得到的机械故障特征往往不够直观且对于故障早期诊断可靠性低。针对具有循环平稳特性的滚动轴承振动信号，本文研究了基于时间-频率二维信息的特征提取方法。尝试根据其谱相关密度函数与Wigner-Ville分布之间的函数关系，利用长数据序列计算得到循环谱密度重构Wigner-Ville分布。结果证明基于谱相关密度函数的Wigner-Ville分布可以极大削弱噪声对时频图的干扰，并且有很好的时频聚集性。
(4)在滚动轴承的早期故障监测过程中，由于微弱损伤激发的能量很小，易于淹没在背景噪声和较强的干扰之中，使得故障信息提取的难度加大，有时采用二阶循环统计量也不能有效地提取故障特征。因此采用的信号分析方法的抗噪性能显得尤为重要。理论上，在保证足够采样数据长度的情况下，高阶循环统计量对于任何高斯与非高斯噪声都是自然免疫的。
高阶循环统计量从实用的角度考虑，最常用的是三阶循环矩、三阶循环累积量、三阶循环矩谱、三阶循环累积量谱。本文重点研究了三阶循环累积量谱。三阶循环累积量谱，也称循环双谱，是含有三个参变量的多维函数。除了利用理论推导之外，用传统的谱分析表述方法很难将循环双谱表述清楚。若完整表述它则需要三根不同的频率轴——循环频率α轴、时延频率f1轴和时延频率f2轴，在传统的三维空间中无法完全表述其面貌。因此，我们研究了基于循环双谱的双频率二维表示的特征提取与智能诊断技术，将低阶循环平稳分析中的切片分析方法引入到高阶循环平稳分析之中。通过仿真和实验验证了，若选取合适的循环频率所得到的循环双谱的二维表示图谱更有特点。如当α=fn时，所得循环双谱切片图是一个关于中心频率f n成六边形的规则图谱。六边形的顶点与中心频率及故障特征频率之间有特定的关系。可以尝试由此处循环双谱切片进行故障信号特征提取，使高阶循环平稳分析结果更加直观。
由于循环双谱一次切片具有对称性，图谱上重复冗余信息比较多；另外，循环双谱特定频率下的一次切片谱是双频率轴的三维图谱，即便做成等高线图，对于故障特征的展示也不清晰和直接。在证明了循环双谱一次切片的有效性的基础上，本文尝试按照传统的双谱的分析方法，对特定循环频率α对应的循环双谱一次切片做进一步的切片，使其成为一个清晰的二维图谱。我们称最后得到的二维图谱为一个循环双谱的二次切片。
With the development of technology, rotating machinery possesses more and morecomplex structure, which asks for accurate operation situation to ensure long-term saferunning. As vital parts of rotating machinery, rolling element bearing plays a veryimportant role in the normal running of overall system. Their any deviation from thenormal situation that is caused by defects, no matter how light they are, will disturb therunning of connected components. Consequently, more components will be involved inand the performance of the system will deteriorate gradually together with a series of faults.Therefore, picking up fault characters of rolling element bearing as early as possibleguarantees the normal operation of overall system. But, it is not an easy task. Early faultsof them are weak, and fault information always buries under environment noise.Monitoring their occurrence and evolution is an arduous challenge. Parameters of rotatingmachinery are periodically time-varying, especially for those under failure situation.Periodical time-variance implies cyclostationarity. Therefore, studying the cyclostationarycharacters of rolling element bearing could clarify the fault essence and has easier access topicking up weak fault information.
To realize the early feature extraction of bearing faults, fault bearing signal model andcyclic statistics theories are investigated, the cyclostationary nature of bearing vibrationsignals is analyzed. Fault feature signal is separated from background noise and otherinterferences through the second order and third order cyclostationary analysis, thus theearly and weak fault signatures are identified objectively and effectively. The contents areas follows:
(1) The characteristics of incipient fault of rolling element bearing are analyzed, andits fault signal model is introduced. The signal model has two components, deterministicand random, whose frequency characteristics are studied: the deterministic part has discretespectrum while the random one has continuous spectrum. It is analyzed that the uncertaintyof impulse period, which is caused by variation of rotation speed or contact angle of rollingelements, can cause the decrease of discrete spectrum and make it very difficult tohighlight the fault characteristic frequency in power spectrum of rolling element bearings.
(2) Cyclostationary phenomena and basic concepts of cyclic statistics are brieflytalked about. Based on the theories of cyclic statistics, the second order cyclostationaryfeature is obtained for the rolling element bearing fault signal model. The methods basedon spectral correlation density function and cyclic autocorrelation function analysis forearly fault detecting of bearing is investigated. And both the methods are focus on thecyclic frequency-frequency plane or cyclic frequency-time lag plane.
(3) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. And statistical properties of the signals change periodically with time. Theaccurate analysis of time-varying signals is an essential pre-request for the fault diagnosisand hence safe operation of rolling element bearings. The Wigner distribution (WD) isprobably most widely used among the Cohen’s class in order to describe how the spectralcontent of a signal changes over time. However, the basic nature of such signals causessignificant interfering cross-terms, which do not permit a straightforward interpretation ofthe energy distribution. To overcome this difficulty, the Wigner-Ville distribution based onthe cyclic spectral density is discussed in this paper. It is shown that the improvedWigner-Ville distribution, which based on cyclic spectral density of a long time series, canrender the time-frequency distribution less susceptible to noise, and restrain the cross-termsin the time-frequency domain. Simulation and experiment of the rolling element bearingfault diagnosis are performed, and the results indicate the validity of the Wigner-Villedistribution based on cyclic spectral density in time-frequency analysis for bearing faultdetection.
(4) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. However, because the background noise is very heavy when the earlyfault occurs, it is difficult to disclose the latent periodic components successfully evenusing the second order cyclostationary analysis. To overcome this difficulty, the cyclicbispectrum (CBS), an alternative approach based on third-order cyclostationarity analysis,is discussed in this paper. Furthermore, the slice spectrum analysis of the CBS is proposed.
The CBS is a third-order cyclic statistical parameter, in the frequency domain. TheCBS gives full play to the advantage which is provided from the higher order cyclicstatistical methods. It can restrain noise and provide more information than classicalmethods such as amplitude spectrum analysis and envelope analysis when the fault at anearly stage. However, the CBS is four-dimensional. So, the Slices Spectrum Analysis of theCBS is introduced to fault diagnosis. According to the algorithm by C.T. Yiakopoulos andI.A. Antoniadis, the actual CBS analysis is a set of specific values for cyclic frequency α.And, each of them corresponds to a specific cyclic frequency α. We called each of them tothe once slice of the CBS. That is, the once slice of the CBS, which is3D structure, issliced along the cyclic frequency axis firstly. The CBS corresponding one cyclic frequencyis called the once slice of the CBS. Simulation and experiment of the rolling elementbearing fault diagnosis are performed, and the results indicate the feasibility and validity ofthe once slice of the CBS analysis in rolling element bearing early fault diagnosis.
However the information in the once slice is redundant and indirect for fault diagnosis.So the twice slice of the CBS, as the horizontal slice of the once slice (HSCBS), thevertical slice of the once slice (VSCBS) and the diagonal slice of the once slice (DSCBS), which is sliced along one frequency axis in the once slice is studied. By analysis, thehorizontal slice of the once slice of the CBS (HSCBS) which is at a special given cyclicfrequency is proposed to resolve the contradiction. Additionally, the less computation ofHSCBS is also appealing.
引文
[1]陈进.机械设备振动监测与故障诊断[M].上海:上海交通大学出版社,1999.
[2]亨利基尔,马任全,杨殿伦.滚动轴承故障分析[J].润滑与密封,1978,4):81-9.
[3]吴翘平.关于轴承松动故障的分析与排除[J].洪都科技,1980,1):22-4.
[4]王振华.滚动轴承运行状态的监测技术[J].轴承,1987,4):50-7.
[5]雷继尧,张思复,何世德.滚动轴承疲劳故障的在线监视和诊断技术[J].重庆大学学报（自然科学版）,1988,2):
[6] SUNNERSJ C S. Rolling bearing vibrations—The effects of geometricalimperfections and wear [J]. Journal of Sound and Vibration,1985,98(4):455-74.
[7] SUNNERSJO C S. Varying compliance vibrations of rolling bearings [J]. Journalof Sound and Vibration,1978,58(3):
[8] SU Y-T, LIN M-H, LEE M-S. The Effects of Surface Irregularities on RollerBearing Vibrations [J]. Journal of Sound and Vibration,1993,165(3):455-66.
[9] HOWARD I M: Department of Defence, Aeronautical and Maritime ResearchLaboratory,1994.
[10] MCFADDEN P D. Advances in the Vibration Monitoring of Gears and RollingElement Bearings; proceedings of the Institution of Engineers, Australia/RoyalAeronautical Society Joint National Symposium, F,1985[C].
[11] MCFADDEN P D, SMITH J D. Information from the vibration of rolling bearings;proceedings of the Condition Monitoring, F,1984[C].
[12] MCFADDEN P D, SMITH J D: Engineering Department, Cambridge University,1983.
[13] MCFADDEN P D, SMITH J D. Model for the vibration produced by a single pointdefect in a rolling element bearing [J]. Journal of Sound and Vibration,1984,96(1):69-82.
[14] TANDON N, CHOUDHURY A. A theoretical model to predict the vibrationresponse of rolling bearings in a rotor bearing system to distributed defects underradial load [J]. Journal of Tribology-Transactions of the Asme,2000,122(3):609-15.
[15] SOPANEN J T, MIKKOLA A M. Ball bearing vibration analysis includinglocalized and distributed defects; proceedings of the19th Biennial Conference onMechanical Vibration and Noise, F,2003[C].
[16] LI J C, MA J. Bearing localized defect detection through wavelet decomposition of机械系统与振动国家重点实验室127vibrations [J]. Sensors and Signal Processing for Manufacturing,1992,55(187-96.
[17] SHI L, RANDALL R B, ANTONI J. Rolling element bearing fault detection usingimproved envelope analysis [J]. Eighth International Conference on Vibrations inRotating Machinery (IMechE Conference Transactions2004-2),2004,
[18]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,2001.
[19]何正嘉,警艳阳,孟庆丰, et al.机械设备非平稳信号的故障诊断原理及应用
[M].北京:高等教育出版社,2001.
[20]闻邦椿,武新华,丁千, et al.故障旋转机械非线性动力学的理论与实验[M].北京:科学出版社.,2004.
[21]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[22]杨江天,陈家骥,曾子平.基于高阶谱的旋转机械故障征兆提取[J].振动工程学报,2001,14(1):13-7.
[23] COLLIS W B, WHITE P R, HAMMOND J K. Higher-order spectra: Thebispectrum and trispectrum [J]. Mechanical Systems and Signal Processing,1998,12(3):375-94.
[24] FONOLIOSA J R, NIKIAS C L. Wigner higher order moment spectra: definition,properties, computation and application to transient signal analysis [J]. IEEETransactions on Signal Processing,1993,41(1):
[25] LEE S K, WHITE P R. Higher-order time-frequency analysis and its application tofault detection in rotating machinery [J]. Mechanical Systems and SignalProcessing,1997,11(4):637-50.
[26] COHEN L. Time-frequency distributions-a review [J]. Proceedings of the IEEE,1989,77(7):
[27] QIAN S. Introduction to time-frequency and wavelet transforms [M]. Beijing:China Machine Press,2005.
[28]张晔.信号时频分析及应用[M].哈尔滨:哈尔滨工业大学出版社,2006.
[29] RIOUL O, VETTERLI M. Wavelets and signal processing [J]. IEEE SignalProcessing Magazine,1991,8(4):14-38.
[30]崔锦泰,程正兴.小波分析导论[M].西安:西安交通大学出版社,1995.
[31]李建平.小波分析与信号处理[M].重庆:重庆出版社,1997.
[32]范剑青,姚琦伟,陈敏.非线性时间序列[M].北京:高等教育出版社,2005.
[33]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征综合优化（续一）[J].机械研究与应用,1998,11(3):12-3.
[34]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征提取(一)[J].机械研究128机械系统与振动国家重点实验室与应用,1998,11(12):12-3.
[35]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征提取的研究[J].西安交通大学学报,1999,33(1):88-92.
[36]王海燕.非线性时间序列分析及其应用[M].北京:科学出版社,2006.
[37]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用综述[J].振动工程学报,2001,14(2):125-38.
[38]张严,王树勋.非线性相位耦合的切片谱分析方法[J].电子学报,1998,26(10):104-9.
[39]张严,王树勋,李生红.二次相位耦合的3/2维谱分析[J].电子学报,1996,24(4):109-12.
[40] KOIZUMI T, KISO M, TANIGUCHI R. Preventive maintenance for roller andjournal bearing of induction motor based on the diagnostic signature analysis [J].Journal of Vibration, Acoustics, Stress, and Reliability in Design,1986,108(26-30.
[41]陈进.机械故障诊断中关于特征提取的若干研究前沿[J].面向21世纪的中国振动工程研究-中国科协第30次“青年科学家论坛”报告文集,1999,110~22.
[42]丁玉兰,石来德.机械设备故障诊断技术[M].上海:上海科学技术文献出版社,1993.
[43]黄文虎,夏松波,刘瑞岩.设备故障诊断原理、技术及应用[M].北京:科学出版社.1996.
[44]徐敏.设备故障诊断手册[M].西安:西安交通大学出版社,1998.
[45] BADAOUI M E, ANTONI J, GUILLET F, et al. Use of the moving cepstrumintegral to detect and localise tooth spalls in gears [J]. Mechanical Systems andSignal Processing,2001,15(5):873-85.
[46] HARTING D R. Incipient failure detection by demodulated resonance analysisindustrial machines [J]. Instrumentation Technology,1977,24(9):
[47] MCFADDEN P D. Detection fatigue cracks in gears by amplitude and phasedemodulation of the meshing vibration [J]. Journal of Vibration, Acoustics, stressand Reliability in Design,1986,108(165-70.
[48] MCFADDEN P D, SMITH J D. Vibration monitoring of rolling element bearingsby the high-frequency resonance technique—A review [J]. Tribology International,1984,17(1):3-10.
[49]丁康,米林,王志杰.调制分析在故障诊断中应用的局限性问题[J].振动工程学报,1997,10(1):13-20.
[50]林京,刘红星.信号包络特征识别在故障诊断中的应用[J].振动测试与诊断,1998,18(1):34-8.
[51]郑晓溪,丁康,江利旗.希尔伯特变换解调分析在故障诊断中应用的局限性研究[J].汕头大学学报,1999,14(2):40-6.
[52] LOUGHLIN P J, BERNARD G D. Cohen-Posch (positive) time-frequencydistributions and their application to machine vibration analysis [J]. MechanicalSystems and Signal Processing,1997,11(4):561-76.
[53]王秉仁.希尔伯特变换在机械故障诊断中的应用[J].水利电力机械,2000,1):43-5.
[54] BRIE D, TOMCZAK M, OEHLMANN H, et al. GEAR CRACK DETECTION BYADAPTIVE AMPLITUDE AND PHASE DEMODULATION [J]. MechanicalSystems and Signal Processing,1997,11(1):149-67.
[55] SHEEN Y T. A complex filter for vibration signal demodulation in bearing defectdiagnosis [J]. Journal of Sound and Vibration,2004,276(1-2):105-19.
[56] WANG W Y. Early detection of gear tooth cracking using the resonancedemodulation technique [J]. Mechanical Systems and Signal Processing,2001,15(5):887-903.
[57] EDGAR G, CORD D,1984.
[58] KAISHNAPPA G. Gear fault detection parameter development based onmodulation techniques; proceedings of the Fifth International Congress on Soundand Vibration, F,1997[C].
[59] RRAUN S, DATNER B. Analysis of roller/ball bearing vibrations [J]. Journal ofMechanical Design,1979,101(118-25.
[60] DALPIAZ G, RIVOLA A. Condition monitoring and diagnostics in automaticmachines: Comparison of vibration analysis techniques [J]. Mechanical Systemsand Signal Processing,1997,11(1):53-73.
[61] MCFADDEN P D, COOK J G, FORSTER L M. Decomposition of gear vibrationsignals by the generalised S transform [J]. Mechanical Systems and SignalProcessing,1999,13(5):691-707.
[62] YA W, DU R. Feature extraction and assessment using wavelet packets formonitoring of machining processes [J]. Mechanical Systems and Signal Processing,1996,10(1):
[63]刘占生,武新华,夏松波.小波分析法在旋转机械故障诊断中的应用[J].汽轮机技术,1996,38(6):326-9.
[64]朱利民,钟秉林,贾民平.振动信号短时分析方法及在机械故障诊断中的应用[J].振动工程学报,2000,13(3):400-5.
[65] YOSHIDA A, OHUE Y, ISHIKAWA H. Diagnosis of tooth surface failure bywavelet transform of dynamic characteristics [J]. Tribology International,2000,33(3-4):273-9.
[66] BONATO P, CERAVOLO R, DESTEFANO A, et al. Bilinear time-frequencytransformations in the analysis of damaged structures [J]. Mechanical Systems andSignal Processing,1997,11(4):509-27.
[67] DALIANIS S A, HAMMOND J K. Time-frequency spectra forfrequency-modulated processes [J]. Mechanical Systems and Signal Processing,1997,11(4):621-35.
[68] STASZEWSKI W J, WORDEN K, TOMLINSON G R. Time-frequency analysis ingearbox fault detection using the Wigner-Ville distribution and pattern recognition[J]. Mechanical Systems and Signal Processing,1997,11(5):673-92.
[69] TANDON N, CHOUDHURY A. A review of vibration and acoustic measurementmethods for the detection of defects in rolling element bearings [J]. TribologyInternational,1999,32(8):469-80.
[70] LI C J, MA J. Wavelet decomposition of vibrations for detection ofbearing-localized defects [J]. NDT&E International,1997,30(3):143-9.
[71] OEHLMANN H, BRIE D, TOMCZAK M, et al. A method for analysing gearboxfaults using time-frequency representations [J]. Mechanical Systems and SignalProcessing,1997,11(4):529-45.
[72]胡劲松,杨世锡,周方洁.旋转机械振动信号基于EMD的HT和Winger分布时频分析比较[J].汽轮机技术,2003,45(5):307-9.
[73]沈松,应怀樵,刘进明.用小波变换识别机械故障中的通过振动[J].振动与冲击,1999,18(2):1-4.
[74] YANG D M, STRONACH A F, MACCONNELL P. The application of advancedsignal processing techniques to induction motor bearing condition diagnosis [J].Meccanica,2003,38(2):297-308.
[75]钱立军,蒋东翔.小波变换在横向裂纹转子升速过程状态监测中的应用[J].中国机电工程学报,2003,23(5):86-9.
[76]徐敏强,王日新,张嘉钟.基于梳状小波的旋转机械振动信号降噪方法的研究[J].振动工程学报,2003,15(1):90-2.
[77]钟掘,卓志红,杨平.包络-小波分析法用于滚动轴承故障诊断的研究[J].中国有色金属学报,1996,6(4):163-5.
[78] CHOUDHURY A, TANDON N. A theoretical model to predict vibration responseof rolling bearings to distributed defects under radial load [J]. Journal of Vibrationand Acoustics-Transactions of the Asme,1998,120(1):214-20.
[79] MCFADDEN P D, SMITH J D. The vibration produced by multiple point defectsin a rolling element bearing [J]. Journal of Sound and Vibration,1985,98(2):263-73.
[80] MCCORMICK A C. Cyclostationary and higher-order statistical sgianl processingalgorithms for machine condition monitoring [D]; University of Strathclyde,1998.
[81] MCCORMICK A C, NANDI A K. Cyclostationarity in rotating machine vibrations[J]. Mechanical Systems and Signal Processing,1998,12(2):225-42.
[82] ZHOU F C, CHEN J, HE J, et al. Fault early diagnosis of rolling element bearingscombining wavelet filtering and degree of cyclostationarity analysis [J]. Journal ofShanghai Jiaotong University (Science),2005,10E(4):446-8+55.
[83] ZHOU F C, CHEN J, HE J, et al. Cyclic statistics based neural network for earlyfault diagnosis of rolling element bearings [J]. Lecture Notes in Computer Science,2004,3174/2004(Advances in Neural Networks-ISNN2004):183-201.
[84]周福昌,陈进,何俊, et al.循环自相关函数的解调特性分析及其在故障诊断中的应用[J].振动工程学报,2004,17(280-3.
[85] JIANG M, CHEN J. Performance analysis of second-order statistics forcyclostationary signals [J]. Journal of Shanghai Jiaotong University (EnglishEdition),2002, E-7(2):
[86]姜鸣.循环统计量理论及其在滚动轴承故障诊断中的应用研究[D].上海;上海交通大学,2002.
[87]姜鸣,陈进,周福昌.一种改进的循环自相关函数分析方法; proceedings of the2002年全国振动（诊断、模态、噪声与结构动力学）工程及应用学术会议, F,2002
[C].
[88]李力,屈梁生.循环统计量方法在滚动轴承故障诊断中的应用[J].振动、测试与诊断,2003,23(2):116-9.
[89] JIANG M, CHEN J. Research on fault diagnosis of rolling element bearing basedon second-order cyclic statistics analysis; proceedings of the First InternationalWorkshop on Diagnosis, Analysis and Control of Vibration and Noise, F,2001[C].
[90] JIANG M, CHEN J, QIN K. A new method for rolling element bearing faultdiagnosis based on cyclostationary theory [J]. International Journal of PlantEngineering and Management,2001,6(3):136-42.
[91]姜鸣,陈进,秦恺.时变调幅信号的循环平稳特征[J].上海交通大学学报,2001,35(12):1798-801.
[92]姜鸣,陈进,秦恺.循环周期图在滚动轴承故障诊断中的应用[J].机械科学与技术,2002,21(1):108-10.
[93]姜鸣,陈进.循环自相关函数的解调性能分析[J].上海交通大学学报,2002,36(6):43-6.
[94]李力,屈梁生.二阶循环统计量在机械故障诊断中的应用[J].西安交通大学学报,2002,36(9):943-6.
[95]秦恺陈,姜鸣.一种滚动轴承故障特征提取的新方法——谱相关密度[J].振动与冲击,2001,20(1):34-7.
[96] LI L, QU L S. Cyclic statistics in rolling bearing diagnosis [J]. Journal of Soundand Vibration,2003,267(2):253-65.
[97]何俊,陈进,毕果, et al.循环自相关函数及其切片的解调原理分析[J].振动工程学报,2004,359-62.
[98]李力,屈梁生.循环域解调方法在滚动轴承故障诊断中的应用[J].轴承,2003,10):33-6.
[99] ANTONI J, RANDALL R B. A stochastic model for simulation and diagnostics ofrolling element bearings with localized faults [J]. Transactions of the ASMEJournal of Vibration and Acoustics,2003,125(3):
[100] HO D, RANDALL R B. Optimisation of bearing diagnostic techniques usingsimulated and actual bearing fault signals [J]. Mechanical Systems and SignalProcessing,2000,14(5):763-88.
[101] RANDALL R B, ANTONI J, CHOBSAARD S. A comparison of cyclostationaryand envelope analysis in the diagnostics of rolling element bearings; proceedings ofthe IEEE International Conference on Acoustics, Speech, and Signal Processing,Istanbul, Turkey, F,2000[C].
[102] RANDALL R B, ANTONI J, CHOBSAARD S. The relationship between spectralcorrelation and envelope analysis in the diagnostics of bearing faults and othercyclostationary machine signals [J]. Mechanical Systems and Signal Processing,2001,15(5):945-62.
[103] GARDNER W A. SPECTRAL CORRELATION THEORY OFCYCLOSTATIONARY TIME-SERIES [J]. Signal Processing,1986,11(1):13-36.
[104] GARDNER W A. Statistical spectral analysis: a non-probabilistic theory [M]. NewJersey: Prentice-Hall,1987.
[105] GARDNER W A. Rice's representation for cyclostationary processes [J]. IEEETransactions on Communications,1987, COM-35(1):
[106] GARDNER W A. Exploitation of spectral correlation in cyclostationary signals [J].Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling (CatNo88CH2633-6),1988,
[107] GARDNER W A, FRANKS L E. Characterization of cyclostationary random signalprocesses [J]. IEEE Transactions on Information Theory,1975, IT-21(1):
[108] ANTONI J, BONNARDOT F, RAAD A, et al. Cyclostationary modelling ofrotating machine vibration signals [J]. Mechanical Systems and Signal Processing,2004,18(6):1285-314.
[109] ANTONIADIS I, GLOSSIOTIS G. Cyclostationary analysis of rolling-elementbearing vibration signals [J]. Journal of Sound and Vibration,2001,248(5):829-45.
[110] BONNARDOT F, RANDALL R B, GUILLET F O. Extraction of second-ordercyclostationary sources-Application to vibration analysis [J]. Mechanical Systemsand Signal Processing,2005,19(6):1230-44.
[111] ANTONI J, RANDALL R B. Differential diagnosis of gear and bearing faults [J].Journal of Vibration and Acoustics,2002,124(2):165-71.
[112] ANTONI J, RANDALL R B. On the use of the cyclic power spectrum in rollingelement bearings diagnostics [J]. Journal of Sound and Vibration,2005,281(1-2):463-8.
[113]陈仲生,杨拥民,胡政, et al.基于循环统计量的直升机齿轮箱轴承故障早期检测[J].航空学报,2005,26(3):371-5.
[114] GARDNER W A. Introduction to random processing with applications to signalsand systems [M]. New York: McGraw-Hill,1990.
[115] SPOONER C M, GARDNER W A. The cumulant theory of cyclostationarytime-series. II. Development and applications [J]. IEEE Transactions on SignalProcessing,1994,42(12):
[116]沈凤麟,钱玉美.信号统计分析基础[M].合肥:中国科学技术出版社,1989.
[117] GARDNER W A. Stationarizable random processes [J]. IEEE Transactions onInformation Theory,1978,24(8-22.
[118] GARDNER W A. The spectral correlation theory of cyclostationary time-series [J].Signal Processing,1986,11(1):
[119] GARDNER W A. Spectral correlation of modulated signals. I. Analog modulation[J]. IEEE Transactions on Communications,1987, COM-35(6):
[120] GARDNER W A. Signal interception: a unifying theoretical framework for featuredetection [J]. IEEE Transactions on Communications,1988,36(8):
[121] BROWN W A. On the theory of cyclostationary signals [D]; Unversity ofCalifornia,1986.
[122] GARDNER W A, BROWN W A. Frequency-shift filtering theory for adaptiveco-channel interference removal [J]. Conference Record Twenty-Third AsilomarConference on Signals, Systems ands Computers (IEEE Cat No89-CH2836-5),1989,
[123] ZIVANOVIC G D, GARDNER W A. Degrees of cyclostationarity and theirapplication to signal detection and estimation [J]. Signal Processing,1991,22(3):
[124] HASSELMANN K, BARNETT T P. Techniques of linear prediction for systemswith periodic statistics [J]. Journal of the Atmospheric Sciences,1981,38(10):
[125] SKINNER B J, INGELS F M, DONOHOE J P, et al. STATIONARY ANDCYCLOSTATIONARY RANDOM PROCESS MODELS [M].1994.
[126] TIAO G C, GRUPE M R. Hidden periodic autoregressive-moving average modelsin time series data [J]. Biometrika,1980,67(2):
[127] TROUTMAN B M. Some results in periodic autoregression [J]. Biometrika,1979,66(2):219-28.
[128] AGEE B G, SCHELL S V, GARDNER W A. Spectral self-coherence restoral: anew approach to blind adaptive signal extraction using antenna arrays [J].Proceedings of the IEEE,1990,78(4):
[129] BOYLES R A, GARDNER W A. Cycloergodic properties of discrete-parameternonstationary stochastic processes [J]. IEEE Transactions on Information Theory,1983, IT-29(1):
[130] NEWTON H J. Using periodic autoregressions for multiple spectral estimation [J].Technometrics,1982,24(2):109-16.
[131] ADLARD J F. Frequency Shift Filtering for Cyclostationary Signals [D];University of York,2000.
[132] FREDERICK T J. Time-Frequency estimation for cyclostationary signals [D];Florida Atlantic University,1997.
[133]张贤达.现代信号处理[M].北京:清华大学出版社,1995.
[134] DANDAWATE A V, GIANNAKIS G B, JOHNS HOPKINS U. ERGODICITYRESULTS FOR NONSTATIONARY SIGNALS-CUMULANTS, AMBIGUITYFUNCTIONS AND WAVELETS [J]. Proceedings of the25th Annual Conferenceon Information Sciences and Systems,1991,976-83.
[135]王宏禹.非平稳随机信号分析与处理[M].北京:国防工业出版社,1999.
[136]张桂才史铁林,杨叔子.基于高阶统计量的机械故障特征提取方法研究[J].华中理工大学学报,1999,27(3):6-8.
[137] DANDAWATE A V, GIANNAKIS G B. Nonparametric identification of linear(almost) periodically time-varying systems using cyclic-polyspectra [J]. IEEE SixthSP Workshop on Statistical Signal and Array Processing Conference Proceedings(Cat No92TH0410-1),1992,
[138] DANDAWATE A V, GIANNAKIS G B. Nonparametric polyspectral estimators forkth-order (almost) cyclostationary processes [J]. IEEE Transactions on InformationTheory,1994,40(1):
[139] RANDALL R B, ANTONI J, CHOBSAARD S. The relationship between spectralcorrelation and envelope analysis in the diagnostics of bearing faults and othercyclostationary machine signals [J]. Mech Syst Signal Pr,2001,15(5):945-62.
[140]毕果,陈进,周福昌, et al.调幅信号谱相关密度分析中白噪声影响的研究[J].振动与冲击,2006,25(2):75-8.
[141] ANTONI J. Cyclic spectral analysis of rolling-element bearing signals: Facts andfictions [J]. Journal of Sound and Vibration,2007,304(3-5):497-529.
[142]董广明.滚动轴承早期局部冲击故障的特征提取方法研究[M].上海交通大学博士后研究出站报告,2009.
[143] ANTONI J. Cyclostationarity by examples [J]. Mech Syst Signal Pr,2009,23(4):987-1036.
[144] LI L, QU L S. Cyclic statistics in rolling bearing diagnosis [J]. Journal of Soundand Vibration,2003,267(2):253~65.
[145]何俊,陈进,毕果.循环平稳度解调频原理分析及其在齿轮故障诊断中的应用[J].上海交通大学学报,2007,41(11):1862-6.
[146]丁康,孔正国,何志达.振动调幅信号的循环平稳解调原理与应用[J].振动工程学报,2005,03):304-8.
[147] BI G, CHEN J, ZHOU F C, et al. Application of slice spectral correlation density togear defect detection [J]. P I Mech Eng C-J Mec,2006,220(9):1385-92.
[148]毕果,陈进,李富才, et al.谱相关密度分析在轴承点蚀故障诊断中的研究[J].振动工程学报,2006,19(3):388-93.
[149]周福昌,陈进,何俊, et al.基于小波滤波与循环平稳度分析的滚动轴承早期故障诊断方法[J].振动与冲击,2006,25(4):91-3.
[150]贾民平,杨建文.滚动轴承振动的周期平稳性分析及故障诊断[J].机械工程学报,2007,43(1):144-7.
[151]崔玲丽,高立新,蔡力钢, et al.基于循环平稳解调的齿轮裂纹早期故障诊断研究[J].振动工程学报,2008,03):274-8.
[152] CAPDESSUS C, SIDAHMED M, LACOUME J L. Cyclostationary processes:Application in gear faults early diagnosis [J]. Mech Syst Signal Pr,2000,14(3):371-85.
[153]毕果.基于循环平稳的滚动轴承及齿轮微弱故障特征提取应用研究[M].上海交通大学博士学位论文,2007.
[154] RAAD A, ANTONI J, SIDAHMED M. Indicators of cyclostationarity: Theory andapplication to gear fault monitoring [J]. Mech Syst Signal Pr,2008,22(3):574-87.
[155]商铁军,张文明,刘立, et al.齿轮局部损伤振动信号的循环平稳性分析[J].北京科技大学学报,2009,03):388-93.
[156] DONG G M, CHEN J. Study on Cyclic Energy Indicator for DegradationAssessment of Rolling Element Bearings [J]. J Vib Control,2010,(已录用)(
[157] SEJDIC E, DJUROVIC I, JIANG J. Time-frequency feature representation usingenergy concentration: An overview of recent advances [J]. Digit Signal Prog,2009,19(1):153-83.
[158]董广明.结构损伤全局检测若干方法研究及应用[M].上海交通大学博士学位论文,2007.
[159]邹剑,陈进,董广明.基于Wigner-Ville分布裂纹转子识别中的仿真[J].上海交通大学学报,2004,38(7):1207-10.
[160]赵发刚,陈进,董广明.匹配追踪在齿轮故障诊断中的应用[J].上海交通大学学报,2009,43(6):0910-3.
[161] LOUGHLIN P, CAKRAK F, COHEN L. Conditional moments analysis oftransients with application to helicopter fault data [J]. Mech Syst Signal Pr,2000,14(4):511-22.
[162] WANG C D, ZHANG Y Y, ZHONG Z Y. Fault diagnosis for diesel valve trainsbased on time-frequency images [J]. Mech Syst Signal Pr,2008,22(8):1981-93.
[163] BARANIUK R G, FLANDRIN P, JANSSEN A J E M, et al. Measuringtime-frequency information content using the Renyi entropies [J]. Ieee T InformTheory,2001,47(4):1391-409.
[164] CHO K, COATS D, ABRAMS J, et al. Applications of Time-Frequency Analysisfor Aging Aircraft Component Diagnostics and Prognostics-art. no.70740Y;proceedings of the Advanced Signal Processing Algorithms, Architectures, andImplementations Xviii, Proceedings of the Society of Photo-OpticalInstrumentation Engineers (Spie), F,2008[C].
[165] GRALL-MAES E, BEAUSEROY P. Mutual information-based feature extractionon the time-frequency plane [J]. Ieee T Signal Proces,2002,50(4):779-90.
[166] GARDNER W A. Introduction to random processes with applications to signalsand systems (Chapter12Cyclostationary processes)[M]. Second Edition ed.:McGraw-Hill, Inc,1990.
[167] GIANNAKIS G B. Digital Signal Processing Handbook (Chapter17Cyclostationary signal analysis)[M]. CRC Press&IEEE Press,1998.
[168] WILBUR J, BONO J. Wigner/cycle spectrum analysis of spread spectrum anddiversity transmissions [J]. IEEE Journal of Oceanic Engineering,1991,16(1):98-106.
[169] LALL B, JOSHI S D, BHATT R K P. Second-order statistical characterization ofthe filter bank and its elements [J]. Ieee T Signal Proces,1999,47(6):1745-9.
[170] WANG J D, CHEN T W, HUANG B. On spectral theory of cyclostationary signalsin multirate systems [J]. Ieee T Signal Proces,2005,53(7):2421-31.
[171] ANTONI J. Cyclic spectral analysis in practice [J]. Mech Syst Signal Pr,2007,21(2):597-630.
[172] DONG G, CHEN J, ZHAO F, et al. Comparative Study on Time FrequencyAnalysis of Rolling Element Bearing Signals for Fault Diagnosis; proceedings ofthe13th Asia Pacific Vibration Conference, University of Canterbury, New Zealand,F22-25November,2009[C].
[173] DONG G M, CHEN J, LEI X Y, et al. Global-based structure damage detectionusing LVQ neural network and bispectrum analysis [J]. Advances in NeuralNetworks-Isnn2005, Pt3, Proceedings,2005,3498(531-7.
[174]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用[J].振动工程学报,2001,02):125-34.
[175] BOUILLAUT L, SIDAHMED M. Cyclostationary approach and bilinear approach:Comparison, applications to early diagnosis for helicopter gearbox andclassification method based on hocs [J]. Mech Syst Signal Pr,2001,15(5):923-43.
[176]陈仲生.直升机旋转部件故障特征提取的高阶统计量方法研究[M].国防科学技术大学博士学位论文,2004.
[177] ZHU Z K, FENG Z H, KONG F R. Cyclostationarity analysis for gearboxcondition monitoring: Approaches and effectiveness [J]. Mech Syst Signal Pr,2005,19(3):467-82.
[178]夏天,王新晴,赵慧敏, et al.基于高阶循环平稳的柴油发动机曲轴轴承振动信号分析[J].内燃机学报,2009,06):552-6.
[179] YIAKOPOULOS C T, ANTONIADIS I A. Cyclic bispectrum patterns of defectiverolling element bearing vibration response [J]. Forschung im Ingenieurwesen,2005,70(2):90-104.
[180] ZHOU Y, CHEN J, DONG G M. Fault Diagnosis of Rolling Element BearingsBased on Cyclic Bispectrum; proceedings of the23rd International Congress onCondition Monitoring and Diagnostic Engineering Management, F,2010[C].
[181] GARDNER W A, NAPOLITANO A, PAURA L. Cyclostationarity: Half a centuryof research [J]. Signal Processing,2006,86(4):639-97.
[182] GARDNER W A. Measurement of Spectral Correlation，IEEE Trans. On Acoustic,Speech, and Signal Processing，1986,34:1111~1123
[183] Dandawate A.V. and Giannakis G.B. Asymptotic Theory of Mixed Time Averagesand Kth-Order Cyclic-Moment and Cumulant Statistics，IEEE Trans. OnInformation Theory，1995,41(1):216~232
[184] Hurd H.L. and Gerr N.L. Graphical Methods for Determining the PresenceProcesses，Journal of Time Series Analysis，1991,12(4):337~350
[185] Grossmann A., Morlet J. Decomposition of hardy functions into square integrablewavelets of constant shape, SIAM J. Math. Anal.,1984,15:723-736
[186] RAAD A. Sidahmed M. Estimation of cyclic bispectrum: Algorithms andApplications. SURVEILLANCE4. In:4thInternational Conference on Acoustical
and Vibratory Surveillance Methods and Diagnostic techniques. Compiegne,
France (2001)
[2]亨利基尔,马任全,杨殿伦.滚动轴承故障分析[J].润滑与密封,1978,4):81-9.
[3]吴翘平.关于轴承松动故障的分析与排除[J].洪都科技,1980,1):22-4.
[4]王振华.滚动轴承运行状态的监测技术[J].轴承,1987,4):50-7.
[5]雷继尧,张思复,何世德.滚动轴承疲劳故障的在线监视和诊断技术[J].重庆大学学报（自然科学版）,1988,2):
[6] SUNNERSJ C S. Rolling bearing vibrations—The effects of geometricalimperfections and wear [J]. Journal of Sound and Vibration,1985,98(4):455-74.
[7] SUNNERSJO C S. Varying compliance vibrations of rolling bearings [J]. Journalof Sound and Vibration,1978,58(3):
[8] SU Y-T, LIN M-H, LEE M-S. The Effects of Surface Irregularities on RollerBearing Vibrations [J]. Journal of Sound and Vibration,1993,165(3):455-66.
[9] HOWARD I M: Department of Defence, Aeronautical and Maritime ResearchLaboratory,1994.
[10] MCFADDEN P D. Advances in the Vibration Monitoring of Gears and RollingElement Bearings; proceedings of the Institution of Engineers, Australia/RoyalAeronautical Society Joint National Symposium, F,1985[C].
[11] MCFADDEN P D, SMITH J D. Information from the vibration of rolling bearings;proceedings of the Condition Monitoring, F,1984[C].
[12] MCFADDEN P D, SMITH J D: Engineering Department, Cambridge University,1983.
[13] MCFADDEN P D, SMITH J D. Model for the vibration produced by a single pointdefect in a rolling element bearing [J]. Journal of Sound and Vibration,1984,96(1):69-82.
[14] TANDON N, CHOUDHURY A. A theoretical model to predict the vibrationresponse of rolling bearings in a rotor bearing system to distributed defects underradial load [J]. Journal of Tribology-Transactions of the Asme,2000,122(3):609-15.
[15] SOPANEN J T, MIKKOLA A M. Ball bearing vibration analysis includinglocalized and distributed defects; proceedings of the19th Biennial Conference onMechanical Vibration and Noise, F,2003[C].
[16] LI J C, MA J. Bearing localized defect detection through wavelet decomposition of机械系统与振动国家重点实验室127vibrations [J]. Sensors and Signal Processing for Manufacturing,1992,55(187-96.
[17] SHI L, RANDALL R B, ANTONI J. Rolling element bearing fault detection usingimproved envelope analysis [J]. Eighth International Conference on Vibrations inRotating Machinery (IMechE Conference Transactions2004-2),2004,
[18]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,2001.
[19]何正嘉,警艳阳,孟庆丰, et al.机械设备非平稳信号的故障诊断原理及应用
[M].北京:高等教育出版社,2001.
[20]闻邦椿,武新华,丁千, et al.故障旋转机械非线性动力学的理论与实验[M].北京:科学出版社.,2004.
[21]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[22]杨江天,陈家骥,曾子平.基于高阶谱的旋转机械故障征兆提取[J].振动工程学报,2001,14(1):13-7.
[23] COLLIS W B, WHITE P R, HAMMOND J K. Higher-order spectra: Thebispectrum and trispectrum [J]. Mechanical Systems and Signal Processing,1998,12(3):375-94.
[24] FONOLIOSA J R, NIKIAS C L. Wigner higher order moment spectra: definition,properties, computation and application to transient signal analysis [J]. IEEETransactions on Signal Processing,1993,41(1):
[25] LEE S K, WHITE P R. Higher-order time-frequency analysis and its application tofault detection in rotating machinery [J]. Mechanical Systems and SignalProcessing,1997,11(4):637-50.
[26] COHEN L. Time-frequency distributions-a review [J]. Proceedings of the IEEE,1989,77(7):
[27] QIAN S. Introduction to time-frequency and wavelet transforms [M]. Beijing:China Machine Press,2005.
[28]张晔.信号时频分析及应用[M].哈尔滨:哈尔滨工业大学出版社,2006.
[29] RIOUL O, VETTERLI M. Wavelets and signal processing [J]. IEEE SignalProcessing Magazine,1991,8(4):14-38.
[30]崔锦泰,程正兴.小波分析导论[M].西安:西安交通大学出版社,1995.
[31]李建平.小波分析与信号处理[M].重庆:重庆出版社,1997.
[32]范剑青,姚琦伟,陈敏.非线性时间序列[M].北京:高等教育出版社,2005.
[33]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征综合优化（续一）[J].机械研究与应用,1998,11(3):12-3.
[34]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征提取(一)[J].机械研究128机械系统与振动国家重点实验室与应用,1998,11(12):12-3.
[35]苏文斌,史维祥,温熙森.故障诊断中非线性耦合特征提取的研究[J].西安交通大学学报,1999,33(1):88-92.
[36]王海燕.非线性时间序列分析及其应用[M].北京:科学出版社,2006.
[37]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用综述[J].振动工程学报,2001,14(2):125-38.
[38]张严,王树勋.非线性相位耦合的切片谱分析方法[J].电子学报,1998,26(10):104-9.
[39]张严,王树勋,李生红.二次相位耦合的3/2维谱分析[J].电子学报,1996,24(4):109-12.
[40] KOIZUMI T, KISO M, TANIGUCHI R. Preventive maintenance for roller andjournal bearing of induction motor based on the diagnostic signature analysis [J].Journal of Vibration, Acoustics, Stress, and Reliability in Design,1986,108(26-30.
[41]陈进.机械故障诊断中关于特征提取的若干研究前沿[J].面向21世纪的中国振动工程研究-中国科协第30次“青年科学家论坛”报告文集,1999,110~22.
[42]丁玉兰,石来德.机械设备故障诊断技术[M].上海:上海科学技术文献出版社,1993.
[43]黄文虎,夏松波,刘瑞岩.设备故障诊断原理、技术及应用[M].北京:科学出版社.1996.
[44]徐敏.设备故障诊断手册[M].西安:西安交通大学出版社,1998.
[45] BADAOUI M E, ANTONI J, GUILLET F, et al. Use of the moving cepstrumintegral to detect and localise tooth spalls in gears [J]. Mechanical Systems andSignal Processing,2001,15(5):873-85.
[46] HARTING D R. Incipient failure detection by demodulated resonance analysisindustrial machines [J]. Instrumentation Technology,1977,24(9):
[47] MCFADDEN P D. Detection fatigue cracks in gears by amplitude and phasedemodulation of the meshing vibration [J]. Journal of Vibration, Acoustics, stressand Reliability in Design,1986,108(165-70.
[48] MCFADDEN P D, SMITH J D. Vibration monitoring of rolling element bearingsby the high-frequency resonance technique—A review [J]. Tribology International,1984,17(1):3-10.
[49]丁康,米林,王志杰.调制分析在故障诊断中应用的局限性问题[J].振动工程学报,1997,10(1):13-20.
[50]林京,刘红星.信号包络特征识别在故障诊断中的应用[J].振动测试与诊断,1998,18(1):34-8.
[51]郑晓溪,丁康,江利旗.希尔伯特变换解调分析在故障诊断中应用的局限性研究[J].汕头大学学报,1999,14(2):40-6.
[52] LOUGHLIN P J, BERNARD G D. Cohen-Posch (positive) time-frequencydistributions and their application to machine vibration analysis [J]. MechanicalSystems and Signal Processing,1997,11(4):561-76.
[53]王秉仁.希尔伯特变换在机械故障诊断中的应用[J].水利电力机械,2000,1):43-5.
[54] BRIE D, TOMCZAK M, OEHLMANN H, et al. GEAR CRACK DETECTION BYADAPTIVE AMPLITUDE AND PHASE DEMODULATION [J]. MechanicalSystems and Signal Processing,1997,11(1):149-67.
[55] SHEEN Y T. A complex filter for vibration signal demodulation in bearing defectdiagnosis [J]. Journal of Sound and Vibration,2004,276(1-2):105-19.
[56] WANG W Y. Early detection of gear tooth cracking using the resonancedemodulation technique [J]. Mechanical Systems and Signal Processing,2001,15(5):887-903.
[57] EDGAR G, CORD D,1984.
[58] KAISHNAPPA G. Gear fault detection parameter development based onmodulation techniques; proceedings of the Fifth International Congress on Soundand Vibration, F,1997[C].
[59] RRAUN S, DATNER B. Analysis of roller/ball bearing vibrations [J]. Journal ofMechanical Design,1979,101(118-25.
[60] DALPIAZ G, RIVOLA A. Condition monitoring and diagnostics in automaticmachines: Comparison of vibration analysis techniques [J]. Mechanical Systemsand Signal Processing,1997,11(1):53-73.
[61] MCFADDEN P D, COOK J G, FORSTER L M. Decomposition of gear vibrationsignals by the generalised S transform [J]. Mechanical Systems and SignalProcessing,1999,13(5):691-707.
[62] YA W, DU R. Feature extraction and assessment using wavelet packets formonitoring of machining processes [J]. Mechanical Systems and Signal Processing,1996,10(1):
[63]刘占生,武新华,夏松波.小波分析法在旋转机械故障诊断中的应用[J].汽轮机技术,1996,38(6):326-9.
[64]朱利民,钟秉林,贾民平.振动信号短时分析方法及在机械故障诊断中的应用[J].振动工程学报,2000,13(3):400-5.
[65] YOSHIDA A, OHUE Y, ISHIKAWA H. Diagnosis of tooth surface failure bywavelet transform of dynamic characteristics [J]. Tribology International,2000,33(3-4):273-9.
[66] BONATO P, CERAVOLO R, DESTEFANO A, et al. Bilinear time-frequencytransformations in the analysis of damaged structures [J]. Mechanical Systems andSignal Processing,1997,11(4):509-27.
[67] DALIANIS S A, HAMMOND J K. Time-frequency spectra forfrequency-modulated processes [J]. Mechanical Systems and Signal Processing,1997,11(4):621-35.
[68] STASZEWSKI W J, WORDEN K, TOMLINSON G R. Time-frequency analysis ingearbox fault detection using the Wigner-Ville distribution and pattern recognition[J]. Mechanical Systems and Signal Processing,1997,11(5):673-92.
[69] TANDON N, CHOUDHURY A. A review of vibration and acoustic measurementmethods for the detection of defects in rolling element bearings [J]. TribologyInternational,1999,32(8):469-80.
[70] LI C J, MA J. Wavelet decomposition of vibrations for detection ofbearing-localized defects [J]. NDT&E International,1997,30(3):143-9.
[71] OEHLMANN H, BRIE D, TOMCZAK M, et al. A method for analysing gearboxfaults using time-frequency representations [J]. Mechanical Systems and SignalProcessing,1997,11(4):529-45.
[72]胡劲松,杨世锡,周方洁.旋转机械振动信号基于EMD的HT和Winger分布时频分析比较[J].汽轮机技术,2003,45(5):307-9.
[73]沈松,应怀樵,刘进明.用小波变换识别机械故障中的通过振动[J].振动与冲击,1999,18(2):1-4.
[74] YANG D M, STRONACH A F, MACCONNELL P. The application of advancedsignal processing techniques to induction motor bearing condition diagnosis [J].Meccanica,2003,38(2):297-308.
[75]钱立军,蒋东翔.小波变换在横向裂纹转子升速过程状态监测中的应用[J].中国机电工程学报,2003,23(5):86-9.
[76]徐敏强,王日新,张嘉钟.基于梳状小波的旋转机械振动信号降噪方法的研究[J].振动工程学报,2003,15(1):90-2.
[77]钟掘,卓志红,杨平.包络-小波分析法用于滚动轴承故障诊断的研究[J].中国有色金属学报,1996,6(4):163-5.
[78] CHOUDHURY A, TANDON N. A theoretical model to predict vibration responseof rolling bearings to distributed defects under radial load [J]. Journal of Vibrationand Acoustics-Transactions of the Asme,1998,120(1):214-20.
[79] MCFADDEN P D, SMITH J D. The vibration produced by multiple point defectsin a rolling element bearing [J]. Journal of Sound and Vibration,1985,98(2):263-73.
[80] MCCORMICK A C. Cyclostationary and higher-order statistical sgianl processingalgorithms for machine condition monitoring [D]; University of Strathclyde,1998.
[81] MCCORMICK A C, NANDI A K. Cyclostationarity in rotating machine vibrations[J]. Mechanical Systems and Signal Processing,1998,12(2):225-42.
[82] ZHOU F C, CHEN J, HE J, et al. Fault early diagnosis of rolling element bearingscombining wavelet filtering and degree of cyclostationarity analysis [J]. Journal ofShanghai Jiaotong University (Science),2005,10E(4):446-8+55.
[83] ZHOU F C, CHEN J, HE J, et al. Cyclic statistics based neural network for earlyfault diagnosis of rolling element bearings [J]. Lecture Notes in Computer Science,2004,3174/2004(Advances in Neural Networks-ISNN2004):183-201.
[84]周福昌,陈进,何俊, et al.循环自相关函数的解调特性分析及其在故障诊断中的应用[J].振动工程学报,2004,17(280-3.
[85] JIANG M, CHEN J. Performance analysis of second-order statistics forcyclostationary signals [J]. Journal of Shanghai Jiaotong University (EnglishEdition),2002, E-7(2):
[86]姜鸣.循环统计量理论及其在滚动轴承故障诊断中的应用研究[D].上海;上海交通大学,2002.
[87]姜鸣,陈进,周福昌.一种改进的循环自相关函数分析方法; proceedings of the2002年全国振动（诊断、模态、噪声与结构动力学）工程及应用学术会议, F,2002
[C].
[88]李力,屈梁生.循环统计量方法在滚动轴承故障诊断中的应用[J].振动、测试与诊断,2003,23(2):116-9.
[89] JIANG M, CHEN J. Research on fault diagnosis of rolling element bearing basedon second-order cyclic statistics analysis; proceedings of the First InternationalWorkshop on Diagnosis, Analysis and Control of Vibration and Noise, F,2001[C].
[90] JIANG M, CHEN J, QIN K. A new method for rolling element bearing faultdiagnosis based on cyclostationary theory [J]. International Journal of PlantEngineering and Management,2001,6(3):136-42.
[91]姜鸣,陈进,秦恺.时变调幅信号的循环平稳特征[J].上海交通大学学报,2001,35(12):1798-801.
[92]姜鸣,陈进,秦恺.循环周期图在滚动轴承故障诊断中的应用[J].机械科学与技术,2002,21(1):108-10.
[93]姜鸣,陈进.循环自相关函数的解调性能分析[J].上海交通大学学报,2002,36(6):43-6.
[94]李力,屈梁生.二阶循环统计量在机械故障诊断中的应用[J].西安交通大学学报,2002,36(9):943-6.
[95]秦恺陈,姜鸣.一种滚动轴承故障特征提取的新方法——谱相关密度[J].振动与冲击,2001,20(1):34-7.
[96] LI L, QU L S. Cyclic statistics in rolling bearing diagnosis [J]. Journal of Soundand Vibration,2003,267(2):253-65.
[97]何俊,陈进,毕果, et al.循环自相关函数及其切片的解调原理分析[J].振动工程学报,2004,359-62.
[98]李力,屈梁生.循环域解调方法在滚动轴承故障诊断中的应用[J].轴承,2003,10):33-6.
[99] ANTONI J, RANDALL R B. A stochastic model for simulation and diagnostics ofrolling element bearings with localized faults [J]. Transactions of the ASMEJournal of Vibration and Acoustics,2003,125(3):
[100] HO D, RANDALL R B. Optimisation of bearing diagnostic techniques usingsimulated and actual bearing fault signals [J]. Mechanical Systems and SignalProcessing,2000,14(5):763-88.
[101] RANDALL R B, ANTONI J, CHOBSAARD S. A comparison of cyclostationaryand envelope analysis in the diagnostics of rolling element bearings; proceedings ofthe IEEE International Conference on Acoustics, Speech, and Signal Processing,Istanbul, Turkey, F,2000[C].
[102] RANDALL R B, ANTONI J, CHOBSAARD S. The relationship between spectralcorrelation and envelope analysis in the diagnostics of bearing faults and othercyclostationary machine signals [J]. Mechanical Systems and Signal Processing,2001,15(5):945-62.
[103] GARDNER W A. SPECTRAL CORRELATION THEORY OFCYCLOSTATIONARY TIME-SERIES [J]. Signal Processing,1986,11(1):13-36.
[104] GARDNER W A. Statistical spectral analysis: a non-probabilistic theory [M]. NewJersey: Prentice-Hall,1987.
[105] GARDNER W A. Rice's representation for cyclostationary processes [J]. IEEETransactions on Communications,1987, COM-35(1):
[106] GARDNER W A. Exploitation of spectral correlation in cyclostationary signals [J].Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling (CatNo88CH2633-6),1988,
[107] GARDNER W A, FRANKS L E. Characterization of cyclostationary random signalprocesses [J]. IEEE Transactions on Information Theory,1975, IT-21(1):
[108] ANTONI J, BONNARDOT F, RAAD A, et al. Cyclostationary modelling ofrotating machine vibration signals [J]. Mechanical Systems and Signal Processing,2004,18(6):1285-314.
[109] ANTONIADIS I, GLOSSIOTIS G. Cyclostationary analysis of rolling-elementbearing vibration signals [J]. Journal of Sound and Vibration,2001,248(5):829-45.
[110] BONNARDOT F, RANDALL R B, GUILLET F O. Extraction of second-ordercyclostationary sources-Application to vibration analysis [J]. Mechanical Systemsand Signal Processing,2005,19(6):1230-44.
[111] ANTONI J, RANDALL R B. Differential diagnosis of gear and bearing faults [J].Journal of Vibration and Acoustics,2002,124(2):165-71.
[112] ANTONI J, RANDALL R B. On the use of the cyclic power spectrum in rollingelement bearings diagnostics [J]. Journal of Sound and Vibration,2005,281(1-2):463-8.
[113]陈仲生,杨拥民,胡政, et al.基于循环统计量的直升机齿轮箱轴承故障早期检测[J].航空学报,2005,26(3):371-5.
[114] GARDNER W A. Introduction to random processing with applications to signalsand systems [M]. New York: McGraw-Hill,1990.
[115] SPOONER C M, GARDNER W A. The cumulant theory of cyclostationarytime-series. II. Development and applications [J]. IEEE Transactions on SignalProcessing,1994,42(12):
[116]沈凤麟,钱玉美.信号统计分析基础[M].合肥:中国科学技术出版社,1989.
[117] GARDNER W A. Stationarizable random processes [J]. IEEE Transactions onInformation Theory,1978,24(8-22.
[118] GARDNER W A. The spectral correlation theory of cyclostationary time-series [J].Signal Processing,1986,11(1):
[119] GARDNER W A. Spectral correlation of modulated signals. I. Analog modulation[J]. IEEE Transactions on Communications,1987, COM-35(6):
[120] GARDNER W A. Signal interception: a unifying theoretical framework for featuredetection [J]. IEEE Transactions on Communications,1988,36(8):
[121] BROWN W A. On the theory of cyclostationary signals [D]; Unversity ofCalifornia,1986.
[122] GARDNER W A, BROWN W A. Frequency-shift filtering theory for adaptiveco-channel interference removal [J]. Conference Record Twenty-Third AsilomarConference on Signals, Systems ands Computers (IEEE Cat No89-CH2836-5),1989,
[123] ZIVANOVIC G D, GARDNER W A. Degrees of cyclostationarity and theirapplication to signal detection and estimation [J]. Signal Processing,1991,22(3):
[124] HASSELMANN K, BARNETT T P. Techniques of linear prediction for systemswith periodic statistics [J]. Journal of the Atmospheric Sciences,1981,38(10):
[125] SKINNER B J, INGELS F M, DONOHOE J P, et al. STATIONARY ANDCYCLOSTATIONARY RANDOM PROCESS MODELS [M].1994.
[126] TIAO G C, GRUPE M R. Hidden periodic autoregressive-moving average modelsin time series data [J]. Biometrika,1980,67(2):
[127] TROUTMAN B M. Some results in periodic autoregression [J]. Biometrika,1979,66(2):219-28.
[128] AGEE B G, SCHELL S V, GARDNER W A. Spectral self-coherence restoral: anew approach to blind adaptive signal extraction using antenna arrays [J].Proceedings of the IEEE,1990,78(4):
[129] BOYLES R A, GARDNER W A. Cycloergodic properties of discrete-parameternonstationary stochastic processes [J]. IEEE Transactions on Information Theory,1983, IT-29(1):
[130] NEWTON H J. Using periodic autoregressions for multiple spectral estimation [J].Technometrics,1982,24(2):109-16.
[131] ADLARD J F. Frequency Shift Filtering for Cyclostationary Signals [D];University of York,2000.
[132] FREDERICK T J. Time-Frequency estimation for cyclostationary signals [D];Florida Atlantic University,1997.
[133]张贤达.现代信号处理[M].北京:清华大学出版社,1995.
[134] DANDAWATE A V, GIANNAKIS G B, JOHNS HOPKINS U. ERGODICITYRESULTS FOR NONSTATIONARY SIGNALS-CUMULANTS, AMBIGUITYFUNCTIONS AND WAVELETS [J]. Proceedings of the25th Annual Conferenceon Information Sciences and Systems,1991,976-83.
[135]王宏禹.非平稳随机信号分析与处理[M].北京:国防工业出版社,1999.
[136]张桂才史铁林,杨叔子.基于高阶统计量的机械故障特征提取方法研究[J].华中理工大学学报,1999,27(3):6-8.
[137] DANDAWATE A V, GIANNAKIS G B. Nonparametric identification of linear(almost) periodically time-varying systems using cyclic-polyspectra [J]. IEEE SixthSP Workshop on Statistical Signal and Array Processing Conference Proceedings(Cat No92TH0410-1),1992,
[138] DANDAWATE A V, GIANNAKIS G B. Nonparametric polyspectral estimators forkth-order (almost) cyclostationary processes [J]. IEEE Transactions on InformationTheory,1994,40(1):
[139] RANDALL R B, ANTONI J, CHOBSAARD S. The relationship between spectralcorrelation and envelope analysis in the diagnostics of bearing faults and othercyclostationary machine signals [J]. Mech Syst Signal Pr,2001,15(5):945-62.
[140]毕果,陈进,周福昌, et al.调幅信号谱相关密度分析中白噪声影响的研究[J].振动与冲击,2006,25(2):75-8.
[141] ANTONI J. Cyclic spectral analysis of rolling-element bearing signals: Facts andfictions [J]. Journal of Sound and Vibration,2007,304(3-5):497-529.
[142]董广明.滚动轴承早期局部冲击故障的特征提取方法研究[M].上海交通大学博士后研究出站报告,2009.
[143] ANTONI J. Cyclostationarity by examples [J]. Mech Syst Signal Pr,2009,23(4):987-1036.
[144] LI L, QU L S. Cyclic statistics in rolling bearing diagnosis [J]. Journal of Soundand Vibration,2003,267(2):253~65.
[145]何俊,陈进,毕果.循环平稳度解调频原理分析及其在齿轮故障诊断中的应用[J].上海交通大学学报,2007,41(11):1862-6.
[146]丁康,孔正国,何志达.振动调幅信号的循环平稳解调原理与应用[J].振动工程学报,2005,03):304-8.
[147] BI G, CHEN J, ZHOU F C, et al. Application of slice spectral correlation density togear defect detection [J]. P I Mech Eng C-J Mec,2006,220(9):1385-92.
[148]毕果,陈进,李富才, et al.谱相关密度分析在轴承点蚀故障诊断中的研究[J].振动工程学报,2006,19(3):388-93.
[149]周福昌,陈进,何俊, et al.基于小波滤波与循环平稳度分析的滚动轴承早期故障诊断方法[J].振动与冲击,2006,25(4):91-3.
[150]贾民平,杨建文.滚动轴承振动的周期平稳性分析及故障诊断[J].机械工程学报,2007,43(1):144-7.
[151]崔玲丽,高立新,蔡力钢, et al.基于循环平稳解调的齿轮裂纹早期故障诊断研究[J].振动工程学报,2008,03):274-8.
[152] CAPDESSUS C, SIDAHMED M, LACOUME J L. Cyclostationary processes:Application in gear faults early diagnosis [J]. Mech Syst Signal Pr,2000,14(3):371-85.
[153]毕果.基于循环平稳的滚动轴承及齿轮微弱故障特征提取应用研究[M].上海交通大学博士学位论文,2007.
[154] RAAD A, ANTONI J, SIDAHMED M. Indicators of cyclostationarity: Theory andapplication to gear fault monitoring [J]. Mech Syst Signal Pr,2008,22(3):574-87.
[155]商铁军,张文明,刘立, et al.齿轮局部损伤振动信号的循环平稳性分析[J].北京科技大学学报,2009,03):388-93.
[156] DONG G M, CHEN J. Study on Cyclic Energy Indicator for DegradationAssessment of Rolling Element Bearings [J]. J Vib Control,2010,(已录用)(
[157] SEJDIC E, DJUROVIC I, JIANG J. Time-frequency feature representation usingenergy concentration: An overview of recent advances [J]. Digit Signal Prog,2009,19(1):153-83.
[158]董广明.结构损伤全局检测若干方法研究及应用[M].上海交通大学博士学位论文,2007.
[159]邹剑,陈进,董广明.基于Wigner-Ville分布裂纹转子识别中的仿真[J].上海交通大学学报,2004,38(7):1207-10.
[160]赵发刚,陈进,董广明.匹配追踪在齿轮故障诊断中的应用[J].上海交通大学学报,2009,43(6):0910-3.
[161] LOUGHLIN P, CAKRAK F, COHEN L. Conditional moments analysis oftransients with application to helicopter fault data [J]. Mech Syst Signal Pr,2000,14(4):511-22.
[162] WANG C D, ZHANG Y Y, ZHONG Z Y. Fault diagnosis for diesel valve trainsbased on time-frequency images [J]. Mech Syst Signal Pr,2008,22(8):1981-93.
[163] BARANIUK R G, FLANDRIN P, JANSSEN A J E M, et al. Measuringtime-frequency information content using the Renyi entropies [J]. Ieee T InformTheory,2001,47(4):1391-409.
[164] CHO K, COATS D, ABRAMS J, et al. Applications of Time-Frequency Analysisfor Aging Aircraft Component Diagnostics and Prognostics-art. no.70740Y;proceedings of the Advanced Signal Processing Algorithms, Architectures, andImplementations Xviii, Proceedings of the Society of Photo-OpticalInstrumentation Engineers (Spie), F,2008[C].
[165] GRALL-MAES E, BEAUSEROY P. Mutual information-based feature extractionon the time-frequency plane [J]. Ieee T Signal Proces,2002,50(4):779-90.
[166] GARDNER W A. Introduction to random processes with applications to signalsand systems (Chapter12Cyclostationary processes)[M]. Second Edition ed.:McGraw-Hill, Inc,1990.
[167] GIANNAKIS G B. Digital Signal Processing Handbook (Chapter17Cyclostationary signal analysis)[M]. CRC Press&IEEE Press,1998.
[168] WILBUR J, BONO J. Wigner/cycle spectrum analysis of spread spectrum anddiversity transmissions [J]. IEEE Journal of Oceanic Engineering,1991,16(1):98-106.
[169] LALL B, JOSHI S D, BHATT R K P. Second-order statistical characterization ofthe filter bank and its elements [J]. Ieee T Signal Proces,1999,47(6):1745-9.
[170] WANG J D, CHEN T W, HUANG B. On spectral theory of cyclostationary signalsin multirate systems [J]. Ieee T Signal Proces,2005,53(7):2421-31.
[171] ANTONI J. Cyclic spectral analysis in practice [J]. Mech Syst Signal Pr,2007,21(2):597-630.
[172] DONG G, CHEN J, ZHAO F, et al. Comparative Study on Time FrequencyAnalysis of Rolling Element Bearing Signals for Fault Diagnosis; proceedings ofthe13th Asia Pacific Vibration Conference, University of Canterbury, New Zealand,F22-25November,2009[C].
[173] DONG G M, CHEN J, LEI X Y, et al. Global-based structure damage detectionusing LVQ neural network and bispectrum analysis [J]. Advances in NeuralNetworks-Isnn2005, Pt3, Proceedings,2005,3498(531-7.
[174]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用[J].振动工程学报,2001,02):125-34.
[175] BOUILLAUT L, SIDAHMED M. Cyclostationary approach and bilinear approach:Comparison, applications to early diagnosis for helicopter gearbox andclassification method based on hocs [J]. Mech Syst Signal Pr,2001,15(5):923-43.
[176]陈仲生.直升机旋转部件故障特征提取的高阶统计量方法研究[M].国防科学技术大学博士学位论文,2004.
[177] ZHU Z K, FENG Z H, KONG F R. Cyclostationarity analysis for gearboxcondition monitoring: Approaches and effectiveness [J]. Mech Syst Signal Pr,2005,19(3):467-82.
[178]夏天,王新晴,赵慧敏, et al.基于高阶循环平稳的柴油发动机曲轴轴承振动信号分析[J].内燃机学报,2009,06):552-6.
[179] YIAKOPOULOS C T, ANTONIADIS I A. Cyclic bispectrum patterns of defectiverolling element bearing vibration response [J]. Forschung im Ingenieurwesen,2005,70(2):90-104.
[180] ZHOU Y, CHEN J, DONG G M. Fault Diagnosis of Rolling Element BearingsBased on Cyclic Bispectrum; proceedings of the23rd International Congress onCondition Monitoring and Diagnostic Engineering Management, F,2010[C].
[181] GARDNER W A, NAPOLITANO A, PAURA L. Cyclostationarity: Half a centuryof research [J]. Signal Processing,2006,86(4):639-97.
[182] GARDNER W A. Measurement of Spectral Correlation，IEEE Trans. On Acoustic,Speech, and Signal Processing，1986,34:1111~1123
[183] Dandawate A.V. and Giannakis G.B. Asymptotic Theory of Mixed Time Averagesand Kth-Order Cyclic-Moment and Cumulant Statistics，IEEE Trans. OnInformation Theory，1995,41(1):216~232
[184] Hurd H.L. and Gerr N.L. Graphical Methods for Determining the PresenceProcesses，Journal of Time Series Analysis，1991,12(4):337~350
[185] Grossmann A., Morlet J. Decomposition of hardy functions into square integrablewavelets of constant shape, SIAM J. Math. Anal.,1984,15:723-736
[186] RAAD A. Sidahmed M. Estimation of cyclic bispectrum: Algorithms andApplications. SURVEILLANCE4. In:4thInternational Conference on Acoustical
and Vibratory Surveillance Methods and Diagnostic techniques. Compiegne,
France (2001)
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