李康强等：迭代生成微分方程分解方法研究 ·1583· ted gear fault of planetary gearboxes.Proc CSEE,2013,33(2): FM representations:An asymptotically exact approach.IEEE T 118 Audio Speech Language Process,2007,15(3):823 (冯志鹏，褚福磊.行星齿轮箱齿轮分布式故障振动频谱特 [9]Gianfelici F,Turchetti C,Crippa P.Multicomponent AM-FM de- 征.中国电机工程学报，2013,33(2)：118) modulation:the state of the art after the development of the itera- [2]Feng Z P,Zhao LL,Chu F L.Frequency demodulation analysis ted Hilbert transform /IEEE International Conference on Signal for fault diagnosis of planetary gearboxes.Proe CSEE,2013,33 Processing and Communications.Dubai,2007:1471 (8):107 [10]Qin Y,Ren B.Li N,et al.An improved iterative Hilbert trans- (冯志鹏，赵镭镭，褚福磊.行星齿轮箱故障诊断的频率解调 form and its application to rolling bearing fault diagnosis.J Vib 分析方法.中国电机工程学报，2013,33(8)：107) Shock,2013,32(11):83 [3] Feng Z P,Zhao LL,Chu F L.Vibration spectral characteristics (秦毅，任兵，李宁，等.改进的迭代希尔伯特变换及滚动轴 of localized gear fault of planetary gearboxes.Proc CSEE,2013, 承故障诊断应用.振动与冲击，2013,32(11)：83) 33(5):119 [11] Qin Y.Multicomponent AM-FM demodulation based on energy (冯志鹏，赵镭镭，褚福磊。行星齿轮箱齿轮局部故障振动频 separation and adaptive filtering.Mech Syst Signal Process, 谱特征.中国电机工程学报，2013,33(5)：119) 2013,38(2):440 [4]Huang N E,Shen Z,Long S R,et al.The empirical mode de- [12]Tang G J.Pang B.Research on mechanical fault diagnosis based composition and the Hilbert spectrum for non-linear and non-sta- on iterated energy operator.China Measur Text Technol,2016, tionary time series anaysis.Proc R Soc Lond A,1998.454:903 42(3):85 [5]Feldman M.Time-varying vibration decomposition and analysis (唐贵基，庞彬.迭代能量算子机械故障诊断研究.中国测 based on the Hilbert transform.J Sound Vib,2006,295(3-5): 试，2016,42(3)：85) 518 [13]Zayezdny A,Druckmann I.A new method of signal description [6]Feldman M.Theoretical analysis and comparison of the Hilbert and its applications to signal processing.Signal Process,1991, transform decomposition methods.Mech Syst Signal Process, 22(2):153 2008,22(3):509 [14]Zayezdny A,Tiunov S.Extrapolation of time series by their [7]Braun S,Feldman M.Decomposition of non-stationary signals into structural properties.Signal Process,1993,32(3):285 varying time scales:some aspects of the EMD and HVD methods. [15]Zayezdny A.Tiunov S,Bronstein A.Extrapolation of real-time Mech Syst Signal Process,2011,25(7):2608 processes by their structural properties.Signal Process,1994,38 [8]Gianfelici F,Biagetti G.Crippa P,et al.Multicomponent AM- (2):231李康强等: 迭代生成微分方程分解方法研究 ted gear fault of planetary gearboxes. Proc CSEE, 2013, 33(2): 118 (冯志鹏, 褚福磊. 行星齿轮箱齿轮分布式故障振动频谱特 征. 中国电机工程学报, 2013, 33(2): 118) [2] Feng Z P, Zhao L L, Chu F L. Frequency demodulation analysis for fault diagnosis of planetary gearboxes. Proc CSEE, 2013, 33 (8): 107 (冯志鹏, 赵镭镭, 褚福磊. 行星齿轮箱故障诊断的频率解调 分析方法. 中国电机工程学报, 2013, 33(8): 107) [3] Feng Z P, Zhao L L, Chu F L. Vibration spectral characteristics of localized gear fault of planetary gearboxes. Proc CSEE, 2013, 33(5): 119 (冯志鹏, 赵镭镭, 褚福磊. 行星齿轮箱齿轮局部故障振动频 谱特征. 中国电机工程学报, 2013, 33(5): 119) [4] Huang N E, Shen Z, Long S R, et al. The empirical mode de鄄 composition and the Hilbert spectrum for non鄄linear and non鄄sta鄄 tionary time series anaysis. Proc R Soc Lond A, 1998, 454: 903 [5] Feldman M. Time鄄varying vibration decomposition and analysis based on the Hilbert transform. J Sound Vib, 2006, 295 (3鄄5): 518 [6] Feldman M. Theoretical analysis and comparison of the Hilbert transform decomposition methods. Mech Syst Signal Process, 2008, 22(3): 509 [7] Braun S, Feldman M. Decomposition of non鄄stationary signals into varying time scales: some aspects of the EMD and HVD methods. Mech Syst Signal Process, 2011, 25(7): 2608 [8] Gianfelici F, Biagetti G, Crippa P, et al. Multicomponent AM鄄鄄 FM representations: An asymptotically exact approach. IEEE T Audio Speech Language Process, 2007, 15(3): 823 [9] Gianfelici F, Turchetti C, Crippa P. Multicomponent AM鄄鄄FM de鄄 modulation: the state of the art after the development of the itera鄄 ted Hilbert transform / / IEEE International Conference on Signal Processing and Communications. Dubai, 2007: 1471 [10] Qin Y, Ren B, Li N, et al. An improved iterative Hilbert trans鄄 form and its application to rolling bearing fault diagnosis. J Vib Shock, 2013, 32(11): 83 (秦毅, 任兵, 李宁, 等. 改进的迭代希尔伯特变换及滚动轴 承故障诊断应用. 振动与冲击, 2013, 32(11): 83) [11] Qin Y. Multicomponent AM鄄鄄 FM demodulation based on energy separation and adaptive filtering. Mech Syst Signal Process, 2013, 38(2): 440 [12] Tang G J, Pang B. Research on mechanical fault diagnosis based on iterated energy operator. China Measur Text Technol, 2016, 42(3): 85 (唐贵基, 庞彬. 迭代能量算子机械故障诊断研究. 中国测 试, 2016, 42(3):85) [13] Zayezdny A, Druckmann I. A new method of signal description and its applications to signal processing. Signal Process, 1991, 22(2): 153 [14] Zayezdny A, Tiunov S. Extrapolation of time series by their structural properties. Signal Process, 1993, 32(3): 285 [15] Zayezdny A, Tiunov S, Bronstein A. Extrapolation of real鄄time processes by their structural properties. Signal Process, 1994, 38 (2): 231 ·1583·