基于时间—小波能量谱及交叉小波变换的振动信号分析
|
摘要
振动信号分析是对旋转机械进行故障诊断的最主要途径,由于受各种因素影响,如工况变化和设备自身故障等,振动信号中一般都含有非平稳成分。这些非平稳成分往往都包含有丰富的故障信息,因此,对这部分信号分析就显得非常重要。在许多分析方法中,Fourier变换是使用最为普遍也最为成熟的一种,遗憾的是它对非平稳信号的分析能力有限,不能很好地揭示非平稳信号所包含的信息。短时Fourier变换的出现为解决这个问题提供了一个好的开始,但由于其基函数的变换窗口固定不变,在一定程度上限制了非平稳信号的分析。相比较而言,小波变换在非平稳信号分析中具有独特优点。本论文的主要内容是在小波变换理论基础上,提出时间-小波能量谱及交叉小波变换两种信号处理方法,并将它们分别用于齿轮、滚动轴承故障诊断及水轮机振动信号分析。
冲击信号发生的频率信息是诊断齿轮、滚动轴承故障的重要依据之一,通过对齿轮、滚动轴承等故障机理研究,在小波变换理论的基础之上提出了时间-小波能量谱分析方法。运用时间-小波能量谱对缺齿、磨损等齿轮故障信号及外圈、内圈、滚珠等滚动轴承故障信号进行分析,并将分析结果与传统的包络解调分析及Hilbert-Huang变换的结果进行对比。结果表明:时间-小波能量频谱能够有效的提取出其他分析方法无法提取的故障特性信息,在齿轮、滚动轴承等故障诊断中取得了很好的分析结果。
水压脉动是影响水力发电机组振动的主要因素之一,分析水压脉动与机组振动之间的相关性对于研究水压脉动对机组振动的影响机理具有重要意义。基于小波变换理论的交叉小波变换是一种在时频空间中分析两个信号相关性的分析方法。论文中将交叉小波变换用于分析水轮机导轴承振动和尾水管出口、蜗壳进口、顶盖下等三处典型水压脉动之间的相关性,并将分析结果与传统的互相关分析进行对比。结果表明:交叉小波变换能够提取出不同水压脉动对机组振动的影响的频率成分及时间信息,而互相关分析无法达到这样的分析效果。
Fault diagnostics is useful for ensuring the safe running of rotating machines and vibration signal analysis has been widely used for fault diagnostics. Various kinds of factors, such as the change of the environment and the faults from the machine itself, often make the vibration signal of the running machine contain non-stationary components. So it is important to analyze the non-stationary signals. Among many signal processing methods, the most common tool utilized in real-signal applications is the Fourier transform(FT) which decomposes a given signal into its frequency components. Unfortunately, this technique requires that a signal to be examined is stationary, i.e. without time-evolution of the frequency content. FT-based methods are not suitable for non-stationary signal analysis, with an intermittent and changing frequency pattern. The limitation of the Fourier analysis can be partly resolved by using a short-time Fourier transform(STFT). One critical limitation of the STFT appears when windowing the signal mainly due to the violation of the uncertainty principle. More precisely, if the window is too narrow, the frequency resolution will be poor, whereas if the window is too wide, the time localization will be less precise. So STFT is not suitable for analyzing signals involving different scales or range of frequencies. Compared with the STFT, the wavelet transform has many distinct advantages for vibration signal analysis. Time-wavelet Spectrum analysis and Cross-wavelet Transform based on the wavelet transform theory are brought out. The main aim of the present dissertation is to extract the feature information of the gear and bearing fault by using time-wavelet spectrum analysis and analyze the vibration signal of hydraulic turbine by using cross-wavelet transform.
The impulses in vibration signals and their spectral features are important in diagnosing localized damage of gear and bearing. A new method, so called time-wavelet energy spectrum which is based on the theory of wavelet transform, is proposed for gear and bearing fault diagnosis. It can extract the feature of impulses in both time domain and frequency domain. It is applied to analyze the vibration signals of a gearbox under worn and broken statuses and bearing with outer ring fault, inner ring fault and ball fault. Envelope-demodulation analysis and Hilbert-Huang tranform are also used to analyze those signals. The result shows that the time-wavelet energy spectrum is more effective in extracting the impulse features produced by gear and bearing damage than other methods of signal processing.
Hydaulic pressure fluctuation is one of major factors influencing the vibration of hydraulic turbines. Correlation analysis of the hydaulic pressure fluctuation and the turbine vibration is important to reveal the hydaulic pressure fluctuation induced vibration. Cross-wavelet transform based on the wavelet theory is used to analyze the two signals’correlation in time-frequency domain. In this dissertation, cross-wavelet transform is used to analyze the vibration at water turbine guide bearing and the hydaulic pressure fluctuation at draft tube, spiral case and headcover in time-frequency joint domain. The time-frequency correlation between the vibration and the hydaulic pressure fluctuation are extracted. The traditional cross-correlation analysis is also used to analyze those signals. The result shows that cross-wavelet transform can extract not only the time information but also the frequency information of the correlation of two signals, which the traditional cross-correlation analysis cannot.
冲击信号发生的频率信息是诊断齿轮、滚动轴承故障的重要依据之一,通过对齿轮、滚动轴承等故障机理研究,在小波变换理论的基础之上提出了时间-小波能量谱分析方法。运用时间-小波能量谱对缺齿、磨损等齿轮故障信号及外圈、内圈、滚珠等滚动轴承故障信号进行分析,并将分析结果与传统的包络解调分析及Hilbert-Huang变换的结果进行对比。结果表明:时间-小波能量频谱能够有效的提取出其他分析方法无法提取的故障特性信息,在齿轮、滚动轴承等故障诊断中取得了很好的分析结果。
水压脉动是影响水力发电机组振动的主要因素之一,分析水压脉动与机组振动之间的相关性对于研究水压脉动对机组振动的影响机理具有重要意义。基于小波变换理论的交叉小波变换是一种在时频空间中分析两个信号相关性的分析方法。论文中将交叉小波变换用于分析水轮机导轴承振动和尾水管出口、蜗壳进口、顶盖下等三处典型水压脉动之间的相关性,并将分析结果与传统的互相关分析进行对比。结果表明:交叉小波变换能够提取出不同水压脉动对机组振动的影响的频率成分及时间信息,而互相关分析无法达到这样的分析效果。
Fault diagnostics is useful for ensuring the safe running of rotating machines and vibration signal analysis has been widely used for fault diagnostics. Various kinds of factors, such as the change of the environment and the faults from the machine itself, often make the vibration signal of the running machine contain non-stationary components. So it is important to analyze the non-stationary signals. Among many signal processing methods, the most common tool utilized in real-signal applications is the Fourier transform(FT) which decomposes a given signal into its frequency components. Unfortunately, this technique requires that a signal to be examined is stationary, i.e. without time-evolution of the frequency content. FT-based methods are not suitable for non-stationary signal analysis, with an intermittent and changing frequency pattern. The limitation of the Fourier analysis can be partly resolved by using a short-time Fourier transform(STFT). One critical limitation of the STFT appears when windowing the signal mainly due to the violation of the uncertainty principle. More precisely, if the window is too narrow, the frequency resolution will be poor, whereas if the window is too wide, the time localization will be less precise. So STFT is not suitable for analyzing signals involving different scales or range of frequencies. Compared with the STFT, the wavelet transform has many distinct advantages for vibration signal analysis. Time-wavelet Spectrum analysis and Cross-wavelet Transform based on the wavelet transform theory are brought out. The main aim of the present dissertation is to extract the feature information of the gear and bearing fault by using time-wavelet spectrum analysis and analyze the vibration signal of hydraulic turbine by using cross-wavelet transform.
The impulses in vibration signals and their spectral features are important in diagnosing localized damage of gear and bearing. A new method, so called time-wavelet energy spectrum which is based on the theory of wavelet transform, is proposed for gear and bearing fault diagnosis. It can extract the feature of impulses in both time domain and frequency domain. It is applied to analyze the vibration signals of a gearbox under worn and broken statuses and bearing with outer ring fault, inner ring fault and ball fault. Envelope-demodulation analysis and Hilbert-Huang tranform are also used to analyze those signals. The result shows that the time-wavelet energy spectrum is more effective in extracting the impulse features produced by gear and bearing damage than other methods of signal processing.
Hydaulic pressure fluctuation is one of major factors influencing the vibration of hydraulic turbines. Correlation analysis of the hydaulic pressure fluctuation and the turbine vibration is important to reveal the hydaulic pressure fluctuation induced vibration. Cross-wavelet transform based on the wavelet theory is used to analyze the two signals’correlation in time-frequency domain. In this dissertation, cross-wavelet transform is used to analyze the vibration at water turbine guide bearing and the hydaulic pressure fluctuation at draft tube, spiral case and headcover in time-frequency joint domain. The time-frequency correlation between the vibration and the hydaulic pressure fluctuation are extracted. The traditional cross-correlation analysis is also used to analyze those signals. The result shows that cross-wavelet transform can extract not only the time information but also the frequency information of the correlation of two signals, which the traditional cross-correlation analysis cannot.
引文
[1]虞和济.故障诊断的基本原理.北京:冶金工业出版社,1989
[2]黄文虎,夏松波,刘瑞岩.设备故障诊断原理、技术及应用.北京:科学出版社,1996
[3]郝如江.声发射和形态学方法在滚动轴承故障诊断中的应用:[博士学位论文].北京:清华大学精密仪器与机械学系,2008
[4]钟秉林,黄仁.机械故障诊断学.北京:机械工业出版社,2007
[5]张新明.声发射技术在滚动轴承故障诊断中的应用:[硕士学位论文].北京:清华大学精密仪器与机械学系,2006
[6]成琼.基于小波分析的齿轮故障诊断研究:[硕士学位论文].湖南:湖南大学,2001
[7]王万岗,吴广宁,雷栋.水轮机振动在线监测系统设计.仪表技术与传感器,2009,7:36-38
[8]王庆禹.小波分析在故障诊断及状态监测中应用研究:[硕士学位论文].北京:清华大学精密仪器与机械学系,2000
[9]李国华,张永忠.机械故障诊断.北京:化学工业出版社,1999
[10]寇惠,原培新.故障诊断中的振动信号处理.北京:冶金工业出版社,1989
[11]李力.机械信号处理及其应用.湖北:华中科技大学出版社,2007
[12]徐科军.信号分析与处理.北京:清华大学出版社,2006
[13]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1988
[14]寿海飞.基于小波分析的齿轮故障诊断研究:[硕士学位论文].浙江:浙江工业大学,2007
[15] Russell P C, Cosgrave J, Tomtsis, et al. Extraction of information from acoustic vibration signals using Gabor transform type devices. Measurement Science and Technology. 1998, 9(8):1282-1290
[16] Brie D, Oehlmann H, Vogt M, et al. Application of the local smoothed pseudo-Wigner-Ville distribution to gear tooth vibration signature analysis. Applied Signal Processing. 1997, 4(3): 168~78
[17] Wang W J, McFadden P D. Application of wavelets to gearbox vibration signals for fault detection. Journal of Sound and Vibration. 1996, 192(5):927-939
[18] Ma J. A neural network approach to real-time pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence. 2001, 15(6):937-947
[19] Kang S L, Zhang H Z. Detection and localization of turbine-generator bearing vibration using wavelet neural network. Proceedings of the 2009 IEEE International Conference onMechatronics and Automation. 2009:4414-4418
[20] Wang W J, Mcfadden P D. Application of orthogonal wavelets to early gear damage dedection. Mechanical Systems and Signal Processing. 1995, 9(5):497-507
[21] Rafiee J, Rafiee M A, Tse P W. Application of mother wavelet functions for automatic gear and bearing fault diagnosis. Expert Systems with Applications. 2010, 37(6):4568-4579
[22] Saravanan N, Ramachandran K I. Incipient gear box fault diagnosis using discrete wavelet transform for feature extraction and classification using artificial neural network. Expert Systems with Applications. 2010, 37(6):4168-4181
[23] Fan Xianfeng, Zuo M J. Gearbox fault detection using Hilbert and wavelet packet transform. Mechanical Systems and Signal Processing. 2006, 20(4): 966-982
[24] Staszewski W J, Worden K, Tomlinson G R. Time–frequency analysis in gearbox fault detection using the Wigner–Ville distribution and pattern recognition. Mechanical Systems and Signal Processing. 1997, 11(5): 673-692
[25] Rai V K, Mohanty A R. Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform. Mechanical Systems and Signal Processing, 2007, 21(6): 2607-2615
[26] Sawalhi N, Randall R B, Endo H. The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis. Mechanical Systems and Signal Processing, 2007, 21(6):2616-2633
[27] Zareia J, Poshtan J. Bearing fault detection using wavelet packet transform of induction motor stator current. Tribology International. 2007, 40(5):763-769
[28] Yang H, Mathew J, Ma L. Fault diagnosis of rolling element bearings using basis pursuit. Mechanical Systems and Signal Processing. 2005, 19(2):341-356
[29]赵婷.基于小波分析的机械振动故障分析:[硕士学位论文].辽宁:沈阳工业大学,2008
[30]周洋.小波分析在旋转机械振动信号监测和故障诊断中的应用研究:[硕士学位论文].上海:同济大学,2007
[31]潘罗平,周叶,唐封,等.水轮发电机组状态监测技术的现状及展望.水电站机电技术,2008,31(6):1-7
[32]冯志鹏,刘立,张文明.基于小波时频框架分解方法的滚动轴承故障诊断.振动与冲击,2008,27(2):110-114
[33] Feng Z P, Chu F L. Application of atomic decomposition to gear damage detection. Journal of Sound and Vibration, 2007, 302:138-151
[34]郝如江,卢文秀,褚福磊.滚动轴承故障信号的多尺度形态学分析.机械工程学报,2008,44(11):160-165
[35]郝如江,卢文秀,褚福磊.形态滤波器用于滚动轴承故障信号的特征提取.中国机械工程,2009,20(2):197-201
[36]彭志科.小波分析在旋转设备故障诊断中的应用:[博士学位论文].北京:清华大学精密仪器与机械学系,2002
[37]王晓冬,何正嘉,訾艳阳.滚动轴承故障诊断的多小波谱峭度方法.西安交通大学学报,2010,44(3):77-81
[38]孟庆丰,蒋晓玲,何正嘉,等.滚动轴承和齿轮故障的时频域识别.重型机械,1998,1:57-62
[39]丁锋,何正嘉,张新运.小波包分析在滚动轴承信号消噪处理中的应用.西安工业学院学报,2006,26(1):8-12
[40] Cheng J, Yang Y, Yu D. The envelope order spectrum based on generalized demodulation time–frequency analysis and its application to gear fault diagnosis. Mechanical Systems and Signal Processing. 2010, 24(2): 508-521
[41]于德介,程军圣,杨宇. Hilbert-Huang变换在齿轮故障诊断中的应用.机械工程学报, 2005,41(6):102-107
[42]刘坚,彭富强,于德介.基于线调频小波路径追踪阶比跟踪算法的齿轮箱故障诊断研究.机械工程学报,2009,45(7):81-86
[43]杨宇,于德介,程军圣.基于Hilbert边际谱的滚动轴承故障诊断方法.振动与冲击,2005,24(1):70-72
[44]程军圣,于德介,杨宇,等.尺度-小波能量谱在滚动轴承故障诊断中的应用.振动工程学报,2004,17(1):82-85
[45] Zheng H, Li Z,Chen X. Gear fault diagnosis based on continuous wavelet transform. Mechanical Systems and Signal Processing. 2002, 16(2-3):447-457
[46]郑海波,李志远,陈心昭.基于连续小波变换的齿轮故障诊断方法研究.机械工程学报,2002,38(3):69-73
[47]冯志鹏,朱萍玉,刘立,等.基追踪在齿轮损伤识别中的应用.北京科技大学学报,2008,30(1):84-89
[48]来五星,轩建平,史铁林,等. Wigner-Ville时频分布研究及其在齿轮故障诊断中的应用.振动工程学报,2003,16(2):247-250
[49]冯志鹏,褚福磊.基于Hilbert-Huang变换的水轮机非平稳压力脉动信号分析.中国电机工程学报,2005,25(10):111-115
[50]韩凤琴,陈林刚,桂中华,等.基于小波包提取尾水管水压脉动特征的研究.水电能源科学,2005,23(1):31-33
[51]吴子英,李郁侠,刘宏昭,等.短时傅立叶变换在大型水轮发电机组振动分析中的应用.水力发电学报,2005,24(6):115-120
[52]贺志龙,常黎.小波分析在水电机组状态检测中的应用研究.华中电力,2003,2(16):4-6
[53]胡广书.数字信号处理:理论、算法与实现.北京:清华大学出版社,2003
[54]郑君里,应启珩,杨为理.信号与系统(上册).北京:高等教育出版社,2009
[55]李德葆,陆秋海.工程振动试验分析.北京:清华大学出版社,2004
[56] Pan M C, Sas P. Transient analysis on machinery condition monitoring. International Conference on Signal Processing Proceeding ICSP. 1996, 2:1723-1726
[57]褚福磊,彭志科,冯志鹏,等.机械故障诊断中的现代信号处理方法.北京:科学出版社,2009
[58]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法.北京:科学出版社,2006
[59]杨福生.小波变换的工程分析与应用.北京:科学出版社,1999
[60]张德丰. MATLAB与小波分析.北京:机械工业出版社,2009
[61]林京,屈梁生.基于连续小波变换的信号检测技术与故障诊断.机械工程学报, 2000,36(12):95–100
[62] Daubechies I. Where do wavelet come from?-A person point of view. Proceeding of the IEEE. 1996, 84(4):510-513
[63] Polikar R. The story of wavelets. IMACS/IEEE CSCC. 1999, 5481-5786
[64]程正兴.小波分析算法与应用.西安:西安交通大学出版社,1998
[65] Boulahbal D, Farid G M, Ismail F. Amplitude and phase wavelet maps for thedetection of cracks in geared systems. Mechanical Systems and Signal Processing. 1999, 13(3):423-436
[66] Lin J, Qu L S. Feature extraction based on Morlet wavelet and its application formechanical fault diagnosis. Journal of Sound and Vibration. 2000, 234(1):135-148
[67]何正嘉,訾艳阳,张周锁,等.大型机械设备变工况非平稳动态分析与监测诊断关键技术.中国机械工程,1999,10(9):978-981
[68] Ruiz D, Nougues J M, Calderon Z, et al. Neural network based framework forfault diagnosis in batch chemical plants. Computers and Chemical Engineering. 2000, 24(2):777-784
[69] Donoho D L, Johnson I M. Ideal Spatial Adaptaion via Wavelet Shrinkage. Biometrika. 1994, 81:428~455
[70] Altmann J, Mathew J. Multiple band-pass autoregressive demodulation forrolling-element bearing fault diagnosis. Mechanical Systems and Signal Processing. 2001, 15(5):963-977
[71]徐敏强,王日新,张嘉钟.基于梳妆小波的旋转机械振动信号降噪方法的研究.振动工程学报,2002,15(1):90-93
[72]马元奎,陆颂元.小波分解及嵌入式小波系数零树编码在振动数据压缩中的应用研究.汽轮机技术, 2001,43(02):87-92
[73]任震,何建军,黄雯莹,等.基于小波包算法的电机故障信号的压缩和重构.中国电机工程学报,2001,21(1):25-29
[74] Robertson A N, Park K C, Alvin K F. Identification of structural dynamics modelsusing wavelet-generated impulse response data. Journal of Vibration andAcoustics, Transactions of the ASME. 1998, 120(1):261-266
[75]郑兆昌.机械振动(上册).清华大学工程力学系,1978
[76]程军圣,于德介,邓乾旺,等.时间-小波能量谱在滚动轴承诊断中的应用.振动与冲击,2004,23(2):34-36
[77] Peng Z K, Chu F L. Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography. Mechanical Systems and Signal Processing. 2004, (18):199-221
[78] Gennaro D M, Stefano S, Maria C C, et al. Cross-correlation time-frequency analysis for multiple EMG signals in Parkinson’s disease: a wavelet approach. Medical Engineering & Physics. 2003, 25:361–369
[79] Jan F A. River flow forecasting using wavelet and cross-wavelet transform models. Hydrological Process. 2008, 22:4877–4891
[80] Jordan D A, Hajj M R, Tieleman H W. Wavelet analysis of the relation between atmospheric wind and pressure fluctuations on a low-rise building. Journal of Wind Engineering and Industrial Aercodynamics. 1997, 69-71:647-655
[81] Horodko L. Identification Of Rotating Pressure Waves in a Centrifugal Compressor Diffuser by Means of The Wavelet Cross-Correlation. International Journal of Wavelets, Multiresolution and Information Processing. 2006, 4(2):373-382
[82] Kyprianou A, Staszewski W J. On The Cross Wavelet Analysis of Duffing Oscillator. Journal of Sound and Vibration. 1999, 228(1):199-210
[83]孙卫国,程炳岩.交叉小波变换在区域气候分析中的应用.应用气象学报,2008,19(4):479-487
[84]南峰,李有利,张宏升.新疆玛纳斯河径流波动与北大西洋涛动的关系.北京大学学报(自然科学版),2006,42(4):534-541
[85]洪梅,张韧等.基于交叉小波与小波相干分析对影响“0801暴雪”的副热带高压的时延相关分析.中国气象学会2008年年会极端天气气候事件与应急气象服务分会场论文集,2008
[86]彭志科,何永勇,褚福磊.小波尺度谱在振动信号分析中的应用研究.机械工程学报,2002,38(3):123-126
[87]丁康,李巍华,朱小勇.齿轮及齿轮箱故障诊断实用技术.北京:机械工业出版社,2005
[88]盛兆顺,尹琦岭.设备状态监测与故障诊断技术及应用.北京:化学工业出版社,2003
[89]陈长征,胡立新,周勃,等.设备振动分析与故障诊断技术.北京:科学出版社,2007
[90]屈梁生,何正嘉.机械故障诊断学.上海:上海科学技术出版社,1986
[91] Rubini R, Meneghetti U. Application of the envelope and wavelet transform analysis for the diagnosis of incipient faults in ball bearings.Mechanical Systems and Signal Processing. 2001, 15(2):287-302
[92]罗文波,王莉,夏松波.利用小波变换提取水轮机轴系动态特性信息.哈尔滨工业大学学报,1998,30(2):47-50
[93]冯志鹏,李学军,褚福磊.基于平稳小波包分解的水轮机非平稳振动信号希尔伯特谱分析.中国电机工程学报,2006,26(12):79-84
[94]冯志鹏,朱萍玉,褚福磊.基于自适应多尺度线性调频小波分解的水轮机非平稳振动信号分析.中国电机工程学报,2008,28(8):105-110
[95]沈东.水利机组故障分析.北京:中国水利水电出版社,1996
[96]孙建平,代开锋.基于连续小波变换的水轮机振动信号检测.水电能源科学,2005,23(2):44-47
[2]黄文虎,夏松波,刘瑞岩.设备故障诊断原理、技术及应用.北京:科学出版社,1996
[3]郝如江.声发射和形态学方法在滚动轴承故障诊断中的应用:[博士学位论文].北京:清华大学精密仪器与机械学系,2008
[4]钟秉林,黄仁.机械故障诊断学.北京:机械工业出版社,2007
[5]张新明.声发射技术在滚动轴承故障诊断中的应用:[硕士学位论文].北京:清华大学精密仪器与机械学系,2006
[6]成琼.基于小波分析的齿轮故障诊断研究:[硕士学位论文].湖南:湖南大学,2001
[7]王万岗,吴广宁,雷栋.水轮机振动在线监测系统设计.仪表技术与传感器,2009,7:36-38
[8]王庆禹.小波分析在故障诊断及状态监测中应用研究:[硕士学位论文].北京:清华大学精密仪器与机械学系,2000
[9]李国华,张永忠.机械故障诊断.北京:化学工业出版社,1999
[10]寇惠,原培新.故障诊断中的振动信号处理.北京:冶金工业出版社,1989
[11]李力.机械信号处理及其应用.湖北:华中科技大学出版社,2007
[12]徐科军.信号分析与处理.北京:清华大学出版社,2006
[13]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1988
[14]寿海飞.基于小波分析的齿轮故障诊断研究:[硕士学位论文].浙江:浙江工业大学,2007
[15] Russell P C, Cosgrave J, Tomtsis, et al. Extraction of information from acoustic vibration signals using Gabor transform type devices. Measurement Science and Technology. 1998, 9(8):1282-1290
[16] Brie D, Oehlmann H, Vogt M, et al. Application of the local smoothed pseudo-Wigner-Ville distribution to gear tooth vibration signature analysis. Applied Signal Processing. 1997, 4(3): 168~78
[17] Wang W J, McFadden P D. Application of wavelets to gearbox vibration signals for fault detection. Journal of Sound and Vibration. 1996, 192(5):927-939
[18] Ma J. A neural network approach to real-time pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence. 2001, 15(6):937-947
[19] Kang S L, Zhang H Z. Detection and localization of turbine-generator bearing vibration using wavelet neural network. Proceedings of the 2009 IEEE International Conference onMechatronics and Automation. 2009:4414-4418
[20] Wang W J, Mcfadden P D. Application of orthogonal wavelets to early gear damage dedection. Mechanical Systems and Signal Processing. 1995, 9(5):497-507
[21] Rafiee J, Rafiee M A, Tse P W. Application of mother wavelet functions for automatic gear and bearing fault diagnosis. Expert Systems with Applications. 2010, 37(6):4568-4579
[22] Saravanan N, Ramachandran K I. Incipient gear box fault diagnosis using discrete wavelet transform for feature extraction and classification using artificial neural network. Expert Systems with Applications. 2010, 37(6):4168-4181
[23] Fan Xianfeng, Zuo M J. Gearbox fault detection using Hilbert and wavelet packet transform. Mechanical Systems and Signal Processing. 2006, 20(4): 966-982
[24] Staszewski W J, Worden K, Tomlinson G R. Time–frequency analysis in gearbox fault detection using the Wigner–Ville distribution and pattern recognition. Mechanical Systems and Signal Processing. 1997, 11(5): 673-692
[25] Rai V K, Mohanty A R. Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform. Mechanical Systems and Signal Processing, 2007, 21(6): 2607-2615
[26] Sawalhi N, Randall R B, Endo H. The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis. Mechanical Systems and Signal Processing, 2007, 21(6):2616-2633
[27] Zareia J, Poshtan J. Bearing fault detection using wavelet packet transform of induction motor stator current. Tribology International. 2007, 40(5):763-769
[28] Yang H, Mathew J, Ma L. Fault diagnosis of rolling element bearings using basis pursuit. Mechanical Systems and Signal Processing. 2005, 19(2):341-356
[29]赵婷.基于小波分析的机械振动故障分析:[硕士学位论文].辽宁:沈阳工业大学,2008
[30]周洋.小波分析在旋转机械振动信号监测和故障诊断中的应用研究:[硕士学位论文].上海:同济大学,2007
[31]潘罗平,周叶,唐封,等.水轮发电机组状态监测技术的现状及展望.水电站机电技术,2008,31(6):1-7
[32]冯志鹏,刘立,张文明.基于小波时频框架分解方法的滚动轴承故障诊断.振动与冲击,2008,27(2):110-114
[33] Feng Z P, Chu F L. Application of atomic decomposition to gear damage detection. Journal of Sound and Vibration, 2007, 302:138-151
[34]郝如江,卢文秀,褚福磊.滚动轴承故障信号的多尺度形态学分析.机械工程学报,2008,44(11):160-165
[35]郝如江,卢文秀,褚福磊.形态滤波器用于滚动轴承故障信号的特征提取.中国机械工程,2009,20(2):197-201
[36]彭志科.小波分析在旋转设备故障诊断中的应用:[博士学位论文].北京:清华大学精密仪器与机械学系,2002
[37]王晓冬,何正嘉,訾艳阳.滚动轴承故障诊断的多小波谱峭度方法.西安交通大学学报,2010,44(3):77-81
[38]孟庆丰,蒋晓玲,何正嘉,等.滚动轴承和齿轮故障的时频域识别.重型机械,1998,1:57-62
[39]丁锋,何正嘉,张新运.小波包分析在滚动轴承信号消噪处理中的应用.西安工业学院学报,2006,26(1):8-12
[40] Cheng J, Yang Y, Yu D. The envelope order spectrum based on generalized demodulation time–frequency analysis and its application to gear fault diagnosis. Mechanical Systems and Signal Processing. 2010, 24(2): 508-521
[41]于德介,程军圣,杨宇. Hilbert-Huang变换在齿轮故障诊断中的应用.机械工程学报, 2005,41(6):102-107
[42]刘坚,彭富强,于德介.基于线调频小波路径追踪阶比跟踪算法的齿轮箱故障诊断研究.机械工程学报,2009,45(7):81-86
[43]杨宇,于德介,程军圣.基于Hilbert边际谱的滚动轴承故障诊断方法.振动与冲击,2005,24(1):70-72
[44]程军圣,于德介,杨宇,等.尺度-小波能量谱在滚动轴承故障诊断中的应用.振动工程学报,2004,17(1):82-85
[45] Zheng H, Li Z,Chen X. Gear fault diagnosis based on continuous wavelet transform. Mechanical Systems and Signal Processing. 2002, 16(2-3):447-457
[46]郑海波,李志远,陈心昭.基于连续小波变换的齿轮故障诊断方法研究.机械工程学报,2002,38(3):69-73
[47]冯志鹏,朱萍玉,刘立,等.基追踪在齿轮损伤识别中的应用.北京科技大学学报,2008,30(1):84-89
[48]来五星,轩建平,史铁林,等. Wigner-Ville时频分布研究及其在齿轮故障诊断中的应用.振动工程学报,2003,16(2):247-250
[49]冯志鹏,褚福磊.基于Hilbert-Huang变换的水轮机非平稳压力脉动信号分析.中国电机工程学报,2005,25(10):111-115
[50]韩凤琴,陈林刚,桂中华,等.基于小波包提取尾水管水压脉动特征的研究.水电能源科学,2005,23(1):31-33
[51]吴子英,李郁侠,刘宏昭,等.短时傅立叶变换在大型水轮发电机组振动分析中的应用.水力发电学报,2005,24(6):115-120
[52]贺志龙,常黎.小波分析在水电机组状态检测中的应用研究.华中电力,2003,2(16):4-6
[53]胡广书.数字信号处理:理论、算法与实现.北京:清华大学出版社,2003
[54]郑君里,应启珩,杨为理.信号与系统(上册).北京:高等教育出版社,2009
[55]李德葆,陆秋海.工程振动试验分析.北京:清华大学出版社,2004
[56] Pan M C, Sas P. Transient analysis on machinery condition monitoring. International Conference on Signal Processing Proceeding ICSP. 1996, 2:1723-1726
[57]褚福磊,彭志科,冯志鹏,等.机械故障诊断中的现代信号处理方法.北京:科学出版社,2009
[58]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法.北京:科学出版社,2006
[59]杨福生.小波变换的工程分析与应用.北京:科学出版社,1999
[60]张德丰. MATLAB与小波分析.北京:机械工业出版社,2009
[61]林京,屈梁生.基于连续小波变换的信号检测技术与故障诊断.机械工程学报, 2000,36(12):95–100
[62] Daubechies I. Where do wavelet come from?-A person point of view. Proceeding of the IEEE. 1996, 84(4):510-513
[63] Polikar R. The story of wavelets. IMACS/IEEE CSCC. 1999, 5481-5786
[64]程正兴.小波分析算法与应用.西安:西安交通大学出版社,1998
[65] Boulahbal D, Farid G M, Ismail F. Amplitude and phase wavelet maps for thedetection of cracks in geared systems. Mechanical Systems and Signal Processing. 1999, 13(3):423-436
[66] Lin J, Qu L S. Feature extraction based on Morlet wavelet and its application formechanical fault diagnosis. Journal of Sound and Vibration. 2000, 234(1):135-148
[67]何正嘉,訾艳阳,张周锁,等.大型机械设备变工况非平稳动态分析与监测诊断关键技术.中国机械工程,1999,10(9):978-981
[68] Ruiz D, Nougues J M, Calderon Z, et al. Neural network based framework forfault diagnosis in batch chemical plants. Computers and Chemical Engineering. 2000, 24(2):777-784
[69] Donoho D L, Johnson I M. Ideal Spatial Adaptaion via Wavelet Shrinkage. Biometrika. 1994, 81:428~455
[70] Altmann J, Mathew J. Multiple band-pass autoregressive demodulation forrolling-element bearing fault diagnosis. Mechanical Systems and Signal Processing. 2001, 15(5):963-977
[71]徐敏强,王日新,张嘉钟.基于梳妆小波的旋转机械振动信号降噪方法的研究.振动工程学报,2002,15(1):90-93
[72]马元奎,陆颂元.小波分解及嵌入式小波系数零树编码在振动数据压缩中的应用研究.汽轮机技术, 2001,43(02):87-92
[73]任震,何建军,黄雯莹,等.基于小波包算法的电机故障信号的压缩和重构.中国电机工程学报,2001,21(1):25-29
[74] Robertson A N, Park K C, Alvin K F. Identification of structural dynamics modelsusing wavelet-generated impulse response data. Journal of Vibration andAcoustics, Transactions of the ASME. 1998, 120(1):261-266
[75]郑兆昌.机械振动(上册).清华大学工程力学系,1978
[76]程军圣,于德介,邓乾旺,等.时间-小波能量谱在滚动轴承诊断中的应用.振动与冲击,2004,23(2):34-36
[77] Peng Z K, Chu F L. Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography. Mechanical Systems and Signal Processing. 2004, (18):199-221
[78] Gennaro D M, Stefano S, Maria C C, et al. Cross-correlation time-frequency analysis for multiple EMG signals in Parkinson’s disease: a wavelet approach. Medical Engineering & Physics. 2003, 25:361–369
[79] Jan F A. River flow forecasting using wavelet and cross-wavelet transform models. Hydrological Process. 2008, 22:4877–4891
[80] Jordan D A, Hajj M R, Tieleman H W. Wavelet analysis of the relation between atmospheric wind and pressure fluctuations on a low-rise building. Journal of Wind Engineering and Industrial Aercodynamics. 1997, 69-71:647-655
[81] Horodko L. Identification Of Rotating Pressure Waves in a Centrifugal Compressor Diffuser by Means of The Wavelet Cross-Correlation. International Journal of Wavelets, Multiresolution and Information Processing. 2006, 4(2):373-382
[82] Kyprianou A, Staszewski W J. On The Cross Wavelet Analysis of Duffing Oscillator. Journal of Sound and Vibration. 1999, 228(1):199-210
[83]孙卫国,程炳岩.交叉小波变换在区域气候分析中的应用.应用气象学报,2008,19(4):479-487
[84]南峰,李有利,张宏升.新疆玛纳斯河径流波动与北大西洋涛动的关系.北京大学学报(自然科学版),2006,42(4):534-541
[85]洪梅,张韧等.基于交叉小波与小波相干分析对影响“0801暴雪”的副热带高压的时延相关分析.中国气象学会2008年年会极端天气气候事件与应急气象服务分会场论文集,2008
[86]彭志科,何永勇,褚福磊.小波尺度谱在振动信号分析中的应用研究.机械工程学报,2002,38(3):123-126
[87]丁康,李巍华,朱小勇.齿轮及齿轮箱故障诊断实用技术.北京:机械工业出版社,2005
[88]盛兆顺,尹琦岭.设备状态监测与故障诊断技术及应用.北京:化学工业出版社,2003
[89]陈长征,胡立新,周勃,等.设备振动分析与故障诊断技术.北京:科学出版社,2007
[90]屈梁生,何正嘉.机械故障诊断学.上海:上海科学技术出版社,1986
[91] Rubini R, Meneghetti U. Application of the envelope and wavelet transform analysis for the diagnosis of incipient faults in ball bearings.Mechanical Systems and Signal Processing. 2001, 15(2):287-302
[92]罗文波,王莉,夏松波.利用小波变换提取水轮机轴系动态特性信息.哈尔滨工业大学学报,1998,30(2):47-50
[93]冯志鹏,李学军,褚福磊.基于平稳小波包分解的水轮机非平稳振动信号希尔伯特谱分析.中国电机工程学报,2006,26(12):79-84
[94]冯志鹏,朱萍玉,褚福磊.基于自适应多尺度线性调频小波分解的水轮机非平稳振动信号分析.中国电机工程学报,2008,28(8):105-110
[95]沈东.水利机组故障分析.北京:中国水利水电出版社,1996
[96]孙建平,代开锋.基于连续小波变换的水轮机振动信号检测.水电能源科学,2005,23(2):44-47