Wavelets for fault diagnosis of rotary machines: A review with applications

Over the last 20 years, particularly in last 10 years, great progress has been made in the theory and applications of wavelets and many publications have been seen in the field of fault diagnosis. This paper attempts to provide a review on recent applications of the wavelets with focus on rotary machine fault diagnosis. After brief introduction of the theoretical background on both classical wavelet transform and second generation wavelet transform, applications of wavelets in rotary machine fault diagnosis are summarized according to the following categories: continuous wavelet transform-based fault diagnosis, discrete wavelet transform-based fault diagnosis, wavelet packet transform-based fault diagnosis, and second generation wavelet transform-based fault diagnosis. In addition, some new research trends, including wavelet finite element method, dual-tree complex wavelet transform, wavelet function selection, new wavelet function design, and multi-wavelets that advance the development of wavelet-based fault diagnosis are also discussed.

[1]  Jiang Hongkai,et al.  A sliding window feature extraction method for rotating machinery based on the lifting scheme , 2007 .

[2]  Wenxian Yang,et al.  Detecting Impulses in Mechanical Signals by Wavelets , 2004, EURASIP J. Adv. Signal Process..

[3]  I. S. Bozchalooi,et al.  A joint resonance frequency estimation and in-band noise reduction method for enhancing the detectability of bearing fault signals , 2008 .

[4]  Chen Peng,et al.  Gearbox fault diagnosis using adaptive redundant Lifting Scheme , 2006 .

[5]  Dejie Yu,et al.  A gear fault diagnosis using Hilbert spectrum based on MODWPT and a comparison with EMD approach , 2009 .

[6]  D. Osypiw,et al.  On-Line Vibration Analysis with Fast Continuous Wavelet Algorithm for Condition Monitoring of Bearing , 2003 .

[7]  Debin Zhao,et al.  Performance prediction methodology based on pattern recognition , 2011, Signal Process..

[8]  Iqbal Gondal,et al.  Inchoate Fault Detection Framework: Adaptive Selection of Wavelet Nodes and Cumulant Orders , 2012, IEEE Transactions on Instrumentation and Measurement.

[9]  Yanyang Zi,et al.  Multiwavelet denoising with improved neighboring coefficients for application on rolling bearing fault diagnosis , 2011 .

[10]  Satish C. Sharma,et al.  Rolling element bearing fault diagnosis using wavelet transform , 2011, Neurocomputing.

[11]  Tet Hin Yeap,et al.  A joint wavelet lifting and independent component analysis approach to fault detection of rolling element bearings , 2007 .

[12]  Robert X. Gao,et al.  Wavelet packet base selection for gearbox defect severity classification , 2010, 2010 Prognostics and System Health Management Conference.

[13]  Guang-Ming Xian,et al.  Corrigendum to "An intelligent fault diagnosis method based on wavelet packet analysis and hybrid support vector machines" [Expert Systems with Applications 36 (10) (2009) 12131-12136] , 2010, Expert Syst. Appl..

[14]  Y. Zi,et al.  Gear fault detection using customized multiwavelet lifting schemes , 2010 .

[15]  Yi Qin,et al.  Feature extraction method of wind turbine based on adaptive Morlet wavelet and SVD , 2011 .

[16]  Bo-Suk Yang,et al.  Wavelet support vector machine for induction machine fault diagnosis based on transient current signal , 2008, Expert Syst. Appl..

[17]  Fulei Chu,et al.  Morphological undecimated wavelet decomposition for fault diagnostics of rolling element bearings , 2009 .

[18]  Geok Soon Hong,et al.  Wavelet analysis of sensor signals for tool condition monitoring: A review and some new results , 2009 .

[19]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[20]  Chuan Li,et al.  Multi-scale autocorrelation via morphological wavelet slices for rolling element bearing fault diagnosis , 2012 .

[21]  Konstantinos Gryllias,et al.  A Peak Energy Criterion (P. E.) for the Selection of Resonance Bands in Complex Shifted Morlet Wavelet (Csmw) Based Demodulation of Defective Rolling Element Bearings Vibration Response , 2009, Int. J. Wavelets Multiresolution Inf. Process..

[22]  A. R. Mohanty,et al.  Fault Detection in a Multistage Gearbox by Demodulation of Motor Current Waveform , 2006, IEEE Transactions on Industrial Electronics.

[23]  Pavle Boškoski,et al.  Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures , 2012 .

[24]  Zi Yanyang,et al.  Bearing condition monitoring based on shock pulse method and improved redundant lifting scheme , 2008 .

[25]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Zhengjia He,et al.  Modeling of wave propagation in one-dimension structures using B-spline wavelet on interval finite element , 2012 .

[27]  J. Rafiee,et al.  Application of mother wavelet functions for automatic gear and bearing fault diagnosis , 2010, Expert Syst. Appl..

[28]  Guang-ming Xian.  Mechanical failure classification for spherical roller bearing ofhydraulic injection molding machine using DWT-SVM , 2010, Expert Syst. Appl..

[29]  E. Schukin,et al.  The optimisation of wavelet transform for the impulse analysis in vibration signals , 2004 .

[30]  Zhigang Wang,et al.  A Resonance Demodulation Method Based on Harmonic Wavelet Transform for Rolling Bearing Fault Diagnosis , 2010 .

[31]  Robert X. Gao,et al.  Multi-Scale Enveloping Spectrogram for Bearing Defect Detection , 2005 .

[32]  Ruqiang Yan,et al.  Tutorial 21 wavelet transform: a mathematical tool for non-stationary signal processing in measurement science part 2 in a series of tutorials in instrumentation and measurement , 2009, IEEE Instrumentation & Measurement Magazine.

[33]  Dong Wang,et al.  Robust health evaluation of gearbox subject to tooth failure with wavelet decomposition , 2009 .

[34]  I. S. Bozchalooi,et al.  A smoothness index-guided approach to wavelet parameter selection in signal de-noising and fault detection , 2007 .

[35]  Robert X. Gao,et al.  PCA-based feature selection scheme for machine defect classification , 2004, IEEE Transactions on Instrumentation and Measurement.

[36]  Patrick S. K. Chua,et al.  Vibration analysis with lifting scheme and generalized cross validation in fault diagnosis of water hydraulic system , 2007 .

[37]  Robert X. Gao,et al.  Unified time–scale–frequency analysis for machine defect signature extraction: Theoretical framework , 2009 .

[38]  Ingrid Daubechies,et al.  Where do wavelets come from? A personal point of view , 1996, Proc. IEEE.

[39]  Daren Yu,et al.  Mechanical equipment fault diagnosis based on redundant second generation wavelet packet transform , 2010, Digit. Signal Process..

[40]  P. Tse,et al.  Singularity analysis of the vibration signals by means of wavelet modulus maximal method , 2007 .

[41]  Robert X. Gao,et al.  Energy-Based Feature Extraction for Defect Diagnosis in Rotary Machines , 2009, IEEE Transactions on Instrumentation and Measurement.

[42]  Cristina Castejón,et al.  Automated diagnosis of rolling bearings using MRA and neural networks , 2010 .

[43]  Robert X. Gao,et al.  An efficient approach to machine health diagnosis based on harmonic wavelet packet transform , 2005 .

[44]  K. I. Ramachandran,et al.  Fault diagnosis of spur bevel gear box using discrete wavelet features and Decision Tree classification , 2009, Expert Syst. Appl..

[45]  Wei He,et al.  Bearing fault detection based on optimal wavelet filter and sparse code shrinkage , 2009 .

[46]  Guang Meng,et al.  Wavelet Transform-based Higher-order Statistics for Fault Diagnosis in Rolling Element Bearings , 2008 .

[47]  Huaqing Wang,et al.  Intelligent Gearbox Diagnosis Methods Based on SVM, Wavelet Lifting and RBR , 2010, Sensors.

[48]  Amiya R Mohanty,et al.  Monitoring gear vibrations through motor current signature analysis and wavelet transform , 2006 .

[49]  Y-S Hong,et al.  Component-level fault diagnostics of a bevel gear using a wavelet packet transform , 2011 .

[50]  Zhengjia He,et al.  A study of multiscale wavelet-based elements for adaptive finite element analysis , 2010, Adv. Eng. Softw..

[51]  Ruqiang Yan,et al.  Harmonic wavelet-based data filtering for enhanced machine defect identification , 2010 .

[52]  Baoping Tang,et al.  A novel fault diagnosis model for gearbox based on wavelet support vector machine with immune genetic algorithm , 2013 .

[53]  Fadi Al-Badour,et al.  Vibration analysis of rotating machinery using time-frequency analysis and wavelet techniques , 2011 .

[54]  Huaqing Wang,et al.  Intelligent Diagnosis Method for Rotating Machinery Using Wavelet Transform and Ant Colony Optimization , 2012, IEEE Sensors Journal.

[55]  Jinwu,et al.  NEW METHOD OF EXTRACTING WEAK FAILURE INFORMATION IN GEARBOX BY COMPLEX WAVELET DENOISING , 2008 .

[56]  Pizhong Qiao,et al.  On the wavelet–fractal nonlinear damage diagnosis of mechanical systems , 2009 .

[57]  Wenxian Yang,et al.  Cost-Effective Condition Monitoring for Wind Turbines , 2010, IEEE Transactions on Industrial Electronics.

[58]  A Yoshida,et al.  Application of the wavelet transform to health monitoring and evaluation of dynamic characteristics in gear sets , 2004 .

[59]  Lei Guo,et al.  Robust bearing performance degradation assessment method based on improved wavelet packet–support vector data description , 2009 .

[60]  Ming Liang,et al.  Fault severity assessment for rolling element bearings using the Lempel–Ziv complexity and continuous wavelet transform , 2009 .

[61]  Jian-Da Wu,et al.  Fault gear identification using vibration signal with discrete wavelet transform technique and fuzzy-logic inference , 2009, Expert Syst. Appl..

[62]  Girish Kumar Singh,et al.  Isolation and identification of dry bearing faults in induction machine using wavelet transform , 2009 .

[63]  Jun Ni,et al.  A comparative study on damage detection in speed-up and coast-down process of grinding spindle-typed rotor-bearing system , 2007 .

[64]  Yixiang Huang,et al.  A lean model for performance assessment of machinery using second generation wavelet packet transform and Fisher criterion , 2010, Expert Syst. Appl..

[65]  Robert X. Gao,et al.  Wavelet transform with spectral post-processing for enhanced feature extraction [machine condition monitoring] , 2003, IEEE Trans. Instrum. Meas..

[66]  Jian-Da Wu,et al.  Fault gear identification and classification using discrete wavelet transform and adaptive neuro-fuzzy inference , 2009, Expert Syst. Appl..

[67]  Yaguo Lei,et al.  EEMD method and WNN for fault diagnosis of locomotive roller bearings , 2011, Expert Syst. Appl..

[68]  J. Sanz,et al.  Fault diagnosis of rotating machinery based on auto-associative neural networks and wavelet transforms , 2007 .

[69]  Weiguo Huang,et al.  Adaptive Parameter Identification Based on Morlet Wavelet and Application in Gearbox Fault Feature Detection , 2010, EURASIP J. Adv. Signal Process..

[70]  C. Nagaraju,et al.  Application of 3D wavelet transforms for crack detection in rotor systems , 2009 .

[71]  Stéphane Mallat,et al.  Wavelets for a vision , 1996, Proc. IEEE.

[72]  Wensheng Su,et al.  Rolling element bearing faults diagnosis based on optimal Morlet wavelet filter and autocorrelation enhancement , 2010 .

[73]  K. I. Ramachandran,et al.  A comparative study on classification of features by SVM and PSVM extracted using Morlet wavelet for fault diagnosis of spur bevel gear box , 2008, Expert Syst. Appl..

[74]  Zi Yanyang,et al.  Construction of adaptive redundant multiwavelet packet and its application to compound faults detection of rotating machinery , 2012 .

[75]  Robert X. Gao,et al.  Design of an impulse wavelet for structural defect identification , 2010, 2010 Prognostics and System Health Management Conference.

[76]  Y. Zi,et al.  Adaptive multiwavelets via two-scale similarity transforms for rotating machinery fault diagnosis , 2009 .

[77]  Robert X. Gao,et al.  Wavelet transform with spectral post-processing for enhanced feature extraction , 2002, IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.00CH37276).

[78]  F. Ma,et al.  Bearing system health condition monitoring using a wavelet cross-spectrum analysis technique , 2012 .

[79]  Hui Li,et al.  Bearing fault diagnosis based on amplitude and phase map of Hermitian wavelet transform , 2011 .

[80]  Jae-Seob Kwak,et al.  Application of wavelet transform technique to detect tool failure in turning operations , 2006 .

[81]  Leonid M. Gelman,et al.  Novel detection of local tooth damage in gears by the wavelet bicoherence , 2012 .

[82]  Yanhui Feng,et al.  Normalized wavelet packets quantifiers for condition monitoring , 2009 .

[83]  Mustafa Sabuncu,et al.  Early Detection of Pitting Damage in Gears using Mean Frequency of Scalogram , 2008 .

[84]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[85]  Shibin Wang,et al.  Synchronous Enhancement of Periodic Transients on Polar Diagram for Machine Fault Diagnosis , 2009, Int. J. Wavelets Multiresolution Inf. Process..

[86]  Yanyang Zi,et al.  Rotating machinery fault diagnosis using signal-adapted lifting scheme , 2008 .

[87]  Yaguo Lei,et al.  A Combination of WKNN to Fault Diagnosis of Rolling Element Bearings , 2009 .

[88]  Qiao Hu,et al.  Fault diagnosis of rotating machinery based on improved wavelet package transform and SVMs ensemble , 2007 .

[89]  N. Kingsbury.  Complex Wavelets for Shift Invariant Analysis and Filtering of Signals , 2001 .

[90]  Mir Mohammad Ettefagh,et al.  Asynchronous input gear damage diagnosis using time averaging and wavelet filtering , 2008 .

[91]  Farag K. Omar,et al.  Dynamic wavelet-based tool for gearbox diagnosis , 2012 .

[92]  Hong-kai Jiang,et al.  Wavelet design for extracting weak fault feature based on lifting scheme , 2006 .

[93]  Jie Liu.  Shannon wavelet spectrum analysis on truncated vibration signals for machine incipient fault detection , 2012 .

[94]  Liu Wei,et al.  Continuous wavelet grey moment approach for vibration analysis of rotating machinery , 2006 .

[95]  M. Zuo,et al.  Feature separation using ICA for a one-dimensional time series and its application in fault detection , 2005 .

[96]  K. P. Ramachandran,et al.  Rolling element bearing faults diagnosis based on autocorrelation of optimized: wavelet de-noising technique , 2009 .

[97]  Yanyang Zi,et al.  Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform , 2010 .

[98]  P. Konar,et al.  Bearing fault detection of induction motor using wavelet and Support Vector Machines (SVMs) , 2011, Appl. Soft Comput..

[99]  B Liu.  Selection of wavelet packet basis for rotating machinery fault diagnosis , 2005 .

[100]  Robert X. Gao,et al.  A hybrid approach to bearing defect diagnosis in rotary machines , 2012 .

[101]  J. Flašker,et al.  Determining cracks in gears using adaptive wavelet transform approach , 2010 .

[102]  Wenyi Liu,et al.  A hybrid time-frequency method based on improved Morlet wavelet and auto terms window , 2011, Expert Syst. Appl..

[103]  N. Hamzaoui,et al.  Detection of rolling bearing defects using discrete wavelet analysis , 2008 .

[104]  Zhengjia He,et al.  Quantitative Identification of Rotor Cracks Based on Finite Element of B-spline Wavelet on the Interval , 2009, Int. J. Wavelets Multiresolution Inf. Process..

[105]  P. K. Kankar,et al.  Rolling element bearing fault diagnosis using autocorrelation and continuous wavelet transform , 2011 .

[106]  Ning Li,et al.  Anti-aliasing lifting scheme for mechanical vibration fault feature extraction , 2009 .

[107]  Jong-Duk Son,et al.  Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal , 2008, Expert Syst. Appl..

[108]  Zhongkui Zhu,et al.  Detection of signal transients based on wavelet and statistics for machine fault diagnosis , 2009 .

[109]  Jian-Da Wu,et al.  Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network , 2009, Expert Syst. Appl..

[110]  P. Tse,et al.  A comparison study of improved Hilbert–Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing , 2005 .

[111]  Jing Yuan,et al.  Improved spectral kurtosis with adaptive redundant multiwavelet packet and its applications for rotating machinery fault detection , 2012 .

[112]  Javad Poshtan,et al.  Bearing fault detection using wavelet packet transform of induction motor stator current , 2007 .

[113]  Mousa Rezaee,et al.  Development of vibration signature analysis using multiwavelet systems , 2003 .

[114]  Ming Liang,et al.  Separation of fault features from a single-channel mechanical signal mixture using wavelet decomposition , 2007 .

[115]  Robert X. Gao,et al.  Multi-scale enveloping spectrogram for vibration analysis in bearing defect diagnosis , 2009 .

[116]  Robert X. Gao,et al.  Spindle Health Diagnosis Based on Analytic Wavelet Enveloping , 2006, IEEE Transactions on Instrumentation and Measurement.

[117]  K. I. Ramachandran,et al.  Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN) , 2010, Expert Syst. Appl..

[118]  Hui Li,et al.  Application of Hermitian wavelet to crack fault detection in gearbox , 2011 .

[119]  Bing Li,et al.  An adaptive morphological gradient lifting wavelet for detecting bearing defects , 2012 .

[120]  Zhongsheng Wang,et al.  Robust incipient fault identification of aircraft engine rotor based on wavelet and fraction , 2010 .

[121]  Feng Ding,et al.  An effective approach to rolling bearing diagnosis based on Adaptive Redundant Second-Generation Wavelet , 2008 .

[122]  Jun-Hong Zhou,et al.  Wavelet-based correlation modelling for health assessment of fluid dynamic bearings in brushless DC motors , 2009 .

[123]  Richard Baraniuk,et al.  The Dual-tree Complex Wavelet Transform , 2007 .

[124]  Ricardo Perera,et al.  Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks , 2012, Appl. Soft Comput..

[125]  Wei Guo,et al.  Fault diagnosis based on optimized node entropy using lifting wavelet packet transform and genetic algorithms , 2010 .

[126]  Gang Yu,et al.  Machine fault diagnosis using a cluster-based wavelet feature extraction and probabilistic neural networks , 2009 .

[127]  Huaqing Wang,et al.  Study and Application of Acoustic Emission Testing in Fault Diagnosis of Low-Speed Heavy-Duty Gears , 2011, Sensors.

[128]  K. Loparo,et al.  Bearing fault diagnosis based on wavelet transform and fuzzy inference , 2004 .

[129]  Ming J. Zuo,et al.  GEARBOX FAULT DIAGNOSIS USING ADAPTIVE WAVELET FILTER , 2003 .

[130]  Cheng Junsheng,et al.  Application of an impulse response wavelet to fault diagnosis of rolling bearings , 2007 .

[131]  Robert X. Gao,et al.  Experimental Evaluation of a Unified Time-Scale-Frequency Technique for Bearing Defect Feature Extraction , 2009 .

[132]  Rajesh Kumar,et al.  Outer race defect width measurement in taper roller bearing using discrete wavelet transform of vibration signal , 2013 .

[133]  Robert X. Gao,et al.  Customized Wavelet for Bearing Defect Detection , 2004 .

[134]  Fulei Chu,et al.  Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography , 2004 .

[135]  Peter W. Tse,et al.  Use of autocorrelation of wavelet coefficients for fault diagnosis , 2009 .

[136]  P. Tse,et al.  Machine fault diagnosis through an effective exact wavelet analysis , 2004 .

[137]  Li Li,et al.  Haar wavelet for machine fault diagnosis , 2007 .

[138]  K. I. Ramachandran,et al.  A case study on classification of features by fast single-shot multiclass PSVM using Morlet wavelet for fault diagnosis of spur bevel gear box , 2009, Expert Syst. Appl..

[139]  Zhengjia He,et al.  Rotor crack detection based on high-precision modal parameter identification method and wavelet finite element model , 2009 .

[140]  Robert X. Gao,et al.  Base Wavelet Selection for Bearing Vibration Signal Analysis , 2009, Int. J. Wavelets Multiresolution Inf. Process..

[141]  Jie Liu,et al.  An Extended Wavelet Spectrum for Bearing Fault Diagnostics , 2008, IEEE Transactions on Instrumentation and Measurement.

[142]  Qinghua Hu,et al.  Mechanical fault diagnosis based on redundant second generation wavelet packet transform, neighborhood rough set and support vector machine , 2012 .

[143]  Ruqiang Yan,et al.  Aeroengine Rub-Impact Fault Diagnosis Based on Wavelet Packet Transform and the Local Discriminate Bases , 2012 .

[144]  N Li,et al.  Mechanical faulty signal denoising using a redundant non-linear second-generation wavelet transform , 2011 .

[145]  J. Rafiee,et al.  A novel technique for selecting mother wavelet function using an intelligent fault diagnosis system , 2009, Expert Syst. Appl..

[146]  Li,et al.  Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method , 2010 .

[147]  V. Purushotham,et al.  Multi-fault diagnosis of rolling bearing elements using wavelet analysis and hidden Markov model based fault recognition , 2005 .

[148]  A. Cohen,et al.  Wavelets: the mathematical background , 1996, Proc. IEEE.

[149]  Fanrang Kong,et al.  Multiscale slope feature extraction for rotating machinery fault diagnosis using wavelet analysis , 2013 .

[150]  Bing Li,et al.  Fault feature extraction of gearbox by using overcomplete rational dilation discrete wavelet transform on signals measured from vibration sensors , 2012 .

[151]  O. Rioul,et al.  Wavelets and signal processing , 1991, IEEE Signal Processing Magazine.

[152]  Ming Yang,et al.  A wavelet approach to fault diagnosis of a gearbox under varying load conditions , 2010 .

[153]  Robert X. Gao,et al.  A hybrid diagnostic method based on wigner-ville distribution and wavelet packet transform , 2010, 2010 International Conference on Wavelet Analysis and Pattern Recognition.

[154]  Feng Ding,et al.  End milling tool breakage detection using lifting scheme and Mahalanobis distance , 2008 .

[155]  Zhengjia He,et al.  The construction of wavelet finite element and its application , 2004 .

[156]  Konstantinos Gryllias,et al.  Estimation of the instantaneous rotation speed using complex shifted Morlet wavelets , 2013 .

[157]  Nguyen Phong Dien,et al.  Fault diagnosis in gears operating under non-stationary rotational speed using polar wavelet amplitude maps , 2004 .

[158]  Wenyi Liu,et al.  Wind turbine fault diagnosis based on Morlet wavelet transformation and Wigner-Ville distribution , 2010 .

[159]  Duan Chen-dong,et al.  A lifting undecimated wavelet transform and its applications , 2008 .

[160]  K. P. Ramachandran,et al.  Application of the Laplace-Wavelet Combined With ANN for Rolling Bearing Fault Diagnosis , 2008 .

[161]  Satish C. Sharma,et al.  Fault diagnosis of ball bearings using continuous wavelet transform , 2011, Appl. Soft Comput..

[162]  Hai Qiu,et al.  Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics , 2006 .

[163]  Chao Liu,et al.  Machine Condition Classification Using Deterioration Feature Extraction and Anomaly Determination , 2011, IEEE Transactions on Reliability.

[164]  Sirish L. Shah,et al.  Time domain averaging across all scales: A novel method for detection of gearbox faults , 2008 .

[165]  K. P. Ramachandran,et al.  Rolling Element Bearing Fault Diagnosis Using Laplace-Wavelet Envelope Power Spectrum , 2007, EURASIP J. Adv. Signal Process..

[166]  Zhongkui Zhu,et al.  Transient modeling and parameter identification based on wavelet and correlation filtering for rotating machine fault diagnosis , 2011 .

[167]  Li Li,et al.  Virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method , 2011 .

[168]  Wei He,et al.  Rolling element bearing fault detection based on optimal antisymmetric real Laplace wavelet , 2011 .

[169]  Yanyang Zi,et al.  The principle of second generation wavelet for milling cutter breakage detection , 2008 .

[170]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[171]  Robert X. Gao,et al.  Non-stationary signal processing for bearing health monitoring , 2006, Int. J. Manuf. Res..

[172]  W. Sweldens.  Wavelets: What Next? , 1997 .

[173]  Yanyang Zi,et al.  Multiwavelet construction via an adaptive symmetric lifting scheme and its applications for rotating machinery fault diagnosis , 2009 .

[174]  Robert X. Gao,et al.  Wavelet domain principal feature analysis for spindle health diagnosis , 2011 .

[175]  Liu Chengliang,et al.  Adaptive wavelet filtering for bearing monitoring based on block bootstrapping and white noise test , 2012 .

[176]  Chuan Li,et al.  A generalized synchrosqueezing transform for enhancing signal time-frequency representation , 2012, Signal Process..

[177]  K. Loparo,et al.  Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling : A method for bearing prognostics , 2007 .

[178]  Li Zhen,et al.  Customized wavelet denoising using intra- and inter-scale dependency for bearing fault detection , 2008 .

[179]  Yixiang Huang,et al.  An enhanced feature extraction model using lifting-based wavelet packet transform scheme and sampling-importance-resampling analysis , 2009 .

[180]  Jin Chen,et al.  Bearing performance degradation assessment based on lifting wavelet packet decomposition and fuzzy c-means , 2010 .

[181]  Guang-Ming Xian,et al.  An intelligent fault diagnosis method based on wavelet packer analysis and hybrid support vector machines , 2009, Expert Syst. Appl..