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Research Papers

Incipient Bearing Fault Feature Extraction Based on Minimum Entropy Deconvolution and K-Singular Value Decomposition

[+] Author and Article Information
Guangming Dong

State Key Laboratory of Mechanical
Systems and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: gmdong@sjtu.edu.cn

Jin Chen

State Key Laboratory of Mechanical
Systems and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Fagang Zhao

Shanghai Institute of Satellite Engineering,
251 Huaning Road,
Minhang District,
Shanghai 200240, China

Manuscript received January 13, 2017; final manuscript received June 29, 2017; published online August 24, 2017. Assoc. Editor: Ivan Selesnick.

J. Manuf. Sci. Eng 139(10), 101006 (Aug 24, 2017) (12 pages) Paper No: MANU-17-1020; doi: 10.1115/1.4037419 History: Received January 13, 2017; Revised June 29, 2017

Machinery condition monitoring and fault diagnosis are essential for early detection of equipment malfunctions or failures, which insure productivity, quality, and safety in the manufacturing process. This paper aims at extracting fault features of rolling element bearings at the incipient fault stage. K-singular value decomposition (K-SVD), one technique for sparse representation of signals, is used for study. In K-SVD, its dictionary is trained from data by machine learning techniques, which allows more flexibility to adapt to variation of real signals than the predefined dictionaries. Analysis on simulated bearing signals and real signals shows that K-SVD can give better bearing fault features than the predefined dictionaries such as wavelet dictionaries. However, during our simulation study, K-SVD was found to have large representation error under heavy noise. To reduce the noise effect, minimum entropy deconvolution (MED) is used as a prefilter. The combination of MED and K-SVD is proposed for incipient bearing fault detection. The method is verified by simulation and experimental study. It is shown that the proposed method can effectively extract the impulsive fault feature of the tested bearing at its incipient fault stage.

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References

Ho, D. , and Randall, R. , 2000, “ Optimisation of Bearing Diagnostic Techniques Using Simulated and Actual Bearing Fault Signals,” Mech. Syst. Signal Process., 14(5), pp. 763–788. [CrossRef]
Antoni, J. , and Randall, R. B. , 2006, “ The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines,” Mech. Syst. Signal Process., 20(2), pp. 308–331. [CrossRef]
Antoni, J. , 2006, “ The Spectral Kurtosis: A Useful Tool for Characterising Non-Stationary Signals,” Mech. Syst. Signal Process., 20(2), pp. 282–307. [CrossRef]
Randall, R. B. , Antoni, J. , and Chobsaard, S. , 2001, “ The Relationship Between Spectral Correlation and Envelope Analysis in the Diagnostics of Bearing Faults and Other Cyclostationary Machine Signals,” Mech. Syst. Signal Process., 15(5), pp. 945–962. [CrossRef]
Cocconcelli, M. , Zimroz, R. , Rubini, R. , and Bartelmus, W. , 2012, “ STFT Based Approach for Ball Bearing Fault Detection in a Varying Speed Motor,” Condition Monitoring of Machinery in Non-Stationary Operations, Springer, Berlin, pp. 41–50. [CrossRef]
Lou, X. S. , and Loparo, K. A. , 2004, “ Bearing Fault Diagnosis Based on Wavelet Transform and Fuzzy Inference,” Mech. Syst. Signal Process., 18(5), pp. 1077–1095. [CrossRef]
Peng, Z. K. , and Chu, F. L. , 2004, “ Application of the Wavelet Transform in Machine Condition Monitoring and Fault Diagnostics: A Review With Bibliography,” Mech. Syst. Signal Process., 18(2), pp. 199–221. [CrossRef]
Feng, Y. H. , and Schlindwein, F. S. , 2009, “ Normalized Wavelet Packets Quantifiers for Condition Monitoring,” Mech. Syst. Signal Process., 23(3), pp. 712–723. [CrossRef]
Baydar, N. , and Ball, A. , 2001, “ A Comparative Study of Acoustic and Vibration Signals in Detection of Gear Failures Using Wigner-Ville Distribution,” Mech. Syst. Signal Process., 15(6), pp. 1091–1107. [CrossRef]
Yu, D. J. , Cheng, J. S. , and Yang, Y. , 2005, “ Application of EMD Method and Hilbert Spectrum to the Fault Diagnosis of Roller Bearings,” Mech. Syst. Signal Process., 19(2), pp. 259–270. [CrossRef]
Li, H. , Zhang, Y. P. , and Zheng, H. Q. , 2009, “ Hilbert-Huang Transform and Marginal Spectrum for Detection and Diagnosis of Localized Defects in Roller Bearings,” J. Mech. Sci. Technol., 23(2), pp. 291–301. [CrossRef]
Olshausen, B. A. , 1996, “ Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images,” Nature, 381(6583), pp. 607–609. [CrossRef] [PubMed]
Rubinstein, R. , Bruckstein, A. M. , and Elad, M. , 2010, “ Dictionaries for Sparse Representation Modeling,” Proc. IEEE, 98(6), pp. 1045–1057. [CrossRef]
Liu, B. , Ling, S. F. , and Gribonval, R. , 2002, “ Bearing Failure Detection Using Matching Pursuit,” NDT&E Int., 35(4), pp. 255–262. [CrossRef]
Yang, H. Y. , Mathew, J. , and Ma, L. , 2005, “ Fault Diagnosis of Rolling Element Bearings Using Basis Pursuit,” Mech. Syst. Signal Process., 19(2), pp. 341–356. [CrossRef]
Feng, Z. P. , and Chu, F. L. , 2007, “ Application of Atomic Decomposition to Gear Damage Detection,” J. Sound Vib., 302(1–2), pp. 138–151. [CrossRef]
Cui, L. , Wang, J. , and Lee, S. , 2014, “ Matching Pursuit of an Adaptive Impulse Dictionary for Bearing Fault Diagnosis,” J. Sound Vib., 333(10), pp. 2840–2862. [CrossRef]
Tosic, I. , and Frossard, P. , 2011, “ Dictionary Learning,” IEEE Signal Process. Mag., 28(2), pp. 27–38. [CrossRef]
Olshausen, B. A. , and Field, D. J. , 1997, “ Sparse Coding With an Overcomplete Basis Set: A Strategy Employed by V1?,” Vision Res., 37(23), pp. 3311–3325. [CrossRef] [PubMed]
Kreutz-Delgado, K. , Murray, J. F. , Rao, B. D. , Engan, K. , Lee, T. W. , and Sejnowski, T. J. , 2003, “ Dictionary Learning Algorithms for Sparse Representation,” Neural Comput., 15(2), pp. 349–396. [CrossRef] [PubMed]
Engan, K. , Aase, S. O. , and Husoy, J. H. , 1999, “ Method of Optimal Directions for Frame Design,” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Phoenix, AZ, Mar. 15–19, pp. 2443–2446.
Aharon, M. , Elad, M. , and Bruckstein, A. , 2006, “ K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process., 54(11), pp. 4311–4322. [CrossRef]
Blumensath, T. , and Davies, M. , 2006, “ Sparse and Shift-Invariant Representations of Music,” IEEE Trans. Audio Speech Lang. Process., 14(1), pp. 50–57. [CrossRef]
Liu, H. N. , Liu, C. L. , and Huang, Y. X. , 2011, “ Adaptive Feature Extraction Using Sparse Coding for Machinery Fault Diagnosis,” Mech. Syst. Signal Process., 25(2), pp. 558–574. [CrossRef]
Tang, H. F. , Chen, J. , and Dong, G. M. , 2014, “ Sparse Representation Based Latent Components Analysis for Machinery Weak Fault Detection,” Mech. Syst. Signal Process., 46(2), pp. 373–388. [CrossRef]
Zhou, H. T. , Chen, J. , Dong, G. M. , and Wang, R. , 2016, “ Detection and Diagnosis of Bearing Faults Using Shift-Invariant Dictionary Learning and Hidden Markov Model,” Mech. Syst. Signal Process., 72–73, pp. 65–79. [CrossRef]
Zhu, K. P. , and Vogel-Heuser, B. , 2014, “ Sparse Representation and Its Applications in Micro-Milling Condition Monitoring: Noise Separation and Tool Condition Monitoring,” Int. J. Adv. Manuf. Technol., 70(1–4), pp. 185–199. [CrossRef]
Chen, X. , Du, Z. , Li, J. , Li, X. , and Zhang, H. , 2014, “ Compressed Sensing Based on Dictionary Learning for Extracting Impulse Components,” Signal Process., 96(Part A), pp. 94–109. [CrossRef]
Feng, Z. P. , and Liang, M. , 2016, “ Complex Signal Analysis for Planetary Gearbox Fault Diagnosis Via Shift Invariant Dictionary Learning,” Measurement, 90, pp. 382–395. [CrossRef]
Elad, M. , and Aharon, M. , 2006, “ Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries,” IEEE Trans. Image Process., 15(12), pp. 3736–3745. [CrossRef] [PubMed]
Wiggins, R. A. , 1978, “ Minimum Entropy Deconvolution,” Geoexploration, 16(1–2), pp. 21–35. [CrossRef]
Endo, H. , and Randall, R. B. , 2007, “ Enhancement of Autoregressive Model Based Gear Tooth Fault Detection Technique by the Use of Minimum Entropy Deconvolution Filter,” Mech. Syst. Signal Process., 21(2), pp. 906–919. [CrossRef]
Sawalhi, N. , Randall, R. B. , and Endo, H. , 2007, “ The Enhancement of Fault Detection and Diagnosis in Rolling Element Bearings Using Minimum Entropy Deconvolution Combined With Spectral Kurtosis,” Mech. Syst. Signal Process., 21(6), pp. 2616–2633. [CrossRef]
Jiang, R. , Chen, J. , Dong, G. , Liu, T. , and Xiao, W. , 2013, “ The Weak Fault Diagnosis and Condition Monitoring of Rolling Element Bearing Using Minimum Entropy Deconvolution and Envelope Spectrum,” Proc. Inst. Mech. Eng., Part C, 227(5), pp. 1116–1129. [CrossRef]
Aharon, M. , 2006, “ Overcomplete Dictionaries for Sparse Representation of Signals,” Ph.D. thesis, Technion-Israel Institute of Technology, Faculty of Computer Science, Haifa, Israel. http://www.cs.technion.ac.il/~michalo/MichalAharonPhDThesis.pdf
Mallat, S. G. , and Zhang, Z. , 1993, “ Matching Pursuits With Time-Frequency Dictionaries,” IEEE Trans. Signal Process., 41(12), pp. 3397–3415. [CrossRef]
Pati, Y. C. , Rezaiifar, R. , and Krishnaprasad, P. S. , 1993, “ Orthogonal Matching Pursuit: Recursive Function Approximation With Applications to Wavelet Decomposition,” IEEE Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, CA, Nov. 1–3, pp. 40–44.
Chen, S. S. B. , Donoho, D. L. , and Saunders, M. A. , 1998, “ Atomic Decomposition by Basis Pursuit,” SIAM J. Sci. Comput., 20(1), pp. 33–61. [CrossRef]
McFadden, P. D. , and Smith, J. D. , 1984, “ Model for the Vibration Produced by a Single Point Defect in a Rolling Element Bearing,” J. Sound Vib., 96(1), pp. 69–82. [CrossRef]
McFadden, P. D. , and Smith, J. D. , 1985, “ The Vibration Produced by Multiple Point Defects in a Rolling Element Bearing,” J. Sound Vib., 98(2), pp. 263–273. [CrossRef]
Antoni, J. , and Randall, R. B. , 2002, “ Differential Diagnosis of Gear and Bearing Faults,” ASME J. Vib. Acoust., 124(2), pp. 165–171. [CrossRef]
Antoni, J. , 2007, “ Cyclic Spectral Analysis of Rolling-Element Bearing Signals: Facts and Fictions,” J. Sound Vib., 304(3–5), pp. 497–529. [CrossRef]
Pan, Y. N. , Chen, J. , and Li, X. L. , 2009, “ Spectral Entropy: A Complementary Index for Rolling Element Bearing Performance Degradation Assessment,” Proc. Inst. Mech. Eng., Part C, 223(5), pp. 1223–1231. [CrossRef]

Figures

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Fig. 1

The process of dictionary learning

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Fig. 2

Input, output, and objective of K-SVD

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Fig. 3

Flowchart of the K-SVD algorithm

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Fig. 4

The simulation bearing signal with inner race fault

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Fig. 5

Nine randomly selected atoms from the learned dictionary

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Fig. 6

The denoised signal using K-SVD method

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Fig. 7

The effect of noise on reconstruction accuracy

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Fig. 8

The effect of total number of atoms on K-SVD: (a) reconstruction accuracy and (b) computation time

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Fig. 9

The comparison of approximation error between K-SVD dictionary and predefined dictionaries

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Fig. 10

Bearing fault feature extraction based on MED and K-SVD

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Fig. 11

The original simulated signal: (a) time waveform and (b) envelope frequency spectrum

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Fig. 12

The denoised signal using MED: (a) time waveform and (b) envelope frequency spectrum

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Fig. 13

The denoised signal using MED and K-SVD: (a) time waveform and (b) envelope frequency spectrum

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Fig. 14

The denoised signal using K-SVD only: (a) time waveform and (b) envelope frequency spectrum

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Fig. 15

The denoised signal using SK filter: (a) time waveform and (b) envelope frequency spectrum

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Fig. 16

Testing object: (a) locations of acceleration sensors and (b) the sketch of sensors installations

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Fig. 17

Experiment equipment

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Fig. 18

Failure on rolling element bearing

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Fig. 19

The root-mean-square (RMS) value during the whole life of the tested bearing

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Fig. 20

The time waveform and its frequency spectrum in each stage: (a) and (b) normal stage; (c) and (d) incipient fault stage; (e) and (f) severe fault stage

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Fig. 21

The original signal at 1877th min: (a) time waveform and (b) frequency spectrum

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Fig. 22

The filtered signal using MED: (a) time waveform and (b) frequency spectrum

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Fig. 23

Nine atoms in K-SVD dictionary

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Fig. 24

The denoised signal using MED and K-SVD: (a) time waveform and (b) envelope frequency spectrum

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Fig. 25

The denoised signal using SK filter: (a) time waveform and (b) envelope frequency spectrum

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Fig. 26

Analysis results using predefined dictionary Db8: (a) denoised signal using MP, (b) envelope spectrum of (a), (c) denoised signal using BP, and (d) envelope spectrum of (c)

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