The sparse decomposition based on matching pursuit is an adaptive sparse expression method for signals. This paper proposes an idea concerning a composite dictionary multi-atom matching decomposition and reconstruction algorithm, and the introduction of threshold de-noising in the reconstruction algorithm. Based on the structural characteristics of gear fault signals, a composite dictionary combining the impulse time-frequency dictionary and the Fourier dictionary was constituted, and a genetic algorithm was applied to search for the best matching atom. The analysis results of gear fault simulation signals indicated the effectiveness of the hard threshold, and the impulse or harmonic characteristic components could be separately extracted. Meanwhile, the robustness of the composite dictionary multi-atom matching algorithm at different noise levels was investigated. Aiming at the effects of data lengths on the calculation efficiency of the algorithm, an improved segmented decomposition and reconstruction algorithm was proposed, and the calculation efficiency of the decomposition algorithm was significantly enhanced. In addition it is shown that the multi-atom matching algorithm was superior to the single-atom matching algorithm in both calculation efficiency and algorithm robustness. Finally, the above algorithm was applied to gear fault engineering signals, and achieved good results.
References
[1]
Capdessus, C; Sidahmed, M; Lacoume, JL. Cyclostationary Processes: Application in Gear Faults Early Diagnosis. Mech. Syst. Sign. Process 2000, 14, 371–385.
[2]
Lin, ST; McFadden, PD. Gear Vibration Analysis by B-spline Wavelet-based Linear Wavelet Transform. Mech. Syst. Sign. Process 1997, 1, 603–609.
[3]
Dalpiaz, G; Rivola, A; Rubini, R. Effectiveness and Sensitivity of Vibration Processing Techniques for Local Fault Detection in Gears. Mech. Syst. Sign. Process 2000, 14, 387–412.
[4]
Staszewski, WJ; Tomlinson, GR. Application of the Wavelet Transform to Fault Detection in a Spur Gear. Mech. Syst. Sign. Process 1994, 8, 289–307.
[5]
Yu, D; Yang, Y; Cheng, J. Application of Time-frequency Entropy Method Based on Hilbert-Huang Transform to Gear Fault Diagnosis. Measurement 2007, 40, 823–830.
[6]
Ricci, R; Pennacchi, P. Diagnosis of Gear Faults Based on EMD and Automatic Selection of Intrinsic Mode Functions. Mech. Syst. Sign. Process 2011, 25, 821–838.
[7]
Wang, WJ; McFadden, PD. Application of Orthogonal Wavelets to Early Gear Damage Detection. Mech. Syst. Sign. Process 1995, 9, 497–507.
[8]
Mallat, S; Zhang, Z. Matching Pursuit with Time-Frequency Dictionaries. IEEE Trans. Sign. Process 1993, 41, 3397–3415.
[9]
Lobo, AP; Loizou, PC. Voiced/Unvoiced Speech Discrimination in Noise Using Gabor Atomic Decomposition. Proceedings of ICASSP ’03: IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, 6–10 April 2003; 1, pp. 820–823.
[10]
Liu, L; Jia, Y; Liao, B. Low Bit-Rate Video Coding Based on Gabor Dictionary. Trans. Beijing Instit. Tech 2007, 27, 594–598.
[11]
McClure, MR; Carin, L. Matching Pursuits with a Wave-Based Dictionary. IEEE Trans. Sign. Process 1997, 45, 2912–2927.
[12]
Gribonval, R. Fast Matching Pursuit with a Multiscale Dictionary. IEEE Trans. Sign. Process 2001, 49, 994–1001.
[13]
Vera-Candeas, P; Ruiz-Reyes, N; Rosa-Zurera, M; Martinez-Munoz, D; Lopez-Ferreras, F. Transient Modeling by Matching Pursuits with a Wavelet Dictionary for Parametric Audio Coding. IEEE Sign. Process. Lett 2004, 11, 349–352.
[14]
Fei, X; Meng, Q; He, Z. Signal Decomposition with Matching Pursuits and Technology of Extracting Machinery Fault Feature Based on Impulse Time-Frequency Atom. J. Vib. Shock 2003, 22, 26–29.
[15]
Pi, W; Yu, D; Peng, F. Generalized Demodulation Method Based on Multi-scale Chirplet and Sparse Signal Decomposition and Its Application to Gear Fault Diagnosis. J. Mech. Eng 2010, 46, 59–64.
[16]
Chu, F; Peng, Z; Feng, Z; Li, Z. Modern Signal Process Method in Mechanical Fault Diagnosis; Beijing Science Press: Beijing, China, 2009; pp. 138–170.
[17]
Meng, Q; Fan, H; Wang, Q; He, Z. Extraction of Fault Features in Reciprocating Machinery Based on Matching Pursuits. J. Xi’an Jiaotong Univ 2001, 35, 696–699.
[18]
Zhao, F; Chen, J; Dong, G. Application of Matching Pursuit in Fault Diagnosis of Gear. J. Shanghai Jiaotong Univ 2009, 43, 910–913.
[19]
Feng, Z; Chu, F. Application of Atomic Decomposition to Gear Damage Detection. J. Sound Vib 2007, 302, 138–151.
[20]
Aharon, M; Elad, M; Bruckstein, A. K-SVD: An Algorithm for Designing over Complete Dictionaries for Sparse Representation. IEEE Trans. Sign. Process 2006, 54, 4311–4322.
[21]
Wang, G; Li, M; Yang, J; Xu, J. Fault Pattern Recognition of Rolling Bearings Based on Characteristic Waveform Sparse Matching. J. Univ. Sci. Tech. Beijing 2010, 32, 390–396.
[22]
Liang, W; Que, P; Chen, L; Lei, H. Residual Ratio Iteration Termination Condition for MP Method. J. Shanghai Jiaotong Univ 2010, 44, 171–175.
[23]
Holland, JH. Adaptation in Natural and Artificial System; University of Michigan Press: Ann Arbor, MI, USA, 1975.
[24]
Wang, W. Early Detection of Gear Tooth Cracking Using the Resonance Demodulation Technique. Mech. Syst. Sign. Process 2001, 15, 887–903.
