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Sparse representation by novel cascaded dictionary for bearing fault diagnosis using bi-damped wavelet

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Abstract

Vibration-based bearing condition monitoring of rotating machinery is of great importance for improving production efficiency and ensuring operational safety in the manufacturing industry. Sparse representation is able to effectively extract inherent impulse features from fault vibration signals corrupted by noise and harmonic interference, of which the performance is directly determined by dictionaries. In this study, the typical drawbacks of commonly used dictionaries are addressed using a novel cascaded dictionary. Period-assisted bi-damped wavelets with specific shapes are employed as the initial dictionary atoms to achieve overall matches with impulse features. Subsequently, the initial atoms are subjected to the K-singular value decomposition (K-SVD) for a secondary learning to obtain a cascaded dictionary that matches the real impulse features globally and locally. Finally, faulty vibration signals are recovered in segments using the cascaded dictionary and orthogonal matching pursuit (OMP). The results on the signals from the simulations, experiments, and real-world engineering confirm that the proposed cascaded dictionary consistently outperforms three other leading methods. Furthermore, the proposed cascaded dictionary is proved to be suitable for practical engineering diagnosis because of its outstanding anti-noise capabilities and self-adaptability.

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Data availability

The data used to support the finding of this study are available from the corresponding author upon request.

Code availability

The algorithm described in this paper is still being studied by the research group, so the code has not been publicly disclosed.

References

  1. Liang M, Cao P, Tang J (2021) Rolling bearing fault diagnosis based on feature fusion with parallel convolutional neural network. Int J Adv Manuf Technol 112(3):819–831. https://doi.org/10.1007/s00170-020-06401-8

    Article  Google Scholar 

  2. Youcef Khodja A, Guersi N, Saadi MN, Boutasseta, N (2020) Rolling element bearing fault diagnosis for rotating machinery using vibration spectrum imaging and convolutional neural networks. Int J Adv Manuf Technol 106(5):1737-1751. https://doi.org/10.1007/s00170-019-04726-7

  3. Ma H, Li S, Lu J, Gong S, Yu T (2022) Impulsive wavelet based probability sparse coding model for bearing fault diagnosis. Measurement 194:110969. https://doi.org/10.1016/j.meaurement.2022.110969

    Article  Google Scholar 

  4. Chen G, Yan C, Meng J, Wang H, Wu L (2021) Improved VMD-FRFT based on initial center frequency for early fault diagnosis of rolling element bearing. Meas Sci Technol 32(11):115024. https://doi.org/10.1088/1361-6501/ac1613

  5. Lu Y, Xie R, Liang S (2019) Bearing fault diagnosis with nonlinear adaptive dictionary learning. Int J Adv Manuf Technol 102(9):4227–4239. https://doi.org/10.1007/s00170-019-03455-1

    Article  Google Scholar 

  6. Song Y, Liu J, Chu N, Wu P, Wu D (2019) A novel demodulation method for rotating machinery based on time-frequency analysis and principal component analysis. J Sound Vib 442:645–656. https://doi.org/10.1016/j.sv.2018.11.024

    Article  Google Scholar 

  7. Li H, Liu T, Wu X, Chen Q (2020) An optimized VMD method and its applications in bearing fault diagnosis. Measurement 166:108185. https://doi.org/10.1016/j.measurement.2020.108185

    Article  Google Scholar 

  8. Wang H, Du W (2021) Early weak fault diagnosis of rolling element bearing based on resonance sparse decomposition and multi-objective information frequency band selection method. J Vib Control. https://doi.org/10.1177/10775463211020205

    Article  Google Scholar 

  9. Chui C, Jiang Q, Li L, Lu J (2021) Analysis of an adaptive short-time Fourier transform-based multicomponent signal separation method derived from linear chirp local approximation. J Comput Appl Math 396:113607. https://doi.org/10.1016/j.cam.2021.11360107

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu D, Cheng W, Wen W (2020) Rolling bearing fault diagnosis via STFT and improved instantaneous frequency estimation method. Procedia Manuf 49:166–172. https://doi.org/10.1016/j.promfg.2020.07.014

    Article  Google Scholar 

  11. Chen B, Shen B, Chen F, Tian H, Xiao W, Zhang F, Zhao C (2019) Fault diagnosis method based on integration of RSSD and wavelet transform to rolling bearing. Measurement 131:400–411. https://doi.org/10.1016/j.measurment.2018.07.0432018.07.043

    Article  Google Scholar 

  12. Zhang K, Ma C, Xu Y, Chen P, Du J (2021) Feature extraction method based on adaptive and concise empirical wavelet transform and its applications in bearing fault diagnosis. Measurement 172:108976. https://doi.org/10.10116/j.measument.2021.108976

    Article  Google Scholar 

  13. Gu J, Peng Y (2021) An improved complementary ensemble empirical mode decomposition method and its application in rolling bearing fault diagnosis. Digital Signal Process 113:103050. https://doi.org/10.1016/j.dsp.2021.-103050

    Article  Google Scholar 

  14. Dogan S, Tuncer T (2021) A novel statistical decimal pattern-based surface electromyogram signal classification method using tunable q-factor wavelet transform. Soft Comput 25(2):1085–1098. https://doi.org/10.1007/s00500-020-05205-y

    Article  Google Scholar 

  15. Zhang S, Liu Z, He S, Wang J, Chen L (2022) Improved double TQWT sparse representation using the MQGA algorithm and new norm for aviation bearing compound fault detection. Eng Appl Artif Intell 110:104741. https://doi.org/10.1016/j.engappai.2022.104741

    Article  Google Scholar 

  16. Mallat SG, Zhang Z (1993) Matching pursuits with time-frequency dictionaries. IEEE Trans Signal Process 41(12):3397–3415. https://doi.org/10.1109/78.258082

    Article  MATH  Google Scholar 

  17. Qin Y, Mao Y, Tang B (2013) Vibration signal component separation by iteratively using basis pursuit and its application in mechanical fault detection. J Sound Vib 332(20):5217–5235. https://doi.org/10.1016/j-.jsv.2013.04.021

    Article  Google Scholar 

  18. Wang S, Selesnick IW, Cai G, Ding B, Chen X (2019) Synthesis versus analysis priors via generalized minimax-concave penalty for sparsity-assisted machinery fault diagnosis. Mech Syst Signal Process 127:202–233. https://doi.org/10.1016/j.ymssp.2019.02.053

    Article  Google Scholar 

  19. Li J, Wang H, Song L (2021) A novel sparse feature extraction method based on sparse signal via dual-channel self-adaptive TQWT. Chin J Aeronaut 34(7):157–169. https://doi.org/10.1016/j.cja.2020.06.013

  20. Song L, Yan R (2019) Bearing fault diagnosis based on cluster-contraction stage-wise orthogonal-matching-pursuit. Measurement 140:240–253. https://doi.org/10.1016/j.measurement.-2019.03.061

    Article  Google Scholar 

  21. Jiang F, Ding K, He G, Du C (2021) Sparse dictionary design based on edited cepstrum and its application in rolling bearing fault diagnosis. J Sound Vib 490:115704. https://doi.org/10.1016/j.jsv.2020.115704

    Article  Google Scholar 

  22. Li Y, Zheng F, Xiong Q, Zhang W (2021) A secondary selection-based orthogonal matching pursuit method for rolling element bearing diagnosis. Measurement 176:109199. https://doi.org/10.1016/j.measurement.2021.109199

    Article  Google Scholar 

  23. Sun R, Yang Z, Zhai Z, Chen X (2019) Sparse representation based on parametric impulsive dictionary design for bearing fault diagnosis. Mech Syst Signal Process 122:737–753. https://doi.org/10.1016/j.ymssp.2018.12.054

    Article  Google Scholar 

  24. Qin Y (2017) A new family of model-based impulsive wavelets and their sparse representation for rolling bearing fault diagnosis. IEEE Trans Industr Electron 65(3):2716–2726. https://doi.org/10.1109/TIE.2017.2736510

    Article  Google Scholar 

  25. Fan W, Cai G, Zhu Z, Shen C, Huang W, Shang L (2015) Sparse representation of transients in wavelet basis and its application in gearbox fault feature extraction. Mech Syst Signal Process 56:230–245. https://doi.org/10.1016/j.ymssp.2014.10.016

    Article  Google Scholar 

  26. Wang S, Huang W, Zhu Z (2011) Transient modeling and parameter identification based on wavelet and correlation filtering for rotating machine fault diagnosis. Mech Syst Sig Process 25(4):1299–1320. https://doi.org/10.1016/j.ymssp.2010.10.013

    Article  Google Scholar 

  27. Deng F, Qiang Y, Yang S, Hao R, Liu Y (2021) Sparse representation of parametric dictionary based on fault impact matching for wheelset bearing fault diagnosis. ISA Trans 110:368–378. https://doi.org/10.1016/j.isatra.-2020.10.034

    Article  Google Scholar 

  28. He G, Li J, Ding K, Zhang Z (2022) Feature extraction of gear and bearing compound faults based on vibration signal sparse decomposition. Appl Acoust 189:108604. https://doi.org/10.1016/j.apacoust.2021.108604

    Article  Google Scholar 

  29. Li J, Tao J, Ding W, Zhang J, Meng Z (2022) Period-assisted adaptive parameterized wavelet dictionary and its sparse representation for periodic transient features of rolling bearing faults. Mech Syst Signal Process 169:108796. https://doi.org/10.1016/j.ymssp.2021

    Article  Google Scholar 

  30. Qin Y, Zou J, Tang B, Wang Y (2019) Transient feature extraction by the improved orthogonal matching pursuit and K-SVD algorithm with adaptive transient dictionary. IEEE Trans Industr Inf 16(1):215–227. https://doi.org/10.1109/TII.2019.2909305

    Article  Google Scholar 

  31. Yuan H, Wu N, Chen X (2021) Mechanical compound fault analysis method based on shift invariant dictionary learning and improved FastICA algorithm. Machines 9(8):144. https://doi.org/10.3390/machines9080144

  32. Li N, Huang W, Guo W, Gao G (2019) Zhu Z (2019) Multiple enhanced sparse decomposition for gearbox compound fault diagnosis. IEEE Trans Instrum Meas 69(3):770–781. https://doi.org/10.1109/TIM.2019.2905043

    Article  Google Scholar 

  33. Cui L, Gong X, Zhang J, Wang H (2016) Double-dictionary matching pursuit for fault extent evaluation of rolling bearing based on the Lempel-Ziv complexity. J Sound Vib 385:372–388. https://doi.org/10.1016/j.jsv.2016.09.-008

    Article  Google Scholar 

  34. He G, Ding K, Lin H (2016) Fault feature extraction of rolling element bearings using sparse representation. J Sound Vib 366:514–527. https://doi.org/10.1016/j.jsv.2015.12.020

    Article  Google Scholar 

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Funding

This work is supported by the National Science Foundation of China (no. 51665013), the Natural Science Foundation of Jiangxi Province (no. 20212BAB204007), and Jiangxi Province Graduate Student Innovation Project (YC2021-S422).

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Authors and Affiliations

  1. Key Laboratory of Conveyance and Equipment of the Ministry of Education of China, East China Jiaotong University, Nanchang, 330013, China

    Long Zhang, Lijuan Zhao & Chaobing Wang

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  1. Long Zhang
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  2. Lijuan Zhao
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  3. Chaobing Wang
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Contributions

Long Zhang: methodology, conceptualisation, resources, writing—review and editing, supervision; Lijuan Zhao: methodology, writing—original draft, software; Chaobing Wang: visualisation, analysis.

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Correspondence to Long Zhang.

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Zhang, L., Zhao, L. & Wang, C. Sparse representation by novel cascaded dictionary for bearing fault diagnosis using bi-damped wavelet. Int J Adv Manuf Technol 124, 2365–2381 (2023). https://doi.org/10.1007/s00170-022-10610-8

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