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Tensor-Based Denoising on Multi-dimensional Diagnostic Signals of Rolling Bearing

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Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Purpose

To improve fault diagnosis efficiency, a multidimensional denoising approach based on tensor decomposition is developed for solving multidimensional signal filtering.

Methods

The monitoring signals are decomposed via truncated high-order singular value decomposition (T-HOSVD) to obtain their factor matrices. With L-curve criterion, the appropriate truncation parameters in the tensor factorization are determined to denoise and reduce dimension of signals. Then, the performance of sequentially truncated HOSVD (ST-HOSVD) is verified to quantify the correlation between the dimension of signal and computation complexity. The proposed ST-HOSVD approach is then applied to reduce noise in torque, current and vibration signals collected on bearing test rig, respectively.

Results

Experimental results show that the performance of the T-HOSVD on signals denoising are poor with the dimension increasing. The ST-HOSVD approach can well remove noise and retain the working status features as much as possible. This tensor-based multidimensional signal filtering will be powerful tool for dealing with heterogeneous and multi-aspect data.

Conclusion

The computation complexity of L-curve algorithm will increase sharply with the dimension of signal increasing while optimizing truncated parameters, but that of ST-HOSVD will not vary so much. When the dimension of the tensor model is not too high, the effectiveness of L-curve-T-HOSVD is higher. Otherwise, the computation cost of the ST-HOSVD is relatively lower. Therefore, the priority should be given to the ST-HOSVD for denoising the higher dimensional diagnostic data set about the rolling bearing.

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Data availability

The data that support the findings of this study are openly avaliable in "https://mb.unipaderborn.de/kat/forschung/datacenter/bearing-datacenter/".

References

  1. Kou L, Qin Y, Zhao X, Chen X (2020) A multi-dimension end-to-end CNN model for rotating devices fault diagnosis on high-speed train Bogie. IEEE Trans Veh Technol 69(3):2513–2524

    Article  Google Scholar 

  2. Iqbal M, Madan AK (2022) CNC machine-bearing fault detection based on convolutional neural network using vibration and acoustic signal. J Vib Eng Technol 10(5):1613–1621

    Article  Google Scholar 

  3. Zeng C, Ng MK (2020) Decompositions of third-order tensors: HOSVD, T-SVD, and beyond. Numer Linear Algebr with Appl 27:1–15

    MathSciNet  Google Scholar 

  4. Biswas SK, Milanfar P (2016). Linear support tensor machine : pedestrian detection in thermal infrared images. IEEE Transactions on Image Processing. pp. 1–12

  5. Chen X, Zhang B, Gao D (2021) Bearing fault diagnosis base on multi-scale CNN and LSTM model. J Intell Manuf 32(4):971–987

    Article  Google Scholar 

  6. Hu C, Wang Y (2019) Multidimensional denoising of rotating machine based on tensor factorization. Mech Syst Signal Process 122:273–289

    Article  ADS  Google Scholar 

  7. Sharma V, Raghuwanshi NK, Jain AK (2021) Sensitive sub-band selection criteria for empirical wavelet transform to detect bearing fault based on vibration signals. J Vib Eng Technol 9(7):1603–1617

    Article  Google Scholar 

  8. Liu Y, Qian Q, Liu F, Lu S, He Q, Zhao J (2017) Wayside bearing fault diagnosis based on envelope analysis paved with time-domain interpolation resampling and weighted-correlation-coefficient-guided stochastic resonance. Shock Vib 2017:1–17

    Google Scholar 

  9. Wang Z, Jia L, Qin Y (2018) Adaptive diagnosis for rotating machineries using information geometrical Kernel-ELM based on VMD-SVD. Entropy 20(1):73

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  10. Qiao Z, Pan Z (2015) SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient. Measurement Science and Technology. 26:085014

    Article  ADS  Google Scholar 

  11. Unakafov AM, Keller K (2014) Conditional entropy of ordinal patterns. Phys D Nonlinear Phenom 269:94–102

    Article  ADS  MathSciNet  Google Scholar 

  12. Anandkumar A, Hsu D (2014) Tensor decompositions for learning latent variable models. J Mach Learn Res 15:2773–2832

    MathSciNet  Google Scholar 

  13. Yokota T, Lee N, Cichocki A (2017) Robust multilinear tensor rank estimation using higher order singular value decomposition and information criteria. IEEE Trans Signal Process 65(5):1196–1206

    Article  ADS  MathSciNet  Google Scholar 

  14. Miaoyan W, Song YS (2017). Tensor decompositions via two-mode higher-order SVD (HOSVD). The 20th International Conference on Artificial Intelligence and Statistics. PMLR 54:614–622.

  15. Minster R, Saibaba AK, Kilmer ME (2020) Randomized algorithms for low-rank tensor decompositions in the tucker. Siam J Math Data Sci 2(1):189–215

    Article  MathSciNet  Google Scholar 

  16. Zhang Y, Hofmann B (2020) On the second-order asymptotical regularization of linear Ill-posed inverse problems. Apolicable Anal 99(6):1000–1025

    Article  MathSciNet  Google Scholar 

  17. Xiao C, Yang C, Li M (2021) Efficient alternating least squares algorithms for truncated HOSVD of higher-order tensors. J Sci Comput 87(67):1–25

    MathSciNet  Google Scholar 

  18. Noschese S (2014) A modified truncated singular value decomposition method for discrete Ill- posed problems. Numer Linear Algebr with Appl 21(6):813–822

    Article  MathSciNet  Google Scholar 

  19. Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51(3):455–500

    Article  ADS  MathSciNet  Google Scholar 

  20. Mandic DP, Phan AH, Caiafa CF, Zhou G, Zhao Q, Lathauwer LD (2015) Tensor decompositions for signal processing applications. IEEE Signal Process Mag 145(March):145–163

    Google Scholar 

  21. Lu C, Feng J, Chen Y, Liu W, Lin Z (2020) Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans Pattern Anal Mach Intell 42(4):925–938

    Article  PubMed  Google Scholar 

  22. Li Y, Xu M, Wei Y, Huang W (2016) A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree. Meas J Int Meas Confed 77:80–94

    Article  Google Scholar 

  23. Vannieuwenhoven N, Vandebril RAF, Meerbergen K (2012) A new truncation strategy for the higher-order singular value decomposition. SIAM J Sci Comput 34(2):A1027–A1052

    Article  MathSciNet  Google Scholar 

  24. Xiao C, Yang C, Li M (2020) Efficient alternating least squares algorithms for truncated HOSVD of higher-order tensors. arXiv:2004.02583

  25. Rezghi M, Hosseini SM (2009) A new variant of L-curve for Tikhonov regularization. J Comput Appl Math 231(2):914–924

    Article  ADS  MathSciNet  Google Scholar 

  26. Abdelazeem M, Gobashy M (2007) Two dimensions gravity inverse problem using adaptive pruning L-curve. Bull Fac Sci Cairo Univ 75:93–115

    Google Scholar 

  27. Liu W, Wu C (2013) A predictor – corrector iterated Tikhonov regularization for linear Ill-posed inverse problems. Appl Math Comput 221:802–818

    MathSciNet  Google Scholar 

  28. Bernardi, A., Iannacito, M., Rocchini, D (2021) High order singular value decomposition for plant diversity estimation. Boll Unione Mat Ital 14, 557–591

    Article  MathSciNet  Google Scholar 

  29. Lessmeier C, Kimotho JK, Zimmer D, Sextro W (2016) Condition monitoring of bearing damage in electromechanical drive systems by using motor current signals of electric motors: a benchmark data set for data-driven classification. Third Eur Conf Progn Health Manag Soc 2016:152–156

    Google Scholar 

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Acknowledgements

This research is supported by the National Key R&D Program of China (NO. 2020YFB1600701).

Author information

Author notes

  1. Jie Xu and Hui Zhang have contributed equally to this work.

Authors and Affiliations

  1. State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Jie Xu & Hui Zhang

  2. School of Traffic and Transportation, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Jie Xu & Hui Zhang

  3. Jining Planning Design & Research Institute, Jining, 272000, People’s Republic of China

    Chuankai Sun

  4. Henan Rail Transit Research Institute Co., Ltd., Zhengzhou, 450000, People’s Republic of China

    Yihan Shi

  5. Zhengzhou Oil and Gas Transportation Sub-Company, PipeChina North Pipeline Company, Zhengzhou, 450008, People’s Republic of China

    Guanchu Shi

Authors
  1. Jie Xu
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  2. Hui Zhang
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  3. Chuankai Sun
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  4. Yihan Shi
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Correspondence to Jie Xu.

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Xu, J., Zhang, H., Sun, C. et al. Tensor-Based Denoising on Multi-dimensional Diagnostic Signals of Rolling Bearing. J. Vib. Eng. Technol. 12, 1263–1275 (2024). https://doi.org/10.1007/s42417-023-00905-9

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  • DOI: https://doi.org/10.1007/s42417-023-00905-9

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