On multi-fault detection of rolling bearing through probabilistic principal component analysis denoising and Higuchi fractal dimension transformation

Abstract

Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.

Keywords

Probabilistic principal component analysis Higuchi fractal dimension fractal dimension rolling bearing multi-fault detection

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References

Accardo

Affinito

Carrozzi

, et al. (1997) Use of the fractal dimension for the analysis of electroencephalographic time series. Biological Cybernetics 77(5): 339–350.

Antoni

(2006) The spectral kurtosis: a useful tool for characterising non-stationary signals. Mechanical Systems and Signal Processing 20(2): 282–307.

Antoni

Randall

(2006) The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mechanical Systems and Signal Processing 20(2): 308–331.

Cao

(1997) Practical method for determining the minimum embedding dimension of a scalar time series. Physica D Nonlinear Phenomena 110(1–2): 43–50.

Chen

S-X

Chen

J-W

, et al. (2016) A hybrid P/KPCA-based approach for motion capture data automatic segmentation. Journal of Computational Methods in Sciences and Engineering 16(2): 197–206.

Dang

Huang

(2004) Study of the parameters used in calculating correlative dimension based on G. P algorithm. Application Research of Computers 2004(1): 48–51.

David

Joseph

(1996) Using the correlation dimension for vibration fault diagnosis of rolling element bearings. 1. Basic concepts. Mechanical Systems and Signal Processing 10(3): 241–250.

Ding

Zhao

Lin

, et al. (2019) Multi-objective iterative optimization algorithm based optimal wavelet filter selection for multi-fault diagnosis of rolling element bearings. ISA Transactions 88: 199–215.

Esteller

Vachtsevanos

Echauz

, et al. (2001) A comparison of waveform fractal dimension algorithms. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48(2): 177–183.

10.

Falconer

(1997) Techniques in Fractal Geometry. New Jersey: Wiley.

11.

Wang

, et al. (2016) Identification of multiple faults in rotating machinery based on minimum entropy deconvolution combined with spectral kurtosis. Mechanical Systems and Signal Processing 81: 235–249.

12.

Higuchi

(1988) Approach to an irregular time series on the basis of the fractal theory. Physica D: Nonlinear Phenomena 31(2): 277–283.

13.

Nan

Ren

(2018) Rolling bearing weak fault diagnosis based on PPCA and EWT. Journal of Vibration, Measurement and Diagnosis 38(2): 365–370.

14.

Jiang

Xiang

Wang

(2014) Rolling bearing fault diagnosis approach using probabilistic principal component analysis denoising and cyclic bispectrum. Journal of Vibration and Control 22(10): 2420–2433.

15.

Jolliffe

(1986) Principal Component Analysis. New York: Springer-Verlag.

16.

Liang

(2017) Incipient fault feature extraction for rotating machinery based on improved AR-minimum entropy deconvolution combined with variational mode decomposition approach. Entropy 19(7): 26.

17.

Liehr

Massopust

(2020) On the mathematical validity of the Higuchi method. Physica D-Nonlinear Phenomena 402: 9.

18.

Liu

D-d

Cheng

W-d

Wen

W-g

(2019) Demodulation spectrum analysis for multi-fault diagnosis of rolling bearing via chirplet path pursuit. Journal of Central South University 26(9): 2418–2431.

19.

Logan

Mathew

(1996) Using the correlation dimension for vibration fault diagnosis of rolling element bearings. 1. Basic concepts. Mechanical Systems and Signal Processing 10(3): 241–250.

20.

Maragos

Sun

F-K

(1993) Measuring the fractal dimension of signals: morphological covers and iterative optimization. IEEE Transactions on Signal Processing 41(1): 108–121.

21.

Mredhula

Dorairangaswamy

(2016) An effective filtering technique for image denoising using probabilistic principal component analysis (PPCA). Journal of Medical Imaging and Health Informatics 6(1): 194–203.

22.

Orbach

(1986) Dynamics of fractal networks. Science 231(4740): 814–819.

23.

Puchalski

Komorska

(2018) A generalised entropy in multifractal time signals analysis of mechanical vibration. Journal of Vibroengineering 20(4): 1667–1675.

24.

Raghavendra

Dutt

(2010) Signal characterization using fractal dimension. Fractals 18(3): 287–292.

25.

Rui

Yong

Song

(2018) Multi-fault diagnosis of rolling bearings via adaptive projection intrinsically transformed multivariate empirical mode decomposition and high order singular value decomposition. Sensors 18(4): 1210.

26.

Sharma

Amarnath

Kankar

(2019) Nonlinear dynamic analysis of defective rolling element bearing using Higuchi's fractal dimension. Sadhana-Academy Proceedings in Engineering Sciences 44(4): 29.

27.

Shi

Liang

(2015) A fractal-dimension-based envelope demodulation for rolling element bearing fault feature extraction from vibration signals. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 230(18): 3194–3211.

28.

Upadhyay

Kankar

(2018) Diagnosis of bearing defects using tunable Q-wavelet transform. Journal of Mechanical Science and Technology 32(2): 549–558.

29.

Wang

Liang

(2012) Identification of multiple transient faults based on the adaptive spectral kurtosis method. Journal of Sound and Vibration 331(2): 470–486.

30.

Wang

Kou

, et al. (2017) Weak fault diagnosis of wind turbine gearboxes based on MED-LMD. Entropy 19(6): 15.

31.

Zhang

Liu

Wan

, et al. (2020) Multi-faults diagnosis of rolling bearings via adaptive customization of flexible analytical wavelet bases. Chinese Journal of Aeronautics 33(2): 407–417.

32.

Zhao

Lin

, et al. (2014) Multi-fault detection of rolling element bearings under harsh working condition using IMF-based adaptive envelope order analysis. Sensors 14(11): 20320–20346.

33.

Zhu

(1992) Calculating fractal dimension by scale transformation-one of the basic considerations in simple calculation of fractal dimension. Inland Earthquake 6(3): 217–222.