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Research Papers

Extracting Rolling Element Bearing Faults From Noisy Vibration Signal Using Kalman Filter

[+] Author and Article Information
Sidra Khanam

Industrial Tribology, Machine Dynamics,
and Maintenance Engineering Centre (ITMMEC),
Indian Institute of Technology, Delhi,
New Delhi 110 016, India
e-mail: sidra.khanam10@gmail.com

J. K. Dutt

Department of Mechanical Engineering,
Indian Institute of Technology, Delhi,
New Delhi-110 016, India
e-mail: jkrdutt@yahoo.co.in

N. Tandon

Industrial Tribology, Machine Dynamics,
and Maintenance Engineering Centre (ITMMEC),
Indian Institute of Technology, Delhi,
New Delhi 110 016, India
e-mail: ntandon@itmmec.iitd.ernet.in

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 17, 2012; final manuscript received January 29, 2014; published online April 1, 2014. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 136(3), 031008 (Apr 01, 2014) (11 pages) Paper No: VIB-12-1353; doi: 10.1115/1.4026946 History: Received December 17, 2012; Revised January 29, 2014

Vibration analysis has been widely accepted as a common and reliable method for bearing fault identification, however, the presence of noise in the measured signal poses the maximum amount of difficulty. Therefore, for the clearer detection of defect frequencies related to bearing faults, a denoising technique based on the Kalman filtering algorithm is presented in this paper. The Kalman filter yields a linear, unbiased, and minimum mean error variance recursive algorithm to optimally estimate the unknown states of a dynamic system from noisy data taken at discrete real time intervals. The dynamics of a rotor bearing system is presented through a linear model, where displacement and velocity vectors are chosen as states of the system. Process noise and measurement noise in the equations of motion take into account the modeling inaccuracies and vibration from other sources, respectively. The covariance matrix of the process noise has been obtained through the transfer function approach. The efficiency of the proposed technique is validated through experiments. Periodic noise and random noises obeying the white Gaussian, colored Gaussian and non-Gaussian distribution have been simulated and mixed with a clean experimental signal in order to study the efficiency of the standard Kalman filter under various noisy environments. Additionally, external vibrations to the test rig have been imparted through an electromechanical shaker. The results indicate an improvement in the signal to noise ratio, resulting in the clear identification of characteristic defect frequencies after passing the signal through the Kalman filter. The authors find that there is sufficient potential in using the Kalman filter as an effective tool to denoise the bearing vibration signal.

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Figures

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Fig. 1

The Kalman filter loop

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Fig. 5

Transfer characteristics of the bearing system with the outer race defect

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Fig. 6

Transfer characteristics of the bearing system with the inner race defect

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Fig. 7

Different noises and their temporal, spectral, autocovariance, and statistical distribution: (a) white Gaussian noise (WGN), (b) colored Gaussian noise (CGN), (c) non-Gaussian noise (NGN), and (d) periodic noise (PN)

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Fig. 4

Generation of the excitation force vector for the radial vibration measurement

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Fig. 3

(a) Schematic diagram of the test bearing, (b) rolling elements replaced by the spring and dash-pot, and (c) equivalent 2 DOF model representing the rotor bearing setup

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Fig. 2

A sketch of the test setup

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Fig. 8

Flow chart to estimate the states through the Kalman filter

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Fig. 9

Displacement signal of the housing with the defect on the inner race (Ns = 25 Hz) (time, frequency domain, enlarged view of the defect frequency domain)

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Fig. 10

Denoising effect of the Kalman filter for the WGN: (a) inner race defect signal mixed with the WGN (time domain), (b) spectrum of (a), (c) encircled zone of (b) enlarged, (d) Kalman filtered signal (time domain), (e) spectrum of (d), and (f) encircled zone of (e) enlarged

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Fig. 11

Denoising effect of the Kalman filter for the CGN: (a) inner race defect signal mixed with the CGN (time domain), (b) spectrum of (a), (c) encircled zone of (b) enlarged, (d) Kalman filtered signal (time domain), (e) spectrum of (d), and (f) encircled zone of (e) enlarged

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Fig. 12

Denoising effect of the Kalman filter for the NGN: (a) inner race defect signal mixed with the NGN (time domain), (b) spectrum of (a), (c) encircled zone of (b) enlarged, (d) Kalman filtered signal (time domain), (e) spectrum of (d), and (f) encircled zone of (e) enlarged

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Fig. 13

Denoising effect of the Kalman filter for the PN: (a) spectrum of inner race defect signal mixed with the PN, (b) enlarged view of the defect region of (a), (c) the Kalman filtered signal, and (d) encircled zone of (c) enlarged

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Fig. 14

Effect of the Kalman filter to denoise the bearing vibration spectrum with the inner race defect: (a) experimental noisy spectrum, (b) encircled zone of (a) enlarged, (c) denoising effect of the Kalman filter, and (d) encircled zone of (c) enlarged

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Fig. 15

Displacement signal of the housing with the defect on the outer race (Ns = 25 Hz) (time and frequency domain)

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Fig. 16

Outer race defect signal mixed with the WGN and the denoising effect of the Kalman filter: (a) outer race defect signal mixed with the WGN (time and frequency domain), and (b) the Kalman filtered signal (time and frequency domain)

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Fig. 17

Outer race defect signal mixed with the CGN and the denoising effect of the Kalman filter: (a) outer race defect signal mixed with the CGN (time and frequency domain), and (b) the Kalman filtered signal (time and frequency domain)

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Fig. 18

Outer race defect signal mixed with the NGN and the denoising effect of the Kalman filter: (a) outer race defect signal mixed with the NGN (time and frequency domain), and (b) the Kalman filtered signal (time and frequency domain)

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Fig. 19

Effect of the Kalman filter to denoise the bearing vibration spectrum with the outer race defect: (a) experimental noisy spectrum, (b) encircled zone of (a) enlarged, (c) denoising effect of the Kalman filter, and (d) encircled zone of (c) enlarged

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