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TECHNICAL PAPERS

K-Hybrid: A Kurtosis-Based Hybrid Thresholding Method for Mechanical Signal Denoising

[+] Author and Article Information
Hoonbin Hong

Department of Mechanical Engineering, University of Ottawa, 770 King Edward Avenue, Ottawa, Ontario, K1N 6N5, Canada

Ming Liang1

Department of Mechanical Engineering, University of Ottawa, 770 King Edward Avenue, Ottawa, Ontario, K1N 6N5, Canadaliang@eng.uottawa.ca

1

Corresponding author.

J. Vib. Acoust 129(4), 458-470 (Apr 12, 2007) (13 pages) doi:10.1115/1.2748467 History: Received May 05, 2006; Revised April 12, 2007

This paper presents a kurtosis-based hybrid thresholding method, K-hybrid, for denoising mechanical fault signals. The threshold used in the hybrid thresholding method is determined based on kurtosis, which is an important indicator of the signal-to-noise ratio (SNR) of a signal. This together with its sensitivity to outliers and data-driven nature makes a kurtosis-based threshold particularly suitable for on-line detection of mechanical faults featuring impulsive signals. To better reflect the signal composition, the proposed hybrid thresholding rule divides the wavelet transformed input signals into four zones associated with different denoising actions. This alleviates the difficulties present in the simple keep-or-remove and shrink-or-remove approaches adopted by the hard- and soft-thresholding rules. The boundaries of the four zones are on-line adjusted in response to the kurtosis change of the signal. Our simulation results suggest that the mean squared error (MSE) is unable to distinguish the results in terms of the amount of falsely identified impulses. It is therefore inappropriate to use MSE alone for evaluating the denoising results of mechanical signals. As such, a combined criterion incorporating both MSE and false identification power Pfalse is proposed. Our analysis has shown that the proposed K-hybrid approach outperforms the soft, hard, and BayesShrink thresholding methods in terms of the combined criterion. It also compares favorably to the MAP thresholding method for signals with low kurtosis or low SNR. The proposed approach has been successfully applied to noise reduction and fault feature extraction of bearing signals.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flowchart of the wavelet denoising method

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Figure 2

K-hybrid thresholding rule

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Figure 3

K-hybrid thresholding with four different thresholding zones (parameter k determines the width of each zone)

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Figure 4

Limitation of MSE as a criterion for evaluating denoising performance

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Figure 5

Simulated impulses (mean=0), impulse and noise mixtures, and comparisons between histograms of impulse, noise, and their mixture

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Figure 6

Comparison of denoising results (K-hybrid, soft and hard (σn=0.1))

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Figure 7

Comparison of denoising results (K-hybrid, soft and hard (σn=0.3))

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Figure 8

Comparison of K-hybrid, BayesShrink, and MAP denoising results (σn=0.1)

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Figure 9

Comparison of K-hybrid, BayesShrink, and MAP denoising results (σn=0.3)

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Figure 10

Comparison of K-hybrid, BayesShrink, and MAP denoising results (σn=0.4)

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Figure 11

Comparison of K-hybrid, BayesShrink, and MAP denoising results in terms of MSE, Pfalse, and C values

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Figure 12

Healthy bearing (SKF 6205-2RS)

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Figure 13

Denoising results of inner- and outer-race faults (fault size: 0.007in.(0.18mm)dia and 0.011in.(0.28mm) in depth, BPFI=159Hz, BPFO=105Hz)

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Figure 14

Denoising result of nonstationary signal

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