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Research Papers

Some Improvements on a General Particle Filter Based Bayesian Approach for Extracting Bearing Fault Features

[+] Author and Article Information
Dong Wang

School of Aeronautics and Astronautics,
Sichuan University,
Chengdu 610065, China
e-mail: dongwang4-c@my.cityu.edu.hk

Qiang Miao

School of Aeronautics and Astronautics,
Sichuan University,
Chengdu 610065, China
e-mail: mqiang@scu.edu.cn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 10, 2014; final manuscript received February 20, 2015; published online April 22, 2015. Assoc. Editor: John Yu.

J. Vib. Acoust 137(4), 041016 (Aug 01, 2015) (9 pages) Paper No: VIB-14-1387; doi: 10.1115/1.4029994 History: Received October 10, 2014; Revised February 20, 2015; Online April 22, 2015

In our previous work, a general particle filter based Bayesian method was proposed to derive the graphical relationship between wavelet parameters, including center frequency and bandwidth, and to posteriorly find optimal wavelet parameters so as to extract bearing fault features. In this work, some improvements on the previous Bayesian method are proposed. First, the previous Bayesian method strongly depended on an initial uniform distribution to generate random particles. Here, a random particle represented a potential solution to optimize wavelet parameters. Once the random particles were obtained, the previous Bayesian method could not generate new random particles. To solve this problem, this paper introduces Gaussian random walk to joint posterior probability density functions of wavelet parameters so that new random particles can be generated from Gaussian random walk to improve optimization of wavelet parameters. Besides, Gaussian random walk is automatically initialized by the famous fast kurtogram. Second, the previous work used the random particles generated from the initial uniform distribution to generate measurements. Because the random particles used in the previous work were fixed, the measurements were also fixed. To solve this problem, the first measurement used in this paper is provided by the fast kurtogram, and its linear extrapolations are used to generate monotonically increasing measurements. With the monotonically increasing measurements, optimization of wavelet parameters is further improved. At last, because Gaussian random walk is able to generate new random particles from joint posterior probability density functions of wavelet parameters, the number of the random particles is not necessarily set to a high value that was used in the previous work. Two instance studies were investigated to illustrate how the Gaussian random walk based Bayesian method works. Comparisons with the famous fast kurtogram were conducted to demonstrate that the Gaussian random walk based Bayesian method can better extract bearing fault features.

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Figures

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Fig. 1

The flowchart of the Gaussian random walk based Bayesian method for identifying different bearing faults

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Fig. 2

The simulated bearing fault signal mixed with two low-frequency components and noises: (a) the temporal waveform and (b) its corresponding frequency spectrum

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Fig. 3

The paving of the fast kurtogram for processing the simulated bearing fault signal

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Fig. 4

The results obtained by using the fast kurtogram for processing the simulated bearing fault signal: (a) the squared envelope of the signal filtered by the fast kurtogram and (b) the frequency spectrum of the signal shown in (a)

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Fig. 5

The initial joint posterior probability density function of wavelet parameters at iteration 0 for processing the simulated bearing fault signal

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Fig. 6

The joint posterior probability density function of wavelet parameters at iteration 1 for processing the simulated bearing fault signal

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Fig. 7

The joint posterior probability density function of wavelet parameters at iteration 2 for processing the simulated bearing fault signal

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Fig. 8

The joint posterior probability density function of wavelet parameters at iteration 3 for processing the simulated bearing fault signal

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Fig. 9

The joint posterior probability density function of wavelet parameters at iteration 4 for processing the simulated bearing fault signal

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Fig. 10

The joint posterior probability density function of wavelet parameters at iteration 5 for processing the simulated bearing fault signal

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Fig. 11

The frequency spectra of: (a) the optimal wavelet filter and (b) the signal filtered by the optimal filter for processing the simulated bearing fault signal

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Fig. 12

The results obtained by using the Gaussian random walk based Bayesian method for processing the simulated bearing fault signal: (a) the squared envelope of the signal filtered by the optimal wavelet filter and (b) the frequency spectrum of the signal shown in (a)

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Fig. 13

The bearing ball fault signal: (a) the temporal signal and (b) the frequency spectrum of the temporal signal

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Fig. 14

The paving of the fast kurtogram for processing the bearing ball fault signal

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Fig. 15

The results obtained by using the fast kurtogram for processing the bearing ball fault signal: (a) the squared envelope of the signal filtered by the fast kurtogram and (b) the frequency spectrum of the signal shown in (b)

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Fig. 16

The joint posterior probability density function of wavelet parameters at iteration 0 for processing the bearing ball fault signal

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Fig. 17

The joint posterior probability density function of wavelet parameters at iteration 1 for processing the bearing ball fault signal

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Fig. 18

The joint posterior probability density function of wavelet parameters at iteration 2 for processing the bearing ball fault signal

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Fig. 19

The joint posterior probability density function of wavelet parameters at iteration 3 for processing the bearing ball fault signal

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Fig. 20

The joint posterior probability density function of wavelet parameters at iteration 4 for processing the bearing ball fault signal

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Fig. 21

The joint posterior probability density function of wavelet parameters at iteration 5 for processing the bearing ball fault signal

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Fig. 22

The frequency spectra of: (a) the optimal wavelet filter and (b) the signal filtered by the optimal filter for processing the bearing ball fault signal

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Fig. 23

The results obtained by using the proposed Bayesian method for processing the bearing ball fault signal: (a) the squared envelope of the signal filtered by the optimal wavelet filter and (b) the frequency spectrum of the signal shown in (a)

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