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Research Papers

Influence of Poisson White Noise on the Response Statistics of Nonlinear System and Its Applications to Bearing Fault Diagnosis

[+] Author and Article Information
Dawen Huang

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China;
Jiangsu Key Laboratory of Mine
Mechanical and Electrical Equipment,
China University of Mining and Technology,
Xuzhou 221116, China

Jianhua Yang

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China;
Jiangsu Key Laboratory of Mine
Mechanical and Electrical Equipment,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: jianhuayang@cumt.edu.cn

Dengji Zhou

Key Laboratory of Power Machinery
and Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

Grzegorz Litak

Faculty of Mechanical Engineering,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland

Houguang Liu

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 12, 2018; final manuscript received January 9, 2019; published online January 30, 2019. Assoc. Editor: Tsuyoshi Inoue.

J. Comput. Nonlinear Dynam 14(3), 031010 (Jan 30, 2019) (11 pages) Paper No: CND-18-1462; doi: 10.1115/1.4042526 History: Received October 12, 2018; Revised January 09, 2019

In view of complex noise background in engineering practices, this paper presents a rescaled method to detect failure features of bearing structure in the Poisson white noise background. To realize the scale transformation of the fault signal with Poisson white noise, a general scale transformation (GST) method is introduced based on the second-order underdamped nonlinear system. The signal features are successfully extracted through the proposed rescaled method in the simulated and experimental cases. We focus on the influence of Poisson white noise parameters and damping coefficient on the response of nonlinear system. The impulse arrival rate and noise intensity have opposite effects on the realization of stochastic resonance (SR) and the extraction of bearing fault features. Poisson white noise with smaller impulse arrival rate or larger noise intensity is easier to induce SR to extract bearing fault features. The optimal matching between the nonlinear system and the input signal is formed by the optimization algorithm, which greatly improves the extraction efficiency of fault features. Compared with the normalized scale transformation (NST) method, the GST has significant advantages in recognizing the bearing structure failure. The differences and connections between Poisson white noise and Gaussian white noise are discussed in the rescaled system excited by the experiment signal. This paper might provide several practical values for recognizing bearing fault mode in the Poisson white noise.

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Figures

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Fig. 1

Poisson white noise Γ(t): (a) different impulse arrival rates β under the same noise intensity D =0.2 and (b) different noise intensities D under the same impulse arrival rate β = 10

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Fig. 2

SR response affected by Poisson white noise when m =500 and γ = 0.5: (a) SNR depends on noise intensity D for different impulse arrival rates β and (b) SNR depends on impulse arrival rate β for different noise intensities D

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Fig. 3

ASR response affected by Poisson white noise when m =3000 and γ = 0.5: (a) SNR depends on noise intensity D for different impulse arrival rates β and (b) SNR depends on impulse arrival rate β for different noise intensities D

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Fig. 4

The SR output SNR versus the time scale m: (a) different noise intensities D when β = 0.8 and γ = 0.5 and (b) different impulse arrival rates β when D =0.8 and γ = 0.5

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Fig. 5

The ASR output SNR versus the time scale m: (a) different noise intensities D when β = 0.8 and γ = 0.5 and (b) different impulse arrival rates β when D =0.8 and γ = 0.5

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Fig. 6

The SR output SNR depends on the damping factor γ: (a) different noise intensities D when β = 0.8 and m =750 and (b) different impulse arrival rates β when D =0.45 and m =750

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Fig. 7

The ASR output SNR depends on damping factor γ: (a) different noise intensities D when β = 0.8 and m =750 and (b) different impulse arrival rates β when D =0.45 and m =750

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Fig. 8

The experiment rig of defective bearings

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Fig. 9

The defective bearings: (a) inner ring damage (NU306E), (b) rolling element damage (N306E), (c) outer ring damage (N306E), and (d) the position of outer ring damage relative to the sensor

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Fig. 10

Analysis results of the inner ring damage when m =1000 and γ = 0.3: (a) vibration signal with Poisson white noise (D =0.25, β = 10), (b) enveloped signal, (c) high-pass filtered signal (the stop-band frequency is 100 Hz, the pass-band frequency is 105 Hz, the stop-band attenuation is 80 dB, and the pass-band ripple is 1 dB), (d) NST output, and (e) GST output

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Fig. 11

Analysis results of the rolling element damage when m =1000 and γ = 0.1: (a) vibration signal with Poisson white noise (D =0.2, β = 10), (b) enveloped signal, (c) high-pass filtered signal (the stop-band frequency is 63 Hz, the pass-band frequency is 68 Hz, the stop-band attenuation is 80 dB, and the pass-band ripple is 1 dB), (d) NST output, and (e) GST output

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Fig. 12

Analysis results of the outer ring damage when m =2000 and γ = 0.5: (a) vibration signal with Poisson white noise (D =0.1, β = 10), (b) high-pass filtered signal (the stop-band frequency is 55 Hz, the pass-band frequency is 60 Hz, the stop-band attenuation is 80 dB, and the pass-band ripple is 1 dB), (c) NST output, and (d) GST output

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Fig. 13

The fault vibration signals without noise: (a) inner ring damage (NU306E), (b) rolling element damage (N306E), and (c) outer ring damage (N306E)

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Fig. 14

The output SNR of the GST and NST methods when m =1000 and γ = 0.3: (a) SNR in dependence on the noise intensity D for different impulse arrival rates β and (b) SNR in dependence on the impulse arrival rate β for different noise intensities D

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