Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis
Abstract
:1. Introduction
2. Kurtosis and Correlated Kurtosis
2.1. Kurtosis
2.2. Correlated Kurtosis
3. The Proposed Optimal Resonant Band Demodulation Method Based on an Improved Correlated Kurtosis
3.1. Redefinition of Correlated Kurtosis
3.2. An Improved Correlated Kurtosis
3.3. Performance Comparison
- Signal Y1:
- a unit-impulse function δ(20) and its length equals to 40.
- Signal Y2:
- a Dirac comb function composed by unit-impulse functions δ(20), δ(40) and δ(60), its length equals to 80.
- Signal Y3:
- a Dirac comb function composed by unit-impulse functions δ(20), δ(40), δ(60), δ(80) and δ(100), its length equals to 120.
- Signal Y4:
- a sine function and its length equals to 200.
- Signal Y5:
- a Gaussian noise function and its length equals to 200.
3.4. The Optimal Resonant Band Demodulation
- (1)
- Calculating the fault feature frequency according to the geometric parameters of the rolling bearing and operation conditions of the mechanical system.
- (2)
- Determining the searching range of the resonant bandwidth. As the band-pass filtered bandwidth should be greater than three times of the fault feature frequency, the searching range of the resonant bandwidth can be set as .
- (3)
- Determining the searching range of the resonant central frequency. As the filtered range of the Morlet wavelet filter is , the searching range of the resonant central frequency can be set as , where represents the sampling frequency.
- (4)
- Initializing the Particle Swarm Optimization algorithm. The dimension of the particle swarm is set as 2, the size of the particle swarm is set as 30. The initial particle swarm can be achieved in line with the searching settings in step (2) and step (3).
- (5)
- Performing SES analysis on the initial particle swarm, calculating their values of the improved correlated kurtosis and achieving the individual maximum and global maximum.
- (6)
- Updating speed and location of the particle swarm iteratively until the maximum iterations. Achieving the optimal resonant central frequency and bandwidth .
- (7)
- Setting the central frequency of the optimal complex Morlet wavelet filter as , the bandwidth of the optimal complex Morlet wavelet filter as . Achieving the optimal resonant band filtered signal.
- (8)
- Performing the SES of the optimal resonant band filtered signal and diagnosing faults of rolling bearings.
4. Analysis
4.1. Simulation Analysis
4.2. Experimental Analysis
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Signal | K | CK | ReCK |
---|---|---|---|
Y1 | 15.0526 | 0 | 0 |
Y2 | 15.0526 | 0.2222 | 13.3333 |
Y3 | 15.0526 | 0.16 | 16 |
Y4 | 0.2928 | 0.0048 | 0.9694 |
Y5 | −1.5 | 0.0068 | 1.35 |
Signal | SK | SESCK |
---|---|---|
Y1 | 15.0526 | 0 |
Y2 | 15.0526 | 13.3333 |
Y3 | 15.0526 | 16 |
No. | Fault Depth/mm | Fault Diameter/mm | Motor Load/kW | Rotating Speed/rpm | Fault Feature Frequency/Hz |
---|---|---|---|---|---|
IR007-0 | 2.7940 | 0.1778 | 0 | 1797 | 162 |
IR007-1 | 0.7355 | 1772 | 159 | ||
IR007-2 | 1.4710 | 1748 | 157 | ||
IR007-3 | 2.2065 | 1721 | 155 | ||
IR014-0 | 2.7940 | 0.3556 | 0 | 1796 | 162 |
IR014-1 | 0.7355 | 1774 | 160 | ||
IR014-2 | 1.4710 | 1752 | 158 | ||
IR014-3 | 2.2065 | 1728 | 156 | ||
IR021-0 | 2.7940 | 0.5334 | 0 | 1797 | 162 |
IR021-1 | 0.7355 | 1774 | 160 | ||
IR021-2 | 1.4710 | 1752 | 158 | ||
IR021-3 | 2.2065 | 1728 | 156 |
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Chen, X.; Zhang, B.; Feng, F.; Jiang, P. Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis. Sensors 2017, 17, 360. https://doi.org/10.3390/s17020360
Chen X, Zhang B, Feng F, Jiang P. Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis. Sensors. 2017; 17(2):360. https://doi.org/10.3390/s17020360
Chicago/Turabian StyleChen, Xianglong, Bingzhi Zhang, Fuzhou Feng, and Pengcheng Jiang. 2017. "Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis" Sensors 17, no. 2: 360. https://doi.org/10.3390/s17020360
APA StyleChen, X., Zhang, B., Feng, F., & Jiang, P. (2017). Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis. Sensors, 17(2), 360. https://doi.org/10.3390/s17020360