Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy
Abstract
:1. Introduction
2. The Multipoint Optimal Minimum Entropy Deconvolution Adjustment
- Step 1: Loading the raw vibration signal, , measured by an accelerometer and the range of the fault period, .
- Step 2: Selecting the appropriate filter length, , and window size.
- Step 3: Calculating , and from the signal, . Yielding the optimal filter from Equation (3). Obtaining the filtered signal, , from Equation (6).
- Step 4: Building an array of target impulse train vectors, separated by the periods, .
- Step 5: Applying the window function to the target vectors.
- Step 6: Calculating the spectrum of outputs.
- Step 7: Calculating the spectrum of MKurt values for each output.
- Step 8: Finding the maximum value of MKurt and the best match output.
- Step 9: Enveloping the spectrum analysis.
3. The Proposed Method for The Gearbox Fault Diagnosis
3.1. Basic Principle of Permutation Entropy
3.2. Multipoint Reciprocal Permutation Entropy
4. Simulations
5. Experimental Analysis
6. Conclusions
- The diagnoses of weak impact faults in complex faults were achieved using MOMEDA combined with a spectrum analysis.
- The MKurt-MOMEDA and MRPE-MOMEDA were able to identify the multi-faults of rotating machinery using simulation and experimental analysis.
- A comparison of the fault indication between MKurt-MOMEDA and MRPE-MOMEDA was investigated. Compared to MKurt, MRPE had an excellent tracking ability of the sources of impact faults under the same fault conditions. The MRPE values of the different points were greater. The difference of the MKurt values among the different points was small.
- The impact fault frequencies of 46.7 Hz and 45.3 Hz were extracted from the transmission vibration signal by MRPE-MOMEDA.
- Weak feature extraction in composite faults was difficult. There were fewer test failure samples and more different types of faults need to be further verified in the future.
Author Contributions
Acknowledgments
Conflicts of Interest
Abbreviations
MOMEDA | Multipoint Optional Minimum Entropy Deconvolution Adjusted |
MKurt | Multipoint Kurtosis |
MPE | Multipoint Permutation Entropy |
MRPE | Multipoint Reciprocal Permutation Entropy |
SampEn | Sample Entropy |
FIR | Finite Impulse Response |
FFT | Fast Fourier Transformation |
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Parameter | The 4th Gear Pair | Constantly Meshed Gear Pair | ||
---|---|---|---|---|
Drive Wheel | Driven Wheel | Drive Wheel | Driven Wheel | |
Gear number | 34 | 35 | 15 | 77 |
Rotational frequency (Hz) | 46.7 | 45.3 | 45.3 | 8.8 |
Mesh frequency (Hz) | 1586.7 | 679.5 |
Position | foc | fbc | fc | fic |
---|---|---|---|---|
Input shaft | 2.504 | 1.616 | 0.358 | 4.494 |
3.454 | 2.036 | 0.384 | 5.544 | |
Middle shaft | 7.32 | 3.324 | 0.3792 | 11.0808 |
6.61 | 2.9742 | 0.3792 | 9.914 | |
Output shaft | 0.891 | 0.576 | 0.081 | 1.2398 |
0.6748 | 0.435 | 0.075 | 1.0282 |
Data | Speed (r/min) | Sample Rate (k/s) | Frequency/Hz | Samples |
---|---|---|---|---|
1 | 2800 | 25.6 | 46.7 | 548.2 |
2 | 2800 | 25.6 | 45.4 | 563.8 |
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Sun, H.; Wu, C.; Liang, X.; Zeng, Q. Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy. Entropy 2018, 20, 850. https://doi.org/10.3390/e20110850
Sun H, Wu C, Liang X, Zeng Q. Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy. Entropy. 2018; 20(11):850. https://doi.org/10.3390/e20110850
Chicago/Turabian StyleSun, Huer, Chao Wu, Xiaohua Liang, and Qunfeng Zeng. 2018. "Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy" Entropy 20, no. 11: 850. https://doi.org/10.3390/e20110850
APA StyleSun, H., Wu, C., Liang, X., & Zeng, Q. (2018). Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy. Entropy, 20(11), 850. https://doi.org/10.3390/e20110850