Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis
Abstract
:1. Introduction
2. Time Shift Multiscale Fuzzy Entropy and Related Theories
2.1. Multiscale Entropy Method
2.2. Time Shift Multiscale Sample Entropy
2.3. Time Shift Multiscale Fuzzy Entropy
3. Comparison of TSME and TSMFE
3.1. Parameter Selection
3.2. Simulation Analysis
4. TSMFE and LapSVM Based Fault Diagnosis Method for Rolling Bearing
4.1. LapSVM Algorithm
4.2. The Proposed Fault Diagnosis Method
- (1)
- For given p kinds of states of rolling bearing, each state has mp samples and thus the number of whole samples is ;
- (2)
- TSMFE of all the M samples are calculated and the feature sets , are obtained, where represents the p-th feature sets;
- (3)
- The mp samples of the p-th state are randomly divided into h as marked sample sets, i.e., and (mp − h) as unmarked sample sets, i.e., ;
- (4)
- The sensitive fault features sets of training samples: both and are input to the LapSVM classifier for training, learning and testing.
4.3. Experimental Data Analysis
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
Abbreviations
Nomenclature | |||
AppEn | Approximate entropy | Time scale | |
SampEn | Sample entropy | X | Initial time series |
MSE | Multiscale sample entropy | N | Length of data |
SVM | Support vector machine | Embedding dimension | |
LapSVM | Laplace support vector machine | r | Similar tolerances |
FuzzyEn | Fuzzy entropy | k | Initial time point |
TSMFE | Time shift multiscale fuzzy entropy | Interval time | |
TSME | Time shift multiscale entropy | Upper rounding boundary | |
Norm | Normal rolling bearing | l | Number of given marked samples |
ORI | Outer race fault under fault diameters 0.1778 mm | u | Number of given unmarked samples |
BEI | Ball element under fault diameters 0.1778 mm | Manifold regularization item | |
IRI | Inner race fault under fault diameters 0.1778 mm | Manifold regularization framework | |
ORII | Outer race fault under fault diameters 0.5334 mm | Quadratic planning | |
BEII | Ball element under fault diameters 0.5334 mm | p | Number of rolling bearing states |
IRII | Inner race fault under fault diameters 0.5334 mm | M | Total number of samples |
SD | Standard deviation | p-th feature sets | |
L | Laplacian | Marked sample sets | |
V | Hinge loss function | Unmarked sample sets |
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Sample Sets | Faults | LapSVM1 | LapSVM2 | LapSVM3 | LapSVM4 | LapSVM5 | LapSVM6 |
---|---|---|---|---|---|---|---|
T1~T50 | Norm | +1(50) | |||||
T51~T100 | BEI | −1(50) | +1(50) | ||||
T101~T150 | BEII | −1(50) | −1(50) | +1(50) | |||
T151~T200 | IRI | −1(50) | −1(50) | −1(50) | +1(50) | ||
T201~T250 | IRII | −1(50) | −1(50) | −1(50) | −1(50) | +1(50) | |
T251~T300 | ORI | −1(50) | −1(50) | −1(50) | −1(50) | −1(50) | +1(50) |
T301~T350 | ORII | −1(50) | −1(50) | −1(50) | −1(50) | −1(50) | −1(50) |
Sample Sets | Faults | SVM1 | SVM2 | SVM3 | SVM4 | SVM5 | SVM6 |
---|---|---|---|---|---|---|---|
T1~T50 | Norm | +1(40) | |||||
T51~T100 | BEI | −1(40) | +1(40) | ||||
T101~T150 | BEII | −1(40) | −1(40) | +1(36) | |||
T151~T200 | IRI | −1(40) | −1(40) | −1(42) | +1(40) | ||
T201~T250 | IRII | −1(40) | −1(40) | −1(42) | −1(40) | +1(40) | |
T251~T300 | ORI | −1(40) | −1(40) | −1(40) | −1(40) | −1(40) | +1(40) |
T301~T350 | ORII | −1(40) | −1(40) | −1(40) | −1(40) | −1(40) | −1(40) |
Methods | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | |
---|---|---|---|---|---|---|---|---|---|---|---|
4 | MSE | 86.85 | 96.57 | 96.85 | 96.85 | 97.42 | 97.42 | 97.14 | 96.85 | 97.42 | 97.42 |
TSME | 86 | 91.43 | 92 | 92.57 | 93.43 | 96 | 95.71 | 96.29 | 96.29 | 96.87 | |
TSMFE | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | 99.14 | |
8 | MSE | 88.28 | 92.85 | 92.85 | 92.85 | 93.71 | 94.57 | 95.42 | 95.42 | 94.85 | 94.85 |
TSME | 96.29 | 96.57 | 96.29 | 96.86 | 97.14 | 97.43 | 97.43 | 97.71 | 97.71 | 97.71 | |
TSMFE | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
12 | MSE | 87.14 | 89.14 | 87.42 | 88 | 89.14 | 92.85 | 94.57 | 95.42 | 95.71 | 95.71 |
TSME | 92.85 | 93.42 | 93.42 | 94 | 94.28 | 94.57 | 95.14 | 95.71 | 96.57 | 96.28 | |
TSMFE | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
16 | MSE | 87.71 | 89.71 | 88.57 | 89.14 | 89.14 | 90.57 | 92.85 | 92.85 | 94 | 95.42 |
TSME | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | |
TSMFE | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | |
20 | MSE | 87.14 | 90 | 88.28 | 88 | 88.85 | 89.42 | 91.14 | 91.71 | 95.14 | 95.42 |
TSME | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | |
TSMFE | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 | 98.86 |
Methods | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | |
---|---|---|---|---|---|---|---|---|---|---|---|
4 | MSE | 78.26 | 87.01 | 87.07 | 87.14 | 86.84 | 85.31 | 84.87 | 84.82 | 85.23 | 87.24 |
TSME | 86.95 | 93.18 | 93.87 | 92.50 | 90.97 | 92.85 | 91.59 | 92.41 | 93.80 | 93.36 | |
TSMFE | 97.51 | 97.72 | 97.61 | 97.85 | 98.12 | 98.41 | 98.31 | 98.21 | 98.09 | 97.95 | |
8 | MSE | 79.81 | 84.41 | 83.33 | 85.00 | 84.21 | 84.52 | 84.45 | 83.92 | 85.23 | 85.20 |
TSME | 95.03 | 95.45 | 94.21 | 92.85 | 95.48 | 96.03 | 95.79 | 96.42 | 96.66 | 96.42 | |
TSMFE | 98.44 | 98.70 | 98.29 | 98.21 | 98.49 | 98.41 | 98.31 | 98.21 | 98.02 | 97.88 | |
12 | MSE | 77.32 | 84.74 | 85.37 | 84.28 | 85.71 | 83.73 | 84.03 | 83.48 | 83.80 | 84.18 |
TSME | 93.16 | 94.15 | 94.55 | 93.57 | 94.73 | 95.23 | 94.95 | 95.53 | 96.19 | 95.91 | |
TSMFE | 98.13 | 98.70 | 98.63 | 98.57 | 98.49 | 98.41 | 98.31 | 98.21 | 98.09 | 97.95 | |
16 | MSE | 77.32 | 83.11 | 81.63 | 80.00 | 81.95 | 83.73 | 84.45 | 83.48 | 83.33 | 82.65 |
TSME | 79.81 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 68.48 | 57.14 | 57.14 | 57.14 | |
TSMFE | 97.82 | 98.37 | 98.29 | 98.21 | 98.49 | 98.41 | 98.31 | 98.21 | 98.09 | 97.95 | |
20 | MSE | 77.01 | 78.57 | 79.59 | 80.71 | 81.57 | 79.36 | 81.09 | 80.35 | 82.85 | 81.12 |
TSME | 47.20 | 41.88 | 41.83 | 41.78 | 47.74 | 41.66 | 41.59 | 28.57 | 28.57 | 36.22 | |
TSMFE | 97.82 | 98.37 | 98.29 | 98.21 | 98.49 | 98.01 | 98.31 | 98.21 | 98.09 | 97.95 |
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Zhu, X.; Zheng, J.; Pan, H.; Bao, J.; Zhang, Y. Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis. Entropy 2018, 20, 602. https://doi.org/10.3390/e20080602
Zhu X, Zheng J, Pan H, Bao J, Zhang Y. Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis. Entropy. 2018; 20(8):602. https://doi.org/10.3390/e20080602
Chicago/Turabian StyleZhu, Xiaolong, Jinde Zheng, Haiyang Pan, Jiahan Bao, and Yifang Zhang. 2018. "Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis" Entropy 20, no. 8: 602. https://doi.org/10.3390/e20080602
APA StyleZhu, X., Zheng, J., Pan, H., Bao, J., & Zhang, Y. (2018). Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis. Entropy, 20(8), 602. https://doi.org/10.3390/e20080602