Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis
Abstract
:1. Introduction
2. Fractional Order Fuzzy Dispersion Entropy
2.1.
2.2. Parameter Selection
3. Experiments on Simulated Signals
3.1. Noise Signals Experiment
3.2. Chirp Signal Experiment
3.3. MIX Signal Experiment
4. Experiments on Bearing Fault Diagnosis
4.1. Analysis of Experiment Data
4.2. Single Feature Extraction and Classification
4.3. Double Features Extraction and Classification
4.4. Triple Features Extraction and Classification
5. Conclusions
- Fractional order calculation is introduced on the basis of fuzzy dispersion entropy (FuzzDE), and a new entropy called fractional order FDE () is proposed. Simulated experiments have shown that compared with , can provide more features of greater sensitivity to changes in the dynamics of the time series.
- is combined with , as well as to present a mixed features extraction method. For ten classes of bearing signals, the proposed mixed features fault diagnosis method achieves 100% recognition rate at only triple features.
- Regardless of how many features are selected, the proposed in this paper is the most effective in fault diagnosis compared to the other three fractional order entropies, where appears a total of 11 times in the combination of the triple features with the recognition rate of 100%
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
FuzzDE | Fuzzy Dispersion Entropy |
Fractional order fuzzy dispersion entropy | |
PE | Permutation entropy |
Fractional order permutation entropy | |
DE | Dispersion entropy |
Fractional order dispersion entropy | |
FDE | Fluctuation-based dispersion entropy |
Fractional order fluctuation-based dispersion entropy | |
NCDF | Normal cumulative distribution function |
SE | Sample entropy |
FRDE | Fluctuation-based reverse dispersion entropy |
RDE | Reverse dispersion entropy |
FuzzEn | Fuzzy entropy |
RCMDE | Refined composite multiscale dispersion entropy |
Generalized refined composite multiscale fluctuation-based fractional dispersion entropy | |
LM | Linear mapping |
TANSIG | Tangent sigmoid |
LOGSIG | Logarithm sigmoid |
SORT | Sorting method |
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Class | Label | Fault Size (mm) | Selected Data |
---|---|---|---|
Normal | NORM | 0 | 100_normal_3 |
Inner race fault | IR1 | 0.1778 | 108_IR007_3 |
Balling element fault | BE1 | 0.1778 | 121_B007_3 |
Outer race fault | OR1 | 0.1778 | 133_OR007@6_3 |
Inner race fault | IR2 | 0.3556 | 172_IR014_3 |
Balling element fault | BE2 | 0.3556 | 188_B014_3 |
Outer race fault | OR2 | 0.3556 | 200_OR014@6_3 |
Inner race fault | IR3 | 0.5334 | 212_IR021_3 |
Balling element fault | BE3 | 0.5334 | 225_B021_3 |
Outer race fault | OR3 | 0.5334 | 237_OR021@6_3 |
Entropy | Recognition Rates (%) | ||||
---|---|---|---|---|---|
82.8 | 81.6 | 74 | 68.4 | 67.6 | |
76.4 | 79.6 | 76.4 | 71.2 | 66.0 | |
59.6 | 56.8 | 58.4 | 56.8 | 54.0 | |
79.2 | 82.8 | 78.4 | 77.6 | 80.4 |
Feature Extraction Methods | Combinations | Recognition Rate (%) |
---|---|---|
-based | 91.6 | |
-based | 88.4 | |
-based | 58.4 | |
-based | 90.0 | |
Proposed method | & (1 of 3) | 99.6 |
Feature Extraction Methods | Combinations | Recognition Rate (%) |
---|---|---|
-based | 92 | |
-based | 92 | |
-based | 58 | |
-based | 91.6 | |
Proposed method | (1 of 15) | 100 |
Feature | Appear Times |
---|---|
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Li, Y.; Tang, B.; Geng, B.; Jiao, S. Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis. Fractal Fract. 2022, 6, 544. https://doi.org/10.3390/fractalfract6100544
Li Y, Tang B, Geng B, Jiao S. Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis. Fractal and Fractional. 2022; 6(10):544. https://doi.org/10.3390/fractalfract6100544
Chicago/Turabian StyleLi, Yuxing, Bingzhao Tang, Bo Geng, and Shangbin Jiao. 2022. "Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis" Fractal and Fractional 6, no. 10: 544. https://doi.org/10.3390/fractalfract6100544