A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery
Abstract
:1. Introduction
2. Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy
2.1. Multivariate Fluctuating Dispersion Entropy (MFDE)
- (1)
- The multivariate time series is mapped to using a normal distribution function
- (2)
- The linear transformation maps Y to .
- (3)
- According to the definition of Shannon entropy, the multivariate fluctuation dispersion entropy of the original signal is:
2.2. Multivariate Multiscale Fluctuation Dispersion Entropy (MMFDE)
- (1)
- For a multivariable time series, with length L and number of signal channels N. Then, the coarse granulation time series of scale factor is:
- (2)
- MMFDE was obtained by calculating the MFDE of each coarse-grained multivariate time series under the same parameters. By extending the single-scale MFDE to the multi-scale, more information is obtained from the multi-scale coarse-grained time series of different scales to obtain the multi-scale MMFDE. However, in the coarse-grained multivariate time series whose MMFDE scale factor is , only the coarse-grained multivariate time series starting with is considered, and the remaining multivariable time series is missing. The relationship between the coarse-grained time series has not been taken into consideration, resulting in the lack of statistical information.
2.3. Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE)
- (1)
- For a multivariable time series with length L and number of signal channels N, the coarse-grained time series for the given scale factor is , where , where , .
- (2)
- The RCMMFDE of the original multivariable time series is:
2.4. RCMMFDE Feature Analysis
2.4.1. Mixed Analysis of White Noise and 1/f Noise
2.4.2. Analysis of Anti-Noise Performance
2.4.3. RCMMFDE Data Length Sensitivity Analysis
2.5. Fault Diagnosis Based on RCMMFDE
2.5.1. JMIM Feature Selection
2.5.2. RCMMFDE-JMIM-SVM Fault Diagnosis Algorithm
- Step 1.
- Signal acquisition: Through acceleration sensors installed at different positions of the rotating machinery to be monitored, multi-channel vibration signals of the rotating machinery under different speeds are collected. The data samples collected under different running speeds can form a fault sample data set.
- Step 2.
- Feature extraction: RCMMFDE algorithm is used to extract features from fault sample data to form feature data sets, which are divided into training data sets and test data sets.
- Step 3.
- Feature selection: JMIM algorithm is used to select the most sensitive sub-features of the feature.
- Step 4.
- SVM model training: SVM classifier is trained using sensitive features. The SVM classifier includes M-1 dichotomous SVM, where M is the type of fault sample.
- Step 5.
- Fault diagnosis: Input the samples of the test data set into the RCMMFDE-JMIM-SVM classifier to identify the fault types of different bearing samples.
3. Experimental Verification and Analysis
3.1. Validation of Gearbox Fault Data Set
3.1.1. Data Set Description
3.1.2. RCMMFDE-JMIM-SVM Sensitive Feature Number Analysis
3.1.3. RCMMFDE-JMIM-SVM Performance Analysis at Constant Speed
3.1.4. RCMMFDE-JMIM-SVM Performance Verification
3.2. Verification of Rolling Bearing Fault Data
3.2.1. Description of Rolling Bearing Fault Data Set
3.2.2. Rolling Bearing Fault Data Analysis
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Abbreviation | G1 | G2 | G3 | G4 | G5 | G6 | G7 | G8 | |
---|---|---|---|---|---|---|---|---|---|
Shaft | Input | Normal | Normal | Normal | Normal | Normal | ISI | Normal | ISI |
Output | Normal | Normal | Normal | Normal | Normal | Normal | Keyway wear | Normal | |
Bearing | Input shaft—Input end | Normal | Normal | Normal | BBF | BIF | BIF | BIF | Normal |
Intermediate shaft— Input shaft | Normal | Normal | Normal | Normal | BBF | BBF | Normal | BBF | |
Output shaft—Input end | Normal | Normal | Normal | Normal | BOF | BOF | Normal | BOF | |
Input shaft—Output end | Normal | Normal | Normal | Normal | Normal | Normal | Normal | Normal | |
Intermediate shaft— Output end | Normal | Normal | Normal | Normal | Normal | Normal | Normal | Normal | |
Output shaft—Output end | Normal | Normal | Normal | Normal | Normal | Normal | Normal | Normal | |
Gear | 32T | Normal | TSC | Normal | Normal | TSC | Normal | Normal | Normal |
96T | Normal | Normal | Normal | Normal | Normal | Normal | Normal | Normal | |
48T | Normal | GI | GI | GI | GI | Normal | Normal | Normal | |
80T | Normal | Normal | Normal | TRF | TRF | TRF | Normal | Normal |
No | State | Training Samples | Testing Samples | Class Label |
---|---|---|---|---|
1 | G1 | 200 | 100 | 1,0,0,0,0,0,0,0 |
2 | G2 | 200 | 100 | 0,1,0,0,0,0,0,0 |
3 | G3 | 200 | 100 | 0,0,1,0,0,0,0,0 |
4 | G4 | 200 | 100 | 0,0,0,1,0,0,0,0 |
5 | G5 | 200 | 100 | 0,0,0,0,1,0,0,0 |
6 | G6 | 200 | 100 | 0,0,0,0,0,1,0,0 |
7 | G7 | 200 | 100 | 0,0,0,0,0,0,1,0 |
8 | G8 | 200 | 100 | 0,0,0,0,0,0,0,1 |
Method | Parameter | |||||
---|---|---|---|---|---|---|
RCMMFE-JMIM-SVM | = 17 | m = 2 | r = 0.15 | d = 1 | = 25 | f = 2 |
RCMMSE-JMIM-SVM | = 12 | m = 2 | r = 0.15 | d = 1 | = 25 | |
RCMMPE-JMIM-SVM | = 17 | m = 2 | = 17 | |||
RCMMFDE-JMIM-SVM | = 20 | m = 2 | c = 6 | d = 1 | = 25 |
Method | Max Accuracy | Min Accuracy | Average Accuracy | Run Time |
---|---|---|---|---|
RCMMFDE-JMIM-SVM | 99.252 | 98.518 | 98.757 | 1.67 |
RCMMSE-JMIM-SVM | 96.882 | 96.215 | 96.648 | 1.14 |
RCMMPE-JMIM-SVM | 94.045 | 93.217 | 93.554 | 148.79 |
RCMMFE-JMIM-SVM | 97.867 | 97.305 | 97.694 | 8.28 |
State | Testing Samples | Accuracy/% | ||||
---|---|---|---|---|---|---|
RCMMFDE-JMIM-SVM | RCMMFE-JMIM-SVM | RCMMSE-JMIM-SVM | RCMMPE-JMIM-SVM | CFVS-SVM | ||
G1 | 180 | 99.425 | 98.627 | 98.129 | 96.951 | 97.273 |
G2 | 180 | 99.354 | 97.056 | 97.281 | 91.488 | 94.445 |
G3 | 180 | 97.812 | 95.627 | 98.835 | 97.538 | 97.758 |
G4 | 180 | 99.489 | 97.566 | 95.756 | 92.157 | 95.561 |
G5 | 180 | 99.105 | 97.634 | 96.018 | 92.266 | 93.891 |
G6 | 180 | 99.281 | 98.461 | 96.485 | 94.137 | 96.659 |
G7 | 180 | 99.577 | 97.343 | 97.528 | 94.513 | 96.562 |
G8 | 180 | 98.907 | 96.932 | 94.414 | 93.064 | 94.827 |
Total | 900 | 99.173 | 97.782 | 96.619 | 93.751 | 94.658 |
Bearing State | Abbreviation | Fault Width (mm) | Fault Depth (mm) | Threshing Cylinder Speed (r/min) |
---|---|---|---|---|
Normal | Normal | 0 | 0 | 80/160/240/320 |
Outer Ring Fault 1 | IRF07 | 0.7 | 3.7 | 80/160/240/320 |
Outer Ring Fault 2 | IRF10 | 1.0 | 3.7 | 80/160/240/320 |
Outer Ring Fault 3 | IRF12 | 1.2 | 3.7 | 80/160/240/320 |
Outer Ring Fault 4 | IRF15 | 1.5 | 3.7 | 80/160/240/320 |
Outer Ring Fault 1 | ORF07 | 0.7 | 3.2 | 80/160/240/320 |
Outer Ring Fault 2 | ORF10 | 1.0 | 3.2 | 80/160/240/320 |
Outer Ring Fault 3 | ORF12 | 1.2 | 3.2 | 80/160/240/320 |
Outer Ring Fault4 | ORF15 | 1.5 | 3.2 | 80/160/240/320 |
Composite Fault 1 | CF05 | 0.5/0.5 | 3.2/3.7 | 80/160/240/320 |
Composite Fault 2 | CF10 | 1.0/1.0 | 3.2/3.7 | 80/160/240/320 |
Bearing State | Testing Samples | RCMMFDE-JMIM-SVM | RCMMFE-JMIM-SVM | RCMMSE-JMIM-SVM | RCMMPE-JMIM-SVM | CFVS-SVM | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
MCR | Acc/% | MCR | Acc/% | MCR | Acc/% | MCR | Acc/% | MCR | Acc/% | ||
Normal | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | CF05 | 96.00 |
IRF07 | 25 | 0 | 100.00 | 0 | 100.00 | IRF10 | 96.00 | IRF12 | 88.00 | IRF10 | 92.00 |
IRF10 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | IRF07 | 96.00 | 0 | 100.00 |
IRF12 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | IRF10 | 96.00 |
IRF15 | 25 | 0 | 100.00 | 0 | 100.00 | IRF12 | 96.00 | 0 | 100.00 | 0 | 100.00 |
ORF07 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | ORF10 | 88.00 |
ORF10 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | ORF15 | 96.00 | 0 | 100.00 |
ORF12 | 25 | 0 | 100.00 | 0 | 100.00 | ORF12 | 92.00 | ORF10 | 96.00 | 0 | 100.00 |
ORF15 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | ORF12 | 96.00 |
CF05 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | CF10 | 96.00 | 0 | 100.00 |
CF10 | 25 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | 0 | 100.00 | CF05 | 96.00 |
Total | 275 | 0 | 100.00 | 0 | 100.00 | 4 | 99.27 | 7 | 97.46 | 9 | 96.73 |
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Xi, C.; Yang, G.; Liu, L.; Jiang, H.; Chen, X. A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery. Entropy 2021, 23, 128. https://doi.org/10.3390/e23010128
Xi C, Yang G, Liu L, Jiang H, Chen X. A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery. Entropy. 2021; 23(1):128. https://doi.org/10.3390/e23010128
Chicago/Turabian StyleXi, Chenbo, Guangyou Yang, Lang Liu, Hongyuan Jiang, and Xuehai Chen. 2021. "A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery" Entropy 23, no. 1: 128. https://doi.org/10.3390/e23010128