A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM
Abstract
:1. Introduction
- A novel fault feature extraction method based on HRCMFDE is proposed. The method quantifies the high-frequency and low-frequency features of the measured time series by introducing the hierarchical theory algorithm, which effectively overcomes the problem of high-frequency information loss caused by the coarse-grained process. Meanwhile, HRCMFDE maps each element of the time series to different classes and generates different fluctuation dispersion patterns, which not only has strong anti-noise capability but also avoids the defect of losing amplitude information.
- The performance of the proposed rolling bearing fault diagnosis method is verified using two typical rotating machinery fault datasets. The experimental results show that the proposed fault diagnosis method can not only accurately identify the fault types with varying loads, but also have a high fault identification effect even under load migration.
2. Methodologies
2.1. Feature Extraction
2.1.1. Multiscale Fluctuation-Based Dispersion Entropy (MFDE)
2.1.2. Refined Composite Multiscale Fluctuation-Based Dispersion Entropy (RCMFDE)
2.1.3. Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy (HRCMFDE)
- Basic Principle
- Parameter Selection
- 1.
- Embedding dimension .
- 2.
- The number of classes .
- 3.
- Time delay .
- 4.
- Maximum scale factor .
- 5.
- Number of hierarchical layers .
- Simulation Signal Analysis
2.2. Fault Identification
2.2.1. Extreme Learning Machine (ELM)
2.2.2. Particle Swarm Optimization-Based Extreme Learning Machine (PSO-ELM)
3. Proposed Method
3.1. Data Preprocessing
3.2. Training Process
3.3. Testing Process
4. Experiments
4.1. Case 1: CWRU Dataset
4.1.1. Experiment Setup
4.1.2. Feature Extraction
4.1.3. Fault Identification
4.1.4. Performance Comparison
4.1.5. Load Migration
4.2. Case 2: MFPT Fault Dataset
4.2.1. Experiment Setup
4.2.2. Feature Extraction
4.2.3. Fault Identification
4.2.4. Performance Comparison
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AAPE | Amplitude aware permutation entropy |
ANN | Artificial neural network |
ApEn | Approximate entropy |
CMFDE | Composite multiscale fluctuation-based dispersion entropy |
CNN | Convolutional neural network |
CVs | Coefficients of variation |
CWRU | Case Western Reserve University |
CWT | Continuous wavelet transform |
DE | Dispersion entropy |
DLZC | Dispersion Lempel-Ziv complexity |
EEMD | Ensemble empirical mode decomposition |
ELM | Extreme learning machine |
EMD | Empirical mode decomposition |
FDE | Fluctuation-based dispersion entropy |
FDLZC | Fluctuation-based DLZC |
GA-ELM | Genetic algorithm optimized extreme learning machine |
GRCMFE | Generalized refined composite multiscale fuzzy entropy |
GSA-SVM | Gravitational search algorithm optimized support vector machine |
HCNN | Hierarchical convolutional neural network |
HFDE | Hierarchical fluctuation-based dispersion entropy |
HRCMFDE | Hierarchical refined composite multiscale fluctuation-based dispersion entropy |
IFBE | Improved frequency band entropy |
IMFs | Intrinsic mode functions |
KELM | Kernel extreme learning machine |
k-NN | K-nearest neighbor |
LMD | Local mean decomposition |
LSVM | Linear support vector machine |
LZC | Lempel-Ziv complexity |
MAAPE | Multiscale amplitude aware permutation entropy |
MFDE | Multiscale fluctuation-based dispersion entropy |
MFPT | Machinery Fault Prevention Technology |
M-RVM | Multiclass relevance vector machine |
MSE | Multiscale entropy |
MSST | Multi-synchro-squeezing transform |
NCDF | Normal cumulative distribution function |
NPLSSMM | Non-parallel least squares support matrix machine |
PCA | Principal component analysis |
PE | Permutation entropy |
PSO | Particle swarm optimization |
PSO-ELM | Particle swarm optimization-based extreme learning machine |
RCMFDE | Refined composite multiscale fluctuation-based dispersion entropy |
RCMFDLZC | Refined composite multiscale FDLZC |
RNN | Recurrent neural network |
SD | Standard deviation |
SE | Sample entropy |
SFC-DL | Sparse feature coding based on dictionary learning |
SLFN | Single-hidden layer feedforward neural network |
sps | sample per second |
STMSST | Second-order time-reassigned multi-synchro-squeezing transform |
SVM | Support vector machines |
VMD | Variational mode decomposition |
WGN | White Gaussian noise |
WPT | Wavelet packet transform |
WT | Wavelet transform |
WTFD | Wavelet time-frequency diagram |
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n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
m = 2 | 0.0211 | 0.0042 | 0.0066 | 0.0051 | 0.0140 | 0.0134 | 0.0105 | 0.0036 |
m = 3 | 0.0217 | 0.0045 | 0.0070 | 0.0057 | 0.0156 | 0.0132 | 0.0096 | 0.0038 |
m = 4 | 0.0211 | 0.0037 | 0.0067 | 0.0065 | 0.0169 | 0.0137 | 0.0101 | 0.0042 |
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
m = 2 | 0.0951 | 0.0061 | 0.0045 | 0.0048 | 0.0112 | 0.0162 | 0.0116 | 0.0112 |
m = 3 | 0.0972 | 0.0063 | 0.0044 | 0.0051 | 0.0115 | 0.0175 | 0.0134 | 0.0121 |
m = 4 | 0.0970 | 0.0052 | 0.0045 | 0.0055 | 0.0115 | 0.0180 | 0.0140 | 0.0129 |
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
c = 3 | 0.0301 | 0.0061 | 0.0102 | 0.0074 | 0.0950 | 0.1109 | 0.4438 | 0.4776 |
c = 6 | 0.0211 | 0.0042 | 0.0066 | 0.0051 | 0.0140 | 0.0134 | 0.0105 | 0.0036 |
c = 9 | 0.0176 | 0.0038 | 0.0061 | 0.0047 | 0.0108 | 0.0115 | 0.0127 | 0.0123 |
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
c = 3 | 0.1147 | 0.0085 | 0.0096 | 0.0062 | 0.0259 | 0.0533 | 0.1814 | 0.3336 |
c = 6 | 0.0951 | 0.0061 | 0.0045 | 0.0048 | 0.0112 | 0.0162 | 0.0116 | 0.0112 |
c = 9 | 0.0492 | 0.0046 | 0.0056 | 0.0037 | 0.0131 | 0.0208 | 0.0123 | 0.0119 |
Entropy | Embedding Dimension | Number of Classes | Time Delay | Number of Hierarchical Layers | Maximum Scale Factor |
---|---|---|---|---|---|
HFDE | m = 2 | c = 6 | d = 1 | n = 3 | \ |
MFDE | m = 2 | c = 6 | d = 1 | \ | τ max = 20 |
RCMFDE | m = 2 | c = 6 | d = 1 | \ | τ max = 20 |
HRCMFDE | m = 2 | c = 6 | d = 1 | n = 3 | τ max = 20 |
Fault Types | Severity (Inch) | Load (hp) | |||
---|---|---|---|---|---|
0 | 1 | 2 | 3 | ||
Normal | - | √ | √ | √ | √ |
Ball fault | 0.007 | √ | √ | √ | √ |
0.014 | √ | √ | √ | √ | |
0.021 | √ | √ | √ | √ | |
0.028 | √ | √ | √ | √ | |
Inner race fault | 0.007 | √ | √ | √ | √ |
0.014 | √ | √ | √ | √ | |
0.021 | √ | √ | √ | √ | |
0.028 | √ | √ | √ | √ | |
Outer race fault | 0.007 | √ | √ | √ | √ |
0.014 | √ | √ | √ | √ | |
0.021 | √ | √ | √ | √ | |
0.028 | * | * | * | * |
Labels | Fault Types | Abbreviations | Severity (inch) | Number of Training/Testing Samples |
---|---|---|---|---|
1 | Normal | N | - | 20/30 |
2 | Ball fault | B007 | 0.007 | 20/30 |
3 | B014 | 0.014 | 20/30 | |
4 | B021 | 0.021 | 20/30 | |
5 | B028 | 0.028 | 20/30 | |
6 | Inner race fault | I007 | 0.007 | 20/30 |
7 | I014 | 0.014 | 20/30 | |
8 | I021 | 0.021 | 20/30 | |
9 | I028 | 0.028 | 20/30 | |
10 | Outer race fault | O007 | 0.007 | 20/30 |
11 | O014 | 0.014 | 20/30 | |
12 | O021 | 0.021 | 20/30 |
Load | Fault Types | Number of Training Samples | Number of Testing Samples | Average Accuracy |
---|---|---|---|---|
0 hp | N B IR OR | 20 80 80 60 | 30 120 120 90 | 99.86% |
1 hp | N B IR OR | 20 80 80 60 | 30 120 120 90 | 99.78% |
2 hp | N B IR OR | 20 80 80 60 | 30 120 120 90 | 100% |
3 hp | N B IR OR | 20 80 80 60 | 30 120 120 90 | 100% |
Feature Extraction | Fault Identification | Load 0 hp | Load 1 hp | Load 2 hp | Load 3 hp | Average Accuracy |
---|---|---|---|---|---|---|
HFDE [33] | PSO-ELM | 99.72% | 100% | 100% | 99.81% | 99.88% |
MFDE [28] | PSO-ELM | 94.03% | 96.69% | 99.61% | 99.42% | 97.44% |
RCMFDE [31] | PSO-ELM | 98.36% | 99.39% | 100% | 99.92% | 99.42% |
HRCMFDE | PSO-ELM | 99.86% | 99.78% | 100% | 100% | 99.91% |
Num. | Feature Extraction | Fault Identification | Accuracy (%) | Training Time (s) | Testing Time (s) |
---|---|---|---|---|---|
1 | HRCMFDE | ELM [51] | 99.56 ± 0.53 | 0.0285 | 0.0085 |
2 | HRCMFDE | KELM [52] | 97.94 ± 2.87 | 0.0046 | 0.0013 |
3 | HRCMFDE | GA-ELM [53] | 99.86 ± 0.16 | 231.3569 | 28.6741 |
4 | HRCMFDE | PSO-ELM | 99.91 ± 0.11 | 11.3320 | 1.2427 |
Literature | Feature Extraction | Fault Identification | Number of Classes | Average Accuracy (%) |
---|---|---|---|---|
[54] | WTFD | NPLSSMM | 10 | 99.64 |
[55] | VMD+MPE | KPCA+CGOA-KELM | 4 | 99.67 |
[56] | CWT | CNN-SVM | 12 | 98.75 |
[25] | MAAPE | RF | 10 | 96.00 |
[57] | EEMD+PE | M-RVM | 4 | 99.58 |
[11] | RCMFDLZC | DAC | 12 | 96.08 |
This paper | HRCMFDE | PSO-ELM | 12 | 99.91 |
Fault Classes | Fault Types | Load (lb) | Sample Rate (sps) | Sample Time (s) | Data Points |
---|---|---|---|---|---|
Normal | Baseline | 270 | 97,656 | 6 | 585,936 |
Outer Race Fault | Outer Race Fault | 270 | 97,656 | 6 | 585,936 |
More Outer Race Fault | 25 | 48,828 | 3 | 146,484 | |
50 | 48,828 | 3 | 146,484 | ||
100 | 48,828 | 3 | 146,484 | ||
150 | 48,828 | 3 | 146,484 | ||
200 | 48,828 | 3 | 146,484 | ||
250 | 48,828 | 3 | 146,484 | ||
300 | 48,828 | 3 | 146,484 | ||
Inner Race Fault | Inner Race Fault | 0 | 48,828 | 3 | 146,484 |
50 | 48,828 | 3 | 146,484 | ||
100 | 48,828 | 3 | 146,484 | ||
150 | 48,828 | 3 | 146,484 | ||
200 | 48,828 | 3 | 146,484 | ||
250 | 48,828 | 3 | 146,484 | ||
300 | 48,828 | 3 | 146,484 |
Labels | Fault Classes | Number of Total Samples | Number of Training Samples | Number of Testing Samples |
---|---|---|---|---|
1 | Normal | 360 | 144 | 216 |
2 | Outer Race Fault | 790 | 316 | 474 |
3 | Inner race fault | 425 | 170 | 255 |
Num. | Feature Extraction | Fault Identification | Accuracy (%) | Training Time (s) | Testing Time (s) |
---|---|---|---|---|---|
1 | HRCMFDE | ELM | 97.90 ± 0.49 | 0.0318 | 0.0198 |
2 | HRCMFDE | KELM | 97.71 ± 0.49 | 0.0371 | 0.0293 |
3 | HRCMFDE | GA-ELM | 99.49 ± 0.48 | 318.0357 | 150.4896 |
4 | HRCMFDE | PSO-ELM | 99.43 ± 0.38 | 17.6277 | 5.1201 |
Literature | Feature Extraction | Fault Identification | Number of Classes | Average Accuracy (%) |
---|---|---|---|---|
[56] | CWT | CNN-SVM | 3 | 98.89 |
[59] | LMD | SNN | 3 | 99.31 |
[60] | WT | IGoogLeNet | 3 | 99.40 |
[61] | MSST+SFC-DL | LSVM | 3 | 95.83 |
[62] | STMSST | CNN | 3 | 98.67 |
[11] | RCMFDLZC | DAC | 3 | 96.05 |
This paper | HRCMFDE | PSO-ELM | 3 | 99.43 |
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Chen, Y.; Yuan, Z.; Chen, J.; Sun, K. A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM. Entropy 2022, 24, 1517. https://doi.org/10.3390/e24111517
Chen Y, Yuan Z, Chen J, Sun K. A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM. Entropy. 2022; 24(11):1517. https://doi.org/10.3390/e24111517
Chicago/Turabian StyleChen, Yinsheng, Zichen Yuan, Jiahui Chen, and Kun Sun. 2022. "A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM" Entropy 24, no. 11: 1517. https://doi.org/10.3390/e24111517
APA StyleChen, Y., Yuan, Z., Chen, J., & Sun, K. (2022). A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM. Entropy, 24(11), 1517. https://doi.org/10.3390/e24111517