Fault Detection of Wheelset Bearings through Vibration-Sound Fusion Data Based on Grey Wolf Optimizer and Support Vector Machine
Abstract
:1. Introduction
2. Methodology
2.1. Overview of the Proposed Method
2.2. The Description of the GWO-SVM Model
- Select the current candidate i: Choose the i-th wolf from the pack.
- Train SVM model using current candidate: (1) Extract the SVM hyperparameters and from the current candidate; (2) Initialize an SVM model with these parameters; (3) Train the SVM model on the training dataset.
- Evaluate the model on the validation set: (1) Use the validation dataset to predict outcomes; (2) Calculate the accuracy of the predictions, which represents the fitness of the current candidate
- Record the fitness value of the current candidate: Save the fitness value for the current candidate.
- Increment the index i: Move to the next candidate ().
- Repeat Step 3: Continue evaluating the next candidate until all candidates are evaluated.
2.2.1. Basic SVM Formula
2.2.2. GWO Formulas
- -
- D represents the distance between the current wolf and the , , and .
- -
- is the position of the , , and , representing the best solution found so far.
- -
- is the updated position of the wolf, the elements in are essentially combinations of SVM hyperparameters, optimized through the GWO process to find the best parameter settings.
2.2.3. GWO Algorithm Steps
- -
- w is the weight vector that determines the hyperplane for classification.
- -
- b is the bias term.
- -
- is the square norm of the weight vector used to control the complexity of the model.
- -
- is a regularization parameter used to balance the misclassification of training data and model complexity.
- -
- is a slack variable that allows certain samples to be misclassified.
- Initialize the positions of the wolves, for linear kernel, train the SVM with the linear kernel using the wolf’s position parameter ; train the SVM with the RBF kernel using the wolf’s position parameters , , and train the SVM with the Polynomial kernel using the wolf’s position parameters and coefficient term , the degree of polynomial Kernel in this study is confirmed.
- Evaluate the fitness of each wolf based on the classification accuracy of the SVM.
- Update the positions of , , and .
- Update the positions of the other wolves.
- Repeat the above steps until the maximum number of iterations is reached.
2.2.4. Summary
- -
- determines the balance between minimizing the error on the training data and reducing the complexity of the model. A larger value tries to classify every sample correctly, which may lead to overfitting, while a smaller value allows some misclassifications, potentially improving generalization.
- -
- controls the width of the Gaussian kernel. A larger value means higher sensitivity to individual data points, making the model focus more on local patterns, while a smaller value makes the model consider a broader range of data points.
- -
- r adjusts the influence of higher-order terms in the polynomial kernel.
3. Experimental Section
3.1. Experimental Setup and Dataset
3.2. Data Analysis
3.3. Experimental Results
3.3.1. Comparison Performance
3.3.2. Training Loss
4. Discussion
4.1. Evaluation of Different Lengths in Each Segment
4.2. Evaluation of Proposed Method Performance
4.3. Evaluation of Testing Speed
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Abbreviations | Description |
---|---|
CNN | Convolutional Neural Network |
FFT | Fast Fourier Transform |
GWO | Grey Wolf Optimizer |
MFCC | Mel-Frequency Cepstral Coefficients |
PCA | Principal Component Analysis |
PSD | Power Spectral Density |
RBF | Radial Basis Function |
SPL | Sound Pressure Level |
STFT | Short-Time Fourier Transform |
SVM | Support Vector Machine |
Training Group | Testing Group | |
---|---|---|
Validation 1 | 2, 3, 4 | 1 |
Validation 2 | 1, 3, 4 | 2 |
Validation 3 | 1, 2, 4 | 3 |
Validation 4 | 1, 2, 3 | 4 |
SVM Method | Data Types | Length | |||
---|---|---|---|---|---|
256 | 128 | 64 | 32 | ||
Linear SVM | Vibration | 100% | 98% | 98% | 97% |
Sound | 99% | 100% | 99% | 97% | |
Cubic SVM | Vibration | 100% | 100% | 99% | 98% |
Sound | 99% | 100% | 98% | 97% | |
Quadratic SVM | Vibration | 100% | 100% | 98% | 98% |
Sound | 99% | 100% | 98% | 97% | |
Coarse Guassian SVM | Vibration | 100% | 99% | 99% | 97% |
Sound | 99% | 100% | 97% | 93% | |
Medium Gaussian SVM | Vibration | 99% | 99% | 99% | 96% |
Sound | 99% | 100% | 100% | 98% |
Kernel of SVM | Training Model | Vibration Accuracy | Sound Accuracy | Fusion Accuracy |
---|---|---|---|---|
Linear SVM | Matlab | 67.6% | 97.4% | 97.8% |
GWO-SVM | 68% | 97.6% | 98.3% | |
Quadratic SVM | Matlab | 67.4% | 97.2% | 97.9% |
GWO-SVM | 67.7% | 97.3% | 98% | |
Cubic SVM | Matlab | 66.8% | 95.5% | 97.5% |
GWO-SVM | 66.8% | 97.2% | 97.7% | |
Gaussian SVM | Matlab-Medium Gaussian SVM | 68% | 97.6% | 97% |
Matlab-Coarse Gaussian SVM | 67.9% | 95.2% | 94.3% | |
GWO-SVM | 68.1% | 97.7% | 98.1% |
Different Kernel of GWO-SVM | Accuracy | Testing Time for Each Segment | Sampling Time |
---|---|---|---|
Linear SVM | 98.3% | 0.0027 ms | 31.25 ms |
Quadratic SVM | 98% | 0.0034 ms | |
Cubic SVM | 97.7% | 0.0035 ms | |
Gaussian SVM | 98.1% | 0.016 ms |
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Wang, T.; Meng, H.; Zhang, F.; Qin, R. Fault Detection of Wheelset Bearings through Vibration-Sound Fusion Data Based on Grey Wolf Optimizer and Support Vector Machine. Technologies 2024, 12, 144. https://doi.org/10.3390/technologies12090144
Wang T, Meng H, Zhang F, Qin R. Fault Detection of Wheelset Bearings through Vibration-Sound Fusion Data Based on Grey Wolf Optimizer and Support Vector Machine. Technologies. 2024; 12(9):144. https://doi.org/10.3390/technologies12090144
Chicago/Turabian StyleWang, Tianhao, Hongying Meng, Fan Zhang, and Rui Qin. 2024. "Fault Detection of Wheelset Bearings through Vibration-Sound Fusion Data Based on Grey Wolf Optimizer and Support Vector Machine" Technologies 12, no. 9: 144. https://doi.org/10.3390/technologies12090144