Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm
Abstract
:1. Introduction
2. Literature Review
3. Method
3.1. Gray Wolf Optimization
- Step1:
- Calculate the fitness of individual in the population. The best fitness of three wolves in the population were marked as , and . The rest was marked as . In other words, the optimization process of GWO is guided by three optimal solutions () in each generation population.
- Step2:
- Surround the prey. When the wolf group is close to its prey, it will slowly approach and surround the prey. The mathematical expressions are as follows.
- Step3:
- Prey. When wolf which would lead the pack to attack the prey finds its prey. In this case, the wolf , and would attack the prey together, and their positions with the prey can be expressed by the Formulas (6)–(12).
3.2. Modified Gray Wolf Optimization
3.2.1. Chaotic Sequences Based on Tent Map
3.2.2. Sine Wave Dynamic Adaptive Factor
3.3. Steps of Modified Gray Wolf Optimization Algorithm
- (1)
- Initialize the parameters of GWO: set the population number of N; the maximum number of iterations Tmax; candidate solution dimension D, etc.
- (2)
- The chaotic sequences based on tent map was used to the initialization of the GWO, and the fitness value was calculated. According to the fitness value, the gray wolf population was classified into the wolf , , and .
- (3)
- Update parameters a, A and C of GWO.
- (4)
- Update the positions of each wolf and add sine wave dynamic adaptive factor into the final position update formula of each individual.
- (5)
- Rearrange the fitness value and the position of population after update. If the fitness value of the updated position is better, the updated position is retained. Otherwise, the new position is ignored.
- (6)
- Determine whether better convergence accuracy is achieved. If reached, end the search and output the position of . Otherwise, go back to step 2.
3.4. Algorithm Testing
4. Construction of MGWO-SVM Fault Diagnosis Model
4.1. Support Vector Machine
4.2. Model of MGWO-SVM
- Step1:
- Test the “normal” and the other 6 fault states of motor bearing respectively, extract the current signal data of 7 states, and build the current signal data set of the input model accordingly.
- Step2:
- Process the current signal data set of the input model.
- Step3:
- Randomly confuse the data by groups, divide the training data set and the test data set, in order to prepare for better training and testing of SVM model.
- Step4:
- Set the gray wolf population size and iteration times, initialize the gray wolf population, and set the punishment factor C and radial basis kernel function g in SVM as the individual positions of gray Wolf, .
- Step5:
- Take the SVM classification accuracy as the fitness value of the algorithm, calculate the fitness value, and sort the population individual according to the fitness value.
- Step6:
- As the number of iterations of the MGWO is superposition, determine whether the optimal fitness value is reached and determine whether the maximum number of iterations is reached. If not, return step 5.
- Step7:
- The optimal penalty factor C and the radial basis function parameter g obtained from the optimization of the MGWO algorithm were inserted into the SVM model, based on which the fault diagnosis model of the MGWO-SVM was constructed.
- Step8:
- The training data set trained the MGWO-SVM model, and after the training, the model tests the remaining data set.
- Step9:
- Analyze the fault diagnosis results of MGWO-SVM model for motor.
5. Case Studies
5.1. Experimental Data Extraction
- Step1:
- Select 2 qualified motors, 4 qualified motor bearings and fault parts required for testing different states, and clean them with filtered gasoline for standby;
- Step2:
- Test the qualified motor, and extract the current signal;
- Step3:
- Install qualified fault-free bearing on the motor with stator fault for test, and collect stator fault current signal;
- Step4:
- Install qualified fault-free bearing on the motor with rotor fault for test, and collect rotor fault current signal;
- Step5:
- Replace the qualified bearing with a bearing with only holder fault on the qualified motor, and extract the current signal;
- Step6:
- Replace the qualified bearing with a bearing with only rolling element fault on the qualified motor, and extract the current signal;
- Step7:
- Replace the qualified bearing with a bearing with only bearing inner ring fault on the qualified motor, and extract the current signal;
- Step8:
- Replace the qualified bearing with a bearing with only bearing outer ring fault on the qualified motor, and extract the current signal;
- Step9:
- Sort out the extracted current signal, complete the current signal acquisition and test under different states of the motor.
5.2. Data Processing
5.3. Experimental Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Function | Lower | Upper | Global Minimum | Function Type |
---|---|---|---|---|
−100 | 100 | 0 | Unimodal | |
−10 | 10 | 0 | Unimodal | |
−100 | 100 | 0 | Unimodal | |
−100 | 100 | 0 | Multimodal | |
−5.12 | 5.12 | 0 | Multimodal | |
−32 | 32 | 0 | Multimodal |
Function | MGWO | GWO | SFO | PSO | ||||
---|---|---|---|---|---|---|---|---|
Optimum | Average | Optimum | Average | Optimum | Average | Optimum | Average | |
F1 | 0 | 0 | 2..00 × 10−29 | 2.19 × 10−27 | 2.58 × 10−12 | 3.63 × 10−10 | 1.48 × 10−5 | 3.44 × 10−4 |
F2 | 0 | 0 | 2.19 × 10−17 | 9.47 × 10−17 | 4.28 × 10−6 | 8.74 × 10−5 | 1.44 × 10−2 | 4.13 × 10−2 |
F3 | 0 | 0 | 3.05 × 10−9 | 4.72 × 10−6 | 1.22 × 10−12 | 5.31 × 10−8 | 44.80 | 103 |
F4 | 1.87 × 10−6 | 1.07 × 10−4 | 3.55 × 10−4 | 2.32 × 10−3 | 8.75 × 10−5 | 7.00 × 10−4 | 3.90 × 10−2 | 9.47 × 10−2 |
F5 | 0 | 0 | 5.68 × 10−14 | 1.89 × 10−13 | 1.73 × 10−7 | 2.10 × 10−5 | 29.60 | 55.50 |
F6 | 8.88 × 10−16 | 8.88 × 10−16 | 7.55 × 10−14 | 1.08 × 10−13 | 1.34 × 10−7 | 1.23 × 10−5 | 1.59 × 10−3 | 1.63 × 10−2 |
SVM Parameters | Maximum Iterations | Population Number | Dimension | Parameter Range of Penalty Factor | Parameter Range of Kernel Function |
100 | 50 | 2 | [0.1, 1200] | [0.001, 100] | |
SFO-SVM | SF percent | Attack coefficient | Attack coefficient | ||
0.4 | 4 | 0.0001 | |||
ELM | Number of neurons in hidden layer | ||||
250 | |||||
BP | Maximum convergence times | Rate of learning | Convergen-ce objective | ||
100 | 0.01 | 0 |
Model | Accuracy of Different Optimization Number (%) | Average | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
MGWO-SVM | 88.57 | 100.0 | 98.57 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 99.29 | 97.86 | 98.430 |
GWO-SVM | 32.14 | 97.86 | 56.43 | 28.57 | 100.0 | 72.86 | 75.00 | 94.29 | 98.57 | 28.57 | 68.430 |
SFO-SVM | 90.00 | 97.14 | 29.29 | 98.57 | 26.42 | 84.29 | 52.86 | 83.57 | 34.29 | 95.00 | 69.143 |
SVM | 72.14 | 43.57 | 70.00 | 57.86 | 54.29 | 100.0 | 57.14 | 69.29 | 41.43 | 55.71 | 62.143 |
ELM | 54.29 | 50.00 | 47.14 | 53.57 | 51.43 | 52.14 | 52.86 | 51.43 | 50.71 | 45.71 | 50.928 |
BP | 33.33 | 30.00 | 10.00 | 16.67 | 26.67 | 16.67 | 58.33 | 10.00 | 33.33 | 28.33 | 26.333 |
Model | Accuracy of Different Optimization Number (%) | Average | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
MGWO-SVM | 100.0 | 95.00 | 100.0 | 99.29 | 100.0 | 100.0 | 100.0 | 71.43 | 100.0 | 99.29 | 96.500 |
GWO-SVM | 99.29 | 28.57 | 100.0 | 27.86 | 74.29 | 85.00 | 70.00 | 100.0 | 20.00 | 83.57 | 68.857 |
SFO-SVM | 100.0 | 27.14 | 26.43 | 100 | 27.14 | 60.00 | 75.71 | 87.14 | 77.86 | 71.43 | 65.285 |
SVM | 91.43 | 57.86 | 72.14 | 84.29 | 59.29 | 61.43 | 30.71 | 55.71 | 71.43 | 57.14 | 64.143 |
ELM | 52.14 | 54.29 | 56.43 | 60.00 | 55.71 | 50.00 | 50.71 | 52.86 | 50.00 | 54.29 | 53.643 |
BP | 20.00 | 15.00 | 33.33 | 33.33 | 3.33 | 13.33 | 28.33 | 31.67 | 38.33 | 10.00 | 22.665 |
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Li, L.-L.; Liu, J.-Q.; Zhao, W.-B.; Dong, L. Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm. Symmetry 2021, 13, 163. https://doi.org/10.3390/sym13020163
Li L-L, Liu J-Q, Zhao W-B, Dong L. Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm. Symmetry. 2021; 13(2):163. https://doi.org/10.3390/sym13020163
Chicago/Turabian StyleLi, Ling-Ling, Jia-Qi Liu, Wei-Bing Zhao, and Lei Dong. 2021. "Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm" Symmetry 13, no. 2: 163. https://doi.org/10.3390/sym13020163