A Condition-Monitoring Approach for Diesel Engines Based on an Adaptive VMD and Sparse Representation Theory
Abstract
:1. Introduction
2. Methods
2.1. Variational Mode Decomposition
- Initialize , , , and n.
- Update by Equation (3).
- Update by Equation (4).
- Update by Equation (5).
- Repeat steps (2)–(4) until the termination condition is met:
2.2. Adaptive VMD
2.2.1. Correlated Kurtosis
2.2.2. Grey Wolf Optimization
2.2.3. Adaptive VMD Based on GWO
- Load the measured vibration signal.
- Initialize the parameters of GWO, such as the maximum iteration number t = 20 and population size n = 100.
- Extract the mode using VMD, and calculate the fitness of all modes. Use Equation (7) to evaluate the fitness value.
- Determine whether the termination condition was achieved. If not, update the positions of wolves until reaching the termination criterion and continue the iteration.
- Obtain and save the optimal parameters and the minimum fitness.
- Use the optimal parameters for VMD to extract the modes.
- Use the decomposition results further for dictionary learning.
2.3. Sparse Representation Theory
2.3.1. Coefficient Solving
- Initialize the residual and variable ;
- Select most relevant atoms (Equation (16));
- Calculate the coefficient using Equation (17);
- Update the residual r by ;
- Repeat steps (2)–(4) until one of the following termination conditions is met:
2.3.2. Dictionary Learning
- Initialize the iteration counter and column index, and generate either by using random entries or m randomly chosen examples.
- Increase k by 1 and calculate sparse coefficients using Equation (22).
- Define a group of examples using atom .
- Calculate the residual matrix using Equation (23).
- Obtain by restricting corresponding to .
- Apply SVD on
- Repeat (3)–(6) for to update the columns of the dictionary and obtain .
- Repeat (2)–(7) until the predefined threshold or iteration count is reached.
2.4. Fault Diagnosis Workflow
3. Case Study: Valve Clearance and Injection Timing of a Diesel Engine
3.1. Bench Test
3.2. Signal Processing Based on Adaptive VMD
3.3. Dictionary Learning
3.4. Feature Extraction
4. Comparison and Discussion
4.1. Comparison
4.2. Discussions
5. Conclusions and Outlook
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Items | Specifications |
---|---|
Number of cylinders | 6 |
Displacement | 7.14 L |
Stroke | 130 mm |
Max power | 220 kW @ 2300 rpm |
Max torque | 1160 Nm @ 1200–1600 rpm |
Number | Condition Description | Specification |
---|---|---|
1 | Normal | Default value set by manufacturer |
2 | Small valve clearance | 0.25 mm (intake), 0.45 mm (exhaust) |
3 | Large valve clearance | 0.35 mm (intake), 0.55 mm (exhaust) |
4 | Small advance in injection timing | 1 °C A |
5 | Large advance in injection timing | 2 °C A |
6 | Small delay in injection timing | 1 °C A |
7 | Large delay in injection timing | 2 °C A |
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Yang, X.; Bi, F.; Jing, Y.; Li, X.; Zhang, G. A Condition-Monitoring Approach for Diesel Engines Based on an Adaptive VMD and Sparse Representation Theory. Energies 2022, 15, 3315. https://doi.org/10.3390/en15093315
Yang X, Bi F, Jing Y, Li X, Zhang G. A Condition-Monitoring Approach for Diesel Engines Based on an Adaptive VMD and Sparse Representation Theory. Energies. 2022; 15(9):3315. https://doi.org/10.3390/en15093315
Chicago/Turabian StyleYang, Xiao, Fengrong Bi, Yabing Jing, Xin Li, and Guichang Zhang. 2022. "A Condition-Monitoring Approach for Diesel Engines Based on an Adaptive VMD and Sparse Representation Theory" Energies 15, no. 9: 3315. https://doi.org/10.3390/en15093315
APA StyleYang, X., Bi, F., Jing, Y., Li, X., & Zhang, G. (2022). A Condition-Monitoring Approach for Diesel Engines Based on an Adaptive VMD and Sparse Representation Theory. Energies, 15(9), 3315. https://doi.org/10.3390/en15093315