Systematic Development of a Multi-Objective Design Optimization Process Based on a Surrogate-Assisted Evolutionary Algorithm for Electric Machine Applications
Abstract
:1. Introduction
- Development of a Bayesian optimization-based hyperparameter (HP) tuning process to improve the approximation accuracy of SMs;
- Development of new convergence criteria for the transition from FEA to SM;
- Analysis of the effect of the number of FEA calculations on the approximation accuracy of the SM for different objective functions;
- Comparative analysis of three different surrogate modeling techniques: ANN, Kriging, and SVR;
- Development of a clustering-based technique to reduce calculation time for verifying Pareto fronts predicted by an SM.
2. Proposed Surrogate-Assisted Design Optimization Process
3. Experimental Setup
4. Surrogate Model Construction
4.1. Surrogate Modeling Techniques
4.1.1. Kriging
4.1.2. Artificial Neural Network
4.1.3. Support Vector Regression
4.2. Hyperparameters of Surrogate Model
4.3. Transition from FEA-Based to Surrogate-Based Optimization
- Criterion 1: Stop if the RMSE is equal to or less than 0.5%;
- Criterion 2: Stop if the sign of the rate of change changes from negative to positive and RMSE is equal to or less than 3% after 10 iterations (500 FEA calculations);
- Criterion 3: Stop if the number of calculations is greater than 50 iterations (2500 FEA calculations).
4.4. Data Clustering Technique for Pareto Front Verification
5. Optimization Results
5.1. Performance Comparison between SMs
5.2. Comparative Analysis: FEA-Based vs. SM-Based Optimization Process
6. Conclusions and Future Works
- Comparison of three different surrogate modeling techniques, Kriging, ANN, and SVR;
- Introduction of an automated HP tuning process through Bayesian optimization;
- Development of robust three-step stopping criteria that determine the transition from FEA-based to SM-based optimization;
- Detailed analysis of the approximation accuracy of various SMs for four different objective functions considering the number of FEA results used for SM training and HP tuning effect;
- Reduction of calculation time for verification of the Pareto front predicted by SM using the k-means clustering technique;
- Computational time savings of more than 90% with no loss of accuracy compared to FEA-based optimization.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Peak Current Density | 15 Arms/mm2 |
Slot/Pole | 12/10 |
Peak Power/Peak Torque | 15 kW/70 Nm |
Peak Current | 150 Arms |
Series Turns | 17 Turns |
Rotor Diameter | 110 mm |
Airgap Length | 0.75 mm |
Magnet Remanence | 1.1 T at 100 °C |
Magnet Grade | NMX-36EH (Hitachi) |
Lamination Grade | 35JN300 (JFE) |
Design Variables and Their Range |
Type of SM | Parameter (s) | Hyperparameter (s) |
---|---|---|
Kriging | Correlation matrix, vector | |
ANN | Weight, bias | Number of hidden layers, neurons, and activation function |
SVR | Support vector | Regularization hyperparameter, kernel function |
Objective Function | Kriging | ANN | SVR |
---|---|---|---|
Total Mass | 50 | 50 | 50 |
Active Material Cost | 50 | 50 | 100 |
Average Torque | 50 | 200 | 350 |
Torque Ripple | 700 | 950 | 2500 |
Processing Unit | AMD Ryzen 9 5900X 12-Core Processor, 3.70 GHz |
Operating System | Windows 11 Pro (64-bit) |
Random Access Memory | 32 GB DDR4 |
Data Storage Type | SSD SATA |
Graphic Card | NVIDIA GeForce GTX 1650 |
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Choi, M.; Choi, G.; Bramerdorfer, G.; Marth, E. Systematic Development of a Multi-Objective Design Optimization Process Based on a Surrogate-Assisted Evolutionary Algorithm for Electric Machine Applications. Energies 2023, 16, 392. https://doi.org/10.3390/en16010392
Choi M, Choi G, Bramerdorfer G, Marth E. Systematic Development of a Multi-Objective Design Optimization Process Based on a Surrogate-Assisted Evolutionary Algorithm for Electric Machine Applications. Energies. 2023; 16(1):392. https://doi.org/10.3390/en16010392
Chicago/Turabian StyleChoi, Mingyu, Gilsu Choi, Gerd Bramerdorfer, and Edmund Marth. 2023. "Systematic Development of a Multi-Objective Design Optimization Process Based on a Surrogate-Assisted Evolutionary Algorithm for Electric Machine Applications" Energies 16, no. 1: 392. https://doi.org/10.3390/en16010392