Surrogate-Assisted Multi-Objective Optimization of Interior Permanent Magnet Synchronous Motors with a Limited Sample Size
Source abstract
Abstract
Interior permanent magnet synchronous motors (IPMSMs) are critical for electric vehicle traction and industrial systems, yet optimizing their performance under high-dimensional design spaces remains computationally challenging. This study proposes a surrogate-assisted multi-objective optimization framework tailored for limited sample sizes. The methodology integrates random forest (RF) and analysis of variance (ANOVA) for variable importance analysis to reduce model complexity, followed by a Generalized Regression Neural Network (GRNN) to establish an efficient surrogate model. A multi-objective particle swarm optimization (MOPSO) algorithm generates Pareto-optimal solutions, while an entropy-weighted distance metric objectively selects the final design. Experimental results demonstrate that the optimized IPMSM achieves a 4.62% increase in average output torque, a 0.15% improvement in efficiency, and a 10.48% reduction in torque ripple compared to the prototype. Finite element analysis validates the consistency between predicted and simulated outcomes, with relative errors below 2.92%. The framework effectively balances computational efficiency and accuracy, offering a data-driven approach for motor optimization under constrained experimental resources.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Electric Motor Design and Analysis · Induction Heating and Inverter Technology · Sensorless Control of Electric Motors
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Automation, Central South University, Changsha 410083, China
References (40)
Show source-provided references
1. Multi-objective optimization of IPMSM for electric vehicles based on the combinatorial surrogate model and the hierarchical design method10.1016/j.ijepes.2024.110245 ↗
2. Improved Multiphysics Multiobjective Optimization for U-Shaped IPMSM Equipped With Eccentric Rotor10.1109/JESTPE.2023.3298010 ↗
3. Multi-Objective Design Optimization of an IPMSM Based on Multilevel Strategy10.1109/TIE.2020.2965463 ↗
4. Surrogate Model-Based Multiobjective Optimization of High-Speed PM Synchronous Machine: Construction and Comparison10.1109/TTE.2022.3173940 ↗
5. Li, G., Li, R., Hou, H., Zhang, G., and Li, Z. (2024). A Data-Driven Motor Optimization Method Based on Support Vector Regression—Multi-Objective, Multivariate, and with a Limited Sample Size. Electronics, 13.10.3390/electronics13122231 ↗
6. Fast Multi-Objective Optimization of Electromagnetic Devices Using Adaptive Neural Network Surrogate Model
7. Liu, Z., Zhang, G., and Du, G. (2025). An Investigation of Parameter Dimension Reduction Optimization of PMA-Synrm. Appl. Sci., 15.10.3390/app15031529 ↗
8. The Effect of Small Sample Size on Two-Level Model Estimates: A Review and Illustration10.1007/s10648-014-9287-x ↗
9. Hanic, Z., Hanic, A., and Kovacic, M. (2021, January 22–24). The Application of Neural Network Metamodels Interior Permanent Magnet Machine Performance Prediction. Proceedings of the 2021 International Conference on Electrical Drives & Power Electronics (EDPE), Dubrovnik, Croatia.10.1109/EDPE53134.2021.9604055 ↗
10. Liu, X., Li, X., and Huang, S. (2019, January 11–14). Parameters Optimization of the Permanent Magnet Linear Synchronous Machine Using Kriging-based Genetic Algorithm. Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China.10.1109/ICEMS.2019.8922517 ↗
11. Seo, H.S., Park, C.B., Kim, S.H., Lei, G., Guo, Y., and Lee, H.W. (2024). Utilizing MicroGenetic Algorithm for Optimal Design of Permanent-Magnet-Assisted WFSM for Traction Machines. Appl. Sci., 14.10.3390/app14125150 ↗
12. Chai, J., Zhao, T., and Gui, X. (2021). Design and Multi-Objective Optimization for Improving Torque Performance of a Permanent Magnet-Assisted Synchronous Reluctance Motor. World Electr. Veh. J., 12.10.3390/wevj12030131 ↗
13. Yang, F., Li, N., Du, G., Huang, M., and Kang, Z. (2024). Electromagnetic Optimization of a High-Speed Interior Permanent Magnet Motor Considering Rotor Stress. Appl. Sci., 14.10.3390/app14146033 ↗
14. Xing, F., Zhang, J., Zuo, F., and Gao, Y. (2024). Optimization of an Asymmetric-Rotor Permanent Magnet-Assisted Synchronous Reluctance Motor for Improved Anti-Demagnetization Performance. Appl. Sci., 14.10.3390/app142311233 ↗
15. Pei, W., Xiao, P., Pan, J., Li, Z., and Lv, A. (2024). Multi-Objective Optimization Strategy for Commercial Vehicle Permanent Magnet Water Pump Motor Based on Improved Sparrow Algorithm. Appl. Sci., 14.10.3390/app14219666 ↗
16. Hsiao, C.Y., and Htet, S.M. (2024). Multi-Step Design Optimization for the Improvement of an Outer-Rotor Brushless Direct Current Motor. Appl. Sci., 14.10.3390/app14104302 ↗
17. Combined Random Forest and NSGA-II for Optimal Design of Permanent Magnet Arc Motor10.1109/JESTPE.2021.3049242 ↗
18. Accurate and Efficient Surrogate Model-Assisted Optimal Design of Flux Reversal Permanent Magnet Arc Motor10.1109/TIE.2022.3215444 ↗
19. A Review of Data-Driven Surrogate Models for Design Optimization of Electric Motors10.1109/TTE.2024.3366417 ↗
20. Liu, X., Peng, W., Xie, L., and Zhang, X. (2023). Optimization of a Multi-Type PMSM Based on Pyramid Neural Network. Appl. Sci., 13.10.3390/app13116810 ↗
21. Cen, Y., Shen, H., Wang, X., Wu, Y., and Du, J. (2024). Multi-Objective Optimization Analysis of Electromagnetic Performance of Permanent Magnet Synchronous Motors Based on the PSO Algorithm. Energies, 17.10.3390/en17184637 ↗
22. Yu, Y., Zhao, P., Hao, Y., Zeng, D., Hu, Y., Zhang, B., and Yang, H. (2022). Multi Objective Optimization of Permanent Magnet Synchronous Motor Based on Taguchi Method and PSO Algorithm. Energies, 16.10.3390/en16010267 ↗
23. Optimal design of a yoke-less axial flux switching PM motor based on multi-objective PSO10.1108/COMPEL-03-2022-0102 ↗
24. Yang, Q., Zhang, W., and Zhao, C. (2024). Research on Torque Performance of Marine Hybrid Excitation Synchronous Motors Based on PSO Optimization of Magnetic Permeability Structure. J. Mar. Sci. Eng., 12.10.3390/jmse12071064 ↗
25. Systematic application of traffic-signal-control system architecture design and selection using model-based systems engineering and Pareto frontier analysis10.1002/sys.21759 ↗
26. Ranking of Pareto-optimal solutions and selecting the best solution in multi- and many-objective optimization problems using R-method10.1016/j.socl.2021.100015 ↗
27. Multi-objective optimization of composite stiffened panels for mass and buckling load using PNN-NSGA-III algorithm and TOPSIS method10.1016/j.tws.2024.112878 ↗
28. A hybrid two stage Taguchi-regression-NSGA II-AHP-GRA, multi-objective optimization framework for sustainable straight slot milling of AZ31 magnesium alloy10.1016/j.rineng.2025.104451 ↗
29. A mathematical theory of communication10.1002/j.1538-7305.1948.tb01338.x ↗
30. Barberi, E., Cucinotta, F., Forssén, P.E., and Sfravara, F. (2023). DECI: A Differential Entropy-Based Compactness Index for Point Clouds Analysis: Method and Potential Applications. Eng. Proc., 56.10.3390/ASEC2023-15808 ↗
31. Effects of the entropy weight on TOPSIS10.1016/j.eswa.2020.114186 ↗
32. Orthogonal experimental design of liquid-cooling structure on the cooling effect of a liquid-cooled battery thermal management system10.1016/j.applthermaleng.2017.12.115 ↗
33. Correlation and variable importance in random forests10.1007/s11222-016-9646-1 ↗
34. Chen, W., Yang, Q., Wang, L., Liu, D., Han, X., and Meng, G. (2020, January 25–27). Approximate Modeling of Gear Torque of Permanent Magnet Synchronous Motor Based on Improved Latin Hypercube Sampling. Proceedings of the 9th Frontier Academic Forum of Electrical Engineering, Xi’an, China.
35. Multi-objective optimization of squirrel cage fan for range hood based on Kriging model10.1177/0954406221995863 ↗
36. Wind turbine airfoils optimization design by generalized regression neural network under small sample10.1007/s12206-022-1223-2 ↗
37. Li, J., An, L., Cheng, Y., and Wang, H. (2024). Small Sample Sound Quality Prediction Method of Hy-Vo Chain Transmission System Based on Fuzzy Generation. Appl. Sci., 14.10.24425/aoa.2024.148816 ↗
38. A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification10.1016/j.enconman.2024.118392 ↗
39. 25 Years of Particle Swarm Optimization: Flourishing Voyage of Two Decades10.1007/s11831-022-09849-x ↗
40. Lu, T., Hao, M., and Zhang, Z. (2025). Comprehensive Evaluation of Remote Tower Controllers’ Situation Awareness Level Based on the Entropy Weight Method (EWM)–TOPSIS–Gray Relational Analysis Model. Appl. Sci., 15.10.3390/app15052623 ↗