Hierarchical Multiobjective Optimization of Spoke-Type Axial-Flux PMSMs Using Transfer Learning and Improved Grey Wolf Algorithm

This article proposes a computationally efficient and high-fidelity multiobjective optimization framework for the design of spoke-type axial-flux permanent magnet synchronous motors (STAF-PMSMs) targeting in-wheel applications. To address high-dimensional design spaces, conflicting objectives, and costly finite element model (FEM) evaluations, a hierarchical surrogate-assisted strategy is developed. Design variables are decomposed into two levels using Morris sensitivity analysis and crossed factorial analysis of variance (ANOVA). A deep neural network (DNN) surrogate enhanced by transfer learning (TL) is employed to improve prediction accuracy with limited data, while an improved multiobjective grey wolf optimizer (IMOGWO) is used to search for nondominated solutions with enhanced convergence. K-medoids clustering and a hybrid weighting scheme are further applied for solution filtering and selection. The framework is validated on a parameterized STAF-PMSM, achieving a 53.4% increase in torque and a 65.3% reduction in torque ripple, with only moderate increases in loss and cost. Meanwhile, the number of FEM evaluations is reduced from 2600 to 920, confirming the computational efficiency of the method. These results demonstrate that the proposed TL-IMOGWO framework provides a scalable and accurate solution for multiobjective motor design.