###### Abstract  
Recently, a large amount of research on deep learning has been conducted. Related studies have also begun to apply deep learning techniques to the field of electric machines, but such studies have been limited to the field of fault diagnosis. In this study, the shape optimization of a permanent magnet synchronous motor (PMSM) for electric vehicles (EVs) was conducted using a multi-layer perceptron (MLP), which is a type of deep learning model. The target specifications were determined by referring to Renault's Twizy, which is a small EV. The average torque and total harmonic distortion of the back electromotive force were used for the multi-objective functions, and the efficiency and torque ripple were chosen as constraints. To satisfy the multi-objective functions and constraints, the angle between the V-shaped permanent magnets and the rib thickness of the rotor were selected as design variables. To improve the accuracy of the design, the design of experiments was conducted using finite element analysis, and a parametric study was conducted through analysis of means. To verify the effectiveness of the MLP, metamodels was generated using both the MLP and a conventional Kriging model, and the optimal design was determined using the hybrid metaheuristic algorithm. To verify the structural stability of the optimized model, mechanical stress analysis was conducted. Moreover, because this is an optimal design problem with multi-objective functions, the changes in the optimal design results were examined as a function of the changes in the weighting. The optimal design results showed that the MLP technique achieved better predictive performance than the conventional Kriging model and is useful for the shape optimization of PMSMs. deep learning; finite element analysis; PMSM; optimization; metamodeling +
Footnote †: journal: Applied Soft  
The work in [5] involved multi-objective shape optimization of a PMSM based on FEA and a modified particle swarm optimization algorithm. The performance of five PMSMs with different rotor topologies were compared based on several factors including the efficiency, flux-weakening rate, and price. In [6], an optimization process for PMSM design to optimize the weight, output power, and suitability was proposed. This work included shape optimization of the permanent magnets and the rotor core using FEA with the fuzzy inference system strategy. Using a novel memetic algorithm, an optimal design was created based on FEA to minimize torque ripple in a PMSM [7]. In [8], multi-physics and multi-objective optimization of a PMSM based on FEA and an analytical magnetic model were studied. There are two main ways to optimize design variables: either by combining the optimal algorithm with the design methods directly or by combining it with the metamodel resulting from the design of experiments (DOE). A metamodel is a mathematical model that approximates the relationships between design variables and responses. DOE is an application of statistics aimed at designing experimental methods and analyzing the results to identify relationships between design variables and responses. In the case of optimization by creating metamodels using DOE results, it is possible to predict the optimal results by analyzing the sensitivity between design variables and target goals. Moreover, the time taken for the optimization design is clear. However, the numbers of DOE and test points must be selected properly, and the metamodel must be made correctly. Recently, there have been many studies on optimal design using the Kriging model as a metamodeling technique. The Kriging model, which is a representative of the interpolation class of models, generates an approximation function composed of a global model and the local deviation. The Kriging model is based on the empirical method applied by a South African miner named [PERSON]. It has been widely applied in various fields since [PERSON], a French geologist, established its mathematical basis.