## 3 Comparison of Different Surrogate Models and Motor Optimization Design
### Electromagnetic Optimization Design of Motor  
Figure 13 shows the optimization process of this motor. In this paper, two sample point sampling methods and three surrogate model fitting methods were selected for the optimization of the motor. By comparing different sample point sampling methods and surrogate model fitting methods, an optimization method suitable for this kind of motor with a high coupling degree of electromagnetic performance was found. According to the above section, the influence of each design parameter on the electromagnetic performance of the motor was analyzed, and the motor optimization parameters and parameter range were selected, as shown in Table 3.  
Figure 12: Influence of length of air gap on electromagnetic performance. (**a**) Torque ripple. (**b**) Core loss. (**c**) Solid loss. Figure 13: Motor optimization process. The sensitivity of the optimized parameters of the motor structure was obtained by establishing a finite element model for calculation. The histogram of Figure 14 shows the sensitivity values of the two rotor structure optimization parameters. The sensitivity value was larger, indicating that it had a greater impact on the optimization goal. A positive sensitivity value indicates that the optimization objective increased with the increase in the optimization variable, and a negative sensitivity value indicates the opposite trend. The multi-objective optimization of the motor mostly uses the surrogate model, and the optimization results are verified by the finite element method. This method can greatly reduce the multi-objective optimization calculation time. However, it is necessary to select a reasonable experimental design method and a surrogate model fitting method to improve the fitting accuracy of the surrogate model and ensure the accuracy of the optimization results. The central composite design (CCD) and Latin hypercube design (LHS) were selected as the experimental design methods, and the genetic aggregation method (GA), Kriging method and neural network method (ANN) were selected as the surrogate model fitting methods. The proxy model obtained by combining these methods is shown in Figure 15.  
From Figure 15, it can be seen that the accuracy of the surrogate model fitted by CCD-GA was poor, and there was a normal concentration phenomenon in various electromagnetic properties; the electromagnetic properties such as iron loss and torque in the CCD-Kriging surrogate model were also too concentrated, which would have made the optimization results less accurate. The accuracy of the surrogate model of CCD-ANN fitting was very poor, and the fitting of the neural network surrogate model required a large sample space. In motor optimization, a large number of sample space means a huge calculation time, which is unreasonable. The electromagnetic properties such as eddy current loss and efficiency of the surrogate model fitted by LHS-GA also showed normal concentration. The accuracy of the surrogate model fitted by LHS-ANN was very poor; however, the accuracy of the surrogate model of LHS-Kriging fitting was better, which is also the advantage of the stratified sampling strategy of LHS sampling. The neural network surrogate model is a non-parametric model, while CCD and Kriging are based on the data distribution characteristics of using the minimum sample space instead of the overall  
Figure 14: Sensitivity values of structural optimization parameters. \begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Parameter** & **Range** \\ \hline \(Wt\) (mm) & Stator tooth width & [7,9] \\ \(B\)s0 (mm) & Stator slot opening width & [2,5,3.5] \\ \(\alpha_{p}\) & Polar arc coefficient of permanent magnet & [0.65,0.8] \\ \(Tp\) (mm) & Thickness of permanent magnet & [5,10] \\ \(\delta\) (mm) & Length of air gap & [1,3] \\ \hline \end{tabular}
\end{table} 
Table 3: The optimization parameters of the motor and the range of parameter variation. space, and the obtained sampling space has obvious Monte Carlo simulation characteristics.