## 3 Comparison of Different Surrogate Models and Motor Optimization Design
### Electromagnetic Optimization Design of Motor
Finally, from the perspective of the fitting accuracy of the surrogate model, the LHS-Kriging fitting surrogate model was selected for the next multi-objective optimization. The response surface of the motor stator and rotor design parameters to the motor performance is shown in Figure 16. It can be seen that the influence of tooth width and slot opening on torque ripple and iron loss was significant. The pole arc coefficient of the permanent magnet and the thickness of the permanent magnet have a great influence on the kilometer citation, efficiency, torque ripple and eddy current loss of the motor. The air gap has a great influence on torque ripple and iron loss. Therefore, the optimization of the above five stator and rotor design parameters is very necessary. Efficiency is an important criterion for judging the excellence of the motor. The reduction in the amount of permanent magnets can greatly reduce the manufacturing cost, and the suppression of torque ripple can ensure the smooth output torque of the motor. Therefore, the above three indicators were used as optimization objectives. Selecting the torque as the first constraint condition of the rated load should be greater than the rated torque. The no-load back electromotive force of the motor should be slightly less than the rated load voltage to ensure that there is a sufficient excitation magnetic field to complete the electromechanical energy conversion process. In addition, the power factor of the motor is a basic index. For the permanent magnet motor, the power factor should not be less than 0.9. Figure 15: The surrogate model is established by combining different sampling methods and surrogate model fitting methods. (**a**) CCD-GA. (**b**) CCD-Kriging. (**c**) CCD-ANN. (**d**) LHS-GA. (**e**) LHS-Kriging. (**f**) LHS-ANN. \[\text{Objectives}:\ \left\{ \begin{aligned} \max(\eta)\\ \min(PM-weight)\\ \min(Tr)\end{aligned} \right. \tag{1}\]  
where \(\eta\) is the motor efficiency; _PM-weight_ is the weight of the rare earth permanent magnet. _Tr_ is the torque ripple of the motor. \[\text{Constrains}:\ \left\{ \begin{aligned} 22.1\ \text{kNm}\leq T\\ 0.9\leq\cos\varphi\\ 320\ \text{V}\leq E_{Ls}\leq 335\ \text{V}\end{aligned} \right. \tag{2}\]  
where \(T\) is the output torque of the motor, \(cos\varphi\) is the power factor of the motor, and \(E_{LS}\) is the no-load back EMF of the motor. The LHS-Kriging surrogate model was used to optimize the multi-objective optimization of the motor with NSGA-II after the optimization objective and constraint adjustment were defined. The parameters before and after optimization are shown in Table 4.  
Figure 16: Response surface of motor stator and rotor design parameters to motor performance. (**a**) Wt-Bs0-Torque. (**b**) Wt-Bs0-Torque ripple. (**c**) Wt-Bs0-Core loss. (**d**) \(\alpha_{\text{p}}\)-Tp-Power factor. (**e**) \(\alpha_{\text{p}}\)-Tp-Efficiency. (**f**) \(\alpha_{\text{p}}\)-Tp-Torque ripple. (**g**) \(\alpha_{\text{p}}\)-Tp-Solid loss. (**h**) \(\delta\)-\(\alpha_{\text{p}}\)-Torque ripple. (**i**) \(\delta\)-\(\alpha_{\text{p}}\)-Core loss.