## 3 Initial Design Parameters of HSPMM
### Multi-Objective Optimization of Electromagnetic Performance and Losses
is shown in Figure 8. It can be seen from the figure that almost all the different proxy model surfaces reach the maximum motor efficiency in the middle of the optimization parameter range, and the existing optimization parameters on this surface are reasonable and can meet the optimization conditions of each optimization objective. With the gradual increase of each optimization parameter value, the motor efficiency will gradually reach the local maximum value and then gradually decrease, so there are some local non-inferior optimal solutions of motor efficiency that satisfy the multi-objective optimization mathematical model. Figure 8: The response surface of efficiency. (**a**) The effect of sleeve thickness and PM thickness. (**b**) The effect of length of air gap and PM thickness. (**c**) The effect of rotor outer diameter and sleeve thickness. (**d**) The effect of rotor outer diameter and pole embrace. (**e**) The effect of length of air gap and rotor outer diameter. (**f**) The effect of length of air gap and PM thickness. Figure 7: The response surface of permanent magnet loss. (**a**) The effect of PM thickness and sleeve thickness. (**b**) The effect of PM thickness and pole arc coefficient. (**c**) The effect of PM thickness and length of air gap. (**d**) The effect of PM thickness and rotor outer diameter. Each optimized parameter has a great influence on the thermal load of the motor winding, as shown in Figure 9 below. According to practical engineering experience and design requirements, the HSPMM designed in this paper only adopts the heat dissipation method of spiral water cooling of the casing, so the thermal load of the motor windings needs to be kept below 250 A\({}^{2}\)/mm\({}^{3}\), as shown in the light-yellow plane in the figure below. With the increase of the thickness of permanent magnet, the thermal load of motor windings increases first and then decreases. With the increase of sleeve thickness and air gap length, the thermal load of motor windings increases gradually. In the range of rotor diameter, sleeve thickness, pole-arc coefficient, air-gap length and permanent magnet thickness, Kriging proxy surface model of motor winding thermal load has local optimal solution set, which can be optimized to find non-inferior optimal solution. Firstly, the Kriging proxy model of the important parameter subspace X1 of rotor is established by keeping the important parameter subspace X2 of stator unchanged, and the Kriging proxy model is optimized by multi-objective genetic algorithm. The resulting Pareto front is shown in Figure 10.  
According to the distribution of Pareto front surface, the maximum efficiency of the motor can reach 97.44%, the maximum output torque can reach 20.6 Nm, the minimum eddy current loss of permanent magnet is 4.5 W, and the minimum thermal load of the motor is 122 A\({}^{2}\)/mm\({}^{3}\). However, it can be found from Figure 9 that when the motor efficiency is maximum and the motor thermal load is minimum, the permanent magnet eddy current is large and the output torque is small; when the permanent magnet eddy current is minimum and the output torque is maximum, the motor efficiency is small  
Figure 9: The response surface of thermal load. (**a**) The effect of sleeve thickness and PM thickness. (**b**) The effect of length of air gap and sleeve thickness. (**c**) The effect of rotor outer diameter and sleeve thickness. (**d**) The effect of rotor outer diameter and pole arc coefficient. (**e**) The effect of rotor outer diameter and length of air gap. (**f**) The effect of rotor outer diameter and PM thickness. and the motor thermal load is large. Therefore, in multi-objective optimization design, there is not a group of optimal solutions but a compromise choice among all optimization objectives, and the choice space composed of all non-inferior optimal solutions constitutes a Pareto front surface, from which a group of non-inferior optimal solutions satisfying the requirements should be selected as the final optimization scheme.