Due to its high power factor, high torque density, high efficiency, high reliability, and other advantages, PMSM is widely used in electric vehicles, aerospace, and other vital fields [
1,
2,
3]. To design an efficient and reliable PMSM, the researchers optimized both the controller and the body structure of the PMSM. The structure optimization of the PMSM is mainly divided into single-objective optimization [
4,
5] and multi-objective optimization [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26] of the motor. Traditional single-objective optimization methods often consider only individual motor performance. In contrast, the overall performance of the PMSM is affected by output torque, torque ripple, speed range, loss, temperature rise, and many other factors. In [
4,
5], a method for effectively weakening the tooth groove torque of the motor is proposed; however, other performance indicators, such as average torque, loss, efficiency, etc., are not taken into account. Although this single-objective optimization method can significantly improve the particular performance index of the motor, it is always premised on sacrificing other performances of the motor, which is not conducive to the overall performance improvement of the PMSM. Therefore, the current PMSM optimization study is mainly a multi-objective optimization method. In the literature [
6,
7,
8], the parametric scanning method is applied to optimize the performance of the motor. This method can effectively find out the combination of design variables that meet the objective conditions, but this process requires much computation, is very time-consuming, and is not suitable for application in the case of many design variables. In order to reduce the computation time, in the literature [
9,
10,
11], the Taguchi method is introduced to optimize the objective performance of the motor. This method finds the best combination of design variables based on orthogonal test design and analysis. It can effectively optimize the performance of the motor with fewer trials, and the optimization efficiency is high. Therefore, the Taguchi method is often used by designers to optimize the design of mechanical structures. However, in the case of large value ranges of design variables, the Taguchi method has a large span of adjacent value levels in the design space, and many high-quality design variables will be ignored. The optimization accuracy is insufficient. To overcome this difficulty, in the literature [
12,
13], the combination of fuzzy theory and the Taguchi method is introduced to convert multiple objectives to a single objective and update the value ranges of design variables in the optimization process based on the sequential Taguchi method, and then again optimize the performance of the IPMSM, thereby effectively improving the optimization accuracy. However, this method requires much manual calculation with complicated data processing.
To further improve the multi-objective optimization effect of the PMSM, in addition to the aforementioned Taguchi method, the response surface method [
14,
15], and the intelligent optimization algorithm [
17,
18,
19,
20,
21,
22,
23,
24,
25], other methods are also applied in the optimization design of the motor and provide more optimization solutions to improve the performance of the motor. In the literature [
14,
15], the response surface method is adopted to obtain the non-linear relationship between variables and objectives and perform a comprehensive analysis to obtain the best combination of design variables of the performance of the motor. The motor optimization design based on the intelligent optimization algorithm is mainly used to build the surrogate model and then be combined with the optimization algorithm to look for the combination of variables that meet the requirements [
16]. The surrogate models commonly used in optimization problems of the PMSM are the response surface method (RSM) model [
17], the Kriging model [
18], the support vector regression (SVR) model [
19], etc. The reliability of the whole optimization is directly determined by the goodness of the surrogate model. If the surrogate model does not accurately reflect the mapping relationship between the design variables and the optimization objectives, even if it is combined with the optimization algorithm, it cannot produce accurate and effective results. The optimization algorithms commonly used in optimizing the PMSM are genetic algorithms [
20], particle swarm algorithms [
21], etc. In the literature [
22], radial basis function (RBF) neural network and multi-island genetic algorithm (MIGA) are combined for the torque performance optimization of the motor. In the literature [
23], the average torque, the torque ripple, the average suspension force, and the suspension force ripple of the motor are taken as the optimization objectives. In the optimization process, the combination of RSM and improved MOPSO is adopted. The results show that the torque Performance of the motor is improved. However, the RSM usually uses the relationship between the second-order polynomial fitting variables and the objective performance. The fitting accuracy cannot be guaranteed to be high enough when there are many variables. In the literature [
24], to obtain a more accurate approximation relationship between the design variables and the optimization objectives, a variety of different surrogate models are established, analyzed, and compared. The best-performing random forest (RF) surrogate model is selected to optimize the performance indicators of the motor in combination with NSGA-II. Although the surrogate model combined with the intelligent optimization algorithm can effectively obtain the optimal combination of design variables in the optimization design of the PMSM, as the number of design variables increases, the accuracy of the surrogate model decreases, and the convergence of the optimization algorithm is more difficult. It is a challenge to obtain the optimal value. In this case, the optimization strategy of the PMSM is very critical. By taking into account many design variables [
25], the sensitivity analysis method can be used to divide the design variables into two layers of sensitivity and insensitivity and then optimize them, respectively. The results show that this strategy can effectively solve the optimization problem of many design variables. However, in that paper, only the torque performance of the motor is considered. In the literature [
26], a strategy for optimizing the structure of the IPM motor based on deep learning is proposed. The process trains the model by inputting a cross-sectional image of the rotor structure of the motor and the corresponding output performance data. Then it selects the best combination of design variables based on the trained model. However, the data samples required by the method are too large, and the technique is very time-consuming.
In this paper, a multi-objective optimization strategy based on a combined surrogate model and the optimization algorithm is proposed to optimize the average torque, the torque ripple, and the loss of the IPMSM. The rest of this paper is as follows: The FEM model of the IPMSM is established, and the optimization process of IPMSM is introduced in
Section 2. In
Section 3, the optimization variables and objectives are determined, and the optimization variables are divided into high-sensitivity variables and low-sensitivity variables according to the comprehensive sensitivity analysis. The high-sensitivity variables are optimized by using the surrogate model in combination with NSGA-II, and the low-sensitivity variables are optimized by using the Taguchi method. In
Section 4, the performances of the pre-optimization and post-optimization motors are verified and contrasted. Conclusions are drawn in
Section 5.