V-shaped built-in rotor magnetic steel groove optimization method based on multi-objective optimization

Abstract

A V-shaped built-in rotor magnetic steel slot optimization method based on multi-objective optimization rapidly identifies design parameters having significant influence on motor performance through sensitivity analysis, and then systematically optimizes the parameters by using an optimization algorithm to improve the motor performance. According to the optimization method, the performance of the motor can be remarkably improved, the number of design iterations and the design period are greatly reduced, and an efficient and systematic optimization method is provided for motor design; besides, the application of the method is not limited to a V-shaped built-in rotor magnetic steel groove, can also be expanded to design optimization of other types of motors, and has a wide application prospect.

Description

Technical Field

[0001] The invention belongs to the technical field of motor design, and in particular relates to a rotor magnetic steel slot optimization design method for improving the performance of a V-shaped built-in permanent magnet synchronous motor. Background Art

[0002] In the field of motor design, V-shaped built-in rotor magnetic steel slots are one of the key structures that affect motor performance. Since the motor needs to maintain high efficiency and stability during operation, high requirements are placed on the precise design of the rotor magnetic steel slots. Traditional design methods have problems such as low optimization efficiency, long time consumption, and low optimization accuracy. With the development of computing technology, finite element analysis (FEA) has gradually become an important tool in motor design. It can accurately simulate the electromagnetic field inside the motor and thus predict the performance of the motor. However, the direct application of finite element analysis for parameter optimization is computationally expensive, especially when the parameter dimension is high, which requires a lot of computing resources and time. Therefore, there is an urgent need for an efficient and systematic design optimization method to improve this situation. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention provides a V-shaped built-in rotor magnetic steel slot optimization method based on multi-objective optimization, which quickly identifies the design parameters that significantly affect the motor performance through sensitivity analysis, and then uses the optimization algorithm to systematically optimize these parameters to improve the performance of the motor. The optimization method of the present invention can not only significantly improve the performance of the motor, but also greatly reduce the number of design iterations and design cycles, providing an efficient and systematic optimization method for motor design. In addition, the application of this method is not limited to V-shaped built-in rotor magnetic steel slots, but can also be extended to the design optimization of other types of motors, and has broad application prospects.

[0004] The technical solution adopted by the present invention to solve its technical problem is:

[0005] A V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization comprises the following steps:

[0006] S1: Select optimization parameters, determine optimization targets, and establish a motor finite element model;

[0007] S2: The design variables are sampled using the BBD sampling method, the optimization target results are calculated through FEA, the sensitivity between the design variables and the optimization target is analyzed using the Spearman correlation coefficient method, and the design variables are divided into high sensitivity and low sensitivity parts;

[0008] S3: Design low-sensitivity parameter factor levels through the Taguchi method, conduct orthogonal experiments and analyze their mean values ​​and variances to determine the optimal design variable combination level values;

[0009] S4: Sample highly sensitive parameter samples and optimize the target results through FEA calculation. Use AdaBoost algorithm and Gray Wolf optimization algorithm to optimize BP neural network and build a proxy model between highly sensitive design variables and optimization targets. Determine whether the accuracy of the proxy model meets the requirements. If not, increase the number of sample sampling;

[0010] S5: Combine the GWO-BPNN-AdaBooost agent model and NSGA-II to perform multi-objective optimization on high-sensitivity parameters and determine the optimal high-sensitivity design variable parameters;

[0011] S6: Analyze and compare the motor performance before and after optimization.

[0012] Furthermore, in S1, the motor is a 4-pole 6-slot internal permanent magnet synchronous motor. The motor rotor structure is optimized under the premise of keeping the inner and outer diameters of the motor rotor and the amount of permanent magnets constant. Based on the improvement of the electromagnetic performance of the motor, three optimization goals are selected: 1) minimizing the cogging torque; 2) increasing the output torque; and 3) reducing the torque pulsation.

[0013] In S2, the Spearman method is used to analyze the sensitivity between the design variables and the optimization objectives, and the three optimization objectives are comprehensively considered, and the weight coefficient is used to evaluate each variable.

[0014] In S3, the low sensitivity parameter optimization process based on the Taguchi method is as follows:

[0015] 3.1 Design low sensitivity parameter factor levels;

[0016] 3.2 Orthogonal experimental design;

[0017] 3.3 Average value analysis;

[0018] 3.4 Analysis of variance.

[0019] In S4, the process of optimizing the high sensitivity parameters based on the proxy model and NSGA-Π is as follows:

[0020] 4.1 Construction of agent model: The agent model of motor optimization design is constructed using the GWO-BPNN-AdaBoost model;

[0021] 4.2 Evaluation of proxy model, regression model evaluation index is: determination coefficient R 2 , root mean square error RMSE, mean absolute error MAE, mean absolute percentage error MAPE.

[0022] In S5, the multi-objective optimization process is:

[0023] 5.1 Mathematical model of motor optimization

[0024] The objective function of motor optimization is:

[0025]

[0026] The constraints for motor optimization are set as:

[0027]

[0028] 5.2 NSGA-II Optimization

[0029] According to the established GWO-BPNN-AdaBoost proxy model and the mathematical model of motor optimization, the NSGA-Π algorithm is used to optimize the highly sensitive parameters.

[0030] In S6, the optimization results are analyzed as follows:

[0031] 6.1 Cogging torque comparison: After optimization, the peak value of cogging torque is greatly reduced from 32.53 to 17.79 mN·m, which is 45.32% weaker. The optimization effect is obvious.

[0032] 6.2 Output performance comparison: While reducing the cogging torque, the motor output torque is increased and the torque pulsation is reduced. After optimization, the average output torque of the motor changes from 195.69mN·m to 210.88mN·m, and the torque pulsation decreases from 10.63% to 7.22%.

[0033] The beneficial effects of the present invention are mainly manifested in that it can not only significantly improve the performance of the motor, but also greatly reduce the number of design iterations and the design cycle, providing an efficient and systematic optimization method for motor design. In addition, the application of this method is not limited to V-shaped internal rotor magnetic steel slots, but can also be extended to the design optimization of other types of motors, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization.

[0035] Figure 2 It is a schematic diagram of the main design parameters of the rotor topology structure.

[0036] Figure 3 It is a schematic diagram of parameter sensitivity analysis.

[0037] Figure 4 This is a schematic diagram of the GWO-BP-AdaBoost integrated model. DETAILED DESCRIPTION

[0038] The present invention will be further described below in conjunction with the accompanying drawings.

[0039] Reference Figure 1 , a V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization, comprising the following steps:

[0040] S1: Select optimization parameters, determine optimization targets, and establish a motor finite element model;

[0041] In S1, the motor is a 4-pole 6-slot internal permanent magnet synchronous motor, and the motor rotor structure is optimized under the premise of keeping the inner and outer diameters of the motor rotor and the amount of permanent magnets constant. Figure 1 It is a schematic diagram of the main design parameters of the rotor topology structure, and Table 1 is the main design parameters related to its built-in rotor;

[0042]

[0043] Table 1

[0044] from Figure 2 It can be seen that there are seven parameters in the rotor topology parameters, namely D1, O1, O2, Rib, Dmin, HRib, and B1. If all these parameters are analyzed by variables, there will be cross-interference between the variables, which will not only increase the complexity of the simulation, but also may cause the simulation process to be abnormally time-consuming. Therefore, in order to improve the optimization efficiency and shorten the simulation time, it is necessary to weigh the influence of each parameter on the optimization target and fix the parameters with less obvious influence. In this way, we can focus on the key parameters that have a significant impact on the optimization target, thereby achieving more efficient and targeted design optimization.

[0045] Based on the improvement of the electromagnetic performance of the motor, three optimization goals are selected: 1) Minimize the cogging torque: Cogging torque is a non-ideal torque caused by the tooth structure of the stator and rotor. It is an undesirable torque because it will cause vibration and noise during the operation of the motor, affecting the stability and efficiency of the motor. Therefore, in the motor design stage, it is necessary to minimize its negative impact on the motor performance through optimization design; 2) Improve the output torque: The output torque of the motor is directly related to its driving ability and is one of the important indicators for measuring the performance of the motor. Improving the output torque means that the motor can provide greater power at lower energy consumption; 3) Reduce torque pulsation: Torque pulsation is the phenomenon of torque fluctuation during the operation of the motor. It will cause the dynamic response of the motor to be unstable, affecting the control accuracy and operation smoothness. Reducing torque pulsation can not only improve the operating efficiency of the motor, but also extend its service life.

[0046] The formula for calculating the cogging torque is:

[0047]

[0048] Where: z is the number of stator slots, L ais the axial length of the stator core, μ0 is the relative magnetic permeability, R1 is the inner radius of the stator, R2 is the outer radius of the stator, G n is the Fourier decomposition coefficient of the square of the relative air gap permeance, B rnz / 2p is the Fourier decomposition coefficient of the square of the air gap flux generated by the permanent magnet, n is the order of the cogging torque, and is the least common multiple of the number of stator slots z and the number of poles 2p.

[0049] The electromagnetic torque calculation formula is:

[0050]

[0051] Where: T em is the electromagnetic torque; p is the number of pole pairs; ψ f is the permanent magnet flux; L d , L q is the motor d-axis and q-axis inductance; i d 、i q are the motor d-axis and q-axis currents.

[0052] Average torque T avg and torque ripple T rip It is expressed as:

[0053] T avg =avg(T em )

[0054]

[0055] Where: T em_max 、T em_min They are the maximum peak value of electromagnetic torque and the minimum peak value of electromagnetic torque respectively.

[0056] According to the type of motor to be simulated, import the CAD model into Maxwell or directly draw the geometric structure of the motor, including the stator, rotor, magnetic steel, winding, etc.; assign material properties to each component of the motor, including magnetic permeability, electrical conductivity, etc.; define the boundary conditions of the motor and set the excitation source of the motor; set the initial conditions at the beginning of the simulation, and set the appropriate time step and total simulation time according to the motor speed and the dynamic process to be observed; mesh the geometric model and select the appropriate mesh size to ensure calculation accuracy and efficiency; solve the cogging torque under transient no-load and the electromagnetic torque under transient load respectively; after the simulation is completed, analyze the changes of the motor's cogging torque and electromagnetic torque over time to obtain the maximum cogging torque, average output torque and torque pulsation. Table 2 shows the motor structural materials,

[0057]

[0058] Table 2

[0059] S2: The design variables are sampled using the BBD sampling method, the optimization target results are calculated through FEA, the sensitivity between the design variables and the optimization target is analyzed using the Spearman correlation coefficient method, and the design variables are divided into high sensitivity and low sensitivity parts;

[0060] In S2, in order to reduce the dimension of the multi-objective optimization problem and improve the efficiency of finite element calculation, sensitivity analysis is applied to the first step of optimization, because it can effectively identify the degree to which each design variable affects the motor performance. The Spearman method is used to analyze the sensitivity between the design variables and the optimization objectives, and the correlation threshold is set to 0.5. The sensitivity analysis results are shown in Figure 3 shown.

[0061] The calculation formula of Spearman correlation coefficient is as follows:

[0062]

[0063] Where: d i —The difference in rank values ​​of the i-th data pair; n—the total number of observed samples.

[0064] The value range of the Spearman correlation coefficient is [-1,1]. When the coefficient is greater than zero, it indicates that there is a positive correlation between the variable and the optimization target, and when it is less than zero, it indicates a negative correlation between the two. The sensitivity between the variable and the optimization target is determined by the absolute value of the correlation coefficient. The closer it is to 1, the stronger the sensitivity, and the closer it is to 0, the weaker the sensitivity.

[0065] Taking the three optimization objectives into consideration, the weight coefficient is used to evaluate each variable. The comprehensive sensitivity index S(x i ), expressed as

[0066]

[0067] The design variables x are i To T avg , T rip , T cog sensitivity value; w1, w2, w3 are T avg , T rip , T cog The weight coefficient is w1+w2+w3=1;

[0068] According to the actual demand for the motor optimization target, the weight coefficients w1, w2, and w3 of the optimization target are selected as 0.3, 0.3, and 0.4 respectively. The calculation results of the comprehensive sensitivity index are shown in Table 3.

[0069]

[0070] Table 3

[0071] 0.2 is selected as the sensitivity threshold, that is, the high-sensitivity design variables are O2, B1, Rib, and D1, and the low-sensitivity design variables are O1, HRib, and Dmin.

[0072] Table 4 shows the parameter sensitivity classification;

[0073]

[0074]

[0075] Table 4

[0076] S3: Design low-sensitivity parameter factor levels through the Taguchi method, conduct orthogonal experiments and analyze their mean values ​​and variances to determine the optimal design variable combination level values;

[0077] In S3, the low sensitivity parameter optimization process based on the Taguchi method is as follows:

[0078] 3.1 Design low sensitivity parameter factor levels, as shown in Table 5:

[0079]

[0080] Table 5

[0081] 3.2 Orthogonal experimental design

[0082] Orthogonal test design is often used to analyze multivariate problems. The most representative points are obtained based on the orthogonal table. As can be seen from the table, the number of variables is 3 and the level value is 5. If the full factorial test point scheme is used, 3 5 If an orthogonal experimental design is used, only 25 experimental points need to be calculated, and the orthogonal table can be used L 25 (5 3 ) indicates, refer to Table 6.

[0083]

[0084]

[0085] Table 6

[0086] 3.3 Average value analysis

[0087] After constructing the orthogonal experiment table and calculating the FEA results of each experiment, the total average value of each optimization target is calculated according to the table. The calculation formula is expressed as:

[0088]

[0089] Where: M is the total average value of the optimization target; ni —Number of experiments; M i —FEA results of the i-th optimization target. The calculation results are shown in Table 7.

[0090] Optimization goals <![CDATA[T avg (mN·m)]]> <![CDATA[T rip (%)]]> <![CDATA[T cog (mN·m)]]> M 195.72 10.65 32.626

[0091] Table 7

[0092] In order to analyze the effect of each optimization variable level on T avg , T rip and T cog To understand the influence trend of each optimization variable, we need to calculate the average value of the optimization target when each optimization variable takes each level value. For example, when the optimization variable O1 has a level value of 1, the corresponding T avg The average value calculation can be expressed as:

[0093]

[0094] The calculation is performed according to the above formula, and the calculation results are shown in Table 8.

[0095]

[0096]

[0097] Table 8

[0098] T cog Obtain the value of O1 and T in the optimal combination of variable level values avg , T rip Therefore, further analysis of the effect of O1 on T is needed. avg , T rip and T cog , thereby determining the optimal combination of variable level values.

[0099] 3.4 Analysis of variance

[0100] In order to comprehensively consider the above combinations, variance analysis is needed to find out the variables with greater correlation with the optimization target to determine the optimal variable level combination. The variance calculation formula is:

[0101]

[0102] Where: T—optimization target; Q—number of levels of optimization variables; M T(j) —The average value of T at level j of the optimization variable x.

[0103] Table 9 shows the variance and proportion of optimization variables and optimization targets.

[0104]

[0105] Table 9

[0106] According to the variance and weight, we can determine which optimization target each variable has the greatest impact on. From the table, we can see that variable O1 has the greatest impact on T avg The impact on T is slightly greater than that on cog The influence ratio of T is small, but the difference between them is small. Combined with the weight of the previous optimization target, T avg The weight coefficient is less than T cog , so the median value is taken for O1, that is, the optimal combination of variable level values ​​is: O1(3)Dmin(1)HRib(1).

[0107] S4: Sample highly sensitive parameter samples and optimize the target results through FEA calculation. Use AdaBoost algorithm and Gray Wolf optimization algorithm to optimize BP neural network and build a proxy model between highly sensitive design variables and optimization targets. Determine whether the accuracy of the proxy model meets the requirements. If not, increase the number of sample sampling;

[0108] In S4, the process of optimizing the high sensitivity parameters based on the proxy model and NSGA-Π is as follows:

[0109] 4.1 Building a proxy model

[0110] In high-dimensional, nonlinear optimization problems, if parameter scanning or evolutionary algorithms are directly used to search within the value range of the optimization variable, the time cost of FEA calculation is huge. Therefore, the present invention greatly improves the subsequent optimization efficiency by establishing a high-precision proxy model.

[0111] BPNN is a multi-layer feedforward network trained by the error back propagation algorithm. It has strong nonlinear processing capabilities and is one of the most widely used neural networks. However, BPNN has relatively poor generalization ability and is prone to fall into local minima during the optimization process. It also has poor robustness and slow convergence of the learning process. Based on the above shortcomings, various optimization algorithms have been introduced to optimize the parameters of BPNN and have achieved good results.

[0112] The AdaBoost algorithm can train multiple BPNNs as weak classifiers, making them complement each other and integrated into a strong classifier with strong robustness. The Grey Wolf Algorithm (GWO) can optimize the initial value and threshold of BPNN and further improve the performance of BPNN. Therefore, the GWO-BPNN-AdaBoost model is used to construct the proxy model for the motor optimization design.

[0113] The Gray Wolf Optimization (GWO) algorithm simulates the hierarchy mechanism and hunting behavior of gray wolf populations in nature. Four types of gray wolves (α, β, δ, ω) are used to simulate social hierarchy. The solution with the best, second-best, and third-best fitness values ​​of the population are regarded as α wolf, β wolf, and δ wolf, respectively, and the remaining solutions are regarded as ω wolf. The α wolf, β wolf, and δ wolf are responsible for leading, and the ω wolf follows the α wolf, β wolf, and δ wolf to complete the hunting optimization by searching, encircling, chasing, and attacking prey, and finally obtain the optimal solution. The process of the GWO algorithm is as follows:

[0114] (1) Find and surround prey

[0115] During hunting, the gray wolf group will first surround the prey. The mathematical model of this behavior can be expressed as:

[0116]

[0117] Where t is the number of current iterations, is the position vector of the prey in the tth iteration, is the position vector of the gray wolf in the tth iteration. and is the synergy vector, and the calculation formula is:

[0118]

[0119] Among them, the components in a decrease linearly from 2 to 0 during the iteration process, and is a random vector in [0,1].

[0120] (2) Chasing prey

[0121] After the prey is surrounded, the wolf pack begins to hunt. The hunting process is led by wolf α, and wolf β and wolves δ follow the lead of wolf α and lead the wolf pack to surround the prey. The mathematical formula for the position of α wolf, β wolf and δ wolf in hunting the prey is as follows:

[0122]

[0123] in, and Respectively represent the distances between α wolf, β wolf and δ wolf and other individual gray wolves (including ω wolf). and Represent the current positions of α wolf, β wolf and δ wolf respectively. represents a random vector.

[0124]

[0125] in, and Represents the vectors of other gray wolves in the wolf pack moving towards wolf α, wolf β, and wolf δ respectively, according to the calculation and The final locations of other gray wolf individuals can be determined.

[0126]

[0127] Finally, the wolf pack gradually approaches the prey. When the prey stops moving, the gray wolf will attack and complete the hunt.

[0128] BPNN is a network system with strong nonlinear mapping capabilities and is often used by researchers to build agent models in optimization design problems.

[0129] Neuron z c The received signal is represented as:

[0130]

[0131] Where: w mc —Input layer neuron x m and the hidden layer neuron z c The weight between .

[0132] Input to neuron y n The signal is represented as:

[0133]

[0134] Where: w cn —Neuron z c With neuron y n The weight between c —Neuron z c Output.

[0135] y n The output and mean square error are:

[0136]

[0137] Where: θ n —Threshold of the output layer.

[0138] The process of the AdaBoost algorithm is:

[0139] (1) Data selection and network initialization

[0140] Determine the BPNN network structure according to the input and output dimensions, initialize the BPNN weights and thresholds, and initialize the distribution weights D of the m sets of training data sets i :

[0141]

[0142] Where: D i —The initial weight of the sample, i=1,2,3,...,m.

[0143] (2) Weak classifier prediction

[0144] When training the t-th BPNN weak classifier, the prediction error and e of the output g(t) are obtained by predicting the training data. t :

[0145] e t =∑ i D i (i) i=1,2,...,n(g(t)≠y)

[0146] Among them, y is the expected classification result.

[0147] (3) Calculate the prediction sequence weight

[0148] According to the prediction error and e obtained in the previous step t Calculate the weight α of the predicted sequence t :

[0149]

[0150] (4) Adjust weight D i

[0151] According to the prediction sequence weight α obtained in the previous step t Adjust the weights for the next round of training:

[0152]

[0153] In the formula, B t It is a normalization factor, the purpose of which is to make the sum of the distribution weights equal to 1 no matter how the weights change.

[0154] (5) Strong classifier

[0155] After T rounds of training, the weak classifier function f(g(t),α t ), and then combine these weak classifiers into the final strong classifier h(x):

[0156]

[0157] GWO-BP-AdaBoost integrated model reference Figure 4 .

[0158] 4.2 Evaluation Agent Model

[0159] The regression model evaluation index is: determination coefficient R 2, root mean square error RMSE, mean absolute error MAE, mean absolute percentage error MAPE. Among them, R 2 It is the evaluation index that best reflects the degree of fit. The closer it is to 1, the better the fit. Secondly, the smaller the values ​​of RMSE, MAE, and MAPE are, the better the model effect is. The calculation formulas for these evaluation indicators are:

[0160]

[0161] Where: m—number of samples in the test set; y i —actual value of the test set sample; f(x i )—test set sample prediction value; —The average value of the actual value of the test set samples. The evaluation indicators are shown in Table 10.

[0162]

[0163]

[0164] Table 10

[0165] According to the evaluation indicators of the three proxy models for each optimization objective in Table 10, it can be concluded that the R of the prediction model constructed by the GWO-BPNN-AdaBoost proxy model for the three optimization objectives of average torque, torque ripple, and cogging torque is 2 It is close to 1, indicating that the prediction model has strong fitting ability and high prediction accuracy. MAPE and RMSE are close to 0, indicating that the model prediction error is small, the prediction result can be close to the actual value, and the performance is improved compared with BPNN and BPNN-AdaBoost. Therefore, the three prediction models constructed by GWO-BPNN-AdaBoost have high prediction accuracy and can be used as proxy models for this motor optimization design.

[0166] S5: Combine the GWO-BPNN-AdaBooost agent model and NSGA-II to perform multi-objective optimization on high-sensitivity parameters and determine the optimal high-sensitivity design variable parameters;

[0167] In S5, the multi-objective optimization process is:

[0168] 5.1 Mathematical model of motor optimization

[0169] The objective function of this motor optimization is:

[0170]

[0171] The constraints for this motor optimization are set as follows:

[0172]

[0173] 5.2 NSGA-II Optimization

[0174] According to the established GWO-BPNN-AdaBoost agent model and the mathematical model of motor optimization, the NSGA-Π algorithm is used to optimize the highly sensitive parameters, with a population size of 200, 100 iterations, a crossover probability of 0.8, and a mutation probability of 0.2. The Pareto frontier of the optimization target is obtained.

[0175] According to the Pareto frontier, the optimal high-sensitivity design variable parameters are determined, as shown in Table 11.

[0176]

[0177] Table 11

[0178] S6: Analyze and compare the motor performance before and after optimization.

[0179] In S6, the optimization results are analyzed as follows:

[0180] 6.1 Cogging torque comparison: After optimization, the peak value of cogging torque is greatly reduced from 32.53 to 17.79 mN·m, which is weakened by 45.32%. The optimization effect is obvious.

[0181] 6.2 Output performance comparison: While reducing the cogging torque, the motor output torque is increased and the torque pulsation is reduced. After optimization, the average output torque of the motor changes from 195.69mN·m to 210.88mN·m, and the torque pulsation decreases from 10.63% to 7.22%.

[0182] The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective sensitivity analysis in this embodiment optimizes the rotor magnetic steel slot of the V-shaped internal permanent magnet synchronous motor by comprehensively considering the three optimization objectives of cogging torque, average torque and torque ripple. The motor performance is significantly improved through the following steps:

[0183] 1. Parameter sensitivity analysis: The Spearman correlation coefficient method was used to identify key structural parameters that have a significant impact on motor performance, including the magnetic isolation bridge width, the distance from the rotor inner diameter to the magnetic isolation bridge, the magnetic isolation width, the magnet end distance, the magnetic isolation bridge length, the magnetic steel slot width, and the magnetic steel slot limiting diameter.

[0184] 2. Application of optimization algorithm: The Taguchi method was used to optimize the low-sensitivity parameters, and the optimal parameter combination was determined through orthogonal experimental design and variance analysis. At the same time, a high-precision proxy model was constructed using the BP neural network and AdaBoost algorithm optimized by the Gray Wolf algorithm, providing an effective prediction model for the optimization of high-sensitivity parameters.

[0185] 3. Multi-objective optimization: The NSGA-II algorithm was used to perform multi-objective optimization on highly sensitive parameters, and the Pareto optimal solution set that met the three optimization objectives was successfully found.

[0186] 4. Optimization effect verification: The electromagnetic performance of the motor before and after optimization was compared and analyzed by finite element analysis. The results showed that the peak value of the motor cogging torque after optimization was reduced by 45.32%, the average torque was increased by 7.68%, and the torque pulsation was reduced by 3.17%, proving the effectiveness and practicality of the optimization method.

[0187] In summary, this study not only improves the performance of V-type interior permanent magnet synchronous motors, but also significantly reduces the number of design iterations and design cycles, providing an efficient and systematic optimization method for motor design. Future work can further explore more parameters and more complex motor models to achieve wider applications and deeper performance improvements.

[0188] The contents described in the embodiments of this specification are merely enumerations of implementation forms of the inventive concept and are for illustrative purposes only. The protection scope of the present invention should not be considered to be limited to the specific forms described in this embodiment, and the protection scope of the present invention also extends to equivalent technical means that can be thought of by ordinary technicians in this field based on the inventive concept.

Claims

1. A V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization, characterized in that: The method comprises the following steps: S1: Select optimization parameters, determine optimization targets, and establish a motor finite element model; S2: The design variables are sampled using the BBD sampling method, the optimization target results are calculated through FEA, the sensitivity between the design variables and the optimization target is analyzed using the Spearman correlation coefficient method, and the design variables are divided into high sensitivity and low sensitivity parts; S3: Design low-sensitivity parameter factor levels through the Taguchi method, conduct orthogonal experiments and analyze their mean values ​​and variances to determine the optimal design variable combination level values; S4: Sample highly sensitive parameter samples, calculate the optimization target results through FEA, optimize the BP neural network using the AdaBoost algorithm and the gray wolf optimization algorithm, build a proxy model between the highly sensitive design variables and the optimization target, and determine whether the accuracy of the proxy model meets the requirements. If not, increase the number of sample sampling; S5: Combine the GWO-BPNN-AdaBooost agent model and NSGA-II to perform multi-objective optimization on high-sensitivity parameters and determine the optimal high-sensitivity design variable parameters; S6: Analyze and compare the motor performance before and after optimization.

2. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1, characterized in that: In S1, the motor is a 4-pole 6-slot internal permanent magnet synchronous motor. The motor rotor structure is optimized under the premise of keeping the inner and outer diameters of the motor rotor and the amount of permanent magnets constant. Based on the improvement of the electromagnetic performance of the motor, three optimization goals are selected: 1) minimizing the cogging torque; 2) increasing the output torque; and 3) reducing the torque pulsation.

3. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1 or 2, characterized in that: In S2, the Spearman method is used to analyze the sensitivity between the design variables and the optimization objectives, and the three optimization objectives are comprehensively considered, and the weight coefficient is used to evaluate each variable.

4. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1 or 2, characterized in that: In S3, the low sensitivity parameter optimization process based on the Taguchi method is as follows: 3.1 Design low sensitivity parameter factor levels; 3.2 Orthogonal experimental design; 3.3 Average value analysis; 3.4 Analysis of variance.

5. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1 or 2, characterized in that: In S4, the process of optimizing the high sensitivity parameters based on the proxy model and NSGA-Π is as follows: 4.1 Construction of agent model: The agent model of motor optimization design is constructed using the GWO-BPNN-AdaBoost model; 4.2 Evaluation of proxy model, regression model evaluation index is: determination coefficient R 2 , root mean square error RMSE, mean absolute error MAE, mean absolute percentage error MAPE.

6. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1 or 2, characterized in that: In S5, the multi-objective optimization process is: 5.1 Mathematical model of motor optimization The objective function of motor optimization is: The constraints for motor optimization are set as: 5.2 NSGA-II Optimization According to the established GWO-BPNN-AdaBoost proxy model and the mathematical model of motor optimization, the NSGA-Π algorithm is used to optimize the highly sensitive parameters.

7. The V-shaped internal rotor magnetic steel slot optimization method based on multi-objective optimization according to claim 1 or 2, characterized in that: In S6, the optimization results are analyzed as follows: 6.1 Cogging torque comparison: After optimization, the peak value of cogging torque is greatly reduced from 32.53 to 17.79 mN·m, which is 45.32% weaker. The optimization effect is obvious. 6.2 Output performance comparison: While reducing the cogging torque, the output torque of the motor is increased and the torque pulsation is reduced. After optimization, the average output torque of the motor changes from 195.69mN·m to 210.88mN·m, and the torque pulsation is reduced from 10.63% to 7.22%.

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