Motor multi-objective optimization design method and system based on Kriging agent model

Abstract

The invention discloses a motor multi-objective optimization design method and system based on a Kriging agent model. Comprising the following steps: constructing an initial data set through an experimental design method and finite element simulation calculation, so as to train an initial Kriging agent model which takes a motor design variable combination as an input variable and takes motor performance as an output response; the proxy model serves as a target function, a multi-target optimization problem is solved, the proxy model is updated, and an updating strategy is as follows: after each round of optimization is finished, a high-error solution in a current Pareto solution set is screened based on a Kriging model prediction mean square error, a finite element response of the high-error solution is obtained and supplemented to a data set, and the proxy model is updated and trained; and repeating the process until the optimization result converges. According to the method, high-uncertainty region samples are selectively supplemented, the calculation cost is remarkably reduced while the local prediction precision of the proxy model at the Pareto leading edge is improved, and the method has good practicability and economical efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor body optimization design, and relates to a motor multi-objective optimization design method and system based on a Kriging surrogate model. BACKGROUND

[0002] Motor design is a complex multi-variable and multi-objective optimization problem. Traditional optimization methods usually rely on finite element analysis for motor performance evaluation, but due to the large amount of calculation and long time consumption, the multi-objective optimization solving efficiency is extremely low, which is difficult to meet the time efficiency requirement of engineering design. In order to improve this problem, a surrogate model is introduced into the motor optimization design, which is used to replace the finite element for motor performance prediction under given design parameters. As a kind of spatial interpolation model, the Kriging model can fit the mapping relationship between the input variables and the output response through the known sampling data, and provide the prediction value and the uncertainty measure (such as mean square error) of the prediction at any point, which has the advantages of high precision and small amount of calculation, and has been widely used in engineering design.

[0003] In the multi-objective optimization of the motor, the designer often pays more attention to the solutions near the Pareto front. However, the global Kriging surrogate model obtained by training a limited number of samples usually has the problem of insufficient prediction accuracy in the key region, and the optimization results obtained directly based on the global Kriging surrogate model may have a large deviation from the true optimal solution. Therefore, it is necessary to dynamically update the surrogate model during the optimization process to improve its prediction accuracy in the key region. The common updating strategy is to perform finite element calculation on all Pareto solution sets obtained by the optimization algorithm, and supplement the results to the surrogate model training data set, and repeat this operation until the termination condition is met. Although this method can improve the local prediction accuracy of the surrogate model, each round of updating needs to perform simulation calculation on a large number of solutions, especially when the size of the Pareto solution set is large or the finite element simulation is time-consuming, the efficiency of the optimization process will be severely restricted. Therefore, under the premise of ensuring the local prediction accuracy of the Pareto front, it is necessary to reduce the number of newly added finite element calculations in the optimization process as much as possible, so as to balance the calculation cost and the optimization accuracy, which has become a technical problem to be solved in the field. SUMMARY

[0004] The purpose of the present application is to provide a motor multi-objective optimization design method and system based on a Kriging surrogate model, which can improve the local prediction accuracy of the surrogate model in the Pareto front while significantly reducing the calculation cost, and has good practicability and economy.

[0005] The technical scheme of the present application comprises the following steps:

[0006] S1, determine the design variables of the motor and their value ranges, and construct a parameterized model of the motor to be optimized;

[0007] S2, generate an initial motor design variable sample set using an experimental design method, for each set of motor design variable values in the initial motor design variable sample set, call the parameterized model of the motor to be optimized for finite element analysis calculation, obtain the corresponding motor performance response, and construct an initial data set;

[0008] S3, the motor design variables are used as the multi-dimensional input variables of the Kriging surrogate model, and the motor performance is used as the output response of the Kriging surrogate model. An initial Kriging surrogate model is trained based on the initial data set to fit the mapping relationship between the combination of motor design variables and the motor performance response. If an initial Kriging surrogate model already exists, the Kriging surrogate model is retrained based on the updated data set;

[0009] S4, use the Kriging surrogate model as one or more objective functions in a multi-objective optimization problem, where the multi-dimensional input variables of the Kriging surrogate model are the decision variables of the optimization problem, the value range of the multi-dimensional input variables of the Kriging surrogate model is the feasible region of the decision variables, and relevant constraint conditions are given to construct an optimization model;

[0010] S5, use a multi-objective optimization algorithm to solve the optimization model and obtain a Pareto optimal solution set for the current round. For each solution in the Pareto optimal solution set, use the Kriging surrogate model to calculate its predicted mean square error as a measure of prediction uncertainty, and according to the size of the predicted mean square error, select solutions higher than the preset threshold to form a simulation sample subset;

[0011] S6, determine whether the hyper volume index of the current round Pareto optimal solution set meets the preset convergence condition: if yes, end the iteration and obtain the final Pareto optimal solution set as the optimization result; if not, go to step S7;

[0012] S7, call the parameterized model of the motor to be optimized for finite element analysis calculation for each sample point in the simulation sample subset, obtain its motor performance response, and add the calculation result to the data set; go to step S3.

[0013] Further, the experimental design method of step S2 is Latin hypercube sampling.

[0014] Further, the Kriging surrogate model of step S3 needs to be preprocessed by value normalization before training;

[0015] The hyperparameter tuning process of the Kriging surrogate model is completed by a particle swarm optimization algorithm or a genetic algorithm.

[0016] Further, the multi-objective optimization algorithm in step S4 includes but is not limited to an NSGA-II algorithm.

[0017] Further, the determination method of the preset threshold in step S5 is:

[0018] Current round of Pareto optimal solution set Mean value of prediction mean square error of all solutions in Standard deviation of prediction mean square error of all solutions in , is a pre-designed value.

[0019] Further, the convergence condition in step S6 is that the hyper volume index of the current round of Pareto optimal solution set The hyper volume index of the last round of Pareto optimal solution set The relative error is less than a set value.

[0020] Further, the motor performance includes but is not limited to an electromagnetic torque.

[0021] The application also provides a motor multi-objective optimization design system based on a Kriging surrogate model, comprising:

[0022] A parameterized model construction unit is configured to determine design variables of a motor and a value range thereof, and construct a parameterized model of a motor to be optimized;

[0023] An initial data set construction unit is configured to generate an initial motor design variable sample set by using an experimental design method, obtain a corresponding motor performance response by calling the parameterized model of the motor to be optimized for each group of motor design variable values in the initial motor design variable sample set for finite element analysis calculation, and construct an initial data set;

[0024] A Kriging surrogate model training unit is configured to take motor design variables as multi-dimensional input variables of a Kriging surrogate model, take motor performance as an output response of the Kriging surrogate model, train an initial Kriging surrogate model based on the initial data set, and fit a mapping relationship between combinations of motor design variables and motor performance responses; if the initial Kriging surrogate model already exists, the Kriging surrogate model is retrained based on an updated data set;

[0025] An optimization model construction unit is configured to use a Kriging surrogate model as one or more objective functions in a multi-objective optimization problem, wherein multi-dimensional input variables of the Kriging surrogate model are decision variables of the optimization problem, a range of values of the multi-dimensional input variables of the Kriging surrogate model is a feasible region of the decision variables, and a relevant constraint condition is given to construct the optimization model;

[0026] An optimization model solution unit is configured to solve the optimization model by using a multi-objective optimization algorithm to obtain a Pareto optimal solution set of a current round, and calculate a prediction mean square error of each solution in the Pareto optimal solution set by using the Kriging surrogate model as a measurement basis of prediction uncertainty, and select a solution higher than a preset threshold value to form a simulation sample subset according to the size of the prediction mean square error.

[0027] A convergence judgment unit is configured to judge whether a hyper volume index of the Pareto optimal solution set of the current round meets a preset convergence condition, and if yes, end the iteration and obtain a final Pareto optimal solution set as an optimization result, and if not, call a motor parameterized model to be optimized to perform finite element analysis calculation on each sample point in the simulation sample subset, obtain a motor performance response, and add a calculation result to a data set.

[0028] The application further provides a computer device including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and the processor implements steps of the motor multi-objective optimization design method based on the Kriging surrogate model when executing the computer program.

[0029] The application further provides a computer readable storage medium storing a computer program, and the computer program implements steps of the motor multi-objective optimization design method based on the Kriging surrogate model when executed by a processor.

[0030] Advantages: Compared with the prior art, the application has the following significant technical effects: (1) the calculation resources are concentrated in a key area near a Pareto front to effectively improve local prediction accuracy of the surrogate model in an optimal solution area, thereby ensuring reliability of an optimization result, and the calculation time of the surrogate model is much smaller than the calculation time of a finite element model, so the application can be widely applied to multi-objective optimization design problems of various types of motors; (2) prediction mean square error information provided by the Kriging model is used to select solutions with high prediction uncertainty in a Pareto optimal solution set to perform simulation, thereby greatly reducing unnecessary and time-consuming finite element calculation in an optimization process, and achieving a balance between calculation cost and optimization accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 This is a flowchart of the method of the present invention;

[0032] Figure 2 This is a three-dimensional structural diagram of a 12-slot, 10-pole axial flux permanent magnet motor according to an embodiment of the present invention.

[0033] Figure 3 This is a single-layer two-dimensional structural diagram of the equivalent linear motor of the 12-slot 10-pole axial flux permanent magnet motor according to an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the high-error solution selected based on the prediction mean square error of the Pareto optimal solution set in an embodiment of the present invention;

[0035] Figure 5 The Pareto optimal solution set two-dimensional hypervolume index of this invention embodiment A schematic diagram of the calculation method;

[0036] Figure 6 This is a schematic diagram of the final optimization result obtained in an embodiment of the present invention;

[0037] Figure 7 This refers to the hypervolume index of the Pareto optimal solution set in each iteration of the embodiments of the present invention and the relative error of the hypervolume index between two adjacent iterations. A diagram illustrating the changes. Detailed Implementation

[0038] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0039] The following uses a 12-slot, 10-pole axial flux motor as an example to illustrate a specific implementation of the multi-objective optimization design method for motors based on the Kriging surrogate model of the present invention.

[0040] The overall implementation process of this invention is as follows: Figure 1 As shown, it includes the following steps:

[0041] S1. Determine the design variables of the motor and their value range, and construct the parametric model of the motor to be optimized;

[0042] In this embodiment, the selected motor design variables, initial values, and value ranges are shown in Table 1.

[0043] Table 1. Design variables, initial values, and value ranges for a 12-slot, 10-pole axial flux motor.

[0044]

[0045] S2. An initial motor design variable sample set is generated using experimental design methods. For each set of motor design variable values ​​in the initial motor design variable sample set, finite element analysis calculations are performed on the parameterized model of the motor to be optimized group by group to obtain the corresponding motor performance response and construct the initial dataset. ;

[0046] In this embodiment, the motor topology to be optimized is a 12-slot, 10-pole axial flux permanent magnet motor, and its three-dimensional structure is as follows: Figure 2 As shown. To improve the efficiency of finite element analysis, a four-layer two-dimensional linear motor parametric model is used to equivalently obtain the motor performance. The single-layer two-dimensional structure of the linear motor is shown in the figure. Figure 3 As shown.

[0047] The motor performance as the output response includes, but is not limited to, electromagnetic torque. In this embodiment, the motor performance response is the average electromagnetic torque during the stable operating period of the motor. The equivalent motor torque obtained through the four-layer two-dimensional linear motor model is the sum of the torques of each layer of the motor model. A sample set of 100 initial motor design variables was obtained through Latin hypercube sampling. For each set of motor design variable values, finite element analysis was performed using the four-layer two-dimensional linear motor parametric model to obtain the corresponding motor torque value.

[0048] S3. Use motor design variables as multidimensional input variables for the Kriging surrogate model. Motor performance is used as the output response of the Kriging surrogate model. Based on the initial dataset Training the initial Kriging proxy model This is used to fit the mapping relationship between the combination of motor design variables and the motor performance response; if an initial Kriging surrogate model already exists... Then based on the updated dataset Retrain the Kriging agent model ;

[0049] In this embodiment, the dataset is processed before each training of the proxy model. The maximum and minimum values ​​are normalized before processing. During each training of the surrogate model, the hyperparameter tuning process of the Kriging surrogate model is completed by the particle swarm optimization algorithm or the genetic algorithm. In this embodiment, the hyperparameter tuning process is completed by the particle swarm optimization algorithm.

[0050] S4, using the Kriging proxy model As one or more objective functions in a multi-objective optimization problem, where the multidimensional input variables of the Kriging surrogate model are... These are the decision variables in the optimization problem. The value range of the multi-dimensional input variable of the Kriging surrogate model is taken as the decision variable , and a related constraint condition is given to construct an optimization model

[0051] In this embodiment, two objective functions are defined, the objective function 1 to be maximized is the Kriging surrogate model representing the average torque of the motor , and the objective function 2 to be minimized is the effective mass of the motor calculated according to the motor size parameters , including the stator and rotor core mass, the permanent magnet mass, and the winding mass, the motor design variables and the value range shown in Table 1 are selected as the decision variable and the feasible region thereof , and the volume constraint condition shown in Table 2 is set, and the multi-objective optimization model constructed is as follows:

[0052]

[0053] , wherein is the objective function 1, is the objective function 2, is the constraint condition 1, is the constraint condition 2, is the constraint condition 3, is the total volume of the motor, is the volume of the permanent magnet, is the volume of the copper wire, is the total volume constraint of the motor, is the volume constraint of the permanent magnet, is the volume constraint of the copper wire.

[0054] Table 2 Volume constraint of 12-slot 10-pole axial flux motor

[0055]

[0056] S5, a multi-objective optimization algorithm is used to solve the optimization model to obtain a Pareto optimal solution set of the current round , For each solution in the Pareto optimal solution set , the Kriging surrogate model is used to calculate the prediction mean square error thereof as a measurement basis for prediction uncertainty, and according to the size of the prediction mean square error, a solution (i.e., a high error solution) higher than a preset threshold is selected to form a simulation sample subset

[0057] In this embodiment, the multi-objective optimization algorithm used to solve the optimization model is the NSGA-II algorithm, and in the algorithm parameters, the population size is set to 50, the maximum evolution generation is set to 100, and 50 groups of Pareto optimal solution sets are obtained. As shown in Fig. 2, the 50 groups of Pareto optimal solution sets are plotted in the objective function 1-2 spaceFigure 4 As shown in the figure, the 50 data points represent the Pareto optimal solution set obtained by the multi-objective optimization algorithm. The Kriging surrogate model is used to calculate the prediction mean square error of the solutions in the Pareto optimal solution set. Points with a prediction mean square error higher than a preset threshold are selected as high-error solutions and marked with red triangles. The method for determining the preset threshold is as follows:

[0058] Pareto optimal solution set for the current round The average of the prediction mean square errors of all solutions + The standard deviation of the predicted mean square error of all solutions × , In this embodiment, the value is a pre-designed value. The value of is 0.

[0059] S6. Determine the Pareto optimal solution set for the current round. over-volume index Does the preset convergence condition hold? If yes, end the iteration and obtain the final Pareto optimal solution set. As an optimization result; if not, proceed to step S7;

[0060] The convergence condition is set as: the hypervolume index of the Pareto optimal solution set in the current round. Hypervolume index compared to the previous Pareto optimal solution set relative error The two-dimensional hypervolume index in this embodiment is less than the set value. The calculation formula is:

[0061]

[0062] in, Based on reference point The Pareto optimal solution set obtained by calculation Two-dimensional hypervolume index, This represents the number of solutions in the Pareto optimal solution set, in this embodiment... It is 50; Let be the sorted Pareto optimal solution set, where The first in the Pareto optimal solution set One solution. For the Pareto optimal solution set, the th The x-coordinate of each solution, For the Pareto optimal solution set, the th The ordinates of each solution; As a reference point, The x-coordinate of the reference point The longitudinal coordinate of the reference point must be dominated by the Pareto solution set, which is fixed as (30, 0) in this embodiment ; The first point and the reference point form a rectangular area (remove the overlapping part), as shown in Figure 5 .

[0063] The relative error of the hyper-volume indicator is used as an indicator to judge the convergence of the optimization result, and the calculation formula is as follows:

[0064]

[0065] In this embodiment, the convergence condition is set to be that the relative error of the hyper-volume indicator is less than 1%. After 4 rounds of iteration update, the optimization result converges, the total time consumption of the optimization process is 21.45 hours, and the final optimization result is as shown in Figure 6 . The change of the hyper-volume indicator of each round of Pareto optimal solution set and the relative error of the hyper-volume indicators of adjacent two rounds in the iteration process is as shown in Figure 7 .

[0066] S7, calling the motor parameterized model to be optimized to perform finite element analysis calculation on each sample point in the sample subset to be simulated, obtaining the motor performance response, and adding the calculation result to the data set ; enter step S3.

[0067] Compared with a method (hereinafter referred to as a traditional method) of supplementing the calculation results of all Pareto solution sets obtained by the optimization algorithm into the training data set of the surrogate model, it can be seen that both methods significantly improve the local prediction accuracy of the Kriging surrogate model near the Pareto front. After verification by the finite element model calculation, the average relative error of the surrogate model prediction at the Pareto optimal solution set is reduced from 6.33% to less than 1%; the traditional method converges after three iterations, a total of 150 samples are supplemented, and the total optimization process time is 46.89 hours; while the embodiment of the application converges after four iterations, since only the subset of the screened Pareto optimal solution set is subjected to finite element simulation each time, a total of 60 samples are supplemented, and the total optimization process time is 21.45 hours, which is more than 50% less than the traditional method. The average relative error of the surrogate model prediction of the 50 groups of Pareto optimal solution sets is 0.90%, which meets the engineering design requirements. Therefore, the application significantly reduces the finite element model calculation cost while ensuring the local prediction accuracy of the Pareto front, greatly improves the efficiency of motor multi-objective optimization design, and is more suitable for occasions where the calculation cost and accuracy need to be balanced.

[0068] Table 3 Comparison of effects of the embodiment of the application and the traditional method

[0069]

[0070] Based on the same inventive concept, the embodiment of the application provides a motor multi-objective optimization design system based on a Kriging surrogate model, comprising:

[0071] A parameterized model construction unit is configured to determine design variables of a motor and a value range thereof, and construct a parameterized model of a motor to be optimized.

[0072] An initial data set construction unit is configured to generate an initial motor design variable sample set by using an experimental design method, perform finite element analysis and calculation on the parameterized model of the motor to be optimized for each group of motor design variable values in the initial motor design variable sample set, obtain corresponding motor performance responses, and construct an initial data set.

[0073] A Kriging surrogate model training unit is configured to take motor design variables as multi-dimensional input variables of a Kriging surrogate model, take motor performance as an output response of the Kriging surrogate model, train an initial Kriging surrogate model based on the initial data set, and fit the mapping relationship between the combination of motor design variables and the motor performance response. If an initial Kriging surrogate model already exists, the Kriging surrogate model is retrained based on an updated data set.

[0074] an optimization model construction unit, configured to construct an optimization model by taking a Kriging surrogate model as one or more objective functions in a multi-objective optimization problem, wherein multi-dimensional input variables of the Kriging surrogate model are decision variables of the optimization problem, taking value ranges of the multi-dimensional input variables of the Kriging surrogate model as feasible regions of the decision variables, and giving relevant constraint conditions;

[0075] an optimization model solution unit, configured to solve the optimization model by using a multi-objective optimization algorithm to obtain a Pareto optimal solution set of a current round; for each solution in the Pareto optimal solution set, calculate a prediction mean square error of the solution by using the Kriging surrogate model as a measurement basis of prediction uncertainty, and select solutions with a prediction mean square error higher than a preset threshold to form a simulation sample subset;

[0076] a convergence judgment unit, configured to judge whether a hyper-volume index of the Pareto optimal solution set of the current round meets a preset convergence condition: if yes, end iteration and obtain a final Pareto optimal solution set as an optimization result; if no, call a motor parameterized model to be optimized to perform finite element analysis calculation on each sample point in the simulation sample subset, obtain a motor performance response, and add a calculation result to a data set.

[0077] Based on the same inventive concept, an embodiment of the present application provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements steps of the motor multi-objective optimization design method based on the Kriging surrogate model when executing the computer program.

[0078] Based on the same inventive concept, an embodiment of the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executable on a processor to implement steps of the motor multi-objective optimization design method based on the Kriging surrogate model.

[0079] It should be apparent to those skilled in the art that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage media, etc.) containing computer-usable program code.

[0080] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0081] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0082] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0083] The above embodiments are only illustrative of the technical ideas of the present application, and do not have any limiting effect on the present application. Any person skilled in the art can make any form of equivalent replacement, modification or change to the technical solutions and technical contents disclosed in the present application without departing from the scope of the technical solutions of the present application, and still fall within the protection scope of the present application.

Claims

1. A method for multi-objective optimization design of an electric machine based on a Kriging surrogate model, characterized in that, The method comprises the following steps: S1, determining design variables of the motor and their value ranges, and constructing a parameterized model of the motor to be optimized; S2, generating an initial motor design variable sample set by using an experimental design method, for each set of motor design variable values in the initial motor design variable sample set, calling the parameterized model of the motor to be optimized for finite element analysis calculation, obtaining the corresponding motor performance response, and constructing an initial data set; S3, taking the motor design variables as the multi-dimensional input variables of the Kriging surrogate model and the motor performance as the output response of the Kriging surrogate model, training an initial Kriging surrogate model based on the initial data set, and fitting the mapping relationship between the combination of motor design variables and the motor performance response; If the initial Kriging surrogate model already exists, the Kriging surrogate model is retrained based on the updated data set; S4, taking the Kriging surrogate model as one or more objective functions in a multi-objective optimization problem, wherein the multi-dimensional input variables of the Kriging surrogate model are the decision variables of the optimization problem, the value ranges of the multi-dimensional input variables of the Kriging surrogate model are the feasible region of the decision variables, and relevant constraint conditions are given to construct an optimization model; S5, solving the optimization model by using a multi-objective optimization algorithm to obtain a Pareto optimal solution set of the current round; for each solution in the Pareto optimal solution set, calculating the prediction mean square error of the solution by using the Kriging surrogate model as a measure of prediction uncertainty, and selecting solutions with a prediction mean square error higher than a preset threshold to form a simulation sample subset according to the size of the prediction mean square error; S6, determining whether the hyper volume index of the Pareto optimal solution set of the current round meets a preset convergence condition: if yes, ending the iteration and obtaining the final Pareto optimal solution set as the optimization result; if no, proceeding to step S7; S7, calling the parameterized model of the motor to be optimized for finite element analysis calculation for each sample point in the simulation sample subset, obtaining the motor performance response thereof, and adding the calculation result to the data set; Proceeding to step S3.

2. The motor multi-objective optimization design method based on a Kriging surrogate model according to claim 1, characterized in that, The experimental design method in step S2 is Latin hypercube sampling.

3. The motor multi-objective optimization design method based on Kriging surrogate model according to claim 1, characterized in that, The Kriging surrogate model in step S3 needs to be preprocessed by maximum and minimum normalization before training; The hyperparameter tuning process of the Kriging surrogate model is completed by a particle swarm optimization algorithm or a genetic algorithm.

4. The motor multi-objective optimization design method based on a Kriging surrogate model according to claim 1, characterized in that, The multi-objective optimization algorithm in step S4 includes but is not limited to an NSGA-II algorithm.

5. The motor multi-objective optimization design method based on Kriging surrogate model according to claim 1, characterized in that, The determination method of the preset threshold in step S5 is as follows: Current round Pareto optimal solution set Mean of the prediction mean square error of all solutions in Standard deviation of the prediction mean square error of all solutions in , is a pre-designed value.

6. The motor multi-objective optimization design method based on a Kriging surrogate model according to claim 1, wherein, The convergence condition described in step S6 is that the hyper-volume index of the current round of Pareto optimal solution set The hyper-volume index of the last round of Pareto optimal solution set The relative error is less than a set value.

7. The motor multi-objective optimization design method based on Kriging surrogate model according to claim 1, characterized in that, The motor performance includes but is not limited to electromagnetic torque.

8. A system for multi-objective optimization design of an electrical machine based on a Kriging surrogate model, characterized in that, The method comprises the following steps: A parameterized model construction unit is configured to determine design variables of the motor and their value ranges, and construct a parameterized model of the motor to be optimized; An initial data set construction unit is configured to generate an initial motor design variable sample set by using an experimental design method, for each set of motor design variable values in the initial motor design variable sample set, call the parameterized model of the motor to be optimized for finite element analysis calculation, obtain the corresponding motor performance response, and construct an initial data set; The Kriging surrogate model training unit is configured to take the motor design variables as multi-dimensional input variables of the Kriging surrogate model, take the motor performance as an output response of the Kriging surrogate model, and train an initial Kriging surrogate model based on the initial data set, so as to fit a mapping relationship between the motor design variable combination and the motor performance response. If the initial Kriging surrogate model exists, the Kriging surrogate model is retrained based on the updated data set. The optimization model construction unit is configured to take the Kriging surrogate model as one or more objective functions in a multi-objective optimization problem, take the multi-dimensional input variables of the Kriging surrogate model as decision variables of the optimization problem, take the value range of the multi-dimensional input variables of the Kriging surrogate model as a feasible region of the decision variables, and give a related constraint condition, so as to construct an optimization model. The optimization model solving unit is configured to solve the optimization model by using a multi-objective optimization algorithm to obtain a Pareto optimal solution set of the current round. For each solution in the Pareto optimal solution set, the Kriging surrogate model is used to calculate a prediction mean square error as a measurement basis of prediction uncertainty, and a solution higher than a preset threshold is selected according to the size of the prediction mean square error to form a simulation sample subset. The convergence judgment unit is configured to judge whether a hyper volume index of the Pareto optimal solution set of the current round meets a preset convergence condition. If yes, the iteration is ended and a final Pareto optimal solution set is obtained as an optimization result. If no, each sample point in the simulation sample subset is called to perform a finite element analysis calculation by using the motor parameterized model to be optimized, a motor performance response is obtained, and the calculation result is added to the data set.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The processor executes the computer program to implement the steps of the motor multi-objective optimization design method based on the Kriging surrogate model according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to implement the steps of the motor multi-objective optimization design method based on the Kriging surrogate model according to any one of claims 1 to 7.

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