Multi-objective optimization design method and system for permanent magnet synchronous linear motor

Abstract

The invention relates to a multi-objective optimization design method and system for a permanent magnet synchronous linear motor, and the method comprises the steps: analyzing the influence of motor structure parameters on average thrust and thrust fluctuation, so as to screen out the motor structure parameters of which the significant influence level is not smaller than a specified level. Optimization of motor structure parameters is realized through a method of combining a Kriging agent model and a multi-target whale optimization algorithm, and the two modes have the advantages of low calculation complexity and capability of reducing calculation cost, so that calculation resources are saved, noise interference can be resisted, an over-fitting phenomenon can be avoided, thrust fluctuation is inhibited, and the motor performance is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer modeling, in particular to a multi-objective optimization design method and system for a permanent magnet synchronous linear motor. BACKGROUND

[0002] Multi-parameter optimization design of a motor is an important part of engineering design, specifically referring to selecting an optimal parameter scheme to meet the requirements of motor indicators and performance on the basis that each parameter of the motor meets the requirements (i.e. constraint conditions). The performance optimization methods for permanent magnet synchronous linear motors in the prior art mainly include analytical method, numerical method and surrogate model method.

[0003] The analytical method is based on Maxwell's equations to solve the analytical expression of motor performance, and then to construct an analytical correlation model between motor structural parameters and motor performance. Due to the complexity of the analytical expression and the coupling relationship between multiple parameters, it is difficult to effectively establish an accurate analytical expression between motor structural parameters and performance, resulting in a significant reduction in calculation accuracy and difficulty in obtaining accurate results.

[0004] The numerical method is to analyze various structural parameter combinations by means of finite element simulation software to obtain corresponding motor performance data, and finally to obtain the optimal motor structural scheme by screening all the results. The numerical method has high calculation accuracy, but is only suitable for low-dimensional parameter calculation. If the parameter dimension is high, the calculation amount will increase exponentially, the operation time will be longer, and the calculation cost will be larger.

[0005] The surrogate model method is to use the motor performance data calculated by part of the structural parameter combinations as sample data, to construct a surrogate model that can accurately predict the motor characteristics based on the sample data, and to combine various optimization algorithms to perform global optimization on the objective function to obtain the optimal solution. The surrogate model method has the significant advantages of short calculation period and high efficiency, and can effectively reduce the calculation amount and improve the design and development efficiency in the engineering design field. The most common surrogate models include response surface model, radial basis function model and artificial neural network model.

[0006] The response surface model has the characteristics of simple model structure and fast calculation speed, but its calculation accuracy is relatively low when dealing with high-dimensional, nonlinear and multi-peak problems. The radial basis function model has the advantages of simple algorithm logic, easy implementation and high flexibility, but it is easily disturbed by noise samples and prone to overfitting phenomenon. The artificial neural network model can effectively handle various nonlinear problems and has strong robustness and autonomous learning ability, but the model structure is complex and requires a large amount of sample data as support, which also puts higher requirements on computing resources. SUMMARY

[0007] The technical problem to be solved by the present application is how to overcome the technical defects of low calculation accuracy, high calculation cost, easy interference of noise samples and easy overfitting phenomenon existing in the multi-parameter optimization design technology of the existing motor.

[0008] The present application provides a kind of permanent magnet synchronous linear motor multi-objective optimization design method and system, specifically includes a kind of permanent magnet synchronous linear motor multi-objective optimization design method and a kind of permanent magnet synchronous linear motor multi-objective optimization design system.

[0009] S1: a function model with motor average thrust promotion and thrust fluctuation reduction as optimization target is constructed, and the value range of average thrust and thrust fluctuation is determined according to target demand to obtain an optimal model;

[0010] S2: the influence of motor structure parameters on average thrust and thrust fluctuation is analyzed based on analytical method and finite element method, to screen out the motor structure parameters with significant influence level not less than specified level, and obtain the optimization parameters;

[0011] S3: Latin hypercube sampling method is used to select a plurality of sample points uniformly distributed in the search space of the optimization parameters, and the response value corresponding to each sample point is obtained by finite element simulation calculation;

[0012] S4: all sample points and their corresponding response values obtained in step S3 are used to construct a Kriging surrogate model with linear combination of the optimization parameters as the overall fitting term and the response value as the output;

[0013] S5: multi-objective whale optimization algorithm is used to globally optimize the Kriging surrogate model, and a Pareto frontier solution set of the optimal model is obtained;

[0014] S6: the coefficient of determination of the Kriging surrogate model is obtained by using the coefficient of determination calculation formula, and whether the coefficient of determination exceeds the set value is judged,

[0015] if yes, the next step is executed;

[0016] if no, the step S3 is executed again;

[0017] S7: a Pareto frontier solution is selected from the current obtained Pareto frontier solution set, and the specific value of the optimization parameter corresponding to the Pareto frontier solution is obtained, and the structure of the motor is designed according to the specific value.

[0018] The multi-objective optimization design method of the permanent magnet synchronous linear motor disclosed in the application screens motor structure parameters with an influence level not less than a specified level by analyzing the influence of motor structure parameters on average thrust and thrust fluctuation. The optimization of motor structure parameters is realized by combining a Kriging surrogate model with a multi-objective whale optimization algorithm. Both of the two methods have the advantages of small computational complexity and low calculation cost, which not only saves computing resources, but also resists noise interference, avoids overfitting phenomenon, and further suppresses thrust fluctuation to improve motor performance.

[0019] In a possible implementation, the step S3 comprises the following steps:

[0020] S31: Latin hypercube sampling method is used to select a plurality of sample points uniformly distributed in the search space of the to-be-optimized parameters;

[0021] S32: average thrust and thrust fluctuation data corresponding to each sample point are respectively obtained through finite element simulation calculation;

[0022] S33: each sample point and its corresponding average thrust and thrust fluctuation data are substituted into the function model, and the response value corresponding to each sample point is obtained by using the response value function analytical expression.

[0023] The Latin hypercube sampling method can uniformly select a plurality of sample points and has unbiased characteristics. The response value corresponding to each sample point is obtained by using the function model and the response value function analytical expression, which can simultaneously consider engineering requirements and calculation cost and further reduce the calculation cost.

[0024] In a possible implementation, the mathematical analytical expression of the Kriging surrogate model is:

[0025]

[0026] wherein,

[0027] g is the response value;

[0028] p is the number of the to-be-optimized parameters;

[0029] f i is the i-th to-be-optimized parameter;

[0030] β i is the weight of the i-th to-be-optimized parameter;

[0031] z is a random fitting term.

[0032] The above calculation formula not only ensures the reduction of calculation cost, but also has small calculation deviation, which further improves the calculation accuracy while reducing the calculation cost.

[0033] In a possible implementation, the determination coefficient calculation formula is:

[0034]

[0035] wherein,

[0036] R 2 is a determination coefficient;

[0037] N is the number of sample points;

[0038] y i is a true value of a response value of the ith sample point;

[0039] is a predicted response value of the ith sample point of the Kriging surrogate model;

[0040] is an average value of the true values of the sample point response values.

[0041] The above calculation formula can not only evaluate the prediction accuracy of the surrogate model, but also reduce the calculation loss due to the relatively mature program of the formula.

[0042] In a possible implementation, the process of obtaining the determination coefficient of the Kriging surrogate model by using the determination coefficient calculation formula in the step S6 includes the following steps:

[0043] S61: selecting a plurality of sample points in the search space of the to-be-optimized parameters, and obtaining the response values of the sample points respectively by using the Kriging surrogate model;

[0044] S62: obtaining the true values of the response values of the sample points respectively by using the finite element calculation method;

[0045] S63: substituting the results obtained in the step S61 and the step S62 into the determination coefficient calculation formula to obtain the determination coefficient.

[0046] In the above manner, the determination coefficient of the Kriging surrogate model is obtained by using the determination coefficient calculation formula, which can not only evaluate the prediction accuracy of the surrogate model, but also further avoid the overfitting phenomenon.

[0047] Another technical solution of the present application provides a multi-objective optimization design system of a permanent magnet synchronous linear motor, which comprises, in series:

[0048] An optimization module is configured to allow a user to construct a function model with the motor average thrust improvement and thrust fluctuation reduction as optimization objectives, and to allow the user to determine the value range of the average thrust and the thrust fluctuation, so as to obtain an optimization model.

[0049] a parameter module configured to analyze the influence of motor structure parameters on average thrust and thrust fluctuation based on an analytical method and a finite element method, to screen the motor structure parameters with a significant influence level not less than a specified level, and to obtain to-be-optimized parameters;

[0050] a calculation module configured to select a plurality of sample points uniformly distributed in a search space of the to-be-optimized parameters by using a Latin hypercube sampling method, and to obtain response values corresponding to each sample point through finite element simulation calculation;

[0051] a modeling module configured to construct a Kriging surrogate model with a linear combination of the to-be-optimized parameters as an overall fitting term and with the response values as outputs, by using all the sample points and the corresponding response values;

[0052] an optimization module configured to perform global optimization on the Kriging surrogate model by using a multi-objective whale optimization algorithm, to obtain a Pareto frontier solution set of the optimized model;

[0053] a calculation and judgment module configured to obtain a determination coefficient of the Kriging surrogate model by using a determination coefficient calculation formula, to judge whether the determination coefficient exceeds a set value, and if yes, to output the Pareto frontier solution set, and if not, to pass the result of failure to the calculation module;

[0054] an output module configured to select a Pareto frontier solution from the currently obtained Pareto frontier solution set, and to obtain specific values of the to-be-optimized parameters corresponding to the Pareto frontier solution.

[0055] The system disclosed in the application is provided with an optimization module, a parameter module, a calculation module, a modeling module, an optimization module and a calculation and judgment module. The parameter module is configured to analyze the influence of motor structure parameters on average thrust and thrust fluctuation, to screen the motor structure parameters with a significant influence level not less than a specified level, and to obtain to-be-optimized parameters. The modeling module, the optimization module and the calculation and judgment module are cooperated to realize optimization of motor structure parameters by combining a Kriging surrogate model with a multi-objective whale optimization algorithm. Both of the two methods have the advantages of small calculation complexity and low calculation cost, which can not only save calculation resources, but also resist noise interference, avoid overfitting phenomenon, suppress thrust fluctuation and improve motor performance.

[0056] In a possible implementation, the calculation module comprises units connected in sequence:

[0057] a sampling unit configured to select a plurality of sample points uniformly distributed in a search space of the to-be-optimized parameters by using a Latin hypercube sampling method;

[0058] The simulation unit is configured to obtain the average thrust and thrust fluctuation data corresponding to each sample point respectively through finite element simulation calculation.

[0059] The solving unit is configured to substitute each sample point and the corresponding average thrust and thrust fluctuation data into the function model to obtain the response value corresponding to each sample point by using the response value function analytical expression.

[0060] By setting the sampling unit, a plurality of sample points can be uniformly selected by using the Latin hypercube sampling method, and the sampling unit has the unbiased characteristic. By setting the solving unit, the response value corresponding to each sample point can be obtained by using the function model and the response value function analytical expression, and the engineering requirement and the calculation cost can be simultaneously considered, and the calculation cost is further reduced.

[0061] In a possible implementation, the calculation and judgment module comprises:

[0062] The searching unit is configured to select a plurality of sample points in the search space of the to-be-optimized parameter, and obtain the response value of each sample point by using the Kriging surrogate model.

[0063] The true value unit is configured to obtain the true value of the response value of each sample point by using the finite element calculation method.

[0064] The coefficient unit is configured to substitute the response value and the true value into the decision coefficient calculation formula to obtain the decision coefficient.

[0065] The judgment unit is configured to judge whether the decision coefficient exceeds a set value, and if yes, the Pareto front solution set is output; if no, the non-passing result is transmitted to the calculation module.

[0066] By setting the searching unit, the true value unit and the coefficient unit, the decision coefficient of the Kriging surrogate model is obtained by using the decision coefficient calculation formula, and the judgment unit is used to execute the judgment program, so that the prediction accuracy of the surrogate model can be evaluated, and the overfitting phenomenon can be further avoided. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 A flow chart of a multi-objective optimization design method of a permanent magnet synchronous linear motor is disclosed in Embodiment One of the present application.

[0068] Figure 2 A structural schematic diagram of a multi-objective optimization design system of a permanent magnet synchronous linear motor is disclosed in Embodiment Two of the present application. DETAILED DESCRIPTION

[0069] First, those skilled in the art should understand that these embodiments are only used to explain the technical principles of the embodiments of the present application, and are not intended to limit the protection scope of the embodiments of the present application. Those skilled in the art can make adjustments as needed in order to adapt to specific application occasions.

[0070] In the description of the embodiments of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "electrically connected", "establishing an electrically connected relationship" should be understood in a broad sense, that is, it should be understood that two or more have an electrical relationship, which can be connected by a wire, or wireless electrical connection, or a combination of the two; it can be directly connected, or indirectly connected through an intermediate medium. For those skilled in the art, the specific meaning of the above terms in the embodiments of the present application can be understood according to the specific circumstances. In addition, unless otherwise specified, "model" in the description of the embodiments of the present application refers to a mathematical model.

[0071] In the embodiments of the present application, unless otherwise explicitly specified and limited, the first feature is "on" or "under" the second feature, which can be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, the first feature can be above or obliquely above the second feature, or it can only mean that the horizontal height of the first feature is higher than that of the second feature. The first feature can be below or obliquely below the second feature, or it can only mean that the horizontal height of the first feature is less than that of the second feature.

[0072] The present application will be further described in detail below with two embodiments, and in conjunction with the drawings and specific embodiments.

[0073] Embodiment one:

[0074] Referring to Figure 1 The embodiments of the present application disclose a multi-objective optimization design method of a permanent magnet synchronous linear motor, Figure 1 A flowchart of the method is shown in the figure, and the method comprises the following steps:

[0075] S1: A function model is constructed with the optimization objectives of improving the average thrust of the motor and reducing the thrust fluctuation, and the value range of the average thrust and the thrust fluctuation is determined according to the target requirements, so as to obtain an optimization model.

[0076] After the function model is determined, the minimum value of the average thrust and the maximum value of the thrust fluctuation are determined according to the target requirements, so as to obtain the value range.

[0077] S2: The influence of the motor structure parameters on the average thrust and the thrust fluctuation is analyzed based on the analytical method and the finite element method, so as to screen out the motor structure parameters with a significant influence level not less than a specified level, and obtain the parameters to be optimized.

[0078] Specifically, the influence of motor structure parameters on average thrust and thrust fluctuation is analyzed based on the analytical method and the finite element method, and through sensitivity analysis on the structure parameters, the to-be-optimized parameters which have significant influence on the objective function are screened out.

[0079] S3: Latin hypercube sampling method is used to select a plurality of sample points uniformly distributed in the search space of the to-be-optimized parameters, and the response values corresponding to each sample point are obtained through finite element simulation calculation, and an initial sample database is constructed.

[0080] In this embodiment, step S3 includes the following steps: S31: Latin hypercube sampling method is used to select a plurality of sample points uniformly distributed in the search space of the to-be-optimized parameters; S32: the average thrust and thrust fluctuation data corresponding to each sample point are respectively obtained through finite element simulation calculation; S33: each sample point and its corresponding average thrust and thrust fluctuation data are respectively substituted into the function model, and the response values corresponding to each sample point are obtained by using the response value function analytical expression.

[0081] Specifically in this embodiment, the average thrust of the motor and the thrust fluctuation of the motor are linearly combined to obtain the response value function analytical expression, and the specific combination coefficients can be determined according to engineering requirements. Of course, the nonlinear function of the average thrust of the motor and the thrust fluctuation of the motor can also be used as the response value function analytical expression.

[0082] S4: Using all the sample points and their corresponding response values obtained in step S3, a Kriging surrogate model is constructed, which takes the linear combination of the to-be-optimized parameters as the overall fitting term and takes the response value as the output.

[0083] In this embodiment, the mathematical expression of the Kriging surrogate model is:

[0084]

[0085] wherein g is the response value; p is the number of to-be-optimized parameters; fi is the i-th to-be-optimized parameter; βi is the weight of the i-th to-be-optimized parameter; z is a random fitting term, which is a Gaussian distribution term in this embodiment. i i

[0086] S5: A multi-objective whale optimization algorithm is used to perform global optimization on the Kriging surrogate model to obtain a Pareto front solution set of the optimized model.

[0087] S6: The coefficient of determination of the Kriging surrogate model is calculated by using the coefficient of determination calculation formula, and it is judged whether the coefficient of determination exceeds a set value,

[0088] If yes, the next step is performed;

[0089] ​​If not, the step S3 is executed.

[0090] In the embodiment, the coefficient of determination calculation formula is:

[0091]

[0092] wherein, R 2 is the coefficient of determination; N is the number of sample points; y i is the true value of the response value of the i-th sample point; is the predicted response value of the i-th sample point of the Kriging surrogate model; is the average value of the true value of the response value of the sample points.

[0093] Meanwhile, in step S6, the process of obtaining the coefficient of determination of the Kriging surrogate model by the coefficient of determination calculation formula includes the following steps: S61: selecting a plurality of sample points in the search space of the to-be-optimized parameters, and obtaining the response value of each sample point by the Kriging surrogate model; S62: obtaining the true value of the response value of each sample point by the finite element calculation method; S63: substituting the response value obtained in step S61 and the true value obtained in step S62 into the coefficient of determination calculation formula to obtain the coefficient of determination.

[0094] S7: selecting a Pareto front solution from the currently obtained Pareto front solution set, and obtaining the specific value of the to-be-optimized parameter corresponding to the Pareto front solution, and performing structure design of the motor according to the specific value.

[0095] The multi-objective optimization design method of the permanent magnet synchronous linear motor disclosed in the embodiment screens the motor structure parameters whose influence significant level is not less than a specified level by analyzing the influence of the motor structure parameters on the average thrust and thrust fluctuation. The optimization of the motor structure parameters is realized by the method combining the Kriging surrogate model with the multi-objective whale optimization algorithm. Both of the two methods have the advantages of small calculation complexity and low calculation cost, which not only saves the calculation resources, but also resists the noise interference, avoids the overfitting phenomenon, and further suppresses the thrust fluctuation and improves the motor performance.

[0096] Embodiment two:

[0097] Referring to Figure 2 , the embodiment further discloses a multi-objective optimization design system of a permanent magnet synchronous linear motor, Figure 2A structural schematic diagram of the multi-objective optimization design system is shown in the figure. The multi-objective optimization design system comprises, in series, an optimization module, a parameter module, a calculation module, a modeling module, an optimization module, a calculation and judgment module, and an output module. The optimization module is configured to allow a user to construct a function model with the motor average thrust increase and thrust fluctuation decrease as the optimization objectives, and to allow the user to determine the value range of the average thrust and the thrust fluctuation, so as to obtain an optimization model. The parameter module is configured to analyze the influence of the motor structure parameters on the average thrust and the thrust fluctuation based on the analytical method and the finite element method, so as to screen out the motor structure parameters with a significant influence level not less than a specified level, and obtain the to-be-optimized parameters. The calculation module is configured to use the Latin hypercube sampling method to select a plurality of sample points uniformly distributed in the search space of the to-be-optimized parameters, and obtain the response values corresponding to each sample point through finite element simulation calculation. The modeling module is configured to construct a Kriging surrogate model with the linear combination of the to-be-optimized parameters as the overall fitting term and the response values as the output. The optimization module is configured to use the multi-objective whale optimization algorithm to perform global optimization on the Kriging surrogate model, and obtain a Pareto frontier solution set of the optimization model. The calculation and judgment module is configured to use a decision coefficient calculation formula to obtain the decision coefficient of the Kriging surrogate model, and determine whether the decision coefficient exceeds a set value. If yes, the Pareto frontier solution set is output. If no, the result of not passing is transmitted to the calculation module. The output module is configured to select a Pareto frontier solution from the currently obtained Pareto frontier solution set, and obtain the specific value of the to-be-optimized parameter corresponding to the Pareto frontier solution.

[0098] See Figure 2 In the present embodiment, the calculation module comprises, in series, a sampling unit, a simulation unit, and a solving unit. The sampling unit is configured to use the Latin hypercube sampling method to select a plurality of sample points uniformly distributed in the search space of the to-be-optimized parameters. The simulation unit is configured to obtain the average thrust and the thrust fluctuation data corresponding to each sample point through finite element simulation calculation. The solving unit is configured to substitute each sample point and the corresponding average thrust and thrust fluctuation data into the function model, and obtain the response value corresponding to each sample point by using the response value function analytical expression.

[0099] See Figure 2In the embodiment, the calculation and judgment module comprises a searching unit, a true value unit, a coefficient unit and a judgment unit connected in sequence, wherein the searching unit is configured to select a plurality of sample points in the search space of the parameters to be optimized, and obtain the response values of the sample points by using the Kriging surrogate model; the true value unit is configured to obtain the true values of the response values of the sample points by using the finite element calculation method; the coefficient unit is configured to obtain the decision coefficient by substituting the response values and the true values into the decision coefficient calculation formula; and the judgment unit is configured to judge whether the decision coefficient exceeds the set value, and if yes, output the Pareto front solution set, and if not, pass the result of failure to the calculation module.

[0100] Corresponding to the beneficial effects of the first embodiment, the multi-objective optimization design system disclosed in the embodiment is configured with the optimization module, the parameter module, the calculation module, the modeling module, the optimization module and the calculation and judgment module. The parameter module is configured to analyze the influence of the motor structure parameters on the average thrust and thrust fluctuation, and to screen out the motor structure parameters with a significant influence level not less than a specified level. In addition, under the cooperation of the modeling module, the optimization module and the calculation and judgment module, the optimization of the motor structure parameters is realized by combining the Kriging surrogate model with the multi-objective whale optimization algorithm. Both of the two methods have the advantages of small calculation complexity and low calculation cost, which not only saves the calculation resources, but also resists noise interference, avoids overfitting phenomenon, and further suppresses the thrust fluctuation to improve the motor performance.

[0101] In the description of the embodiments of the present application, it should be noted that in the description of the present application, the terms indicating the direction or position relationship are based on the direction or position relationship shown in the drawings, which is only for the convenience of description, and does not indicate or imply that the device or member must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application.

[0102] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "in the embodiment", "specific example" or "some examples" means that the specific features, mechanisms, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the description, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, mechanisms, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, the skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples without contradiction.

[0103] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited to this. Any changes or replacements within the technical scope disclosed by the present application can be easily conceived by the person skilled in the art, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A multi-objective optimization design method for a permanent magnet synchronous linear motor, characterized in that, Includes the following steps: S1: Construct a function model with the optimization objectives of increasing the average thrust of the motor and reducing thrust fluctuation, and determine the range of values ​​for average thrust and thrust fluctuation according to the objective requirements to obtain the optimal model; S2: Based on analytical and finite element methods, analyze the influence of motor structural parameters on average thrust and thrust fluctuation, and screen out the motor structural parameters whose influence is not less than a specified level to obtain the parameters to be optimized; S3: The Latin hypercube sampling method is used to select multiple uniformly distributed sample points in the search space of the parameters to be optimized, and the response value corresponding to each sample point is obtained by finite element simulation calculation. S4: Using all the sample points and their corresponding response values ​​obtained in step S3, construct a Kriging surrogate model with the linear combination of the parameters to be optimized as the overall fitting term and the response value as the output. S5: The multi-objective whale optimization algorithm is used to perform global optimization on the Kriging surrogate model to obtain the Pareto front solution set of the optimal model; S6: Obtain the determination coefficient of the Kriging proxy model using the determination coefficient calculation formula, and determine whether the determination coefficient exceeds a set value. If so, proceed to the next step; If not, then return to step S3; S7: Select one Pareto front solution from the currently obtained Pareto front solution set, and obtain the specific value of the parameter to be optimized corresponding to this Pareto front solution, and design the motor structure based on the specific value.

2. The multi-objective optimization design method for permanent magnet synchronous linear motors according to claim 1, characterized in that, Step S3 includes the following steps: S31: The Latin hypercube sampling method is used to select multiple uniformly distributed sample points in the search space of the parameter to be optimized. S32: The average thrust and thrust fluctuation data corresponding to each sample point are obtained by finite element simulation calculation; S33: Substitute each sample point and its corresponding average thrust and thrust fluctuation data into the function model, and use the response value function analytical expression to obtain the response value corresponding to each sample point.

3. The multi-objective optimization design method for a permanent magnet synchronous linear motor according to claim 1 or 2, characterized in that, The mathematical expression of the Kriging proxy model is: in, g is the response value; p is the number of parameters to be optimized; f i Let i be the i-th parameter to be optimized; β i Let be the weight of the i-th parameter to be optimized; z is the random fitting term.

4. The multi-objective optimization design method for permanent magnet synchronous linear motors according to claim 3, characterized in that, The formula for calculating the coefficient of determination is: in, R 2 The coefficient of determination; N is the number of sample points; y i This represents the true value of the response value for the i-th sample point. Let i be the predicted response value of the Kriging proxy model at the i-th sample point; This is the average of the true values ​​of the sample point response values.

5. The multi-objective optimization design method for a permanent magnet synchronous linear motor according to claim 1, 2, or 4, characterized in that, In step S6, the process of obtaining the determination coefficients of the Kriging proxy model using the determination coefficient calculation formula includes the following steps: S61: Select multiple sample points in the search space of the parameters to be optimized, and use the Kriging surrogate model to obtain the response value of each sample point respectively; S62: Obtain the true value of the response at each sample point using the finite element method; S63: Substitute the results obtained in steps S61 and S62 into the formula for calculating the coefficient of determination to obtain the coefficient of determination.

6. A multi-objective optimization design system for a permanent magnet synchronous linear motor, characterized in that, The multi-objective optimization design method for permanent magnet synchronous linear motors based on any one of claims 1-5 includes, in series: The optimization module allows users to build a function model with the optimization objectives of increasing the average thrust of the motor and reducing thrust fluctuation, and allows users to determine the range of values ​​for the average thrust and thrust fluctuation in order to obtain the optimization model. The parameter module is set to analyze the influence of motor structural parameters on average thrust and thrust fluctuation based on analytical and finite element methods, in order to screen out the motor structural parameters whose influence is not less than a specified level and obtain the parameters to be optimized. The calculation module is configured to use the Latin hypercube sampling method to select multiple uniformly distributed sample points in the search space of the parameters to be optimized, and to obtain the response value corresponding to each sample point through finite element simulation calculation. The modeling module is configured to use all sample points and their corresponding response values ​​to construct a Kriging surrogate model with a linear combination of the parameters to be optimized as the overall fitting term and the response values ​​as the output. The optimization module is configured to use a multi-objective whale optimization algorithm to perform global optimization on the Kriging surrogate model and obtain the Pareto front solution set of the optimized model. The calculation and judgment module is configured to obtain the determination coefficient of the Kriging proxy model using the determination coefficient calculation formula, and determine whether the determination coefficient exceeds a set value. If it does, the Pareto front solution set is output; otherwise, the failure result is sent to the calculation module. The output module is configured to select one Pareto front solution from the currently obtained Pareto front solution set and obtain the specific value of the parameter to be optimized corresponding to this Pareto front solution.

7. The multi-objective optimization design method for a permanent magnet synchronous linear motor according to claim 6, characterized in that, The computing module comprises the following components connected in series: The sampling unit is configured to use Latin hypercube sampling to select multiple uniformly distributed sample points in the search space of the parameter to be optimized. The simulation unit is set to obtain the average thrust and thrust fluctuation data corresponding to each sample point through finite element simulation calculation; The solution unit is configured to substitute each sample point and its corresponding average thrust and thrust fluctuation data into the function model, and obtain the response value corresponding to each sample point using the analytical expression of the response value function.

8. The multi-objective optimization design method for a permanent magnet synchronous linear motor according to claim 7, characterized in that, The calculation and judgment module includes: The search unit is configured to select multiple sample points in the search space of the parameters to be optimized, and use the Kriging surrogate model to obtain the response value of each sample point respectively. The true value element is set to obtain the true value of the response value of each sample point through the finite element method; The coefficient unit is configured to substitute the response value and the true value into the determination coefficient calculation formula to obtain the determination coefficient; The judgment unit is configured to determine whether the determination coefficient exceeds a set value. If it does, the Pareto front solution set is output; otherwise, the failure result is transmitted to the calculation module.

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