Method, device and storage medium for multi-objective optimization of cylindrical linear motor

Abstract

The application discloses a kind of cylinder linear motor multi-objective optimization method, equipment and storage medium, the average thrust of the cylinder linear motor and thrust fluctuation are optimization target, the design parameter influencing it is analyzed, and the range of its value is determined;Sample library is constructed by optimal Latin hypercube experimental design;Kriging model is established based on the sample library;The expected maximum adding point criterion function and prediction function of model are parallel optimized using NSGA-II algorithm;If the model reaches the set convergence accuracy, the optimal design parameter is obtained by NSGA-II algorithm optimization;Otherwise, the real value is calculated and added to the sample library, and the optimization is repeated.The application combines NSGA-II algorithm and Kriging model, and parallel optimization is carried out on the expected improvement maximum criterion function and prediction function using NSGA-II algorithm, which can quickly improve the model accuracy and improve the optimization efficiency and robustness of the algorithm.

Description

Technical Field

[0001] The present invention relates to the optimization of a cylindrical linear motor, and in particular to a multi-objective optimization method, device and storage medium for a cylindrical linear motor. Background Art

[0002] Cylindrical linear motors have high energy density and thrust density, demonstrating numerous advantages such as high thrust density, fast response speed, and high acceleration. They have great application potential in areas such as CNC machine tools and wave energy generation.

[0003] However, cylindrical linear motors also present unavoidable hazards such as thrust disturbances. The main reasons for large thrust fluctuations are their unique structural and performance characteristics. First, the primary core is broken, resulting in significant end forces due to end effects, which affect dynamic performance. Second, the core slots, where the coils are embedded, create cogging and generate cogging forces. Therefore, optimization of cylindrical linear motors is necessary.

[0004] In the process of optimizing cylindrical linear motors, in order to simultaneously improve average thrust and reduce thrust fluctuations, multi-objective optimization is required to achieve the optimal balance between these objectives. Traditional finite element models and analytical methods for motor optimization suffer from high computational costs and low accuracy, leading to the development of numerous indirect methods, such as surrogate model-based optimization algorithms.

[0005] A surrogate model constructs a nonlinear response function using a certain amount of data samples and predicts the target values ​​of the corresponding factors. This can improve optimization efficiency in multi-objective motor optimization. Existing optimization algorithms based on surrogate models include radial basis function neural networks, the k-nearest neighbor model based on machine learning theory, and support vector machines. However, in these algorithms, the sample size and model accuracy of the surrogate model are mutually constrained. Specifically, if the sample size is too small, the constructed model will have significant errors, and the predicted target values ​​will be unrepresentative. If the sample size is too large, obtaining the target values ​​through finite element simulation of the motor will be very time-consuming.

[0006] Therefore, in the multi-objective optimization process of the cylindrical linear motor structural parameters, how to alleviate the mutual constraints between sample size and model accuracy, solve the problem of low model accuracy caused by small sample size, and improve the optimization efficiency are difficult problems that technical personnel in this field are committed to solving. Summary of the Invention

[0007] The embodiment of the present application provides a multi-objective optimization method for a cylindrical linear motor, which solves the technical problem of low model accuracy caused by small sample size in the optimization algorithm based on the proxy model in the prior art. On the basis of constructing the proxy model, the point addition criterion is improved to improve the optimization efficiency.

[0008] The embodiment of the present application provides a multi-objective optimization method for a cylindrical linear motor, comprising the following steps:

[0009] Step S1: Taking the average thrust and thrust fluctuation of the cylindrical linear motor as optimization targets, analyzing the design parameters that affect the average thrust and thrust fluctuation, and determining the value ranges of the average thrust and thrust fluctuation;

[0010] Step S2: constructing a sample library through optimal Latin hypercube experimental design;

[0011] Step S3: establishing a Kriging model based on the sample library;

[0012] Step S4: Using the NSGA-Ⅱ algorithm to perform parallel optimization on the expected maximum addition criterion EI function and the prediction function Fp of the Kriging model;

[0013] Step S5: Determine whether the model has reached the set convergence accuracy; if so, the optimal design parameters are obtained through the NSGA-II algorithm; otherwise, the true value of the point obtained by the optimization in step S4 is calculated and added to the sample library in step S2, and steps S3 to S5 are repeated.

[0014] Preferably, in step S1, the design parameters affecting the average thrust and thrust fluctuation include the slot width, permanent magnet length, permanent magnet thickness, pole pitch, air gap width, and mover core thickness of the cylindrical linear motor.

[0015] Preferably, in step S2, based on φ q Standard Latin hypercube experimental design was performed.

[0016] More preferably, the q The specific method for standard Latin hypercube experimental design is as follows:

[0017]

[0018] Among them, n p is the number of samples, d ij is the distance between sample points, q is a positive integer index, where i and j represent the i-th and j-th samples;

[0019] By minimizing φ qThe distance between sample points is maximized to ensure the spatial uniformity of the sample points.

[0020] Preferably, the specific process of step S3 is: extracting samples from the sample library and constructing a Kriging proxy model of the objective function of each sample.

[0021] Preferably, the step S4 specifically includes the following sub-steps:

[0022] Step S41: Calculate the EI function value of the Kriging proxy model of the objective function of each sample, and use the NSGA-Ⅱ algorithm to calculate the Pareto solution set of each EI function value. The solutions on the optimization solution set are all optimal solutions, and the new sample point Sei is determined according to the number of added points;

[0023] Step S42: Obtain the prediction function Fp based on the Kriging proxy model of the objective function of each sample, calculate the Pareto solution set of each prediction function Fp using the NSGA-II algorithm, and all solutions on the optimized solution set are optimal solutions. Determine the new sample point Sp based on the number of added points.

[0024] Preferably, the step S5 specifically includes the following sub-steps:

[0025] Step S51: Determine whether the model has reached the set convergence accuracy;

[0026] If the set convergence accuracy is achieved, proceed to step S52; otherwise, calculate the true target values ​​of the new sample points Sei and Sp optimized in step S4, and add the new sample points Sei, Sp and their true target values ​​to the sample library in step S2, and return to step S3;

[0027] Step S52: constructing a Kriging proxy model using all sample points in the sample library, and calculating the prediction function Fp of each objective function based on the Kriging proxy model;

[0028] Step S53: Calculate the Pareto solution set of the prediction function Fp in step S52 using the NSGA-II algorithm, and finally obtain the Pareto solution set of the multi-objective problem.

[0029] Furthermore, in step S51, the accuracy of the test model is tested using the complex correlation coefficient R 2 , which is expressed as follows:

[0030]

[0031] Among them, n is the number of value points, y i is the true model response value, is the predicted value of the approximate model, is the average value of the true response value; when R2 The closer the value of is to 1, the higher the global accuracy of the model.

[0032] An embodiment of the present application further provides an electronic device, comprising a processor, a memory, and a communication bus, wherein the processor and the memory communicate with each other via the communication bus;

[0033] The memory is used to store computer programs;

[0034] The processor is used to execute the program stored in the memory to implement the above-mentioned multi-objective optimization method of the cylindrical linear motor.

[0035] An embodiment of the present application further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned multi-objective optimization method for a cylindrical linear motor.

[0036] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0037] 1. Combining the NSGA-II algorithm with the Kriging model, using the Kriging proxy model, and establishing a model with a certain number of samples, this approach avoids the time-consuming finite element simulation of multiple sample points. The NSGA-II algorithm is also integrated to perform parallel optimization of the criterion function with the maximum expected improvement and the prediction function. Multiple points are added to the sample library in each iteration, rapidly improving the model accuracy until convergence, thereby enhancing the algorithm optimization efficiency.

[0038] 2. A nonlinear relationship between design variables and optimization objectives is established through the surrogate model, solving the accuracy problem caused by sample size.

[0039] 3. Use the optimal Latin square experimental design for sampling to ensure the uniformity of sample points in space, so that the results obtained later are stable.

[0040] 4. Combining the Kriging proxy model and NSGA-Ⅱ for multi-objective optimization avoids falling into local optimality during the optimization process, improves the running speed of the optimization algorithm, and enhances the robustness of the solution set. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the multi-objective optimization method for a cylindrical linear motor provided in Example 1 of the present application;

[0042] Figure 2 This is a specific flow chart for performing parallel optimization of the expected maximum addition criterion function and the prediction function of the Kriging model using the NSGA-II algorithm in Example 1 of the present application;

[0043] Figure 3 This is a diagram of the design variables of the cylindrical linear motor in Example 1 of the present application;

[0044] Figure 4 Schematic diagram of the Pareto optimal solution set in Example 1 of this application. DETAILED DESCRIPTION

[0045] The embodiment of the present application solves the technical problem of low model accuracy caused by small sample size in the optimization algorithm based on the proxy model in the prior art by providing a multi-objective optimization method for a cylindrical linear motor.

[0046] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows:

[0047] The Kriging model is a dynamic surrogate model that purposefully adds new sample points to the design region using a point-adding criterion function, continuously iterating until convergence. The Kriging surrogate model offers relatively accurate predictions, excellent nonlinear fitting capabilities, and unique error estimation capabilities, enabling high-precision calculation of the objective function response. However, in the Kriging surrogate model, points are added to the sample library one by one using a point-adding criterion. Each addition requires rebuilding the model. Adding too many points requires multiple optimization runs, resulting in low optimization efficiency.

[0048] The non-dominated sorting genetic algorithm with elite strategy (NSGA-Ⅱ) inherits the characteristics of genetic algorithm and obtains the optimal value through the collective evolution of the population, which is conducive to obtaining an optimized global solution and avoiding falling into local optimality. When solving multi-objective problems, it can obtain the Pareto optimal solution set and has the advantages of fast running speed and good solution set convergence.

[0049] To improve the optimization efficiency and accuracy of cylindrical linear motors, this application combines the NSGA-Ⅱ algorithm with the Kriging model. Using the Kriging proxy model, the model is established with a certain number of samples to avoid the time-consuming finite element simulation of multiple sample points. The NSGA-Ⅱ algorithm is integrated to perform parallel optimization of the expected improvement maximum criterion (EI) function and the prediction function. Each iteration adds multiple points to the sample library, rapidly improving the model accuracy until convergence and achieving convergence accuracy. This method improves the previous defect of the Kriging proxy model, which used the point-adding criterion to add points one by one, avoids the problem of low model accuracy caused by a small number of samples, accelerates the convergence of the Kriging model, and improves optimization efficiency.

[0050] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0051] Example 1

[0052] Figure 1 This is a flow chart of the multi-objective optimization method for a cylindrical linear motor provided in Example 1 of the present application. The multi-objective optimization method for a cylindrical linear motor includes the following steps:

[0053] Step S1: Taking the average thrust and thrust fluctuation of the cylindrical linear motor as optimization targets, analyzing the design parameters that affect the average thrust and thrust fluctuation, and determining the value ranges of the average thrust and thrust fluctuation;

[0054] The design parameters that affect the average thrust and thrust fluctuation include but are not limited to the slot width, permanent magnet length, permanent magnet thickness, pole pitch, air gap width, mover core thickness, etc. of the cylindrical linear motor.

[0055] Step S2: Construct a sample library through optimal Latin hypercube experimental design.

[0056] The optimal Latin hypercube is designed through experiments to sample the sample space, and the objective function value is calculated using co-simulation. The obtained samples and their response values ​​are stored in the sample point database.

[0057] Before building a surrogate model, an experimental design (DoE) method is first required to obtain the location of the initial sample points in the design variable space, and then build a surrogate model based on the initial sample points and their response values.

[0058] A good experimental design must satisfy both spatial uniformity and projection uniformity, with the goal of using less sample point information to accurately predict the response of the entire design area. q The standard Latin hypercube experimental design is as follows:

[0059]

[0060] In formula (1), n p is the number of samples, d ij is the distance between sample points, q is a positive integer index, where i and j represent the i-th and j-th samples. By minimizing φ q Maximize the distance between points to ensure the spatial uniformity of sample points.

[0061] Step S3: Establish a Kriging model based on the sample library.

[0062] Extract samples from the sample point database. In an optional implementation, assume that the sample is n p Construct a Kriging surrogate model of m objective functions, where m is a positive integer.

[0063] The Kriging model is an interpolation technique that uses known sample points and sample spatial location information to obtain unbiased estimates of unknown points and minimize the estimated variance. As a semi-parametric model, the model consists of two parts: regression and random parts. The expression is:

[0064] K(x)=F(β,x)+z(x)=f T (x)β+z(x) (2)

[0065] In formula (2), F(β,x) is the regression part, which provides the global prediction of the model, and f T (x) is the basis function of the regression function, β is the coefficient of the basis function, the choice of regression function will affect the accuracy of the model, the higher the order, the higher the accuracy. z(x) is the variance (i.e. σ 2 ) is a static random process with a mean of 0, which is locally estimated based on regression prediction and has the following characteristics:

[0066]

[0067] In formula (3), E[z(x)] represents the mean of z(x), var[z(x)] represents its variance, and cov[z(x i ), z(x j )] represents its covariance, x i and x j Represents the i-th sample and the j-th sample respectively, and the covariance is related to the parameter θ, R(θ,x i ,x j ) is the correlation function about the parameter θ. In this embodiment, R(θ,x i ,x j ) choose to use the Gaussian kernel function,

[0068]

[0069] In formula (4), and Represents sample x respectively i and x j The kth component of , k is a positive integer; θ k is the correlation parameter, which is determined by the maximum likelihood estimate of the correlation function; || indicates the absolute value.

[0070] During the dynamic update of the proxy model, a point addition criterion is needed to determine the location of the next sample point. The location of the newly added point directly affects the optimization efficiency and results of the proxy model. The criterion for maximum expected improvement is expressed as follows:

[0071]

[0072] In formula (5), y min represents the minimum value in the sample, It is expressed as the sample mean, s is the sample standard deviation, and They represent the probability distribution function and density function of the standard normal distribution respectively.

[0073] Step S4: Use the NSGA-Ⅱ algorithm to perform parallel optimization on the expected maximum addition criterion function and the prediction function.

[0074] In this embodiment, the NSGA-Ⅱ algorithm is used to optimize the Kriging model, and the improved multi-point addition method is used to optimize and update the proxy model, taking into account the global optimization and local optimization capabilities of the EI function, and at the same time finding the Pareto optimal set of the objective function. The specific optimization process of the algorithm is as follows Figure 2 As shown, the following steps are included:

[0075] S41: Obtain the EI function value (Fei = [f1ei, f2ei, …, fmei]) of the Kriging proxy model for each objective function, and use the NSGA-Ⅱ algorithm to calculate the Pareto solution set of each EI function value Fei. Since the solutions on the optimization solution set are all optimal solutions, the new sample point Sei is determined based on the number of added points.

[0076] S42: According to the Kriging model of the m objective functions, the prediction function Fp = [f1p, f2p, …, fmp] is obtained, and the Pareto solution set of each prediction function Fp is calculated using the NSGA-Ⅱ algorithm. Since the solutions on the optimization solution set are all optimal solutions, the new sample point Sp is determined according to the number of added points.

[0077] Step S5: Determine whether the model has reached the set convergence accuracy. If so, the NSGA-II algorithm is used to find the optimal design parameters.

[0078] Otherwise, the calculation step S4 optimizes the true target values ​​of the new sample points Sei and Sp, and adds the new sample points Sei, Sp and their true target values ​​to the sample library of step S2, constructs the Kriging proxy model of its objective function, and calculates its EI function value. Continue with the subsequent steps until the model reaches the set convergence accuracy.

[0079] Specifically, the steps include:

[0080] Step S51: Convergence accuracy judgment;

[0081] In this embodiment, the accuracy of the test model is tested using the multiple correlation coefficient R 2,When the value approaches 1, it indicates that the global accuracy of the model is higher. Its expression is as follows,

[0082]

[0083] In formula (6), n is the number of value points, y i is the true model response value, is the predicted value of the approximate model, is the mean of the true response values.

[0084] In this embodiment, when the accuracy of the model R 2 When it reaches 0.95, the convergence accuracy is achieved and the iteration stops.

[0085] If the convergence accuracy is reached, the process proceeds to step S52 . If the convergence accuracy is not reached, the newly obtained sample points Sei and Sp are added to the sample database, the proxy model is reconstructed, and the process returns to step S3 to continue with the following steps.

[0086] S52: Construct a proxy model using all existing sample points, and calculate each objective function prediction function Fp based on the proxy model.

[0087] S53: Calculate the Pareto solution set of the prediction function Fp in step S45 using the NSGA-Ⅱ algorithm, and finally obtain the Pareto solution set of the multi-objective problem.

[0088] The following is an example of multi-objective optimization of a specific cylindrical linear motor.

[0089] To optimize the average thrust and thrust fluctuation of the cylindrical linear motor, the slot width w of the cylindrical linear motor is selected. s , permanent magnet length h p , permanent magnet thickness w p , pole pitch τ, air gap width q, mover core thickness w b is the design variable.

[0090] The design variable marking diagram of the cylindrical linear motor is as follows Figure 3 The range of values ​​of the cylindrical linear motor design variables is shown in Table 1.

[0091] Table 1 Design variable value range

[0092]

[0093] According to the number of variables, 60 sample points are taken through optimal Latin hypercube sampling as shown in Table 2. The cylindrical linear motor model is simulated using finite element Maxwell to calculate its average thrust and thrust fluctuation.

[0094] Table 2 data sample table

[0095]

[0096] The proxy model is constructed by matlab programming, and optimization is performed. The optimization method provided in the application is compared with the traditional optimization by EI function single-point adding point criterion. Both methods are iterated 24 times (to avoid too large iteration convergence number, a certain iteration number is selected), and the model accuracy is compared, as shown in Table 3.

[0097] Table 3 comparison of optimization results

[0098]

[0099] As shown in Table 3, when the iteration number is the same, the accuracy of the model constructed by the parallel adding point criterion of the application is higher than that of the model constructed by the traditional single-point adding point criterion. Even if the thrust fluctuation R 2 is far from 1, but when the iteration number is increased, the algorithm used in the application reaches the accuracy convergence condition earlier than the single-point adding point method, which verifies that the method provided in the application improves the optimization efficiency compared with the traditional method.

[0100] After 24 iterations, the pareto optimal solution set obtained by the algorithm optimization is shown in Figure 4 . One solution is selected from the pareto optimal solution set as shown in Figure 4 , and compared with before optimization, and the results are shown in Table 4.

[0101] Table 4 comparison before and after optimization

[0102]

[0103] As shown in Table 4, when the iteration number is 24, after optimization, the average thrust of the cylindrical linear motor and the thrust fluctuation are improved compared with before optimization. The average thrust is increased from 1094.7N to 1319.7N, and the thrust fluctuation is decreased from 151.077N to 142.813N, which verifies the feasibility and effectiveness of the algorithm optimization.

[0104] The embodiment of the application proposes an improved adding point criterion. In the iteration process, the EI function and the prediction function are used to determine the points added to the sample library simultaneously and in parallel, which improves the optimization efficiency of the algorithm compared with the traditional single-point adding method. In addition, the NSGA-II algorithm is used to optimize the EI adding function and the prediction function in parallel, and the pareto solution set of the two functions is obtained intuitively, which facilitates the selection of points in the iteration process, and the obtained results have stability and enhance the robustness of the solution set.

[0105] Example two

[0106] Based on the same concept, this embodiment further provides an electronic device, which includes a processor, a memory, and a communication bus, wherein the processor and the memory communicate with each other via the communication bus.

[0107] The memory stores a computer program that can be executed by the processor, and the processor is used to execute the program stored in the memory to implement the multi-objective optimization method of the cylindrical linear motor as described in the first embodiment.

[0108] The communication bus mentioned in the above electronic device may be a Peripheral Component Interconnect (PCI) bus or an Extended Industrial Standard Architecture (EISA) bus, etc. The communication bus may be divided into an address bus, a data bus, a control bus, etc.

[0109] The memory may include a random access memory RAM, or may include a non-volatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0110] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc., or a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0111] Example 3

[0112] Based on the same concept, this embodiment further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the multi-objective optimization method for the cylindrical linear motor as described in the first embodiment is implemented.

[0113] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0114] 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 means for functionally implementing the steps listed in the flowchart block or blocks.

[0115] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0116] 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 means for functionally implementing the steps listed in the flowchart block or blocks.

[0117] While the preferred embodiments of the application have been described, additional variations and modifications can be employed, as will be appreciated by those of ordinary skill in the art, once armed with the foregoing disclosure. Accordingly, the appended claims as filed and as ultimately allowed in the patent granted are intended to encompass within their scope all such variations and modifications as are appropriate for particular applications.

[0118] Obviously, numerous modifications and variations of the present application are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A multi-objective optimization method for a cylindrical linear motor, characterized in that: The steps include: Step S1: Taking the average thrust and thrust fluctuation of the cylindrical linear motor as optimization targets, analyzing the design parameters that affect the average thrust and thrust fluctuation, and determining the value ranges of the average thrust and thrust fluctuation; The design parameters that affect the average thrust and thrust fluctuation include the slot width, permanent magnet length, permanent magnet thickness, pole pitch, air gap width, and mover core thickness of the cylindrical linear motor; Step S2: constructing a sample library through optimal Latin hypercube experimental design; Step S3: establishing a Kriging model based on the sample library; Step S4: Using the NSGA-Ⅱ algorithm to perform parallel optimization on the expected maximum addition criterion EI function and the prediction function Fp of the Kriging model; specifically including: Step S41: Calculate the EI function value of the Kriging proxy model of the objective function of each sample, and use the NSGA-Ⅱ algorithm to calculate the Pareto solution set of each EI function value. The solutions on the optimization solution set are all optimal solutions, and the new sample point Sei is determined according to the number of added points; Step S42: Obtain the prediction function Fp based on the Kriging proxy model of the objective function of each sample, calculate the Pareto solution set of each prediction function Fp using the NSGA-II algorithm, and all the solutions on the optimized solution set are optimal solutions. Determine the new sample point Sp based on the number of added points. Step S5: Determine whether the model has reached the set convergence accuracy; if so, the optimal design parameters are obtained through the NSGA-II algorithm; otherwise, the true value of the point obtained by the optimization in step S4 is calculated and added to the sample library in step S2, and steps S3 to S5 are repeated.

2. The multi-objective optimization method for a cylindrical linear motor according to claim 1, characterized in that: In step S2, based on Standard Latin hypercube experimental design was performed.

3. The multi-objective optimization method for a cylindrical linear motor according to claim 2, characterized in that: The based The specific method for standard Latin hypercube experimental design is as follows: Among them, n p is the number of samples, d ij is the distance between sample points, q is a positive integer index, where i and j represent the i-th and j-th samples; By minimizing The distance between sample points is maximized to ensure the spatial uniformity of the sample points.

4. The multi-objective optimization method for a cylindrical linear motor according to claim 1, wherein: The specific process of step S3 is: extracting samples from the sample library and constructing a Kriging proxy model of the objective function of each sample.

5. The multi-objective optimization method for a cylindrical linear motor according to claim 1, wherein: The step S5 specifically includes the following sub-steps: Step S51: Determine whether the model has reached the set convergence accuracy; If the set convergence accuracy is achieved, proceed to step S52; otherwise, calculate the true target values ​​of the new sample points Sei and Sp optimized in step S4, and add the new sample points Sei, Sp and their true target values ​​to the sample library in step S2, and return to step S3; Step S52: constructing a Kriging proxy model using all sample points in the sample library, and calculating the prediction function Fp of each objective function based on the Kriging proxy model; Step S53: Calculate the Pareto solution set of the prediction function Fp in step S52 using the NSGA-II algorithm, and finally obtain the Pareto solution set of the multi-objective problem.

6. The multi-objective optimization method for a cylindrical linear motor according to claim 5, characterized in that: In step S51, the accuracy of the test model is tested by using the complex correlation coefficient R 2 , which is expressed as follows: Among them, n is the number of value points, y i is the true model response value, is the predicted value of the approximate model, is the average value of the true response value; when R 2 The closer the value of is to 1, the higher the global accuracy of the model.

7. An electronic device, characterized in that: The processor and the memory communicate with each other via the communication bus. The memory is used to store computer programs; The processor is configured to execute the program stored in the memory to implement the multi-objective optimization method for the cylindrical linear motor according to any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the multi-objective optimization method for a cylindrical linear motor according to any one of claims 1 to 6 is implemented.

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