A method for optimizing permanent magnet motor core size based on particle swarm algorithm

Abstract

The present application relates to the technical field of motor design, and particularly relates to a permanent magnet motor iron core size optimization method based on a particle swarm algorithm. The method comprises the following steps: selecting geometric parameters such as stator tooth width to construct particles and initializing a particle swarm; in each round of iteration, an agent model constructed in advance is used to predict the electromagnetic performance index of the particles and to calculate the fitness value; a gradient vector is constructed by perturbing the global optimal solution, and the maximum value of the cosine similarity of the gradient vectors between geometric parameters is calculated as the correlation attribute value; the speed update logic is dynamically corrected in response to the correlation attribute value: an inertia weight inversely proportional to the correlation attribute value is applied to the strongly coupled parameters to suppress oscillation, and an inertia weight proportional to the gradient module length is applied to the weakly coupled parameters to accelerate convergence; until the convergence condition is met, the optimal iron core size is output. The present application effectively solves the oscillation problem caused by strongly coupled parameters, and significantly improves the optimization accuracy and efficiency.

Description

Technical Field

[0001] This invention relates to the field of motor design technology. More specifically, this invention relates to a method for optimizing the core dimensions of a permanent magnet motor based on a particle swarm optimization algorithm. Background Technology

[0002] With the rapid development of new energy vehicles and industrial automation technology, permanent magnet motors are widely used due to their high power density and high efficiency. The core dimensions of the motor, such as stator tooth width, yoke thickness, and rotor structure, directly determine the magnetic circuit distribution, saturation level, and final output performance. Traditional motor design typically relies on the designer's experience or analytical methods for preliminary estimation, followed by verification using the finite element method. This method is difficult to obtain the globally optimal solution.

[0003] Existing methods for optimizing motor parameters often employ intelligent optimization algorithms, such as the standard particle swarm optimization (PSO) algorithm and genetic algorithms. While the standard PSO algorithm has advantages in handling multidimensional nonlinear problems, complex strong coupling relationships often exist between various geometric dimensions in permanent magnet motor design. For example, increasing the stator tooth width reduces the tooth magnetic flux density but decreases the slot area, thus affecting winding design. Traditional PSO algorithms typically use a uniform inertial weighting strategy across all dimensions, ignoring the differences in physical coupling characteristics between parameters. This lack of inter-dimensional differentiation in the search mechanism prevents the algorithm from adaptively adjusting the optimization step size based on the physical sensitivity of each geometric dimension, making it difficult to effectively balance local search accuracy and global optimization capabilities. This results in strong coupling parameters causing algorithm oscillations and difficulty in convergence during optimization, while weak coupling parameters suffer from insufficient search step size and slow convergence. Furthermore, due to the massive computational demands of finite element simulation of motor electromagnetic fields, the algorithm's inefficiency leads to excessively long design cycles, failing to meet engineering requirements. Summary of the Invention

[0004] The purpose of this invention is to propose a method for optimizing the core size of a permanent magnet motor based on the particle swarm optimization algorithm, in order to solve the problems of low optimization efficiency and poor convergence accuracy caused by ignoring the parameter coupling characteristics in the prior art.

[0005] In a first aspect, the present invention provides a method for optimizing the core size of a permanent magnet motor based on a particle swarm optimization algorithm, comprising: using selected geometric parameters as particles, randomly initializing a particle swarm within a preset size tolerance range; driving the particle swarm to perform multiple rounds of iterative optimization, each round of iteration using a pre-constructed surrogate model to predict multiple electromagnetic performance indicators of the particles to calculate fitness values; updating the particle swarm based on the corrected velocity vector until a preset convergence condition is met, and taking the global optimal solution as the optimal core size; wherein, during the iteration process, the global optimal solution is perturbed and finite element simulation is performed to solve the problem, the rate of change of electromagnetic performance indicators relative to each geometric parameter is calculated to construct a gradient vector of any electromagnetic performance indicator, and a coupling correlation index is calculated based on the cosine similarity of the gradient vector, and the electromagnetic performance indicator corresponding to the maximum value of the coupling correlation index is selected as the correlation attribute value; the velocity vector of the particle swarm is dynamically corrected according to the correlation attribute value, and for strongly coupled parameters with correlation attribute values ​​higher than a preset threshold, an inertial weight inversely proportional to the correlation attribute value is applied; for weakly coupled parameters with correlation attribute values ​​lower than a preset threshold, an inertial weight proportional to the magnitude of the gradient vector is applied.

[0006] By constructing gradient vectors and calculating associated attribute values, the physical coupling strength between motor geometric parameters was accurately identified. During the speed update phase, an anisotropic dynamic inertia weighting strategy was adopted: applying inverse weights to strongly coupled parameters effectively suppressed numerical oscillations caused by parameter correlation, enhancing algorithm stability; applying proportional weights to weakly coupled parameters leveraged their high sensitivity to increase the search step size, significantly improving convergence speed. This method achieves a deep integration of physical laws and optimization algorithms.

[0007] Optionally, the electromagnetic performance indicators include at least two of the following: the operating efficiency of the motor under rated load conditions; the torque ripple ratio of the motor at a preset speed; and the electromagnetic performance indicators also include the cogging torque of the motor under no-load conditions and the total harmonic distortion rate of the back electromotive force.

[0008] Optionally, the steps for constructing the surrogate model include: acquiring initial sample data and loading it into a finite element simulation environment for solving; establishing an initial database to construct and train the surrogate model, wherein the surrogate model is used to characterize the nonlinear mapping relationship between geometric parameters and electromagnetic performance indicators; in each iteration, inputting the geometric parameters of all particles in the particle swarm into the surrogate model, obtaining the predicted values ​​of the electromagnetic performance indicators and calculating the predicted fitness values; sorting the particles according to the predicted fitness values, and selecting candidate particles with fitness values ​​better than a preset ranking; loading the candidate particles into the finite element simulation environment for solving, obtaining the actual electromagnetic performance indicator values, and feeding back the actual electromagnetic performance indicator values ​​to the surrogate model to update the model parameters.

[0009] This invention introduces a surrogate model-assisted optimization strategy, using Kriging models or neural networks to replace most of the time-consuming finite element simulation calculations. While ensuring the accuracy of electromagnetic field calculations, it improves computational efficiency by several orders of magnitude, effectively solving the technical problem that traditional finite element methods combined with intelligent algorithms are difficult to implement in motor design due to the huge amount of computation required.

[0010] Optionally, the fitness value calculation process includes: obtaining the motor efficiency value and torque ripple value of the current particle; wherein, the values ​​of the candidate particles are obtained from the solution of the finite element simulation environment, and the values ​​of the other particles are obtained from the prediction of the surrogate model; linearly weighting the square inverse of the motor efficiency value with the normalized torque ripple value to generate a basic score; detecting whether the stator slot fill factor value corresponding to the current particle exceeds a preset process allowable upper limit; if it exceeds the process allowable upper limit, then a preset penalty constant value is superimposed on the basic score as the final fitness value; if it does not exceed the limit, then the basic score is directly determined as the final fitness value.

[0011] A process constraint penalty mechanism based on stator slot fill factor was introduced into the fitness calculation. This not only ensures the optimization of electromagnetic performance but also guarantees that the design scheme meets the actual winding process requirements, avoiding the generation of theoretically superior but unmanufacturable solutions, thus improving the engineering practicality of the scheme.

[0012] Optionally, the construction of the gradient vector of the arbitrary electromagnetic performance index includes: for the geometric parameters in the global optimal solution, applying a preset incremental step size based on the current value, keeping the values ​​of the remaining geometric parameters in the particle unchanged, and generating a detection feature vector; loading the detection feature vector into the finite element simulation environment to obtain the response value of the electromagnetic performance index; calculating the difference between the response value and the original electromagnetic performance index value, and dividing the difference by the incremental step size to obtain the sensitivity value corresponding to the geometric parameter; traversing all geometric parameters in the global optimal solution, arranging the sensitivity values ​​corresponding to each geometric parameter in a preset order to form the gradient vector.

[0013] The sensitivity calculation method based on the finite difference method can accurately quantify the influence of each geometric parameter on the electromagnetic performance index, providing a high-precision data foundation for the calculation of the coupling correlation index and improving the accuracy of the algorithm in identifying parameter coupling relationships.

[0014] Optionally, the determination of strongly coupled and weakly coupled parameters includes: for any geometric parameter in the global optimal solution, retrieving all coupling correlation indices between the current geometric parameter and the other geometric parameters; selecting the one with the largest value among all coupling correlation indices and defining it as the correlation attribute value; comparing the correlation attribute value with the preset threshold; when the correlation attribute value is greater than the preset threshold, determining the current geometric parameter as a strongly coupled parameter; when the correlation attribute value is less than or equal to the preset threshold, determining the current geometric parameter as a weakly coupled parameter.

[0015] Optionally, the calculation steps of the coupling correlation index include: for any two geometric parameters, obtaining a first gradient vector corresponding to the first geometric parameter and a second gradient vector corresponding to the second geometric parameter; the dimension of the gradient vector is consistent with the number of electromagnetic performance indicators, and its components are the rates of change of the electromagnetic performance indicators relative to the corresponding geometric parameters; calculating the dot product of the first gradient vector and the second gradient vector; calculating the Euclidean norm of the first gradient vector and the second gradient vector respectively; dividing the dot product by the product of the two Euclidean norms, and the quotient obtained is the coupling correlation index between the two geometric parameters.

[0016] This coupling quantization method based on cosine similarity can effectively measure the degree of consistency in the direction of influence of two geometric parameters on electromagnetic performance indicators. Compared with simple linear correlation analysis, it more accurately reflects the nonlinear coupling characteristics between parameters, providing a scientific basis for determining strong and weak coupling parameters.

[0017] Optionally, the inertia weights applied in proportion to the magnitude of the gradient vector include: calculating the Euclidean norm of the gradient vector corresponding to the weak coupling parameter; setting a preset weight interval, the weight interval being defined by a preset lower limit and a preset upper limit; constructing a monotonically increasing mapping function to map the Euclidean norm to the weight interval; the mapping function is such that as the Euclidean norm increases, the output inertia weight value monotonically increases and is always lower than the preset upper limit.

[0018] Optionally, the step of updating the particle swarm based on the corrected velocity vector specifically includes: constructing a velocity update equation independently for each geometric parameter in each particle; the velocity update equation includes three terms: the first term is the product of the velocity at the previous moment and the corrected inertial weight, the second term is the random cognitive component pointing to the individual's historical best position, and the third term is the random social component pointing to the global historical best position; calculating the updated velocity value and superimposing it on the current position value to generate a new geometric parameter value; determining whether the new geometric parameter value exceeds the preset size tolerance range; if it does, resetting the geometric parameter value to the corresponding boundary limit value.

[0019] Optionally, the preset convergence condition includes at least one of the following judgment logics: the total number of iterations executed by the algorithm reaches a preset threshold; the absolute value of the change of the global optimal fitness value during the iteration process of a consecutive preset number of iterations is always lower than the preset threshold; the variance of the set of fitness values ​​of all particles in the current particle swarm is lower than the preset threshold.

[0020] The beneficial effects of this invention are as follows: This invention dynamically adjusts the inertia weights of the particle swarm optimization algorithm through a coupling correlation index. It employs inverse and direct proportional weight adjustment strategies for strongly coupled and weakly coupled parameters, respectively, achieving an adaptive balance between global exploration capability and local fine-grained search capability. By using the gradient vector cosine similarity metric to quantify parameter coupling relationships, it can accurately identify the complex coupling effects between motor core size parameters. Compared to the traditional fixed-inertia-weight particle swarm optimization algorithm, this significantly improves the convergence speed and global optimization capability of permanent magnet motor core size optimization, effectively avoiding the problem of getting trapped in local optima. Attached Figure Description

[0021] Figure 1 This is a flowchart of a method for optimizing the core size of a permanent magnet motor based on a particle swarm optimization algorithm according to an embodiment of the present invention.

[0022] Figure 2 This is a coupling correlation index diagram of a permanent magnet motor core size optimization method based on particle swarm optimization algorithm according to an embodiment of the present invention.

[0023] Figure 3 This is a convergence curve of a permanent magnet motor core size optimization method based on particle swarm optimization algorithm according to an embodiment of the present invention.

[0024] Figure 4 This is a comparison chart showing the effects of a permanent magnet motor core size optimization method based on particle swarm optimization algorithm according to an embodiment of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Figure 1 The diagram shown is a flowchart of a method for optimizing the core size of a permanent magnet motor based on a particle swarm optimization algorithm according to an embodiment of the present invention.

[0026] S1: Select geometric parameters as particles and initialize the particle swarm.

[0027] First, the stator tooth width, stator yoke thickness, rotor magnetic bridge length, and permanent magnet slot geometry parameters are selected and combined to form particles. The particle swarm is then randomly initialized within a preset dimensional tolerance range. The permanent magnet slot geometry parameters include the permanent magnet width, permanent magnet thickness, and permanent magnet tilt angle.

[0028] For each geometric parameter, its value range is preset based on the motor's rated power and speed. The six geometric parameters are arranged in a preset order. The particle swarm size is initialized to 50 particles. For each particle, an initial position vector and an initial velocity vector are generated using uniformly distributed random numbers within the value range of each geometric parameter. The value range of each component of the initial velocity vector is set to -10% to +10% of the corresponding parameter's value range.

[0029] S2: Drives the particle swarm to perform multiple rounds of iterative optimization and calculates the fitness value.

[0030] After the particle swarm initialization is completed, the particle swarm is driven to perform multiple rounds of iterative optimization. In each round, the particles are loaded into the finite element simulation environment to solve for the values ​​of electromagnetic performance indicators in order to calculate the fitness value.

[0031] The electromagnetic performance indicators include the motor's operating efficiency under rated load conditions and the motor's torque ripple ratio at a preset speed. Alternatively, the electromagnetic performance indicators may also include the motor's cogging torque under no-load conditions and the total harmonic distortion rate of the back electromotive force.

[0032] Before iterating the particle swarm optimization algorithm, initial sample points (50 in this embodiment) are generated within the range of values ​​for each geometric parameter using Latin hypercube sampling. These sample points are then loaded into the ANSYS Maxwell finite element simulation environment for solution. An adaptive mesh refinement strategy is used, with the mesh size set to 0.5 mm for the air gap region and 2 mm for the core region. The solution type is transient electromagnetic field analysis, with a time step of 0.0001 seconds and a total duration of 0.1 seconds. Motor efficiency and torque ripple values ​​are extracted to construct an initial sample database containing the mapping relationship between geometric parameters and electromagnetic performance. Based on this initial sample database, a surrogate model is trained. In this embodiment, a Kriging model is used to establish the nonlinear mapping relationship between six geometric parameters and motor efficiency and torque ripple.

[0033] In each iteration, the position vectors of all particles in the population are input into the surrogate model to quickly calculate the predicted values ​​of efficiency and torque ripple. Based on the predicted values, the predicted fitness is calculated, and the particles are ranked. The top 20% of particles are selected as candidate particles. Only candidate particles are loaded into the finite element simulation environment for accurate solution to obtain true electromagnetic performance indicators. For the remaining particles, the predicted values ​​from the surrogate model are directly used as their performance indicators. The true geometric parameters and true performance indicator data of the candidate particles obtained through finite element solution are added to the sample database, and the surrogate model is retrained using the updated sample database to update the model parameters online.

[0034] The final fitness values ​​of all particles in this round are then calculated. A baseline score is generated by linearly weighting the reciprocal square of the motor efficiency value with the normalized torque ripple value. In this embodiment, the weighting coefficients are set to 0.6 and 0.4, respectively. The formula for calculating the baseline score is as follows:

[0035] ;

[0036] Where F represents the baseline score, which is dimensionless; This represents the motor efficiency value and is dimensionless. This represents the torque pulsation value and is dimensionless. The reference torque ripple value is 0.1 in this embodiment.

[0037] The system checks whether the stator slot fill rate corresponding to the current particle exceeds a preset process allowable upper limit. The stator slot fill rate is calculated by dividing the total cross-sectional area of ​​the conductors by the effective area of ​​the stator slot. In this embodiment, the process allowable upper limit is set to 0.75. If the stator slot fill rate exceeds the process allowable upper limit, a preset penalty constant value is added to the base score as the final fitness value. In this embodiment, the penalty constant value is set to 10. If it does not exceed the limit, the base score is directly determined as the final fitness value.

[0038] S3: Perturb the global optimal solution and construct the gradient vector, then calculate the associated attribute values.

[0039] During the iteration process, the global optimal solution is perturbed and finite element simulation is performed to solve the problem. The rate of change of electromagnetic performance indicators with respect to each geometric parameter is calculated to construct gradient vectors. The cosine similarity between the gradient vectors of any two geometric parameters is calculated as the coupling correlation index.

[0040] For each geometric parameter in the global optimal solution, a preset increment step size is applied based on the current value, while keeping the values ​​of the remaining geometric parameters in the particle unchanged, to generate a detection feature vector. In this embodiment, the increment step size is set to 1% of the corresponding parameter's value range.

[0041] The probe feature vector is loaded into the finite element simulation environment to obtain the response values ​​of the electromagnetic performance indicators. The difference between the response value and the original electromagnetic performance indicator value is calculated, and the difference is divided by the increment step size to obtain the sensitivity value corresponding to the geometric parameter. All geometric parameters in the particle are traversed, and the sensitivity values ​​corresponding to each geometric parameter are arranged in a preset order to form a gradient vector. In this embodiment, the dimension of the gradient vector is 2, corresponding to the two electromagnetic performance indicators of motor efficiency and torque ripple, respectively.

[0042] For any two geometric parameters, obtain the first gradient vector corresponding to the first geometric parameter and the second gradient vector corresponding to the second geometric parameter. The dimension of the gradient vector is consistent with the number of electromagnetic performance indicators, and its components are the rates of change of the electromagnetic performance indicators relative to the corresponding geometric parameters.

[0043] Calculate the dot product of the first and second gradient vectors. Then calculate the Euclidean norm of each gradient vector. Divide the dot product by the product of the two Euclidean norms; the quotient is the coupling correlation index between the two geometric parameters. The specific formula for calculating the coupling correlation index is as follows:

[0044] ;

[0045] in, Indicates the first The geometric parameter and the first The coupling correlation index between the geometric parameters is dimensionless. Indicates the first The gradient vector corresponding to each geometric parameter; Indicates the first The gradient vector corresponding to each geometric parameter; Indicates the first The Euclidean norm of the gradient vectors; Indicates the first The Euclidean norm of a gradient vector. For example... Figure 2 The figure shown is a coupling correlation index diagram of a permanent magnet motor core size optimization method based on particle swarm optimization algorithm according to an embodiment of the present invention.

[0046] For any geometric parameter in the global optimal solution, retrieve all coupling correlation indices between the current geometric parameter and the other geometric parameters, and select the one with the largest value among all coupling correlation indices, and define it as the correlation attribute value.

[0047] The associated attribute value is compared with a preset threshold. In this embodiment, the preset threshold is set to 0.5. When the associated attribute value is greater than the preset threshold, the current geometric parameter is determined to be a strongly coupled parameter; when the associated attribute value is less than or equal to the preset threshold, the current geometric parameter is determined to be a weakly coupled parameter. Alternatively, the central difference method can be used to calculate the sensitivity value, that is, positive and negative increment steps are applied to the current value to improve the accuracy of the sensitivity calculation. Or, the Pearson correlation coefficient can be used to quantify the coupling relationship between parameters.

[0048] S4: Responds to the dynamic adjustment of the associated attribute value update logic and updates the particle swarm.

[0049] The particle swarm velocity update logic is dynamically adjusted in response to the associated attribute values. For strongly coupled parameters with associated attribute values ​​higher than a preset threshold, an inertial weight inversely proportional to the associated attribute value is applied to suppress oscillations; for weakly coupled parameters with associated attribute values ​​lower than a preset threshold, an inertial weight proportional to the magnitude of the gradient vector is applied to accelerate convergence.

[0050] For strongly coupled parameters, a monotonically decreasing nonlinear mapping rule is established, which causes the output inertia weight value to decrease as the input associated attribute value increases. The associated attribute values ​​corresponding to the strongly coupled parameters are obtained and substituted into the nonlinear mapping rule.

[0051] In this embodiment, the nonlinear mapping rule adopts an inverse proportional function form to calculate the correction coefficient. The correction coefficient is used to adjust the basic inertia weight of the particle swarm optimization algorithm, resulting in the inertia weight corresponding to the strongly coupled parameters. The basic inertia weight is set to 0.7.

[0052] For weakly coupled parameters, the Euclidean norm of the gradient vector corresponding to the weakly coupled parameter is calculated. A preset weight interval is set, defined by a preset lower limit and a preset upper limit. In this embodiment, the preset lower limit is set to 0.4, and the preset upper limit is set to 0.9. A monotonically increasing mapping function is constructed to map the Euclidean norm to the weight interval. The mapping function is such that as the Euclidean norm increases, the output inertia weight value monotonically increases and always remains below the preset upper limit. In this embodiment, the mapping function uses a linear mapping or a sigmoid function mapping.

[0053] For each geometric parameter of each particle, an independent velocity update equation is constructed. This equation contains three terms: the first is the product of the previous velocity and the corrected inertial weight; the second is a random cognitive component pointing to the individual's historical best position; and the third is a random social component pointing to the global historical best position. The updated velocity value is calculated and superimposed on the current position value to generate new geometric parameter values. Boundary checks are performed: it is determined whether the new geometric parameter values ​​exceed the preset dimensional tolerance range; if so, the geometric parameter values ​​are reset to the corresponding boundary limit values.

[0054] The preset convergence conditions include at least one of the following decision logics: the total number of iterations performed by the algorithm reaches a preset threshold, which is set to 100 iterations in this embodiment; the absolute value of the change in the global optimal fitness value during a consecutive preset number of iterations is always lower than a preset threshold, which is set to 10 iterations in this embodiment, and the change threshold is set to 0.001; the variance of the set of fitness values ​​of all particles in the current particle swarm is lower than a preset threshold, which is set to 0.0001 in this embodiment. When the preset convergence conditions are met, the iteration stops and the geometric parameters of the global optimal solution are output as the optimal core size. Figure 3 The figure shown is a convergence curve of a permanent magnet motor core size optimization method based on particle swarm optimization according to an embodiment of the present invention. It should be noted that the objective fitness function constructed in this invention minimizes the cost function; that is, the lower the fitness value, the better the overall performance of the motor. Figure 3 As shown, the fitness value exhibits a monotonically decreasing trend and eventually converges as the number of iterations increases.

[0055] like Figure 4 The image shows a comparison of the effects of a permanent magnet motor core size optimization method based on particle swarm optimization according to an embodiment of the present invention. The grouped bar charts show the numerical changes of the two core electromagnetic performance indicators before and after optimization. Red bars represent the initial design performance before optimization, and green bars represent the final performance after optimization. After optimization using the method of the present invention, the motor efficiency is significantly improved, while torque ripple is substantially reduced.

[0056] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be within the scope of protection of the present invention.

Claims

1. A method for optimizing the core size of a permanent magnet motor based on particle swarm optimization, characterized in that, The optimization method includes: The selected geometric parameters are used as particles, and the particle swarm is randomly initialized within the preset size tolerance range. The particle swarm is driven to perform multiple rounds of iterative optimization. In each round of iteration, a pre-built surrogate model is used to predict multiple electromagnetic performance indicators of the particles to calculate the fitness value. The particle swarm is updated based on the corrected velocity vector until the preset convergence condition is met, and the global optimal solution is taken as the optimal core size. In the iterative process, the global optimal solution is perturbed and finite element simulation is performed to solve the problem. The rate of change of electromagnetic performance indicators with respect to each geometric parameter is calculated to construct the gradient vector of any electromagnetic performance indicator. The coupling correlation index is calculated based on the cosine similarity of the gradient vector, and the electromagnetic performance indicator corresponding to the maximum value of the coupling correlation index is selected as the correlation attribute value. The velocity vector of the particle swarm is dynamically corrected according to the correlation attribute value. For strongly coupled parameters with correlation attribute values ​​higher than a preset threshold, an inertial weight that is inversely proportional to the correlation attribute value is applied. For weakly coupled parameters with correlation attribute values ​​lower than a preset threshold, an inertial weight that is proportional to the magnitude of the gradient vector is applied. The construction of the gradient vector for any electromagnetic performance index includes: for the geometric parameters in the global optimal solution, applying a preset incremental step size based on the current value, keeping the values ​​of the remaining geometric parameters in the particle unchanged, and generating a detection feature vector; loading the detection feature vector into the finite element simulation environment to obtain the response value of the electromagnetic performance index; calculating the difference between the response value and the original electromagnetic performance index value, and dividing the difference by the incremental step size to obtain the sensitivity value corresponding to the geometric parameter; traversing all geometric parameters in the global optimal solution, arranging the sensitivity values ​​corresponding to each geometric parameter in a preset order to form a gradient vector.

2. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The electromagnetic performance indicators include at least two of the following: The operating efficiency of the motor under rated load conditions; The torque ripple ratio of the motor at a preset speed; Furthermore, the electromagnetic performance indicators also include the cogging torque value of the motor under no-load conditions and the total harmonic distortion rate value of the back electromotive force.

3. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The steps for constructing the proxy model include: Initial sample data is acquired and loaded into the finite element simulation environment for solution. An initial database is established to construct and train a surrogate model, which is used to characterize the nonlinear mapping relationship between geometric parameters and electromagnetic performance indicators. In each iteration, the geometric parameters of all particles in the particle swarm are input into the surrogate model to obtain the predicted values ​​of the electromagnetic performance index and calculate the predicted fitness value; the particles are sorted according to the predicted fitness value, and candidate particles with fitness values ​​better than the preset ranking are selected; the candidate particles are loaded into the finite element simulation environment for solution to obtain the actual electromagnetic performance index values, and the actual electromagnetic performance index values ​​are fed back to the surrogate model to update the model parameters.

4. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 3, characterized in that, The calculation process for the fitness value includes: Obtain the motor efficiency and torque ripple values ​​of the current particle; wherein, the values ​​of the candidate particles are obtained from the solution of the finite element simulation environment, and the values ​​of the other particles are obtained from the prediction of the surrogate model. The reciprocal square of the motor efficiency value is linearly weighted with the normalized torque ripple value to generate a basic score; the stator slot fill factor value corresponding to the current particle is checked to see if it exceeds the preset process allowable upper limit; if it exceeds the process allowable upper limit, a preset penalty constant value is superimposed on the basic score as the final fitness value; if it does not exceed the limit, the basic score is directly determined as the final fitness value.

5. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The determination of the strong coupling parameter and the weak coupling parameter includes: For any geometric parameter in the global optimal solution, retrieve all coupling correlation indices between the current geometric parameter and the other geometric parameters; Select the one with the largest value from all coupling correlation indices and define it as the correlation attribute value; The associated attribute value is compared with the preset threshold value. When the value of the associated attribute is greater than the preset threshold, the current geometric parameter is determined to be a strongly coupled parameter; When the value of the associated attribute is less than or equal to the preset threshold, the current geometric parameter is determined to be a weakly coupled parameter.

6. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The calculation steps for the coupling correlation index include: For any two geometric parameters, obtain the first gradient vector corresponding to the first geometric parameter and the second gradient vector corresponding to the second geometric parameter; the dimension of the gradient vector is consistent with the number of electromagnetic performance indicators, and its components are the rates of change of the electromagnetic performance indicators relative to the corresponding geometric parameters. Calculate the dot product of the first gradient vector and the second gradient vector; Calculate the Euclidean norms of the first gradient vector and the second gradient vector respectively; Dividing the scalar product by the product of the two Euclidean norms yields the quotient, which is the coupling correlation index between the two geometric parameters.

7. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The inertial weights applied, which are proportional to the magnitude of the gradient vector, include: Calculate the Euclidean norm of the gradient vector corresponding to the weakly coupled parameter; A preset weight range is set, which is defined by a preset lower limit and a preset upper limit; A monotonically increasing mapping function is constructed to map the Euclidean norm to the weight interval; the mapping function outputs an inertia weight value that monotonically increases and is always lower than a preset upper limit value as the Euclidean norm increases.

8. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The step of updating the particle swarm based on the corrected velocity vector specifically includes: For each geometric parameter in each particle, an independent velocity update equation is constructed; the velocity update equation contains three terms: the first term is the product of the velocity at the previous moment and the corrected inertial weight, the second term is the random cognitive component pointing to the individual's historical best position, and the third term is the random social component pointing to the global historical best position. Calculate the updated velocity value and superimpose it onto the current position value to generate a new geometric parameter value; determine whether the new geometric parameter value exceeds the preset dimensional tolerance range; if it does, reset the geometric parameter value to the corresponding boundary limit value.

9. The method for optimizing the core size of a permanent magnet motor based on particle swarm optimization as described in claim 1, characterized in that, The preset convergence condition includes at least one of the following decision logics: The total number of iterations performed by the algorithm reaches a preset threshold; The absolute value of the change in the global optimal fitness value is always lower than the preset threshold during the iterative process of a preset number of rounds. The set variance of the fitness values ​​of all particles in the current particle swarm is lower than a preset threshold.

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