Axial flux motor multi-objective optimization method based on improved holy religious algorithm

Abstract

The invention provides an axial flux motor multi-objective optimization method based on an improved homing religious algorithm. Firstly, key structure parameters are screened through sensitivity analysis, and the optimization range of the key structure parameters is determined; then, sample data is generated by adopting improved Latin hypercube sampling, and a data set is constructed through finite element simulation; then, performing automatic optimization on smooth factors of the generalized regression neural network based on a He-horse optimization algorithm, and establishing a high-precision agent model; improving a horizon algorithm by adopting Tent chaotic mapping, non-dominated sorting and congestion degree distance, and combining the horizon algorithm with the proxy model to carry out multi-objective optimization to generate a Pareto solution set; and finally, selecting an optimal motor parameter according to the target weight. According to the method, parameterized finite element analysis, an optimization agent model and an improved multi-target algorithm are deeply fused, so that the global optimization capability is ensured, the optimization efficiency and precision are remarkably improved, and an effective solution is provided for rapid and accurate design of the axial flux motor.

Description

Technical Field

[0001] This invention relates to the field of motor optimization technology, and in particular to a multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm. Background Technology

[0002] Axial flux motors, especially those with a single stator and dual rotor structure, have shown great potential in high-power applications such as electric vehicles and aerospace due to their superior characteristics, including high power density and high output torque. However, these motors generally suffer from inherent technical challenges during operation, such as large torque ripple and significant heat generation from losses. High torque ripple can cause vibration and noise, affecting the stability and accuracy of system operation; while high losses directly lead to increased motor temperature rise, limiting further improvements in power density and impacting reliability and lifespan. Therefore, how to effectively suppress torque ripple and reduce various losses while increasing motor output torque has become a core problem that urgently needs to be solved in the design of axial flux motors.

[0003] Currently, the traditional methods for optimizing motor performance mainly include the following three: Firstly, relying solely on finite element software for parametric scanning analysis, while intuitive, is extremely computationally expensive and struggles to find the global optimal solution in complex multivariable spaces. Secondly, directly coupling the optimization algorithm with finite element simulation can achieve automatic optimization, but each algorithm iteration requires calling time-consuming finite element calculations, resulting in an excessively long overall optimization cycle and low efficiency. Third, by introducing a surrogate model to replace part of the finite element calculation, although this method can improve efficiency, the prediction accuracy and generalization ability of the surrogate model directly affect the reliability of the optimization results, and its accuracy still needs to be finely adjusted and guaranteed.

[0004] In summary, existing technologies cannot achieve a good balance between optimization efficiency and result accuracy, and there is an urgent need for an efficient and high-precision multi-objective optimization design method that can take both into account. Summary of the Invention

[0005] This invention proposes a multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm, which solves the problem that existing motor performance optimization methods cannot simultaneously balance optimization efficiency and result accuracy.

[0006] The technical solution of this invention is implemented as follows: This invention provides a multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm, comprising the following steps: S1. Perform sensitivity analysis on the motor structural parameters, screen key optimization parameters that are strongly correlated with the optimization target based on the sensitivity magnitude, and determine the optimization range of the key optimization parameters; S2, within the optimization range of the key optimization parameters, multiple sets of sample data are generated using an improved Latin hypercube sampling method, and the optimization target values ​​corresponding to each set of sample data are obtained through finite element simulation to construct a dataset; S3, Based on the Hippo optimization algorithm, the smoothing factor of the generalized regression neural network is automatically optimized, and the optimized generalized regression neural network is used to train the dataset to construct a proxy model of the motor optimization target. S4 improves the single-objective sacred religion algorithm by using Tent chaotic mapping, non-dominated sorting and crowding distance. The improved multi-objective sacred religion algorithm is then combined with the motor proxy model for optimization to generate Pareto solution set. S5. Select the final optimized motor parameters from the Pareto solution set according to the optimization target weights.

[0007] Specifically, in step S1, the sensitivity analysis is used to quantify the influence of each structural parameter on the optimization target, and the formula for calculating the sensitivity is: ; in, Indicates the first i The values ​​of the optimization variables, Indicates the first j The numerical value of the optimization objective. Indicates the first i The optimization variable for the th ... j The sensitivity of an optimization objective. This represents the amount of small perturbation applied to the optimization variable; For each motor structural parameter, its sensitivity across all optimization objectives is ranked, and the parameters with the highest sensitivity are selected as key optimization parameters. Based on the feasibility of the motor's electromagnetic design and manufacturing process, the optimization range of several key optimization parameters is finally determined.

[0008] Furthermore, in step S1, the motor structural parameters include at least several of the following parameters: stator outer diameter, stator inner diameter, air gap length, pole arc coefficient, permanent magnet thickness, rotor back iron thickness, slot height, shoulder height, slot depth, slot width, upper slot width, and lower slot width. The optimization objectives include the motor's average torque, torque ripple, and total losses. The torque ripple is used to measure the smoothness of the motor's output torque, and its expression is: ; in, This refers to the torque pulsation of the motor. , , These represent the average, maximum, and minimum values ​​of the motor torque, respectively. The mathematical expression for the total loss is: ; in, This indicates the total loss of the motor. , , These represent iron loss, copper loss, and permanent magnet eddy current loss, respectively.

[0009] Specifically, step S2 includes: Within the optimization space comprised of the key optimization parameters, a predetermined set of sample points is generated by maximizing the minimum distance between samples and reducing the correlation between parameters. The set of sample points is input into a parameterized finite element model to perform batch simulations, and the values ​​of average torque, torque ripple and total loss corresponding to each sample point are obtained to construct a dataset containing the input optimization parameters and the output optimization objectives.

[0010] Specifically, in step S3, the model expression of the generalized regression neural network is: ; in, n For the input vector in the dataset, This represents the prediction value of the generalized regression neural network for the input vector; n The number of training samples in the dataset. is the smoothing factor for the generalized regression neural network.

[0011] Furthermore, in step S3, the process of automatically optimizing the smoothness factor based on the Hippo optimization algorithm includes: S301, Initialize the population for the Hippo optimization algorithm. The position vector of each individual in the population represents a potential smoothness factor value. S302, during the execution of the optimization loop, simulates three typical hippopotamus behaviors to update the population position: Hippos' habitat location update: Preliminary location adjustments based on current population information; Hippodrome population defense against intruders: Simulating hippopotamus population defense against intruders based on intruder location. With individual location Distance between D Update individual information; Hippos' behavior of seeking safe locations: Individuals move to safer locations, new locations It is generated by the following formula: ; in, A random number between [0,1]. These are normally distributed random numbers. and For the first j Upper and lower bounds for each decision variable; S303, For the updated population, calculate the fitness value of each individual, where the fitness function is: ; in, and These are the mean squared errors of the prediction results of the surrogate model on the training and test sets, respectively. These are the error weighting coefficients. The regularization coefficient is used. S304, repeat steps S302 to S303 until the termination condition is met, and output the smoothness factor value with the best fitness.

[0012] Specifically, in step S4, the method for improving the single-objective sacred religion algorithm using Tent chaotic mapping is as follows: The Tent chaotic sequence is used to initialize the population, ensuring that the initial solutions are distributed as evenly as possible in the solution space, thus increasing population diversity. The Tent chaotic sequence mapping expression is: ; in, and These are the current iteration value and the next iteration value of the chaotic sequence, respectively. It is a random number between the interval [0,1].

[0013] Specifically, in step S4, the method for improving the single-objective sacred religion algorithm using non-dominated sequences and crowding distance includes: S401, after initializing the population, calculate the function value of each individual in the population on multiple optimization objectives; S402, Non-dominated sorting: According to Pareto dominance, all individuals in the population are divided into multiple non-dominated layers; where, if individual A is no worse than individual B in all objective function values ​​and is better than individual B in at least one objective, then A is said to dominate B; the set of individuals not dominated by any other individual constitutes the first non-dominated layer. After removing individuals from this layer, non-dominated individuals are searched again from the remaining individuals to form the second layer, and so on. S403, Crowding Distance Calculation and Ranking: Within the same non-dominated layer, the crowding distance is calculated for each individual. The calculation formula is as follows: ; in, Indicates the first i The degree of crowding of each solution in the target space m To optimize the number of targets, and They were respectively in the second m On the goal of the first i The objective value of two adjacent solutions. and To distinguish the first in the non-dominated layer m The maximum and minimum values ​​of each target; individuals in the same layer are sorted according to the crowding distance, the larger the distance, the smaller the solution density around the individual and the better the diversity; S404, Elite Selection Mechanism: During the algorithm iteration process, when it is necessary to select individuals from parent and child individuals to enter the next generation, individuals with lower non-dominated levels are given priority; for individuals in the same non-dominated level, individuals with larger crowding distance are given priority.

[0014] Specifically, in step S4, the method for generating the Pareto solution set by combining the improved multi-objective sacred religion algorithm with the motor proxy model includes: S405: Use the selected key optimization parameters as optimization variables for the multi-objective sacred religion algorithm, i.e., the various dimensions of the faith vector; S406: In each iteration of the algorithm, a set of candidate motor parameters corresponding to the belief vector of each individual in the current population is input into the motor surrogate model to obtain the predicted value of the optimization objective corresponding to the set of parameters. S407: Using an improved multi-objective sacred religion algorithm, perform the following operations sequentially on multiple predicted values: population partitioning, leader selection, believer evolution, religious events, and elite retention to generate a new generation of population; S408: Repeat steps S406 to S407 until the termination condition is met. The final output non-dominated solution set is the Pareto solution set.

[0015] Further, step S407 includes: Group division: dividing the population into groups. N Individuals are divided into K Within each religious group, individuals are divided into ordinary believers and leader believers based on a hierarchy of non-dominant order and crowding distance. Leader selection: Identify the most influential leaders globally across all groups based on non-dominated ranking hierarchy and crowding distance. ; in, The designation of the most influential leader in the entire organization;F The fitness matrix of the population is expressed as: ; in, For the group j fitness matrix, Representing a group j Inner i The fitness function output value for each believer. , Used to evaluate the quality of a believer's faith value; Obtain the leader's belief vector Based on this, the faith of ordinary believers is updated, and the update formula is: ; in, and Each represents an individual i Faith vectors before and after the update r A random number between [0, 1]; Believer Evolution: Generate a random number r ,like r Less than the selection probability threshold BPSP Then a faith dimension will be randomly selected. And update the attribute values ​​of the current believer in this dimension as follows: ; in, Is the current believer in the dimension New attribute values ​​on The globally optimal leader in the dimension The attribute values ​​on rand It is a random perturbation factor in the interval [0,1]. Religious events: If random numbers r Less than the dynamically changing probability threshold of miracles MP If the probability of a miracle occurs, a new individual with a random belief value is added to the group; otherwise, an attribute is selected from among the believers to replace the corresponding attribute of the current leader; the miracle probability threshold... MP The calculation formula is: ; in, t This represents the current iteration number. This represents the maximum number of iterations. If random number r Greater than the reward probability threshold RP If the attribute is positive, a reward will be given to increase its value; otherwise, a penalty will be imposed. Elite retention: Find the individual with the worst fitness in the group and swap its belief vector with the newly generated individual; if the fitness of the new individual is better than that of the best individual in the current group, then replace the belief vector of the best individual with the belief vector of the new individual.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention overcomes the contradiction between optimization efficiency and result accuracy in traditional methods by deeply integrating parametric finite element analysis, optimized high-precision proxy model and improved multi-objective sacred religious algorithm. This method greatly reduces the direct dependence on time-consuming finite element simulation while ensuring global optimization capability, and provides an effective tool for the rapid and accurate design of motors. (2) By establishing a clear sensitivity analysis screening mechanism, this invention can quickly and accurately identify the key variables that have the greatest impact on performance among many motor structural parameters, effectively reducing the dimension and complexity of the optimization problem, avoiding invalid searches on secondary parameters, and enabling subsequent optimization calculations to focus on the core design space, thereby improving the efficiency and pertinence of the overall optimization process. (3) This invention introduces improved Latin hypercube sampling and constructs an improved generalized regression neural network (HO-GRNN) surrogate model. Based on a small number of finite element simulation samples, it constructs a prediction model that can accurately fit the complex nonlinear performance of motors. This transforms the single performance evaluation from time-consuming finite element calculation to instantaneous prediction by the surrogate model, fundamentally solving the efficiency bottleneck caused by the optimization algorithm calling the simulation model, and laying a speed foundation for subsequent intelligent optimization iterations. (4) This invention improves the Sacred Religion algorithm by using Tent chaotic mapping, non-dominated sorting and crowding distance to achieve multiple objectives, which significantly enhances the global exploration capability and convergence performance of the optimization algorithm. Tent chaotic mapping improves the diversity of the initial population, while the introduction of non-dominated sorting and crowding distance ensures that the algorithm can efficiently search for and maintain a uniformly distributed Pareto optimal solution set that balances multiple performance objectives such as torque, loss and torque ripple. (5) By designing and integrating unique religious behavior simulation mechanisms such as group division, leader selection, and believer evolution, this invention enables the improved multi-objective sacred religious algorithm to converge quickly to the excellent region and effectively escape local optima during the search process, thereby ultimately obtaining a motor design scheme with better overall performance. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm, according to the present invention.

[0019] Figure 2 This is a schematic diagram illustrating the process of automatically optimizing the smoothness factor of a generalized regression neural network using the Hippo optimization algorithm in an embodiment of the present invention.

[0020] Figure 3 This is a flowchart illustrating the improvement of the single-objective sacred religion algorithm in an embodiment of the present invention.

[0021] Figure 4 This is a schematic diagram of the motor dimensions and structural parameters in an embodiment of the present invention.

[0022] Figure 5 This is a sensitivity analysis histogram in an embodiment of the present invention.

[0023] Figure 6 This is a graph showing the fitting effect of the torque model in an embodiment of the present invention.

[0024] Figure 7 This is a diagram showing the fitting effect of the loss model in an embodiment of the present invention.

[0025] Figure 8 This is a fitting effect diagram of the torque ripple model in an embodiment of the present invention.

[0026] Figure 9 This is a diagram showing the determination coefficients of the torque, loss, and torque ripple model in the embodiments of the present invention.

[0027] Figure 10 This is a schematic diagram of the Pareto front solution in an embodiment of the present invention.

[0028] Figure 11 This is a schematic diagram of the torque waveform finite element simulation results of the initial solution and the optimal solution in the embodiment of the present invention. Detailed Implementation

[0029] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0030] Reference Figures 1 to 11 This invention provides a multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm, comprising the following steps: S1. Perform sensitivity analysis on the structural parameters of the motor (in this embodiment, a single-stator dual-rotor axial flux motor is used as an example), screen key optimization parameters that are strongly correlated with the optimization target based on the sensitivity magnitude, and determine the optimization range of the key optimization parameters. By calling the finite element simulation model of a three-dimensional axial flux motor and the optiSLang optimization module, parameter sensitivity analysis and multi-objective optimization design of the axial flux motor are achieved. The optimization parameters and optimization objectives of the ANSYS Maxwell 3D axial flux motor are set and then called in the optiSLang-Sensitivity module.

[0031] The sensitivity analysis is used to quantify the influence of each structural parameter on the optimization objective. The formula for calculating the sensitivity is: ; in, Indicates the first i The values ​​of the optimization variables, Indicates the first j The numerical value of the optimization objective. Indicates the first i The optimization variable for the th ... j The sensitivity of an optimization objective. This represents the amount of small perturbation applied to the optimization variable; in this embodiment, the sensitivity analysis histogram is as follows: Figure 5 As shown.

[0032] The optimization objectives include the motor's average torque, torque ripple, and total losses. The torque ripple is used to measure the smoothness of the motor's output torque, and its expression is: ; in, This refers to the torque pulsation of the motor. , , Let these represent the average, maximum, and minimum values ​​of the motor torque, respectively; the fitting effect of the torque ripple model is as follows: Figure 8 As shown.

[0033] The mathematical expression for the torque of an axial flux motor is: ; in, The number of stator phases; This refers to the armature phase current; This is the polar arc coefficient; Maximum air gap magnetic flux density; This refers to the number of stator turns per phase. The fundamental winding factor; , These are the outer and inner diameters of the stator, respectively. Given the diameter ratio, the torque model fitting effect is as follows: Figure 6 As shown.

[0034] The mathematical expression for the total loss is: ; in, This indicates the total loss of the motor. , , These represent iron loss, copper loss, and permanent magnet eddy current loss, respectively. The fitting effect of the total loss model is as follows: Figure 7 As shown.

[0035] Based on its loss characteristics and generation principle, iron loss can be further subdivided into hysteresis loss, eddy current loss, and additional loss, which is the core loss model commonly used in engineering, expressed as: ; In the formula, It is the hysteresis loss of the iron core; It is the eddy current loss of the iron core; It is the additional loss of the iron core.

[0036] The eddy current losses generated in the permanent magnets of axial flux motors differ from those generated in the iron core, but both are inseparable from the air gap magnetic field. The harmonic components present in the air gap magnetic field are the cause of eddy current losses. The eddy current losses of permanent magnets are calculated by the following formula: ; In the formula, It is the eddy current density of the permanent magnet. It is the conductivity of the permanent magnet. It is the volume of the permanent magnet.

[0037] The copper loss of an axial flux motor mainly originates from the resistive loss in the stator windings, caused by the heat generated when current flows through the windings. The copper loss calculation formula for the axial flux motor designed in this paper is as follows: ; in, m This represents the number of phases in the motor windings.m =3; I This represents the effective value of the phase current in the motor windings. R This represents the phase resistance of the winding.

[0038] For each motor structural parameter, its sensitivity across all optimization objectives is ranked, and the parameters with the highest sensitivity are selected as key optimization parameters. Based on the feasibility of the motor's electromagnetic design and manufacturing process, the optimization range of several key optimization parameters is finally determined.

[0039] like Figure 4 As shown, the motor structural parameters include at least several of the following parameters: stator outer diameter. , stator inner diameter Air gap length e Polar arc coefficient Permanent magnet thickness Rotor back iron thickness Groove height Shoulder height trench depth Groove width Upper width of the groove and the width of the lower part of the groove The initial optimization parameters and ranges for the motor are shown in Table 1 below: Table 1 Motor Parameter Optimization Table

[0040] Based on the sensitivity analysis results, the top 7 parameters in terms of sensitivity (stator outer diameter) were selected. , stator inner diameter Polar arc coefficient Permanent magnet thickness Shoulder height trench depth Groove width () is used as a key optimization parameter.

[0041] S2, within the optimization range of the key optimization parameters, multiple sets of sample data are generated using an improved Latin hypercube sampling method, and the optimization target values ​​corresponding to each set of sample data are obtained through finite element simulation to construct a dataset; specifically including the following steps: The range of values ​​for each parameter is defined as the optimization space, which serves as the search space for the improved genetic algorithm. Within the parameter space, an improved Latin hypercube sampling method is used to generate a set of 500 initial sample points. The improved Latin hypercube sampling method enhances the uniformity and representativeness of sample points by maximizing the minimum distance between samples and reducing parameter correlation. The resulting initial sample points serve as the initial population for the genetic algorithm.

[0042] The sample point set is input into a parametric finite element model to perform batch simulations, obtaining the values ​​of average torque, torque ripple, and total loss for each sample point, and constructing a dataset containing the input optimization parameters and the corresponding output optimization objectives. The initial sample points are then imported into Workbench, and simulation results for 500 initial sample points are obtained through Maxwell-Workbench co-simulation.

[0043] S3, Based on the Hippo optimization algorithm, the smoothing factor of the generalized regression neural network is automatically optimized, and the optimized generalized regression neural network is used to train the dataset to construct a proxy model of the motor optimization target. Design an improved generalized regression neural network (GRNN-HO) and select motor parameters. , , , , , , The value is used as the input to the HO-GRNN model, and the average torque of the motor is selected. Torque pulsation and energy loss The model was trained using the optimized output metrics. The collected dataset was imported to generate training and testing samples (a total of 500 samples were randomly allocated, with 90% used for training and the remaining 10% for testing; all data were standardized to improve training performance). A surrogate model corresponding to the optimization objective was generated. The trained model was tested using the test samples, and parameters were adjusted based on the test set error to achieve the required training accuracy, thus generating and obtaining the optimal motor surrogate model.

[0044] Regression predictions are performed on the test set, and the mean squared regularized error (MSE) and coefficient of determination (R²) are used to measure the goodness of fit between the predicted and actual values, thereby evaluating the model accuracy. The formulas for calculating MSE and R² are as follows: the smaller the values, the better the model fit.

[0045] ; ; In the formula, n This represents the number of test samples; , and They represent the first i The actual value of each sample, the predicted value, and the average of all actual values ​​are given. In this embodiment, the determination coefficients of the torque, loss, and torque ripple model are as follows: Figure 9 As shown.

[0046] The model expression for the generalized regression neural network is: ; in, n For the input vector in the dataset, This represents the prediction value of the generalized regression neural network for the input vector; n The number of training samples in the dataset. is the smoothing factor for the generalized regression neural network.

[0047] In this embodiment, the generalized regression neural network model comprises four layers: an input layer, a pattern layer, a summation layer, and an output layer, which sequentially perform feature extraction and output mapping. The network input and output are as follows: , ; The transfer function of the pattern layer neurons is: ; in, X Input variables for the network, For the first i Each neuron corresponds to a learning sample; The summation layer uses two types of neurons: one type performs arithmetic summation of the pattern layer output, and the other type performs weighted summation. The corresponding transfer functions are shown below: ; , j =1,2,…, k .

[0048] The process of automatically optimizing the smoothness factor based on the Hippo optimization algorithm includes: S301, Initialize the population for the Hippo optimization algorithm. The position vector of each individual in the population represents a potential smoothness factor value. S302, during the execution of the optimization loop, simulates three typical hippopotamus behaviors to update the population position: Hippos' habitat location update: Initial location adjustments are made based on current population information. The initial population location is expressed as follows: ; in, i =1,2,…, N ; j =1,2,…, m ; Location of an individual hippopotamus within the population; N The population size; m Let be the dimension of the decision variables in the problem to be optimized; Hippodrome population defense against intruders: Simulating hippopotamus population defense against intruders based on intruder location. With individual location Distance between D Update individual information; Hippos' behavior of seeking safe locations: Individuals move to safer locations, new locations It is generated by the following formula: ; in, A random number between [0,1]. These are normally distributed random numbers. and For the first j Upper and lower bounds for each decision variable; S303, For the updated population, calculate the fitness value of each individual, where the fitness function is: ; in, and These are the mean squared errors of the prediction results of the surrogate model on the training and test sets, respectively. This is the error weighting coefficient (0.2 in this embodiment). This is the regularization coefficient (0.05 in this embodiment); S304, repeat steps S302 to S303 until the termination condition is met, and output the smoothness factor value with the best fitness.

[0049] S4 improves the single-objective sacred religion algorithm by using Tent chaotic mapping, non-dominated sorting and crowding distance. The improved multi-objective sacred religion algorithm is then combined with the motor proxy model for optimization to generate Pareto solution set. This invention introduces a non-dominated sorting mechanism and a "dominance relationship comparison" rule to classify the solutions in the population into levels, and constructs a global Pareto optimal solution set NDSet based on the non-dominated layer, which effectively supports the collaborative optimization of three objectives: torque, loss, and torque ripple.

[0050] Specifically, in order to improve the diversity and uniformity of the initial solutions of the population, this invention uses Tent chaotic mapping to generate a uniform chaotic sequence between 0 and 1, which is used to initialize the decision variables of each individual, replacing the traditional uniform random initialization method and enhancing the population's ability to traverse the solution space in the early stage.

[0051] The method for improving the single-objective sacred religion algorithm using Tent chaotic mapping is as follows: The Tent chaotic sequence is used to initialize the population, ensuring that the initial solutions are distributed as evenly as possible in the solution space, thus increasing population diversity. The Tent chaotic sequence mapping expression is: ; in, and These are the current iteration value and the next iteration value of the chaotic sequence, respectively. It is a random number between the interval [0,1].

[0052] Specifically, when the number of solutions exceeds a set threshold, a "crowding distance" calculation based on the target space is introduced to prioritize retaining Pareto solutions with large distances to maintain the distribution and diversity of the solution set. The neighborhood density of each non-dominated solution is calculated by defining the crowdingDistance function to ensure a uniform distribution of the Pareto front solution set.

[0053] To ensure numerical scaling consistency across multiple objective functions, the algorithm normalizes and weights different objective values, using this as the basis for leader selection. To improve structural consistency and subsequent resolvability of the solutions, the `remove_extra_fields` function is defined to filter non-core fields in the solution set and enforces standardization of input variables as 1×7 vectors and output variables as 1×3 vectors.

[0054] Methods for improving the single-objective sacred religion algorithm by utilizing non-dominated sequences and crowding distance include: S401, after initializing the population, calculate the function value of each individual in the population on multiple optimization objectives; S402, Non-dominated sorting: According to Pareto dominance, all individuals in the population are divided into multiple non-dominated layers; where, if individual A is no worse than individual B in all objective function values ​​and is better than individual B in at least one objective, then A is said to dominate B; the set of individuals not dominated by any other individual constitutes the first non-dominated layer. After removing individuals from this layer, non-dominated individuals are searched again from the remaining individuals to form the second layer, and so on. S403, Crowding Distance Calculation and Ranking: Within the same non-dominated layer, the crowding distance is calculated for each individual. The calculation formula is as follows: ; in, Indicates the first i The degree of crowding of each solution in the target space m To optimize the number of targets, and They were respectively in the second m On the goal of the first i The objective value of two adjacent solutions. and To distinguish the first in the non-dominated layer m The maximum and minimum values ​​of each target; individuals in the same layer are sorted according to the crowding distance, the larger the distance, the smaller the solution density around the individual and the better the diversity; S404, Elite Selection Mechanism: During the algorithm iteration process, when it is necessary to select individuals from parent and child individuals to enter the next generation, individuals with lower non-dominated levels are given priority; for individuals in the same non-dominated level, individuals with larger crowding distance are given priority.

[0055] Methods for generating Pareto solutions by combining an improved multi-objective sacred religious algorithm with a motor proxy model include: S405: Use the selected key optimization parameters as optimization variables for the multi-objective sacred religion algorithm, i.e., the various dimensions of the faith vector; S406: In each iteration of the algorithm, a set of candidate motor parameters corresponding to the belief vector of each individual in the current population is input into the motor surrogate model to obtain the predicted value of the optimization objective corresponding to the set of parameters. S407: Utilizing an improved multi-objective sacred religion algorithm, perform the following operations sequentially on multiple predicted values: population partitioning, leader selection, believer evolution, religious events, and elite retention, to generate a new generation of population. Specifically, this includes the following steps: Group division: dividing the population into groups. N Individuals are divided into K Within each religious group, individuals are divided into ordinary believers and leader believers based on a hierarchy of non-dominant order and crowding distance. Leader selection: Identify the most influential leaders globally across all groups based on non-dominated ranking hierarchy and crowding distance. ; in, The designation of the most influential leader in the entire organization; F The fitness matrix of the population is expressed as: ; in, For the group j fitness matrix, Representing a group j Inner i The fitness function output value for each believer. , Used to evaluate the quality of a believer's faith value; Obtain the leader's belief vector Based on this, the faith of ordinary believers is updated, and the update formula is: ; in, and Each represents an individual i Faith vectors before and after the update r A random number between [0, 1]; Believer Evolution: Generate a random number r ,like r Less than the selection probability threshold BPSP Then a faith dimension will be randomly selected. And update the attribute values ​​of the current believer in this dimension as follows: ; in, Is the current believer in the dimension New attribute values ​​on The globally optimal leader in the dimension The attribute values ​​on rand It is a random perturbation factor in the interval [0,1]. Religious events: If random numbers r Less than the dynamically changing probability threshold of miracles MP If the probability of a miracle occurs, a new individual with a random belief value is added to the group; otherwise, an attribute is selected from among the believers to replace the corresponding attribute of the current leader; the miracle probability threshold... MP The calculation formula is: ; in, t This represents the current iteration number. This represents the maximum number of iterations. If random number r Greater than the reward probability threshold RP If the attribute is positive, a reward will be given to increase its value; otherwise, a penalty will be imposed. ; in, For believers i Faith value; randn This represents a weak reserve of the original faith value.

[0056] Elite retention: Find the individual with the worst fitness in the group (believer) and swap its faith vector with the newly generated individual; if the fitness of the new individual is better than that of the best individual in the current group, then replace the faith vector of the best individual with the faith vector of the new individual. ; ; in, The faith vector of the weakest believer; The weakest believer is in the first d Attribute values ​​in the faith dimension; This represents the faith vector for newly joined believers.

[0057] S408: Repeat steps S406 to S407 until the termination condition (maximum number of iterations) is met. The final output non-dominated solution set is the Pareto solution set. In this embodiment, the final output Pareto front solution is as follows: Figure 10 As shown.

[0058] S5. Select the final optimized motor parameters from the Pareto solution set according to the optimization target weights.

[0059] Specifically, the expression for the multi-objective optimization function is: ; In the formula, , , These correspond to the optimal solutions for the three optimization objectives. During the optimization process, since the algorithm returns the minimum value for the multi-objective function, the negative value of the average torque objective is taken to maximize the average torque.

[0060] Specifically, an improved Pareto algorithm was adopted, incorporating a multi-objective optimization strategy, to perform multi-objective parameter optimization on the constructed motor performance prediction model, obtaining the Pareto front solution. Based on a comprehensive evaluation of key performance parameters such as average torque, torque ripple, and system losses, the final optimization scheme was determined. The optimization results of the motor structural parameters are shown in Table 2 below: Table 2 Optimization Results of Motor Structural Parameters

[0061] To verify the authenticity and effectiveness of the neural network optimization model and the improved DRA algorithm, this embodiment performs finite element analysis on the motor's state before and after optimization. In this embodiment, the finite element simulation results of the torque waveforms of the initial solution and the optimal solution are as follows: Figure 11 As shown in Table 3 below, the results of motor performance optimization are as follows: Table 3. Results of Motor Performance Optimization

[0062] As shown in the table above, compared with the initial value, the optimized motor torque increased by 20.54%, torque ripple decreased by 21.3%, and losses decreased by 49.5W.

[0063] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm, characterized in that, Includes the following steps: S1. Perform sensitivity analysis on the motor structural parameters, screen key optimization parameters that are strongly correlated with the optimization target based on the sensitivity magnitude, and determine the optimization range of the key optimization parameters; S2, within the optimization range of the key optimization parameters, multiple sets of sample data are generated using an improved Latin hypercube sampling method, and the optimization target values ​​corresponding to each set of sample data are obtained through finite element simulation to construct a dataset; S3, Based on the Hippo optimization algorithm, the smoothing factor of the generalized regression neural network is automatically optimized, and the optimized generalized regression neural network is used to train the dataset to construct a proxy model of the motor optimization target. S4 improves the single-objective sacred religion algorithm by using Tent chaotic mapping, non-dominated sorting and crowding distance. The improved multi-objective sacred religion algorithm is then combined with the motor proxy model for optimization to generate Pareto solution set. S5. Select the final optimized motor parameters from the Pareto solution set according to the optimization target weights.

2. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 1, characterized in that, In step S1, the sensitivity analysis is used to quantify the influence of each structural parameter on the optimization target. The formula for calculating the sensitivity is: ； in, Indicates the first i The values ​​of the optimization variables, Indicates the first j The numerical value of the optimization objective. Indicates the first i The optimization variable for the th ... j The sensitivity of an optimization objective. This represents the amount of small perturbation applied to the optimization variable; For each motor structural parameter, its sensitivity across all optimization objectives is ranked, and the parameters with the highest sensitivity are selected as key optimization parameters. Based on the feasibility of the motor's electromagnetic design and manufacturing process, the optimization range of several key optimization parameters is finally determined.

3. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 1, characterized in that, In step S1, the motor structural parameters include at least several of the following parameters: stator outer diameter, stator inner diameter, air gap length, pole arc coefficient, permanent magnet thickness, rotor back iron thickness, slot height, shoulder height, slot depth, slot width, upper slot width, and lower slot width. The optimization objectives include the motor's average torque, torque ripple, and total losses. The torque ripple is used to measure the smoothness of the motor's output torque, and its expression is: ； in, This refers to the torque pulsation of the motor. , , These represent the average, maximum, and minimum values ​​of the motor torque, respectively. The mathematical expression for the total loss is: ； in, This indicates the total loss of the motor. , , These represent iron loss, copper loss, and permanent magnet eddy current loss, respectively.

4. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 3, characterized in that, Step S2 includes: Within the optimization space comprised of the key optimization parameters, a predetermined set of sample points is generated by maximizing the minimum distance between samples and reducing the correlation between parameters. The set of sample points is input into a parameterized finite element model to perform batch simulations, and the values ​​of average torque, torque ripple and total loss corresponding to each sample point are obtained to construct a dataset containing the input optimization parameters and the output optimization objectives.

5. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 1, characterized in that, In step S3, the model expression of the generalized regression neural network is: ； in, n For the input vector in the dataset, This represents the prediction value of the generalized regression neural network for the input vector; n The number of training samples in the dataset. is the smoothing factor for the generalized regression neural network.

6. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 5, characterized in that, In step S3, the process of automatically optimizing the smoothness factor based on the Hippo optimization algorithm includes: S301, Initialize the population for the Hippo optimization algorithm. The position vector of each individual in the population represents a potential smoothness factor value. S302, during the execution of the optimization loop, simulates three typical hippopotamus behaviors to update the population position: Hippos' habitat location update: Preliminary location adjustments based on current population information; Hippodrome population defense against intruders: Simulating hippopotamus population defense against intruders based on intruder location. With individual location Distance between D Update individual information; Hippos' behavior of seeking safe locations: Individuals move to safer locations, new locations It is generated by the following formula: ； in, A random number between [0,1]. These are normally distributed random numbers. and For the first j Upper and lower bounds for each decision variable; S303, For the updated population, calculate the fitness value of each individual, where the fitness function is: ； in, and These are the mean squared errors of the prediction results of the surrogate model on the training and test sets, respectively. These are the error weighting coefficients. The regularization coefficient is used. S304, repeat steps S302 to S303 until the termination condition is met, and output the smoothness factor value with the best fitness.

7. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 6, characterized in that, In step S4, the method for improving the single-objective sacred religion algorithm using Tent chaotic mapping is as follows: The Tent chaotic sequence is used to initialize the population, ensuring that the initial solutions are distributed as evenly as possible in the solution space, thus increasing population diversity. The Tent chaotic sequence mapping expression is: ； in, and These are the current iteration value and the next iteration value of the chaotic sequence, respectively. It is a random number between the interval [0,1].

8. The multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 7, characterized in that, In step S4, the method for improving the single-objective sacred religion algorithm using non-dominated sequences and crowding distance includes: S401, after initializing the population, calculate the function value of each individual in the population on multiple optimization objectives; S402, Non-dominated sorting: According to Pareto dominance, all individuals in the population are divided into multiple non-dominated layers; where, if individual A is no worse than individual B in all objective function values ​​and is better than individual B in at least one objective, then A is said to dominate B; the set of individuals not dominated by any other individual constitutes the first non-dominated layer. After removing individuals from this layer, non-dominated individuals are searched again from the remaining individuals to form the second layer, and so on. S403, Crowding Distance Calculation and Ranking: Within the same non-dominated layer, the crowding distance is calculated for each individual. The calculation formula is as follows: ； in, Indicates the first i The degree of crowding of each solution in the target space m To optimize the number of targets, and They were respectively in the second m On the goal of the first i The objective value of two adjacent solutions. and To distinguish the first in the non-dominated layer m The maximum and minimum values ​​of each target; individuals in the same layer are sorted according to the crowding distance, the larger the distance, the smaller the solution density around the individual and the better the diversity; S404, Elite Selection Mechanism: During the algorithm iteration process, when it is necessary to select individuals from parent and child individuals to enter the next generation, individuals with lower non-dominated levels are given priority; for individuals in the same non-dominated level, individuals with larger crowding distance are given priority.

9. A multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 8, characterized in that, In step S4, the method for generating the Pareto solution set by combining the improved multi-objective sacred religion algorithm with the motor proxy model includes: S405: Use the selected key optimization parameters as optimization variables for the multi-objective sacred religion algorithm, i.e., the various dimensions of the faith vector; S406: In each iteration of the algorithm, a set of candidate motor parameters corresponding to the belief vector of each individual in the current population is input into the motor surrogate model to obtain the predicted value of the optimization objective corresponding to the set of parameters. S407: Using an improved multi-objective sacred religion algorithm, perform the following operations sequentially on multiple predicted values: population partitioning, leader selection, believer evolution, religious events, and elite retention to generate a new generation of population; S408: Repeat steps S406 to S407 until the termination condition is met. The final output non-dominated solution set is the Pareto solution set.

10. A multi-objective optimization method for axial flux motors based on an improved sacred religious algorithm as described in claim 9, characterized in that, Step S407 includes: Group division: dividing the population into groups. N Individuals are divided into K Within each religious group, individuals are divided into ordinary believers and leader believers based on a hierarchy of non-dominant order and crowding distance. Leader selection: Identify the most influential leaders globally across all groups based on non-dominated ranking hierarchy and crowding distance. ； in, The designation of the most influential leader in the entire organization; F The fitness matrix of the population is expressed as: ； in, For the group j fitness matrix, Representing a group j Inner i The fitness function output value for each believer. , Used to evaluate the quality of a believer's faith value; Obtain the leader's belief vector Based on this, the faith of ordinary believers is updated, and the update formula is: ； in, and Each represents an individual i Faith vectors before and after the update r A random number between [0, 1]; Believer Evolution: Generate a random number r ,like r Less than the selection probability threshold BPSP Then a faith dimension will be randomly selected. And update the attribute values ​​of the current believer in this dimension as follows: ； in, Is the current believer in the dimension New attribute values ​​on The globally optimal leader in the dimension The attribute values ​​on rand It is a random perturbation factor in the interval [0,1]. Religious events: If random numbers r Less than the dynamically changing probability threshold of miracles MP If the probability of a miracle occurs, a new individual with a random belief value is added to the group; otherwise, an attribute is selected from among the believers to replace the corresponding attribute of the current leader; the miracle probability threshold... MP The calculation formula is: ； in, t This represents the current iteration number. This represents the maximum number of iterations. If random number r Greater than the reward probability threshold RP If the attribute is positive, a reward will be given to increase its value; otherwise, a penalty will be imposed. Elite retention: Find the individual with the worst fitness in the group and swap its belief vector with the newly generated individual; if the fitness of the new individual is better than that of the best individual in the current group, then replace the belief vector of the best individual with the belief vector of the new individual.

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