A multi-objective optimization design method for permanent magnet synchronous motor based on physical constraint KAN agent model and adaptive evolutionary algorithm

Abstract

The application discloses a permanent magnet synchronous motor multi-objective optimization design method based on a physical constraint KAN agent model and a self-adaptive evolution algorithm and belongs to the technical field of motor optimization design. The method comprises the following steps: determining optimization targets and initial design variables, performing variable dimension reduction screening by using Pearson correlation coefficients and Morris sensitivity analysis; adopting OLHS combined with finite element analysis to construct an initial sample library; constructing a physical constraint KAN agent model, introducing four electromagnetic physical constraints of magnetic saturation, flux linkage continuity, power balance and electromagnetic torque consistency into a loss function; establishing an active learning feedback mechanism based on a prediction error to realize dynamic updating of the model; taking the updated KAN model as an evaluation engine, introducing a matrix vectorization I-NSGA-II algorithm and a dynamic self-adaptive mutation strategy based on variable sensitivity to perform multi-objective optimization; and finally outputting an optimal design scheme through fuzzy set decision and finite element closed loop verification. The application reduces the finite element calling times from about 16,000 times to more than 300 times, reduces the calculation cost by about 98%, increases the torque by 4.82%, and reduces the pulsation by 6.37%, and has the significant advantages of high calculation efficiency, high prediction accuracy and high optimization reliability.

Description

Technical Field

[0001] This invention belongs to the field of intelligent optimization design technology for permanent magnet synchronous motors, specifically involving a multi-objective optimization design method for high-power permanent magnet synchronous motors that integrates an electromagnetic physical constraint proxy model and an adaptive evolution algorithm. It is applicable to the optimization of electromagnetic structure parameters in drive motors for new energy vehicles, aerospace electric actuators, and high-end industrial servo systems. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in new energy vehicles, aerospace equipment, and high-end industrial servo systems due to their outstanding advantages such as high power density, high efficiency, and wide speed range. However, with the expansion of application scenarios, the development of traditional PMSMs faces challenges such as long design cycles and difficulty in achieving a global trade-off between multiple performance indicators. The complex magnetic saturation, leakage flux, and cogging harmonic effects inside the motor cause the design space to exhibit strong nonlinearity and multi-peak characteristics, making it difficult for traditional surrogate models to accurately describe the local response patterns.

[0003] Meanwhile, traditional evolutionary algorithms employ a uniform mutation strategy, which cannot simultaneously address the search requirements for both high-sensitivity and low-sensitivity parameters. This can easily lead to local convergence or decreased search efficiency. Furthermore, multi-objective optimization designs often rely on finite element analysis, and their efficiency needs improvement in high-dimensional nonlinear space optimization. Therefore, this invention proposes a comprehensive optimization method that integrates data dimensionality reduction, the KAN surrogate model, and matrix vectorization to improve the NSGA-II algorithm. Summary of the Invention

[0004] This invention provides an optimization framework that deeply integrates physical constraints and data-driven approaches. By introducing electromagnetic physics penalty terms (magnetic saturation, power balance) into the loss function of the KAN network, the model output is forced to conform to Maxwell's equations and the fundamental electromagnetic laws of motors, thereby improving the model's generalization accuracy with limited samples. Simultaneously, an active learning feedback mechanism is constructed to address the problem of "drifting" failure of the surrogate model during evolutionary optimization.

[0005] To achieve the above objectives, the solution of this invention is: a multi-objective optimization design method for permanent magnet synchronous motors based on a physically constrained KAN surrogate model and an adaptive evolution algorithm, the method comprising the following steps:

[0006] Step 1: Determine the optimization objective and initial design variables of the motor. Use Pearson correlation coefficient and Morris sensitivity analysis to perform dimensionality reduction screening on the initial design variables and extract key design variables that are strongly correlated with the output objective.

[0007] Step 2: For the key design variables, optimal Latin hypercube sampling (OLHS) combined with finite element analysis is used to generate a sample set, and an original sample library containing key input geometric parameters and output electromagnetic performance indicators is constructed. Step 3: Based on the original sample library, a physical constraint Kolmogorov-Arnold network proxy model is constructed, and its edge-learnable B-spline activation function is used to achieve high-precision mapping from geometric features to physical field performance. An electromagnetic physical constraint penalty term is introduced into the loss function.

[0008] Step 4: Establish an active learning feedback mechanism based on prediction error. When the prediction uncertainty or residual error of the surrogate model in the candidate solution region exceeds the set threshold, high-fidelity finite element calculation is automatically triggered to supplement the sample, so as to realize the dynamic updating and accuracy maintenance of the surrogate model.

[0009] Step 5: Using the KAN surrogate model as a high-frequency evaluator, an improved second-generation non-dominated sorting genetic algorithm (I-NSGA-II) with a reconstruction pure matrix vectorization operator and a dynamic adaptive mutation strategy is introduced to construct an adaptive evolution algorithm based on variable sensitivity to obtain the Pareto solution set.

[0010] Step 6: Implement decision-making and discretization process constraint processing based on fuzzy set theory on the Pareto front solution set, extract the optimal engineering solution, and call finite element simulation to perform fixed-point closed-loop verification of the solution, and output the final motor design scheme.

[0011] In step 1, the optimization objectives are set as maximizing output torque, maximizing efficiency, and minimizing torque ripple. The linear correlation between the variables is calculated using the following Pearson correlation coefficient formula:

[0012]

[0013] in, To design sample values ​​of variables, This represents the corresponding performance indicator response value. The closer the absolute value is to 1, the stronger the linear correlation.

[0014] In step 3, the learnable functions within the KAN surrogate model are parameterized using B-spline basis functions. For a function with n input variables, its representation is as follows:

[0015]

[0016] The parameterized expansion of the edge activation function is as follows:

[0017]

[0018] in, Commonly selected The function serves as the fundamental nonlinear mapping. for spline basis functions These are the control point weights that the network can learn during backpropagation. The overall scaling weight for this edge.

[0019] In step 3, the total loss function and physical constraint loss term of the surrogate model are expanded as follows:

[0020] Total loss function of proxy model

[0021]

[0022] in, This represents the mean squared error between the model's predicted values ​​and the actual samples. To assign adaptive penalty weights to each physical constraint, an automatic adjustment strategy based on validation set error is adopted, which increases the weight of a physical constraint as the degree of violation increases.

[0023] Physical constraint loss term expansion

[0024]

[0025] Magnetic saturation confinement

[0026]

[0027] flux continuity constraint

[0028]

[0029] Power balance constraints

[0030]

[0031] Electromagnetic torque constraint

[0032]

[0033] In the above formula, To predict local magnetic flux density, The saturation magnetic flux density threshold of the material; It is the magnetic flux density vector; These are the motor's input power, output power, and various losses, respectively. To predict electromagnetic torque, p is the number of pole pairs. Here, represents the magnetic flux and current along the d and q axes, respectively.

[0034] In step 4, an active learning feedback mechanism based on prediction error is established. Once the accumulated new samples reach a set batch processing size, finite element simulation is invoked for batch calculations, and the KAN surrogate model parameters are updated using incremental learning. The incremental update strategy for supplementary training samples is expressed as follows:

[0035]

[0036] in, For the original sample set, For the updated sample set, For new solutions in the evolutionary optimization process, For this point, the surrogate model predicts uncertainty or residual error. This is the set error threshold for triggering high-fidelity finite element calculations. Once the cumulative number of new samples reaches 10, a batch of finite element simulations is invoked, and the parameters of the KAN surrogate model are updated using incremental learning.

[0037] In step 5, the pure matrix vectorization evolutionary operation framework is reconstructed in the I-NSGA-II algorithm. This is achieved by directly mapping the population to a continuously stored dense matrix for slicing and parallel tensor computation, eliminating the overhead of iterative loops. Simultaneously, the distribution exponent of its dynamic adaptive polynomial mutation operator is... Iterative algebra g dynamically adjusts nonlinearly:

[0038]

[0039] In the formula, The maximum number of generations; and The values ​​are set to 20 and 60 respectively, which gives the population global exploration capabilities in the early stages of evolution and enables localized in-depth development in the later stages.

[0040] Furthermore, in step 5, the system incorporates a rigid boundary safety shield mechanism: that is, by setting the physical upper and lower limit thresholds for each design variable. Dimensionally truncate all individuals in the population generated by parallel computation:

[0041]

[0042] To prevent the surrogate model from collapsing and diverging at the edge of the sampling space due to extrapolation.

[0043] The beneficial technical effects of this invention are as follows:

[0044] 1. Significantly reduced computational costs: By constructing a small-scale training set using optimal Latin hypercube sampling and introducing a high-fidelity KAN surrogate model to replace iterative optimization of the physical field, the number of finite element method calls is reduced from approximately 16,000 to 300 while ensuring Pareto front accuracy, resulting in a significant reduction of computational costs by approximately 98%.

[0045] 2. Extremely high-dimensional nonlinear representation capability: The KAN network deploys learnable B-spline activation functions at the network edge, overcoming the loss of abrupt features caused by the fixed activation function in traditional neural networks. It can accurately capture and implicitly depict local nonlinear abrupt changes in electromagnetic parameters caused by magnetic bridge saturation, etc., and has extremely high mapping accuracy and physical interpretability.

[0046] 3. Efficient coordination between global exploration and local fine-tuning: By improving the pure matrix vectorization operation of the I-NSGA-II algorithm, the linear degradation of evaluation time is eliminated. Combined with the dynamic adaptive mutation strategy, the local Pareto saturation trap is effectively avoided, and the three-dimensional conflicting objectives of high output torque, high efficiency and low torque ripple are successfully balanced. Attached Figure Description

[0047] Figure 1 This is an overall flowchart of a multi-objective optimization design method for permanent magnet synchronous motors based on the physical constraint KAN surrogate model and the improved NSGA-II algorithm, as described in this invention.

[0048] Figure 2 is a schematic diagram of a KAN network structure and B-spline activation function according to the present invention, wherein (a) is the overall topology of the KAN network, showing the computation path from the input layer to the summation layer through the edge B-spline activation function; (b) is a schematic diagram of the parameterized B-spline curve shape of a single edge activation function, showing the modulation effect of learnable control points on the curve shape.

[0049] Figure 3(a) is a schematic diagram of the Pareto front obtained after optimization by I-NSGA-II in the embodiment of the present invention. (b) is the Pareto front diagram of the optimal engineering solution after optimization. In order to fit the minimum optimization logic of the underlying multi-objective evolution algorithm, the average torque on the horizontal axis is negative. Detailed Implementation

[0050] This embodiment uses a built-in high-power permanent magnet synchronous motor with a rated power of 37kW, a rated voltage of 380V, and a rated speed of 160rpm as the optimization object to describe the execution process of the method of this invention in detail:

[0051] First, parameter selection and sample generation were performed. By analyzing the physical coupling relationship of seven design parameters—slot width, air gap length, slot bottom width, permanent magnet thickness, slot height, magnetic bridge width, and permanent magnet width—Pearson and Morris analyses were used to clarify that average torque and efficiency are dominated by macroscopic dimensions, while torque ripple is highly sensitive to the microscopic dimensions of the tooth groove. The Optimal Latin Hypercube Sampling (OLHS) algorithm was employed to generate 300 uniformly distributed sample points in 7-dimensional space. After finite element simulation, an initial sample library was constructed and proportionally divided into training, validation, and test sets.

[0052] Subsequently, physical constraint KAN modeling is performed: a physical residual term is added to the KAN loss function. A 7-dimensional input, 3-dimensional output KAN network is constructed, and the input geometric variables are processed according to the input feature data... After mapping to the [0, 1] interval, the data is injected into the network. Unlike traditional MLPs, during training, the B-spline curves of KAN's edge nodes adaptively evolve into complex multi-peak nonlinear shapes. Mathematically, this is equivalent to modeling the BH saturation curve and leakage flux fluctuations inside the motor, ultimately improving the model's prediction of torque ripple R. 2 Reaching 0.843, for average torque and efficiency R 2 It achieves accuracy of 0.985 and 0.994 or higher, far exceeding that of traditional algorithms such as SVR and RBF.

[0053] Next, vectorized parallel evolution is performed. An I-NSGA-II population of size 100 is initialized, and the entire population is used as input to a dense matrix. Binary tournament selection and simulated binary crossover are performed using element-wise computation across the entire matrix, significantly improving computational efficiency. Through a defined nonlinear dynamic mutation index, the algorithm exhibits a large perturbation step size in the early stages of evolution, allowing it to escape local optima in the nonlinear response surface. In the mid-to-late stages, the step size is reduced for fine-tuning of sensitive parameters such as magnetic bridges. Simultaneously, the system incorporates a rigid boundary safety shield, which truncates all individuals generated by parallel computation by setting physical upper and lower thresholds for design variables, preventing the surrogate model from collapsing and diverging at the sampling space edges.

[0054] Finally, decision-making and physical layer verification were performed. After generating the Pareto front, a fuzzy satisfaction assessment was introduced, and manufacturing tolerance meshes of 1 mm and 0.5 mm were applied to discretize the solution. The optimal engineering solution was extracted and subjected to finite element closed-loop verification. The results show that the optimized motor's magnetic bridge was reduced from 4 mm to 3 mm, and the permanent magnet thickness increased to 10.4 mm. Finite element verification shows that the average torque increased by 4.82% and the torque ripple decreased significantly by 6.37% after optimization, with prediction errors as low as 0.15% and 5.00%, respectively. This not only meets the stringent requirements of high-power direct-drive equipment for stable low-speed operation but also confirms the high robustness and engineering feasibility of the proposed method throughout the entire process.

Claims

1. A multi-objective optimization design method for permanent magnet synchronous motors based on a physically constrained KAN surrogate model and an adaptive evolution algorithm, comprising the following steps: Step 1: Determine the optimization objective and initial design variables of the motor, and use Pearson correlation coefficient and Morris sensitivity analysis to screen variables and extract key design variables; Step 2: Construct an initial sample library and use optimal Latin hypercube sampling (OLHS) combined with finite element analysis to obtain the corresponding data of input key geometric parameters and output electromagnetic performance indicators; Step 3: Construct a physical constraint Kolmogorov-Arnold network proxy model, use the B-spline activation function as the edge weights, and introduce an electromagnetic physical constraint loss function to achieve a high-precision mapping from geometric features to physical field performance; Step 4: Establish an active learning feedback mechanism based on prediction error. When the prediction error of the surrogate model exceeds the threshold, automatically supplement finite element simulation samples to achieve dynamic model updates. Step 5: Using the dynamically updated KAN proxy model as the high-frequency evaluation engine, the I-NSGA-II algorithm, which combines the reconstruction of pure matrix vectorization operators and dynamic adaptive mutation strategy, is introduced to perform multi-objective collaborative optimization and obtain the Pareto solution set. Step 6: Based on fuzzy set theory, make engineering decisions on the Pareto solution set, extract the optimal engineering solution, and perform finite element closed-loop verification.

2. The method according to claim 1, characterized in that: In step 1, the optimization objective is to maximize the average torque and minimize torque ripple. Key design variables include at least the slot width, air gap length, magnetic bridge width, permanent magnet thickness, permanent magnet width, slot bottom width, and slot height. The formula for calculating the Pearson correlation coefficient is: in, To design sample values ​​of variables, This represents the corresponding performance indicator response value.

3. The method according to claim 1, characterized in that: In step 3, the learnable functions within the KAN surrogate model are represented using local B-spline basis functions. The parameterized expansion of the edge activation function is as follows: in, Commonly selected The function serves as the fundamental nonlinear mapping. for spline basis functions These are the control point weights that the network can learn during backpropagation. The overall scaling weight for this edge.

4. The method according to claim 1, characterized in that: In step 3, the total loss function of the proxy model is: in, This represents the mean squared error between the model's predicted values ​​and the actual samples. The adaptive penalty weights for each physical constraint; The magnetic saturation confinement loss is: The flux continuity constraint loss is: The power balance constraint loss is: The electromagnetic torque constraint loss is: in, To predict local magnetic flux density, The saturation magnetic flux density threshold of the material; It is the magnetic flux density vector; , , These are the motor's input power, output power, and various losses, respectively. To predict electromagnetic torque, p is the number of pole pairs. , , , Here, represents the magnetic flux and current along the d and q axes, respectively.

5. The method according to claim 1, characterized in that: In step 4, the incremental update strategy for supplementing training samples is expressed as follows: in, For the original sample set, For the updated sample set, For new solutions in the evolutionary optimization process, For this point, the surrogate model predicts uncertainty or residual error. This is the set error threshold for triggering high-fidelity finite element calculations. Once the cumulative number of new samples reaches 10, a batch of finite element simulations is invoked, and the parameters of the KAN surrogate model are updated using incremental learning.

6. The method according to claim 1, characterized in that: In step 5, the distribution index of the dynamic adaptive polynomial mutation operator in the I-NSGA-II algorithm's dynamic adaptive polynomial mutation strategy... Dynamic nonlinear adjustment with iteration algebra g: In the formula, The maximum number of generations; and These are set as the lower and upper limits of the variation index, respectively.

7. The method according to claim 1, characterized in that: In step 5, the pure matrix vectorization operator is: to directly map the entire population into a continuously stored dense matrix, and to use the broadcast mechanism of the tensor computing framework to complete the selection, crossover and mutation operations of all individuals at once, eliminating the overhead of loop iteration.

8. The method according to claim 6, characterized in that: In step 5, different design variables are assigned differentiated variance benchmark indices based on the Morris sensitivity analysis results in step 1. High-sensitivity variables are assigned larger variance indices, while low-sensitivity variables are assigned smaller variance indices.

9. The method according to claim 1, characterized in that: In step 5, the system has a built-in rigid boundary safety shield mechanism: that is, by setting the physical upper and lower limit thresholds for each design variable. Dimensionally truncate all individuals in the population generated by parallel computation:

10. The method according to claim 1, characterized in that: In step 6, in the decision-making process based on fuzzy set theory, the first... The solution is at the th solution. The satisfaction level for each objective is: For the maximization objective, The overall satisfaction rate is the weighted sum of the satisfaction rates of each objective, and the solution with the highest overall satisfaction rate is selected as the optimal solution for the project.

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