A high-efficiency design optimization method for a bidirectional magnetic field modulation arc motor

Abstract

The application discloses a kind of high-efficiency design optimization methods for two-way magnetic field modulation arc motor, fusion characteristic complementary BiGRU and XGBoost model, BiGRU can capture parameter two-way complex association, and local fitting effect is good to torque mutation, limit working condition;XGBoost is strong, and conventional working condition prediction is stable.Noise.This application is based on training set prediction residual error variance, to variance reciprocal normalization adaptive to obtain weighting factor, linear superposition double model output, weight is automatically adapted with data set, realize data-driven fusion, avoid artificial tuning.After training, carry out performance verification using multiple error indicators, generate multiple visual charts to evaluate model state, then the prediction results are connected into Newton-Raphson algorithm to complete motor multi-size iterative optimization.The application has the advantages of local fine fitting and global stable prediction, reduces single-point prediction mutation, and the global torque prediction is stable and reliable, which can provide high-precision proxy model for arc motor multivariable size optimization.

Description

Technical Field

[0001] This invention relates to the field of motor performance analysis, and more specifically, to an efficient design optimization method for bidirectional magnetic field modulation arc motors. Background Technology

[0002] In the design and optimization of bidirectional magnetic field modulated arc motors, the finite element method (FEM) is typically used to analyze electromagnetic performance and multiphysics characteristics. However, the FEM suffers from problems such as complex model building, high computational resource consumption, and long single-step solution time. It struggles to meet the demands of rapid iterative evaluation when facing multi-structural-parameter, multi-operating-condition, and multi-objective optimization tasks. Furthermore, existing surrogate models based on single machine learning models are easily limited by their own characteristics when dealing with the complex nonlinear mapping relationship between arc motor structural parameters and electromagnetic performance. This leads to decreased prediction accuracy under certain operating conditions, insufficient fitting ability in local performance variation regions, and poor model generalization stability. Moreover, when using surrogate models to replace the FEM for structural parameter optimization, the non-analytical black-box nature of the surrogate model can cause traditional Newton-type optimization methods to exhibit ill-conditioned Hessian matrices, unstable iteration step sizes, and insufficient convergence during the optimization process.

[0003] Therefore, to address the aforementioned issues, it is necessary to propose an efficient design optimization method for bidirectional magnetic field modulation arc motors. By constructing a hybrid surrogate model with adaptive fusion capabilities, rapid and high-precision prediction of multiple motor performance indicators can be achieved. Furthermore, by combining an improved Newton-Raphson optimization strategy, stable and efficient closed-loop optimization of multiple size parameters can be realized, thereby improving the computational efficiency and optimization reliability of the motor design optimization process. Summary of the Invention

[0004] Large-diameter, heavy-load, and high-positioning-precision direct-drive mechanisms are core requirements of modern high-end manufacturing and precision industries. Arc motors, by eliminating mechanical deceleration links in analytical chains, have become key components for achieving high-rigidity, high-efficiency intelligent drives. However, these motors possess the dual electromagnetic characteristics of linear and rotary motors, and their unique discontinuous structure edge effects and nonlinear cogging effects easily induce significant torque pulsations. In existing modeling systems, analytical methods, while offering millisecond-level response and clear scale mapping, struggle to accommodate complex topologies and core magnetic saturation when simplifying boundaries, limiting their applicability to initial scheme selection. The equivalent magnetic circuit method (MEC), while capable of handling nonlinear magnetic saturation and solving within seconds, suffers from network discretization accuracy highly dependent on engineering experience, failing to accurately characterize fine flow fields such as local magnetic flux density at tooth tips. The finite element method (FEM), with its high precision and ability to accurately analyze complex geometric shapes, cross-saturation, and multi-field coupling details, faces technical challenges such as high computational resource consumption and poor timeliness. To overcome the multi-field computational bottleneck, introducing intelligent algorithms to construct motor proxy models has become a current research hotspot. Machine learning-based surrogate models, by establishing a mapping relationship between input parameters and performance indicators, can predict the electromagnetic and mechanical performance of thousands of motor schemes within milliseconds, greatly improving the search efficiency of the design space. However, multiphysics optimization of arc motors has high-dimensionality and strong nonlinear characteristics, and the prediction accuracy of a single surrogate model (such as using only neural networks or support vector machines) is limited in the global scope. Therefore, this invention proposes a hybrid surrogate model for motor modeling, which can combine the fitting advantages of different basic algorithms, significantly improving the prediction accuracy of various output indicators in multiple fields while maintaining extremely fast computation speed. This is an effective means to achieve efficient and high-precision multi-field coupled optimization of motors.

[0005] The first aspect of this invention provides an efficient design optimization method for a bidirectional magnetic field modulation arc motor, comprising: A topological model of a bidirectional magnetic field modulated arc motor is presented. This topological model consists of two unit motors, one in front and one behind. The two unit motors have identical structures. Each motor consists of a rotor tooth 1, a rotor yoke 2, a rotor permanent magnet 3, a stator yoke 4, a stator winding 5, a stator tooth permanent magnet 6, a stator yoke permanent magnet 7, a stator tooth 8, and a stator auxiliary tooth 9. The stators of the two motors adopt an integrated structure. The rotors of the two motors are staggered by one pole pitch. The permanent magnets in the stator teeth of the two motors are tangentially magnetized, while the permanent magnets in other positions are radially magnetized. The magnetization directions of the permanent magnets at corresponding positions in the two motors are opposite. Based on the topology model, a bidirectional gated cyclic unit-extreme gradient hybrid surrogate model based on variance inverse adaptive weighting is used to predict multiple performance indicators of the motor. The bidirectional gated cyclic unit is a deep learning model that treats motor parameters as sequential data, captures the complex bidirectional relationship between parameters, and fits torque mutation and local intervals of extreme working conditions. The impact of each structural parameter on motor performance is analyzed using an extreme gradient model, and the importance ranking of each structural parameter is output. The training and test sets are imported into the bidirectional gated recurrent unit-extreme gradient hybrid surrogate model for training and prediction. The error variance of the two models is calculated based on the prediction residuals. The weighting coefficients are obtained by normalizing the variance by the inverse. The prediction results of the two models are then linearly superimposed to obtain the final output. After training, a comprehensive performance evaluation was conducted. Multiple error metrics, including R², MSE, MAE, and MAPE, were statistically analyzed for both the single model and the hybrid surrogate model on the training and test sets. Simultaneously, parameter importance histograms, true value prediction comparison curves, fitting scatter plots, and residual distribution plots were generated. A comprehensive objective function was constructed, including predicted average torque, torque ripple, and harmonic distortion rate. Based on the hybrid surrogate model, the gradient and Hessian matrix of the objective function were calculated. The motor structure dimensions were iteratively optimized using the Newton-Raphson algorithm to obtain the final motor prediction performance metrics.

[0006] In this solution, the topology model adopts an integrated stator design, specifically: The front and rear stator segments have no relative displacement and share a common winding structure. The stator windings are arranged in a cross-winding configuration, with the connection phase sequence being ACB, BCA, CAB. The bidirectional magnetic field modulation arc motor adopts a modular stator structure composed of multiple identical unit motors. The mechanical slot pitch angle of 12° under a fully circular 30-slot structure is used as the reference, i.e., the geometric angle corresponding to a single slot is used as the reference. The circumferential physical distance between two adjacent unit motors satisfies S1 and S2. By introducing a reverse compensation angle of 24° equivalent to two mechanical slot pitch angles in the spatial physical arrangement, and coordinating with the circumferential cyclic misalignment of the phase sequence within each unit motor, the induced electromotive force of the in-phase windings of each unit motor remains aligned in electrical angle even under the premise of spatial physical misalignment. S1 and S2 are specifically calculated as follows: (1); in, denoted as the physical angle of the rotor's pole pitch, and k is a preset positive integer.

[0007] In this solution, the bidirectional magnetic field modulation arc motor includes a pole-slot matching design, specifically: Taking 6 slots as the stator slot number for a single unit motor, and considering both the rotor tooth number Nr and the stator slot number Ns, the following formula should be satisfied: (2); To further derive the rotor tooth count, the cogging effect of the front and rear motors is considered. The pole-slot fit of the motor has a significant impact on the cogging torque, thus affecting the motor's performance stability. The arc motor consists of two motors staggered 180 degrees in the rotor structure.° The equation is composed of / p, where p is the number of pole pairs. From this, the formulas for the cogging torque of the front and rear motors are derived: (3); in, Rotor position angle, The total energy stored in the air gap. Air permeability, V: air gap volume and These are the magnetomotive force of the permanent magnet and the air gap permeability, respectively; considering only the stator permanent magnet and the rotor permanent magnet, the cogging torques are as follows: (4); (5); Among them, R si ,R ro : These are the inner radius of the stator and the outer radius of the rotor, respectively; L: axial length of the motor core; N s N r These refer to the number of stator slots and rotor poles (i.e., the number of rotor teeth) of a single unit motor. , , All are corresponding air gap permeability functions; For the cogging torque in equations (4) and (5) to exist effectively, the orders m and n of the Fourier expansion terms must satisfy the spatial periodic matching condition: Then m and n are determined by the following formula: (6); The greatest common divisor; The front motor and the rear motor have a mechanical misalignment angle of 180° / p in their rotor geometry. The cogging torque of the rear motor is shown below: (7); (8); When m and n are odd numbers, the odd harmonics of the cogging torque generated by the front motor and the rear motor are equal in magnitude and opposite in phase, thus canceling each other out when they are superimposed in space. , These represent the cogging torque of a surface-mounted permanent magnet motor, the cogging torque of a built-in permanent magnet motor, the rear cogging torque of a surface-mounted permanent magnet motor, and the rear cogging torque of a built-in permanent magnet motor, respectively. These represent the mth harmonic amplitude of the air gap magnetomotive force of a surface-mounted permanent magnet motor and the nth harmonic amplitude of the air gap magnetomotive force of a built-in permanent magnet motor, respectively.

[0008] In this scheme, the structural parameters are normalized, specifically as follows: (9) Among them, X raw X represents the original dataset. max X min , representing the maximum and minimum values ​​respectively, X raw It is an N×C matrix, where N represents the sample input space quantity and C is the number of motor structural parameters. Let Y represent the output quantity, which is an N×1 matrix. After formula transformation, a new feature matrix X is obtained. s ;X s It arranges the 5-dimensional structural parameters of the motor into a feature sequence according to the geometric and physical topological order from stator to rotor and from radial to circumferential. s =[x1,x2,x3,x4,x5], utilizing BiGRU to correlate cross-dimensional features distributed along physical space, the spatial position dimension of the main magnetic flux closed magnetic circuit of the bidirectional magnetic field modulated arc motor is mapped to the sequence step dimension of the BiGRU network; the sequence step corresponds to the position of each key structure on the magnetic circuit, not the actual physical time step. The BiGRU bidirectional gated cyclic unit is used to learn the forward magnetic flux modulation coupling relationship between each geometric parameter on the magnetic circuit link and the reverse feedback coupling relationship between the rotor side and the stator side, thus setting the time step size to T, where T=C.

[0009] In this scheme, the bidirectional gated loop unit includes deep transient temporal response modeling, specifically: For the normalized dataset X s The process involves setting the number of hidden neurons to H=64, and at each time step t (t=1,2,3,4,5), the input scalar is the normalized feature value of the current step. x t Value, set the positive initial memory vector h 0=0, reverse initial memory vector h 6=0, which internally strictly performs the following matrix and vector-level gated iterative operations: (10); (11); (12); (13); in, It is the Sigmoid activation function. It is the hyperbolic tangent function; An operator that transforms a vector into a diagonal matrix; For the input weight vector, , As the bias vector, iterate sequentially to the endpoint t=C, extract the positive final state feature vector, and retain the positive short-time memory row vector at the final moment. ; , , , These represent the update gate, reset gate, candidate hidden state, and final hidden state, respectively.

[0010] Similarly, the reverse GRU cell element operation is performed, and the operation formula is basically the same as that of the forward operation. When iterating in reverse order to t=1, the reverse short-time memory row vector at the final moment is retained. Finally, the synthesized vector is obtained: (14); After the Dropout layer and two fully connected dense layers for mapping and dimensionality reduction, the intermediate layer neurons... Output layer , inactivation rate : (15); In the formula, , For the synthesized vector, The output after mapping is finally inversely normalized to obtain the predicted value: (16); in, This is the final predicted value. It is used for inverse normalization to predict the maximum and minimum values ​​in the set.

[0011] In this scheme, the extreme gradient model includes static nonlinear tree response modeling, specifically: In the bidirectional gated recurrent unit, while the neural network branches are running, the unnormalized original spatial feature matrix X is... raw Directly input into the XGBoost regressor, XGBoost sets the number of regression trees K=100, and the shrinking step size. , representing the learning rate; the maximum tree depth is 5, and the fitting function for the k-th additive decision tree with a maximum depth of 5 is . For any sample, the final prediction output is a composite matrix equation obtained by recursively summing the previous residuals by fitting them layer by layer through 100 regression decision trees, as shown below:

[0012] (17); in, This represents the final predicted output.

[0013] In this scheme, the weighting coefficients are obtained by normalizing the variance inverse. The multiple error indices are specifically as follows: The number of samples is N tr For a given electromagnetic index Calculate the BiGRU channel and XGBoost channel on the training set respectively. , (18); (19); Introducing a smoothing factor The combination coefficients are solved based on the inverse variance normalization. The final fusion prediction output of index m is denoted as: (20); Multiple evaluation metrics are introduced to compare and calculate the final combined predicted vector with the actual test labels, including the coefficient of determination R. 2 Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE): (twenty one); (twenty two); (twenty three); (twenty four); in, The total number of samples in the Test Set. : The actual simulated true label value of the i-th sample in the test set (the true value of the test set). The hybrid proxy model predicts the final combined output value of the i-th sample in the test set.

[0014] In this scheme, the Newton-Raphson algorithm iteratively optimizes the motor structure dimensions as follows: Using the central finite difference method, the step size of the small perturbation is... Approximate solution of the black box objective function first-order gradient vector With the second-order Hessian matrix The dimensions are respectively , : The approximation terms for the first-order gradient and the partial derivatives of the second-order Hessian matrix are as follows: (25); (26); In the formula: This represents a unit direction vector where the i-th dimension is 1 and all other elements are 0. Incremental damping solution: Introducing a regularization parameter Solve for the Newton-style hill-climbing increment vector. : (27); In the formula: I is The identity matrix; Single-step span truncation constraint: Limits the maximum single-step Euclidean distance adjustment span to no more than [missing information]. : (28); Armijo line search and update termination: This involves updating the state in conjunction with line search and boundary constraints, when the change measure satisfies... Stop iteration when the extreme value converges, and output the optimal set of structure parameters. ; In the formula: The vector of independent variables in the k-th iteration exhibits non-positive definiteness or singularity; The optimization objective of this invention is to maximize the overall performance index of the motor, and the specific objective function is as follows: (29); in: This represents the maximum electromagnetic performance. The average torque is given by , and THD is the current harmonic distortion rate. For torque pulsation, the specific calculation is as follows: (30); (31).

[0015] Where E1 is the fundamental effective value, E2, E3, ..., E n The effective values ​​of the 2nd, 3rd, ..., nth harmonics are T, respectively. out (t) represents the output torque, Max(T) out (t)), Min(T) out (t)), Avg(T) out (t) represents the maximum, minimum and average output torque, respectively.

[0016] A second aspect of the present invention also provides an efficient design optimization system for a bidirectional magnetic field modulated arc motor. The system includes a memory and a processor. The memory includes an efficient design optimization program for a bidirectional magnetic field modulated arc motor. When the efficient design optimization program for a bidirectional magnetic field modulated arc motor is executed by the processor, it implements the steps of the efficient design optimization method for a bidirectional magnetic field modulated arc motor as described in any of the preceding claims.

[0017] A third aspect of the present invention also provides a computer-readable storage medium comprising an efficient design optimization program for a bidirectional magnetic field modulated arc motor, wherein when the efficient design optimization program for a bidirectional magnetic field modulated arc motor is executed by a processor, it implements the steps of the efficient design optimization method for a bidirectional magnetic field modulated arc motor as described in any of the preceding claims.

[0018] This invention discloses an efficient design optimization method for bidirectional magnetic field modulation arc motors, fusing complementary BiGRU and XGBoost models. BiGRU can capture complex bidirectional parameter correlations and provides good local fitting for torque abrupt changes and extreme operating conditions; XGBoost has strong noise resistance and stable prediction under normal operating conditions. This invention calculates the error variance based on the prediction residuals of the training set, adaptively calculates the weighting coefficients using the inverse of the variance normalization, and linearly superimposes the outputs of the two models. The weights are automatically adapted to the dataset, achieving data-driven fusion and avoiding manual parameter tuning. After training, multiple error indices are used for performance verification, generating various types of visual charts to evaluate the model state. The prediction results are then integrated into the Newton-Raphson algorithm to complete iterative optimization of multiple motor dimensions. This invention combines the advantages of local fine fitting and global stable prediction, reducing single-point prediction abrupt changes, and providing stable and reliable global torque prediction, offering a high-precision surrogate model for multi-variable dimension optimization of arc motors. Attached Figure Description

[0019] Figure 1 This is a planar topology diagram of the bidirectional magnetic field modulation arc motor of the present invention; Figure 2 This is a three-dimensional structural schematic diagram of the bidirectional magnetic field modulation arc motor of the present invention; Figure 3 This is a schematic diagram of the cross winding phase sequence design of the bidirectional magnetic field modulation arc motor of the present invention. Figure 4 This is a flowchart illustrating the overall process of modeling and improving the Newton-Raphson optimization of the bidirectional gated loop unit-extreme gradient hybrid proxy model of this invention. Figure 5 A block diagram of an efficient design optimization system for a bidirectional magnetic field modulation arc motor according to the present invention is shown. Detailed Implementation

[0020] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0022] Figure 1 This is a planar topology diagram of the bidirectional magnetic field modulation arc motor of the present invention; Figure 2 This is a three-dimensional structural schematic diagram of the bidirectional magnetic field modulation arc motor of the present invention; Figure 3 This is a schematic diagram of the cross winding phase sequence design of the bidirectional magnetic field modulation arc motor of the present invention. Figure 4 This is a flowchart illustrating the overall process of modeling and improving the Newton-Raphson optimization of the bidirectional gated loop unit-extreme gradient hybrid proxy model of this invention. like Figure 1-4 As shown, the first aspect of the present invention provides an efficient design optimization method for a bidirectional magnetic field modulation arc motor, comprising: A topological model of a bidirectional magnetic field modulated arc motor is presented. This topological model consists of two unit motors, one in front and one behind. The two unit motors have identical structures. Each motor consists of a rotor tooth 1, a rotor yoke 2, a rotor permanent magnet 3, a stator yoke 4, a stator winding 5, a stator tooth permanent magnet 6, a stator yoke permanent magnet 7, a stator tooth 8, and a stator auxiliary tooth 9. The stators of the two motors adopt an integrated structure. The rotors of the two motors are staggered by one pole pitch. The permanent magnets in the stator teeth of the two motors are tangentially magnetized, while the permanent magnets in other positions are radially magnetized. The magnetization directions of the permanent magnets at corresponding positions in the two motors are opposite. Based on the topology model, a bidirectional gated cyclic unit-extreme gradient hybrid surrogate model based on variance inverse adaptive weighting is used to predict multiple performance indicators of the motor. The bidirectional gated cyclic unit is a deep learning model that treats motor parameters as sequential data, captures the complex bidirectional relationship between parameters, and fits torque mutation and local intervals of extreme working conditions. The impact of each structural parameter on motor performance is analyzed using an extreme gradient model, and the importance ranking of each structural parameter is output. The training and test sets are imported into the bidirectional gated recurrent unit-extreme gradient hybrid surrogate model for training and prediction. The error variance of the two models is calculated based on the prediction residuals. The weighting coefficients are obtained by normalizing the variance by the inverse. The prediction results of the two models are then linearly superimposed to obtain the final output. After training, a comprehensive performance evaluation was conducted. Multiple error metrics, including R², MSE, MAE, and MAPE, were statistically analyzed for both the single model and the hybrid surrogate model on the training and test sets. Simultaneously, parameter importance histograms, true value prediction comparison curves, fitting scatter plots, and residual distribution plots were generated. A comprehensive objective function was constructed, including predicted average torque, torque ripple, and harmonic distortion rate. Based on the hybrid surrogate model, the gradient and Hessian matrix of the objective function were calculated. The motor structure dimensions were iteratively optimized using the Newton-Raphson algorithm to obtain the final motor prediction performance metrics.

[0023] It is worth mentioning that in the bidirectional gated recurrent unit-extreme gradient hybrid surrogate model based on variance inverse adaptive weighting, multiple structural parameters such as the inner and outer pole arc coefficients of the motor and the thickness of the permanent magnet are coupled with each other, resulting in complex internal nonlinear relationships. It is difficult to balance local fitting accuracy and generalization ability under unknown operating conditions by using a single prediction model alone. Either the torque prediction deviation in extreme regions is large, or the prediction results fluctuate significantly under new operating conditions. Therefore, this invention selects two complementary basic models for collaborative modeling. The BiGRU bidirectional recurrent network, as a deep learning model, can treat motor parameters as sequential data and capture the complex bidirectional relationships between parameters. It has a fine fitting effect on local intervals such as torque mutation and extreme operating conditions, but it is prone to prediction bias when predicting unfamiliar operating conditions. The XGBoost gradient boosting tree, on the other hand, is a traditional machine learning model that can hierarchically explore the influence of each parameter on motor performance and output the importance ranking of each structural parameter, which is convenient for analyzing key dimensions of the motor in engineering. It has stable prediction and strong noise resistance under normal operating conditions, but the fitting accuracy is insufficient at places with drastic torque changes. To avoid the rigid fusion methods such as manually setting weights and simple averaging, this method does not rely on The algorithm relies on human parameter adjustment and directly calculates the error variance of the two models based on the prediction residuals of the training set. Following the logic that the larger the error variance, the lower the model's reliability, the weighting coefficients are obtained by normalizing the variance inverse. The prediction results of the two models are then linearly superimposed to obtain the final output. The weights are automatically adjusted when the motor operating condition dataset is changed. The entire process is completely data-driven. After the model training is completed, a comprehensive performance test is conducted. Multiple error indicators such as R², MSE, MAE, and MAPE of the single model and the fusion model are statistically analyzed on the training and test sets. At the same time, parameter importance bar charts, true value prediction comparison curves, fitting scatter plots, and residual distribution plots are generated to intuitively judge the model fitting status and error distribution patterns. Finally, the true torque of the test set and the fusion predicted torque are directly connected to the Newton-Raphson optimization algorithm to carry out multi-size iterative optimization of the motor. The fusion model integrates the dual advantages of BiGRU's fine capture of local torque changes and XGBoost's global stable prediction, greatly reducing the problem of single-point prediction mutations. The global torque prediction is more stable and reliable, and it can provide a high-precision, low-fluctuation surrogate response model for multi-variable size optimization of circumferential arc motors.

[0024] It can be understood here that the hybrid proxy model of the present invention is specifically a bidirectional gated recurrent unit-extreme gradient (BiGRU-XGBoost) hybrid proxy model, where BiGRU represents the bidirectional gated recurrent unit model and XGBoost represents the extreme gradient model, specifically, an extreme gradient boosting tree.

[0025] Table 1 below shows the design parameters of the fixed structure of the arc motor to be optimized in this embodiment of the invention: ; Table 1 According to an embodiment of the present invention, the topology model adopts an integrated stator design, specifically: The front and rear stator segments have no relative displacement and share a common winding structure. The stator windings are arranged in a cross-winding configuration, with the connection phase sequence being ACB, BCA, CAB. The bidirectional magnetic field modulation arc motor adopts a modular stator structure composed of multiple identical unit motors. The mechanical slot pitch angle of 12° under a fully circular 30-slot structure is used as the reference, i.e., the geometric angle corresponding to a single slot is used as the reference. The circumferential physical distance between two adjacent unit motors satisfies S1 and S2. By introducing a reverse compensation angle of 24° equivalent to two mechanical slot pitch angles in the spatial physical arrangement, and coordinating with the circumferential cyclic misalignment of the phase sequence within each unit motor, the induced electromotive force of the in-phase windings of each unit motor remains aligned in electrical angle even under the premise of spatial physical misalignment. S1 and S2 are specifically calculated as follows: (1); in, denoted as the physical angle of the rotor's pole pitch, and k is a preset positive integer.

[0026] According to an embodiment of the present invention, the bidirectional magnetic field modulation arc motor includes a pole-slot mating design, specifically: Taking 6 slots as the stator slot number for a single unit motor, and considering both the rotor tooth number Nr and the stator slot number Ns, the following formula should be satisfied: (2); To further derive the rotor tooth count, the cogging effect of the front and rear motors is considered. The pole-slot fit of the motor has a significant impact on the cogging torque, thus affecting the motor's performance stability. The arc motor consists of two motors staggered 180 degrees in the rotor structure. ° The equation is composed of / p, where p is the number of pole pairs. From this, the formulas for the cogging torque of the front and rear motors are derived: (3); in, Rotor position angle, The total energy stored in the air gap. V: Air permeability. and These are the magnetomotive force of the permanent magnet and the air gap permeability, respectively; considering only the stator permanent magnet and the rotor permanent magnet, the cogging torques are as follows: (4); (5); Among them, R si ,R ro : These are the inner radius of the stator and the outer radius of the rotor, respectively; L: axial length of the motor core; N s N r These refer to the number of stator slots and rotor poles (i.e., the number of rotor teeth) of a single unit motor. , , All are corresponding magnetic permeability functions; For the cogging torque in equations (4) and (5) to exist effectively, the orders m and n of the Fourier expansion terms must satisfy the spatial periodic matching condition: Then m and n are determined by the following formula: (6); The greatest common divisor; The front motor and the rear motor have a mechanical misalignment angle of 180° / p in their rotor geometry. The cogging torque of the rear motor is shown below: (7); (8); When m and n are odd numbers, the odd harmonics of the cogging torque generated by the front motor and the rear motor are equal in magnitude and opposite in phase, thus canceling each other out when they are superimposed in space. , , , , respectively represent the cogging torque of a surface-mounted permanent magnet motor, the cogging torque of a built-in permanent magnet motor, the rear cogging torque of a surface-mounted permanent magnet motor, and the rear cogging torque of a built-in permanent magnet motor. , These represent the mth harmonic amplitude of the air gap magnetomotive force of a surface-mounted permanent magnet motor and the nth harmonic amplitude of the air gap magnetomotive force of a built-in permanent magnet motor, respectively.

[0027] It should be noted that if the number of slots is too large, the cross-sectional area of ​​a single slot will be compressed, which not only increases the difficulty of wiring and winding of the armature winding, but also worsens the local heat dissipation conditions of the stator. Conversely, if the number of slots is too small, the ability of the winding to suppress magnetic field harmonics will be significantly reduced, making it difficult to effectively cancel the even-order harmonic components in the flux linkage of a single coil. Through electromagnetic comprehensive optimization analysis, the three-unit arc permanent magnet motor proposed in this invention ultimately determined to have 6 slots as the stator slot number for a single unit motor. In the cogging torque calculation process, when Nr is taken as 10, odd-order harmonics can be effectively eliminated, improving the stability of the motor.

[0028] According to an embodiment of the present invention, the structural parameters are normalized, specifically as follows: (9) Among them, X raw X represents the original dataset. mim X max , representing the maximum and minimum values ​​respectively, X raw It is an N×C matrix, where N represents the amount of sample input space, C is the number of motor structural parameters, and Y represents the output quantity, which is an N×1 matrix. After formula transformation, a new feature matrix X is obtained. s ;X s It arranges the 5-dimensional structural parameters of the motor into a feature sequence according to the geometric and physical topological order from stator to rotor and from radial to circumferential. s =[x1,x2,x3,x4,x5], using BiGRU to obtain cross-dimensional feature associations distributed along the physical space, thus setting the time step to T, where T=C.

[0029] Here, the present invention adopts an adaptive hybrid agent model, including a BiGRU neural network branch and an XGBoost tree model. The two basic learning models run separately in their respective spaces, and the two methods are combined by the inverse variance weighting method, which achieves better prediction results than a single prediction model.

[0030] It should be noted that when building a motor model based on a hybrid surrogate model, the dimensions of multiple structural parameters must be considered first. The dimensions used for the motor's structural parameters include angle, length, dimensionless coefficients, etc. When using different dimensions, the numerical differences can cause large fluctuations in the motor prediction results, making it impossible to truly measure the actual performance contribution of the corresponding motor parameters to the motor performance. Therefore, when building the surrogate model, a numerical normalization method is used to compress the key structural parameters to between 0 and 1. The above is the specific calculation process for normalization.

[0031] Table 2 below shows the range of structural parameters and factor levels for the experimental samples of this invention: ; Table 2 According to an embodiment of the present invention, the bidirectional gated cyclic unit includes deep transient temporal response modeling, specifically: For the normalized dataset X s The process involves setting the number of hidden neurons to H=64, and at each time step t (t=1,2,3,4,5), the input scalar is the normalized feature value of the current step. x t Value, set the positive initial memory vector h 0=0, reverse initial memory vector h 6=0. Internally, it strictly performs the following matrix and vector-level gated iterative operations: (10); (11); (12); (13); in, It is the Sigmoid activation function. It is the hyperbolic tangent function; An operator that transforms a vector into a diagonal matrix; For the input weight vector, , As the bias vector, iterate sequentially to the endpoint t=C, extract the positive final state feature vector, and retain the positive short-time memory row vector at the final moment. ; , , , These represent the update gate, reset gate, candidate hidden state, and final hidden state, respectively.

[0032] Similarly, the reverse GRU cell element operation is performed, and the operation formula is basically the same as that of the forward operation. When iterating in reverse order to t=1, the reverse short-time memory row vector at the final moment is retained. Finally, the synthesized vector is obtained: (14); After the Dropout layer and two fully connected dense layers for mapping and dimensionality reduction, the intermediate layer neurons... Output layer , inactivation rate : (15); In the formula, , For the synthesized vector, The output after mapping is finally inversely normalized to obtain the predicted value: (16); in, This is the final predicted value. It is used for inverse normalization to predict the maximum and minimum values ​​in the set.

[0033] According to an embodiment of the present invention, the extreme gradient model includes static nonlinear tree response modeling, specifically: In the bidirectional gated recurrent unit, while the neural network branches are running, the unnormalized original spatial feature matrix X is... raw Directly input into the XGBoost regressor, XGBoost sets the number of regression trees K=100, and the shrinking step size. , representing the learning rate; the maximum tree depth is 5, and the fitting function for the k-th additive decision tree with a maximum depth of 5 is . For any sample, the final prediction output is a composite matrix equation obtained by recursively summing the previous residuals by fitting them layer by layer through 100 regression decision trees, as shown below: (17); in, This represents the final predicted output.

[0034] According to an embodiment of the present invention, the weighting coefficients are obtained by normalizing the variance inverse, and the multiple error indices are specifically: The number of samples is N tr For a given electromagnetic index Calculate the BiGRU channel and XGBoost channel on the training set respectively. , (18); (19); Introducing a smoothing factor The combination coefficients are solved based on the inverse variance normalization. The final fusion prediction output of index m is denoted as: (20); Multiple evaluation metrics are introduced to compare and calculate the final combined predicted vector with the actual test labels, including the coefficient of determination R. 2 Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE): (twenty one); (twenty two); (twenty three); (twenty four); in, The total number of samples in the Test Set. : The actual simulated true label value of the i-th sample in the test set (the true value of the test set). The hybrid proxy model predicts the final combined output value of the i-th sample in the test set.

[0035] It should be noted that previous hybrid proxy models often used manually set fixed weights or simple arithmetic averages, lacking the flexibility of data-driven approaches; or they relied solely on a single model, which easily led to significant fluctuations in prediction accuracy. This invention integrates a deep learning model (BiGRU) adept at capturing local mutations with a gradient boosting tree (XGBoost) known for its globally stable predictions and strong noise resistance. The method of this invention is entirely data-driven; the weights are automatically updated when different electromagnetic index datasets are used, significantly improving the model's prediction accuracy and robustness.

[0036] According to an embodiment of the present invention, the Newton-Raphson algorithm iteratively optimizes the motor structure dimensions as follows: Using the central finite difference method, the step size of the small perturbation is... Approximate solution of the black box objective function first-order gradient vector With the second-order Hessian matrix The dimensions are respectively , : The approximation terms for the first-order gradient and the partial derivatives of the second-order Hessian matrix are as follows: (25); (26); In the formula: This represents a unit direction vector where the i-th dimension is 1 and all other elements are 0. Incremental damping solution: Introducing a regularization parameter Solve for the Newton-style hill-climbing increment vector. : (27); In the formula: I is The identity matrix; Single-step span truncation constraint: Limits the maximum single-step Euclidean distance adjustment span to no more than [missing information]. : (28); Armijo line search and update termination: This involves updating the state in conjunction with line search and boundary constraints, when the change measure satisfies... Stop iteration when the extreme value converges, and output the optimal set of structure parameters. ; In the formula: The vector of independent variables in the k-th iteration exhibits non-positive definiteness or singularity; The optimization objective of this invention is to maximize the overall performance index of the motor, and the specific objective function is as follows: (29); in: This represents the maximum electromagnetic performance. The average torque is given by , and THD is the current harmonic distortion rate. For torque pulsation, the specific calculation is as follows: (30); (31).

[0037] Where E1 is the fundamental effective value, E2, E3, ..., E n The effective values ​​of the 2nd, 3rd, ..., nth harmonics are T, respectively. out (t) represents the output torque, Max(T) out (t)), Min(T) out (t)), Avg(T) out (t) represents the maximum, minimum and average output torque, respectively.

[0038] It should be noted that the Newton-Raphson algorithm, or simply Newton's method, is a classic second-order numerical iterative optimization algorithm. Its core idea is to use the second-order Taylor expansion to locally approximate the nonlinear objective function, iteratively approaching the function's extreme points. Because the surrogate response surface of a neural network + tree model is a "non-analytical black box," directly calculating the second-order Hessian matrix using the standard Newton method is extremely prone to algorithm divergence and out-of-bounds errors due to matrix singularity or non-positive definiteness. This invention introduces a damping adjustment regularization matrix into the Hessian matrix when solving for the iterative increment, rewriting the iterative equation as follows: By dynamically adjusting the damping coefficient to correct the matrix curvature and limiting the maximum Euclidean distance of the single-step independent variable adjustment span to no more than 0.02, combined with line search technology, the strict monotonically increasing climb of the comprehensive quality score is ensured, avoiding divergence or overstepping of the Newton method on nonlinear manifold surfaces.

[0039] In this scheme, the motor structure and operating parameters are expressed as follows: .

[0040] Table 3 below shows a list of 1024 datasets and their electromagnetic response results generated by the present invention through experiments: ; Table 3 Table 4 below shows the results of four accuracy evaluation metrics of the BiGRU-XGBoost hybrid proxy model of this invention on the test set: ; Table 4 Table 5 below shows the comparison results of the motor structural dimensional parameters before and after using the improved Newton's method for closed-loop optimization in this invention: ; Table 5 Figure 5 A block diagram of an efficient design optimization system for a bidirectional magnetic field modulation arc motor according to the present invention is shown.

[0041] A second aspect of the present invention also provides a high-efficiency design optimization system for a bidirectional magnetic field modulation arc motor. The system includes a memory and a processor. The memory includes a high-efficiency design optimization program for the bidirectional magnetic field modulation arc motor. When executed by the processor, the high-efficiency design optimization program for the bidirectional magnetic field modulation arc motor performs the following steps: When the system is running, it can implement one or more steps of the efficient design optimization method for bidirectional magnetic field modulation arc motors described above.

[0042] A third aspect of the present invention also provides a computer-readable storage medium comprising an efficient design optimization program for a bidirectional magnetic field modulated arc motor, wherein when the efficient design optimization program for a bidirectional magnetic field modulated arc motor is executed by a processor, it implements the steps of the efficient design optimization method for a bidirectional magnetic field modulated arc motor as described in any of the preceding claims.

[0043] This invention addresses the inherent use of a front-and-rear unit combination and an integrated stator design in bidirectional magnetic field modulated arc motors. It constructs a BiGRU-XGBoost hybrid surrogate model based on inverse variance adaptive weighting. This model combines the advantages of deep learning (BiGRU) in capturing local mutations and complex bidirectional relationships between parameters with the global prediction stability, strong noise resistance, and parameter importance assessment capabilities of traditional machine learning (XGBoost). Furthermore, it abandons the manually set weighting method, directly calculating the error variance based on the prediction residuals from the training set, and achieving automatic adaptive weight adjustment through inverse variance normalization. This significantly improves the prediction accuracy and generalization ability for multi-field output indicators.

[0044] In terms of parameter optimization and multi-objective optimization algorithms, this invention proposes a multi-size parameter closed-loop optimization mechanism based on an improved Newton-Raphson algorithm. This method abandons random initial value generation and instead uses the geometric mean center point of the feature space of the historical training set as the iteration starting point. Addressing the black-box characteristic of the hybrid surrogate model lacking analytical derivatives, it approximates the gradient and Hessian matrix using the finite difference method. By introducing a damping adjustment regularization matrix into the Hessian matrix and limiting the single-step iteration span, it solves the matrix singularity and iteration divergence problems, achieving fast and high-precision convergent optimization with the objectives of maximizing average torque and minimizing torque pulsation and harmonic distortion (THD).

[0045] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0046] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0047] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0048] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0049] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0050] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A highly efficient design optimization method for bidirectional magnetic field modulation arc motors, characterized in that, include: The topology model of the bidirectional magnetic field modulated arc motor is composed of two unit motors, front and rear. The two unit motors have the same structure. The front and rear motors are composed of rotor teeth (1), rotor yoke (2), rotor permanent magnet (3), stator yoke (4), stator winding (5), stator tooth permanent magnet (6), stator yoke permanent magnet (7), stator teeth (8), and stator auxiliary teeth (9). The stators of the front and rear motors adopt an integrated structure. The rotors of the front and rear motors are staggered by one pole pitch. The permanent magnets of the stator teeth of the front and rear motors are tangentially magnetized, and the permanent magnets in other positions are radially magnetized. The magnetization directions of the permanent magnets at corresponding positions of the front and rear motors are opposite. Based on the topology model, a bidirectional gated cyclic unit-extreme gradient hybrid surrogate model based on variance inverse adaptive weighting is used to predict multiple performance indicators of the motor. The bidirectional gated cyclic unit is a deep learning model that treats motor parameters as sequential data, captures the complex bidirectional relationship between parameters, and fits torque mutation and local intervals of extreme working conditions. The impact of each structural parameter on motor performance is analyzed using an extreme gradient model, and the importance ranking of each structural parameter is output. The training and test sets are imported into the bidirectional gated recurrent unit-extreme gradient hybrid surrogate model for training and prediction. The error variance of the two models is calculated based on the prediction residuals. The weighting coefficients are obtained by normalizing the variance by the inverse. The prediction results of the two models are then linearly superimposed to obtain the final output. After training, a comprehensive performance evaluation was conducted. Multiple error metrics, including R², MSE, MAE, and MAPE, were statistically analyzed for both the single model and the hybrid surrogate model on the training and test sets. Simultaneously, parameter importance histograms, true value prediction comparison curves, fitting scatter plots, and residual distribution plots were generated. A comprehensive objective function was constructed, including predicted average torque, torque ripple, and harmonic distortion rate. Based on the hybrid surrogate model, the gradient and Hessian matrix of the objective function were calculated. The motor structure dimensions were iteratively optimized using the Newton-Raphson algorithm to obtain the final motor prediction performance metrics.

2. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 1, characterized in that, The aforementioned topology model employs an integrated stator design, specifically: The front and rear stator segments have no relative displacement and share a common winding structure. The stator windings are arranged in a cross-winding configuration, with the connection phase sequence being ACB, BCA, CAB. The bidirectional magnetic field modulation arc motor adopts a modular stator structure composed of multiple identical unit motors. The mechanical slot pitch angle of 12° under a fully circular 30-slot structure is used as the reference, i.e., the geometric angle corresponding to a single slot is used as the reference. The circumferential physical distance between two adjacent unit motors satisfies S1 and S2. By introducing a reverse compensation angle of 24° equivalent to two mechanical slot pitch angles in the spatial physical arrangement, and coordinating with the circumferential cyclic misalignment of the phase sequence within each unit motor, the induced electromotive force of the in-phase windings of each unit motor remains aligned in electrical angle even under the premise of spatial physical misalignment. S1 and S2 are specifically calculated as follows: （1）； in, denoted as the physical angle of the rotor's pole pitch, and k is a preset positive integer.

3. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 2, characterized in that, The bidirectional magnetic field modulated arc motor includes a pole-slot matching design, specifically: Taking 6 slots as the stator slot number for a single unit motor, and considering both the rotor tooth number Nr and the stator slot number Ns, the following formula should be satisfied: （2）； To further derive the rotor tooth count, the cogging effect of the front and rear motors is considered. The pole-slot fit of the motor has a significant impact on the cogging torque, thus affecting the motor's performance stability. The arc motor consists of two motors staggered 180 degrees in the rotor structure. ° The equation is composed of / p, where p is the number of pole pairs. From this, the formulas for the cogging torque of the front and rear motors are derived: （3）； in, Rotor position angle, The total energy stored in the air gap. Air permeability, V: air gap volume and These are the magnetomotive force of the permanent magnet and the air gap permeability, respectively; considering only the stator permanent magnet and the rotor permanent magnet, the cogging torques are as follows: （4）； （5）； Among them, R si ,R ro : These are the inner radius of the stator and the outer radius of the rotor, respectively; L: axial length of the motor core; N s N r These refer to the number of stator slots and the number of rotor poles (i.e., rotor teeth) of a single unit motor. , , All are corresponding magnetic permeability functions; For the cogging torque in equations (4) and (5) to exist effectively, the orders m and n of the Fourier expansion terms must satisfy the spatial periodic matching condition: Then m and n are determined by the following formula: （6）； The greatest common divisor; （7）； （8）； When m and n are odd numbers, the odd-order harmonics of the cogging torque generated by the front motor and the rear motor are equal in magnitude and opposite in phase, thus canceling each other out when they are superimposed in space. , , , , respectively represent the cogging torque of a surface-mounted permanent magnet motor, the cogging torque of a built-in permanent magnet motor, the rear cogging torque of a surface-mounted permanent magnet motor, and the rear cogging torque of a built-in permanent magnet motor. , These represent the mth harmonic amplitude of the air gap magnetomotive force of a surface-mounted permanent magnet motor and the nth harmonic amplitude of the air gap magnetomotive force of a built-in permanent magnet motor, respectively.

4. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 3, characterized in that, The structural parameters are normalized as follows: （9） Among them, X raw X represents the original dataset. max X min , representing the maximum and minimum values ​​respectively, X raw It is an N×C matrix, where N represents the amount of sample input space, C is the number of motor structural parameters, and Y represents the output quantity, which is an N×1 matrix. After formula transformation, a new feature matrix X is obtained. s ;X s It arranges the 5-dimensional structural parameters of the motor into a feature sequence according to the geometric and physical topological order from stator to rotor and from radial to circumferential. s =[x1,x2,x3,x4,x5], using BiGRU to obtain cross-dimensional feature associations distributed along the physical space, the spatial position dimension of the main magnetic flux closed magnetic circuit of the bidirectional magnetic field modulated arc motor is mapped to the sequence step dimension of the BiGRU network; the sequence step corresponds to the position of each key structure on the magnetic circuit, not the actual physical time step. The BiGRU bidirectional gated cyclic unit is used to learn the positive magnetic flux modulation coupling relationship between each geometric parameter on the magnetic circuit link and the reverse feedback coupling relationship between the rotor side and the stator side, so that the time step is set to T, where T=C.

5. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 4, characterized in that, The bidirectional gated cyclic unit includes deep transient temporal response modeling, specifically: For the normalized dataset X s The process involves setting the number of hidden neurons to H=64, and in each time step t, the input scalar is the normalized feature value of the current step. x t Value, set the positive initial memory vector h 0=0, reverse initial memory vector h 6=0, which internally strictly performs the following matrix and vector-level gated iterative operations: （10）； （11）； （12）； （13）； in, It is the Sigmoid activation function. It is the hyperbolic tangent function; An operator that transforms a vector into a diagonal matrix; For the input weight vector, , As the bias vector, iterate sequentially to the endpoint t=C, extract the positive final state feature vector, and retain the positive short-time memory row vector at the final moment. ; , , , These represent the updated door, reset door, candidate hidden state, and final hidden state, respectively. Similarly, the reverse GRU cell element operation is performed, and the operation formula is basically the same as that of the forward operation. When iterating in reverse order to t=1, the reverse short-time memory row vector at the final time is retained. Finally, the synthesized vector is obtained: （14）； After the Dropout layer and two fully connected dense layers for mapping and dimensionality reduction, the intermediate layer neurons... Output layer , inactivation rate : （15）； In the formula, , For the synthesized vector, The output after mapping is finally inversely normalized to obtain the predicted value: （16）； in, This is the final predicted value. It is used for inverse normalization to predict the maximum and minimum values ​​in the set.

6. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 5, characterized in that, The extreme gradient model includes static nonlinear tree response modeling, specifically: In the bidirectional gated recurrent unit, while the neural network branches are running, the unnormalized original spatial feature matrix X is... raw Directly input into the XGBoost regressor, XGBoost sets the number of regression trees K=100, and the shrinking step size. , representing the learning rate; the maximum tree depth is 5, and the fitting function for the k-th additive decision tree with a maximum depth of 5 is . For any sample, the final prediction output is a composite matrix equation obtained by recursively summing the previous residuals by fitting them layer by layer through 100 regression decision trees, as shown below: （17）； in, This represents the final predicted output.

7. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 6, characterized in that, The weighted coefficients are obtained by normalizing the variance using the inverse. The specific multiple error indices are as follows: The number of samples is N tr For a given electromagnetic index Calculate the BiGRU channel and XGBoost channel on the training set respectively. , （18）； （19）； Introducing a smoothing factor The combination coefficients are solved based on the inverse variance normalization. The final fusion prediction output of index m is denoted as: （20）； Multiple evaluation metrics are introduced to compare and calculate the final combined predicted vector with the actual test labels, including the coefficient of determination R. 2 Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE): （21）； （22）； （23）； （24）； in, The total number of samples in the Test Set. : The actual simulated true label value of the i-th sample in the test set. The hybrid proxy model predicts the final combined output value of the i-th sample in the test set.

8. The efficient design optimization method for a bidirectional magnetic field modulation arc motor according to claim 7, characterized in that, The specific method for iteratively optimizing the motor structure dimensions using the Newton-Raphson algorithm is as follows: Using the central finite difference method, the step size of the small perturbation is... Approximate solution of the black box objective function first-order gradient vector With the second-order Hessian matrix The dimensions are respectively , : The approximation terms for the first-order gradient and the partial derivatives of the second-order Hessian matrix are as follows: （25）； （26）； In the formula: This represents a unit direction vector where the i-th dimension is 1 and all other elements are 0. Incremental damping solution: Introducing a regularization parameter Solve for the Newton-style hill-climbing increment vector. : （27）； In the formula: I is The identity matrix; Single-step span truncation constraint: Limits the maximum single-step Euclidean distance adjustment span to no more than [missing information]. : （28）； Armijo line search and update termination: This involves updating the state in conjunction with line search and boundary constraints, when the change measure satisfies... Stop iteration when the extreme value converges, and output the optimal set of structure parameters. ; In the formula: Let be the vector of independent variables in the k-th iteration. For a second-order Hessian matrix that may exhibit non-positive definiteness or singularity at a non-convex nonlinear manifold; The optimization objective is to maximize the overall performance index of the motor, and the specific objective function is as follows: （29）； in: This represents the maximum electromagnetic performance. The average torque is given by , and THD is the current harmonic distortion rate. For torque pulsation, the specific calculation is as follows: （30）； （31）； Where E1 is the fundamental effective value, E2, E3, ..., E n The effective values ​​of the 2nd, 3rd, ..., nth harmonics are T, respectively. out (t) represents the output torque, Max(T) out (t)), Min(T) out (t)), Avg(T) out (t) represents the maximum, minimum and average output torque, respectively.

9. A high-efficiency design optimization system for bidirectional magnetic field modulation arc motors, characterized in that, The system includes a memory and a processor. The memory includes an efficient design optimization program for a bidirectional magnetic field modulated arc motor. When the processor executes the efficient design optimization program for the bidirectional magnetic field modulated arc motor, it implements the steps of the efficient design optimization method for a bidirectional magnetic field modulated arc motor as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes an efficient design optimization program for a bidirectional magnetic field modulated arc motor. When the efficient design optimization program for a bidirectional magnetic field modulated arc motor is executed by a processor, it implements the steps of the efficient design optimization method for a bidirectional magnetic field modulated arc motor as described in any one of claims 1 to 8.

Images