Bayesian active learning method for multi-objective optimization of electrical machines based on physical prior guidance

Abstract

The application provides a kind of motor multi-objective optimization method based on physical priori guidance bayesian active learning, comprising: constructing low-fidelity analytical model and high-fidelity finite element model of linear actuation system motor, defining initial design space;Using low-fidelity model large sample calculation and sensitivity analysis, eliminate low sensitivity variable to determine key design variable;Sampling key variable to obtain high and low fidelity response value, eliminate working condition difference by physical feature reconstruction and calculate nonlinear residual;Constructing heterogeneous kriging model, embedding low-fidelity benchmark into trend item for fundamental wave dominant index and learning residual, using pure data driving for high harmonic dominant index;Optimizing proxy model using multi-objective algorithm, obtaining preliminary Pareto front solution set to establish active sampling mechanism, verifying characteristic solution by high-fidelity model, if not meeting convergence condition, updating model as incremental sample and re-optimizing until converging to output optimal scheme.

Description

Technical Field

[0001] This invention relates to a robotic arm actuation system, and more particularly to a Bayesian active learning method for multi-objective optimization of motors based on physical prior guidance. Background Technology

[0002] As a crucial component of high-end equipment, integrated linear actuation systems require their core drive motors to deliver extremely high explosive thrust and precise motion control within a very small installation envelope. Unlike traditional industrial motors, the design of such motors faces severe challenges: in pursuit of ultimate power density, the motor core often operates in a deep magnetic saturation region, resulting in extremely strong nonlinear characteristics of the magnetic circuit; at the same time, there is an inherent physical contradiction between high thrust and low pulsation and high efficiency.

[0003] The existing motor optimization design methods mainly use analytical models, finite element models, and data-driven proxy models. However, these models have the following shortcomings: (1) Relying solely on analytical models, although the calculation speed is fast, it is based on linear assumptions and cannot accurately calculate the torque output and cogging effect under deep saturation, resulting in large design errors. (2) Relying solely on finite element models, the calculation accuracy is high, but the single simulation takes too long. If combined with genetic algorithms for global optimization, it often requires thousands of calculations, and the design cycle can last for several weeks, which is difficult to meet the needs of rapid iteration in engineering. (3) Conventional data-driven proxy models are "black box" models that rely entirely on data fitting. Under small sample conditions, the model is prone to overfitting or underfitting. Moreover, due to the lack of physical mechanism constraints, the model is prone to predicting false optimal solutions that violate physical common sense in unsampled areas. In addition, the following problems also exist in the design of high power density permanent magnet motors for integrated linear actuation systems: the traditional equivalent magnetic circuit method cannot accurately calculate the nonlinear performance under deep magnetic saturation, while the high-fidelity finite element method takes too long to calculate and cannot support the thousands of iterations required by multi-objective genetic algorithms. Summary of the Invention

[0004] The purpose of this invention is to provide a Bayesian active learning method for multi-objective optimization of motors based on physical prior guidance, comprising the following steps: Step S100: Construct a multi-fidelity physical model for the motor of the linear actuation system. The multi-fidelity physical model includes a low-fidelity analytical model with fast calculation speed and a high-fidelity finite element model with high calculation accuracy, and define the initial design space. Step S200: Use the low-fidelity analytical model to perform large-sample calculations, perform sensitivity analysis on the initial design variables, eliminate low-sensitivity variables to achieve dimensionality reduction of the design space, and determine the key design variables. Step S300: Perform dual-fidelity sampling on key design variables to obtain low-fidelity response values ​​and high-fidelity true values ​​respectively; eliminate the working condition differences between models through physical feature reconstruction, and calculate the residual between the high-fidelity true value and the reconstructed low-fidelity baseline value; Step S400: Construct a physical prior-guided heterogeneous Kriging proxy model. For fundamental-wave dominant performance indicators, embed the low-fidelity benchmark value into the trend term of the Kriging model and train the model to learn the residuals. For higher-harmonic-dominated performance indicators, directly use high-fidelity data to construct a pure data-driven Kriging model. Step S500: A multi-objective optimization algorithm is used to perform global optimization on the heterogeneous Kriging proxy model to obtain a preliminary Pareto front solution set; Step S600: Establish an active sampling closed-loop feedback mechanism based on the sampling strategy of prediction mean and uncertainty. Select the feature solution in the Pareto front and substitute it back into the high-fidelity finite element model for verification. If the prediction error does not meet the convergence condition, use the verification data as incremental samples to update the surrogate model and re-optimize until the convergence condition is met, and output the optimal design scheme.

[0005] Furthermore, the low-fidelity analytical model described in S100 is an equivalent magnetic circuit model constructed based on Hopkinson's law; the high-fidelity finite element model is a finite element simulation model constructed based on two-dimensional transient electromagnetic field theory; both share the same set of geometric parameter variables.

[0006] Furthermore, the sensitivity analysis described in S200 specifically employs statistical correlation analysis, and its calculation formula is as follows: (2) in, The total number of samples, For initial design variables, To optimize the objective; based on The absolute value of the variables is used to sort and filter them.

[0007] Furthermore, the specific calculation method for the physical feature reconstruction described in step S300 is as follows: The rated torque calculated from the low-fidelity analytical model and the corresponding rated current And the constant excitation current set by the high-fidelity finite element model Using the principle of torque constant consistency, the reconstructed physical prior reference torque is calculated. : (3).

[0008] Furthermore, the construction strategy for the heterogeneous kriging proxy model described in S400 includes: For the average torque and efficiency indices, the prediction model is expressed as the sum of the physical prior reference torque and the random residuals. (4) For the torque ripple index, the prediction model represents a purely stochastic process. (5) in, and These are Gaussian random processes under different strategies. μ It is a constant.

[0009] Furthermore, the specific steps of the active sampling closed-loop feedback mechanism described in step S600 include: Select several uniformly distributed characteristic solutions from the Pareto front solution set based on the crowding distance; The true values ​​of the eigenvalues ​​are calculated using a high-fidelity finite element model, and the relative error between the predicted and true values ​​of the heterogeneous kriging surrogate model is also calculated. ; If the maximum relative error If the value exceeds the preset convergence threshold, the feature solution and its true value are added to the sample library, triggering the iterative loop from steps S400 to S600; if the maximum relative error... If the value is less than or equal to the preset convergence threshold, the optimization is considered to have converged.

[0010] Furthermore, the optimal design scheme decision in step S600 also includes: normalizing each optimization objective in the Pareto front solution set, calculating the Euclidean distance from each non-dominated solution to the ideal utopia point, and selecting the solution with the smallest distance as the final motor design scheme.

[0011] Compared with the prior art, the present invention has the following advantages: (1) The present invention proposes a "physical prior guidance" strategy, which uses a low-cost equivalent magnetic circuit model to provide a physical trend benchmark, so that the Gaussian process regression model only needs to fit the nonlinear residuals, effectively solving the technical pain point of insufficient prediction accuracy of the traditional pure data-driven proxy model under small sample conditions. Compared with directly calling high-fidelity finite element for multi-objective optimization, this method shortens the calculation time by more than 90%, and achieves an excellent balance between prediction accuracy and calculation efficiency. (2) In view of the technical problem that motor torque pulsation is difficult to accurately calculate by magnetic circuit method, the present invention innovatively adopts a differentiated heterogeneous modeling strategy, that is, physical fusion modeling is performed on average torque and efficiency, and pure data-driven modeling is performed on torque pulsation, thereby effectively avoiding noise interference introduced by erroneous physical priors and significantly improving the overall robustness of multi-objective collaborative optimization. (3) To overcome the shortcomings of traditional surrogate model open-loop optimization which is prone to deviating from physical reality, this invention introduces a Bayesian active sampling closed-loop feedback mechanism. Through high-fidelity finite element verification, the local deviation of the model near the Pareto front is dynamically corrected, which effectively avoids the "false optimality" phenomenon caused by model prediction distortion and ensures that the final output design scheme has high engineering reliability and physical authenticity. (4) This invention achieves scientific dimensionality reduction of the design space through pre-sensitivity analysis of low-fidelity models, avoiding the ineffective consumption of computing power on secondary variables; and in the final scheme selection stage, the evaluation standard based on the distance of ideal utopia points is used for objective decision-making, overcoming the blindness and subjectivity of traditional manual selection, making the final high power density motor design result more scientific and reasonable. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0013] Figure 2 This is a schematic diagram of the finite element model and RMxprt modeling of the permanent magnet synchronous motor of the present invention.

[0014] Figure 3 This is a schematic diagram of the parametric model of the permanent magnet synchronous motor of the present invention.

[0015] Figure 4 This is a schematic diagram of the sensitivity analysis results of the present invention.

[0016] Figure 5 This is a schematic diagram of the test results of the Kriging proxy model of the present invention.

[0017] Figure 6 This is a schematic diagram of the Pareto front, which is the optimization target of this invention.

[0018] Figure 7 This is a schematic diagram comparing the performance of the initial motor and the optimized motor of the present invention. Detailed Implementation

[0019] Please combine Figures 1 to 7 A Bayesian active learning method for multi-objective optimization of motors based on physical prior guidance includes: Step S1: Construct a multi-fidelity physical model for the motor of the linear actuation system; Step S2: Use the low-fidelity analytical model to perform large-sample calculations, conduct sensitivity analysis on the initial design variables, eliminate low-sensitivity variables to achieve dimensionality reduction of the design space, and determine the key design variables. Step S3: Perform dual-fidelity sampling on key design variables to obtain low-fidelity response values ​​and high-fidelity true values ​​respectively; calculate the residual between the high-fidelity true value and the reconstructed low-fidelity baseline value. Step S4: Construct a physical prior-guided heterogeneous Kriging surrogate model and train the model to learn residuals; for performance indicators dominated by higher harmonics, directly use high-fidelity data to construct a pure data-driven Kriging model. Step S5: Use a multi-objective optimization algorithm to perform global optimization on the heterogeneous Kriging proxy model to obtain a preliminary Pareto front solution set; Step S6: Establish an active sampling closed-loop feedback mechanism based on the sampling strategy of prediction mean and uncertainty. Select the feature solution in the Pareto front and substitute it back into the high-fidelity finite element model for verification. If the prediction error does not meet the convergence condition, use the verification data as incremental samples to update the surrogate model and re-optimize until the convergence condition is met, and output the optimal design scheme.

[0020] This embodiment takes a frameless torque motor in an integrated linear actuation system as an example. The main structural parameters of the motor are shown in Table 1.

[0021] Table 1 Main structural parameters of permanent magnet synchronous motor Step S1: Construct a multi-fidelity parametric physical model. This includes the following steps.

[0022] Step S11, construct a low-fidelity equivalent magnetic circuit model: Utilize the Ansys RMxprt module to construct an analytical magnetic circuit model of the motor. This model, based on Hopkinson's law, equates the stator teeth, stator yoke, air gap, permanent magnets, and rotor yoke of the motor to a nonlinear reluctance network; calculate the main magnetic flux. The specific method is as follows (1) in, The magnetomotive force provided for the permanent magnet. For air gap reluctance, , , These are the nonlinear magnetic reluctances of the stator teeth, rotor teeth, and yoke, respectively. It is the leakage magnetic reluctance.

[0023] Step S12, Construct a high-fidelity finite element model: Generate an Ansys Maxwell 2D transient electromagnetic field finite element model with one click based on the RMxprt model, such as... Figure 2 As shown.

[0024] Step S2 involves performing sensitivity analysis on the low-fidelity model sampling to determine the design variables. This includes the following steps.

[0025] Step S21, perform Latin hypercube sampling on the low-fidelity RMxprt, such as... Figure 3 As shown.

[0026] Step S22: Based on the sampling points, statistical correlation analysis is used to measure the correlation between the structural parameters and the optimization objective within the parameter variation range. The sensitivity analysis formula is as follows: (2) in, The total number of samples is 500. For initial design variables, To optimize the objective; Sort and filter variables based on their absolute values, such as Figure 4 As shown; by introducing weight coefficients to balance the various optimization objectives, a comprehensive correlation coefficient is obtained. , (3) Step S23: The final weighted comprehensive sensitivity score is used to determine the optimization variables and their ranges, as shown in Table 2.

[0027] Table 2 Initial values ​​and range of change of variables Step S3, double-fidelity data acquisition and alignment with the physical reference. This includes the following steps.

[0028] Step S31: Secondary sampling is performed using the Latin hypercube sampling method to generate 70 initial samples within the design space. These 70 small samples will be used, and subsequent incremental supplementation will be achieved through active learning.

[0029] Step S32: For each group of samples, call RMxprt and Maxwell to perform calculations.

[0030] Step S33: Read the rated torque calculated by the low-fidelity analytical model. and the corresponding rated current And the constant excitation current set by the high-fidelity finite element model Using the principle of torque constant consistency, the reconstructed physical prior reference torque is calculated. , (4) Step S34: Calculate the true values ​​of the high-fidelity finite element model. T HF With physical prior reference torque Nonlinear residuals between , (5) Step S35: Package the design variable input samples, optimization target output samples, high-fidelity finite element model true values, and calculated nonlinear residuals together and store them in the dual-fidelity sample library.

[0031] Step S4: Construct a physical prior-guided heterogeneous Kriging agent model, including the following steps.

[0032] Step S41: Extract the design variable input samples and optimization target output samples from the double-fidelity sample library constructed in step S3.

[0033] Step S42: Perform range normalization on the extracted design variable input samples and optimization target output samples, uniformly mapping them to the [-1,1] interval to eliminate the influence of dimensions.

[0034] Step S43: Based on the characteristics of the indicators, construct a Gaussian process regression model. (6) For the average torque and operating efficiency indicators, the reconstructed physical prior reference torque is explicitly used. Set as the global mean function of the Kriging model μ ( x ), using stochastic processes Z ( x Fitting nonlinear residuals ; For the torque ripple index, a purely data-driven strategy is adopted, using the global mean function. μ ( x The mean is set to a constant, and the Kriging model is trained directly using high-fidelity data.

[0035] Step S44: A Gaussian process regression model is constructed using the covariance kernel function to characterize the correlation structure among the input variables, and the model hyperparameters are trained using sample data. (7) in, For the feature length scale, r To control the dynamic adjustment of the attenuation constant of the uncertainty weight, The signal variance is obtained through maximum likelihood estimation (MLE).

[0036] Step S49: Based on the obtained optimal hyperparameters, complete the training of the heterogeneous physics-guided Kriging surrogate model. This model can output the predicted mean and predicted variance for any input variable, such as... Figure 5 As shown.

[0037] Step S5, multi-objective optimization based on the surrogate model, includes the following steps.

[0038] Step S51: Initialize the control parameters of the multi-objective optimization algorithm, and set the population size, maximum number of iterations, crossover probability, and mutation probability; Step S52: Construct the objective function matrix and constraints for multi-objective optimization. (8) in, for The predicted value, This is the predicted value for torque ripple. The physical prior trend of the efficiency index.

[0039] Step S53: Within the geometric boundary constraints, an initial parent population is randomly generated.

[0040] Step S54: Calculate the constraint violation degree of each individual. In fast non-dominated sorting, prioritize dominating individuals with lower constraint violation degrees (CVD). If both individuals are feasible solutions, calculate their crowding distance on each objective dimension m. , (9) in, and For adjacent individuals within the same Pareto level, the predicted value for the m-th objective is given. and These are the maximum and minimum values ​​of the m-th optimization objective function in the current Pareto front solution set, respectively. This mechanism guides the population to evolve towards a physically safe and uniformly distributed region.

[0041] Step S55: Parent individuals are selected using a tournament selection method, and offspring individuals are generated using a simulated binary crossover operator; for parent variables... and The offspring variables it generates and Follows the following distribution, (10) in, The diffusion factor depends on random numbers and the distribution index; then, a multinomial mutation operation is performed to merge parent and child populations and implement an elite preservation mechanism.

[0042] Step S56: Repeat the population evolution and environmental selection process until the set maximum number of generations is reached. Output the set of individuals with the highest non-dominant rank (Rank=1) in the last generation population as the initial Pareto front solution set.

[0043] Step S6: Establish an active sampling closed-loop feedback mechanism based on the sampling strategy of predicted mean and uncertainty, including the following steps.

[0044] Step S61: Construct the Bayesian active learning acquisition function: extract the predicted mean of the preliminary Pareto front solution set. With the predicted standard deviation To balance local development and global exploration, a lower confidence boundary acquisition function is constructed. : (11) in, This is a weighting factor used to adjust the proportion of exploration and development.

[0045] Step S62, based on the above The scores of the acquisition function are sorted, and K feature solutions with high uncertainty or high expected returns are selected from the candidate pool as active learning candidate sample points for this round.

[0046] Step S63: Substitute the geometric parameters of these K candidate sample points back into the high-fidelity finite element model (Maxwell2D) to perform accurate transient electromagnetic field solution and obtain their true performance response values. .

[0047] Step S64: Calculate the high-fidelity true value. Mean predicted by the surrogate model relative deviation between , (12) Judgment error and preset accuracy threshold Relationship: If If the current proxy model is deemed to have insufficient accuracy in the optimal region, these K candidate sample points and their true response values ​​are added as high-value incremental samples to the double-fidelity sample library in step S3, and the process returns to step S4. The hyperparameters of the Kriging model are then re-optimized using the expanded dataset, and the proxy model is updated. Subsequently, the optimization process in step S5 is triggered again. If the Bayesian active learning loop converges, the surrogate model accuracy meets engineering requirements. The iteration loop terminates, and the final Pareto front solution set, rigorously verified by finite element analysis, is output for subsequent decision-making.

[0048] Step S65, Data Normalization: Normalize the torque, efficiency, and ripple data in the solution set to the [0, 1] interval. (13) Step S66, define the ideal utopia point as Calculate each solution arrive Euclidean distance , (14) Step S67, final selection of distance The minimum solution is taken as the final design scheme, such as... Figure 6 As shown, this scheme achieves the best physical trade-off between torque, ripple, and efficiency.

[0049] Regarding electromagnetic torque performance, a comparison of transient field torque before and after optimization is shown, such as... Figure 7 As shown, the average torque before optimization was 2.17 Nm with a torque ripple of 2.20%, while the average torque after optimization was 2.31 Nm with a torque ripple of 1.78%. The average torque increased by 0.14 Nm, while the torque ripple decreased by 0.42%. The motor efficiency also improved.

Claims

1. A Bayesian active learning multi-objective optimization method for motors based on physical prior guidance, characterized in that, Includes the following steps: Step S100: Construct a multi-fidelity physical model for the motor of the linear actuation system. The multi-fidelity physical model includes a low-fidelity analytical model with fast calculation speed and a high-fidelity finite element model with high calculation accuracy, and define the initial design space. Step S200: Use the low-fidelity analytical model to perform large-sample calculations, perform sensitivity analysis on the initial design variables, eliminate low-sensitivity variables to achieve dimensionality reduction of the design space, and determine the key design variables. Step S300: Perform dual-fidelity sampling on key design variables to obtain low-fidelity response values ​​and high-fidelity true values ​​respectively; eliminate the working condition differences between models through physical feature reconstruction, and calculate the residual between the high-fidelity true value and the reconstructed low-fidelity baseline value; Step S400: Construct a physical prior-guided heterogeneous Kriging proxy model. For fundamental-wave dominant performance indicators, embed the low-fidelity benchmark value into the trend term of the Kriging model and train the model to learn the residuals. For higher-harmonic-dominated performance indicators, directly use high-fidelity data to construct a pure data-driven Kriging model. Step S500: A multi-objective optimization algorithm is used to perform global optimization on the heterogeneous Kriging proxy model to obtain a preliminary Pareto front solution set; Step S600: Establish an active sampling closed-loop feedback mechanism based on the sampling strategy of prediction mean and uncertainty. Select the feature solution in Pareto front and substitute it back into the high-fidelity finite element model for verification. If the prediction error does not meet the convergence condition, use the verification data as incremental sample to update the surrogate model and re-optimize until the convergence condition is met, and output the optimal design scheme. The specific calculation method for physical feature reconstruction in step S300 is as follows: The rated torque calculated from the low-fidelity analytical model and the corresponding rated current And the constant excitation current set by the high-fidelity finite element model Using the principle of torque constant consistency, the reconstructed physical prior reference torque is calculated. : （3）； The construction strategy for the heterogeneous kriging proxy model described in S400 includes: For the average torque and efficiency indices, the prediction model is expressed as the sum of the physical prior reference torque and the random residuals. ；（4） For the torque ripple index, the prediction model represents a purely stochastic process. ；（5） in, and These are Gaussian random processes under different strategies. μ It is a constant; The specific steps of the active sampling closed-loop feedback mechanism described in step S600 include: Select several uniformly distributed characteristic solutions from the Pareto front solution set based on the crowding distance; The true values ​​of the eigenvalues ​​are calculated using a high-fidelity finite element model, and the relative error between the predicted and true values ​​of the heterogeneous kriging surrogate model is also calculated. ; If the maximum relative error If the value exceeds the preset convergence threshold, the feature solution and its true value are added to the sample library, triggering the iterative loop from steps S400 to S600; if the maximum relative error... If the value is less than or equal to the preset convergence threshold, the optimization is considered to have converged.

2. The method according to claim 1, characterized in that, The low-fidelity analytical model described in S100 is an equivalent magnetic circuit model constructed based on Hopkinson's law; the high-fidelity finite element model is a finite element simulation model constructed based on two-dimensional transient electromagnetic field theory; both share the same set of geometric parameter variables.

3. The method according to claim 1, characterized in that, The sensitivity analysis described in S200 specifically employs statistical correlation analysis, and its calculation formula is as follows: ，（2） in, The total number of samples, For initial design variables, To optimize the objective; based on The absolute value of the variables is used to sort and filter them.

4. The method according to claim 1, characterized in that, The optimal design scheme decision in step S600 also includes: normalizing each optimization objective in the Pareto front solution set, calculating the Euclidean distance from each non-dominated solution to the ideal utopia point, and selecting the solution with the smallest distance as the final motor design scheme.

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