A multi-objective optimization method for improving torque performance of electric motor

Abstract

This invention belongs to the field of electrical digital data processing technology, specifically relating to a multi-objective optimization method for improving motor torque performance. The method includes: establishing a parameterized model of the motor; extracting geometric harmonic prior features based on the harmonic analysis principle of the motor's air gap magnetic flux density, and using these as a screening criterion to obtain an initial high-quality sample set; constructing a Kriging surrogate model reflecting the mapping relationship between design variables and performance response, introducing an energy efficiency boundary risk function during the construction process; based on the Kriging surrogate model, using a multi-objective optimization algorithm to search for a Pareto front solution set, selecting potential sample points from the Pareto front solution set for simulation verification, and then adaptively updating the Kriging surrogate model until the stopping criterion is met, at which point the target motor design parameters are output. This invention can achieve accurate optimization of electromagnetic parameters by screening samples through geometric harmonic prior features and utilizing the energy efficiency boundary risk function.

Description

Technical Field

[0001] This invention relates to the field of electrical digital data processing technology. More specifically, this invention relates to a multi-objective optimization method for improving the torque performance of a motor. Background Technology

[0002] In the development of high-performance permanent magnet synchronous motors, improving torque density and reducing cogging torque are the core design goals. In existing technologies, engineers usually need to optimize electromagnetic performance by adjusting geometric parameters such as rotor eccentricity, pole arc coefficient and magnetic pole offset. This optimization method mainly relies on orthogonal experimental design or directly uses genetic algorithms to drive finite element simulation software for large-scale iterative search.

[0003] However, to accurately assess the instantaneous overload capacity of a motor under overload conditions, nonlinear magnetic saturation simulations under high current are necessary. Such simulations typically take several minutes per calculation, while conventional genetic algorithms require tens of thousands of iterations, resulting in an overall development cycle of several weeks, which cannot meet the industry's demand for rapid response. Furthermore, national standards such as GB30253 impose mandatory requirements on motor energy efficiency. Existing algorithms often employ a simple "death penalty" mechanism, directly discarding any scheme whose calculated efficiency falls below the standard. This approach ignores the prediction errors inherent in the simulation model itself, easily causing the algorithm to stagnate near local optima with high energy efficiency and low overload, failing to effectively explore boundary regions where energy efficiency barely meets the standard but torque performance is excellent.

[0004] Furthermore, existing methods have poor multi-objective conflict decoupling capabilities and struggle to characterize the sensitivity differences of geometric parameters to the two objectives of cogging torque and average torque, resulting in the final generated scheme often failing to recommend the optimal trade-off solution. Summary of the Invention

[0005] To address the technical challenges of high-performance permanent magnet synchronous motors in design due to the extremely high cost of nonlinear magnetic saturation simulation calculations and the difficulty in balancing energy efficiency standards and torque performance, this invention proposes a multi-objective optimization method to improve motor torque performance. This method can screen samples using geometric harmonic prior features and achieve precise optimization of electromagnetic parameters using energy efficiency boundary risk functions.

[0006] This invention provides a multi-objective optimization method for improving motor torque performance, comprising: establishing a parametric model of the motor; selecting design variables reflecting rotor geometry based on the motor's structural characteristics; extracting geometric harmonic prior features for evaluating harmonic suppression capability under various combinations of design variables based on the harmonic analysis principle of the motor's air gap magnetic flux density, and using these features as a screening criterion to obtain an initial high-quality sample set; obtaining performance response data of the initial high-quality sample set through finite element simulation, and constructing a Kriging surrogate model reflecting the mapping relationship between the design variables and performance response, introducing an energy efficiency boundary risk function during the construction process to assess the risk level of the design scheme meeting energy efficiency standards; based on the Kriging surrogate model, searching the Pareto front solution set using a multi-objective optimization algorithm, and selecting potential sample points from the Pareto front solution set for simulation verification in conjunction with the torque waveform comprehensive utility function, and then adaptively updating the Kriging surrogate model until the stopping criterion is met, and outputting the target motor design parameters to improve motor torque performance.

[0007] By adopting the above technical solutions, geometric harmonic prior features are introduced into the optimization process. Combined with the Kriging proxy model based on the energy efficiency boundary risk function, analytical calculations are used to pre-exclude poor-performing schemes, and probabilistic risk assessment is used to replace hard elimination. This solves the technical problems of high cost of nonlinear magnetic saturation simulation calculation, easy local optima caused by hard energy efficiency constraints, and difficulty in balancing multi-objective conflicts in the design of high-performance permanent magnet synchronous motors.

[0008] Preferably, in the step of extracting the prior features of geometric harmonics, the prior features of geometric harmonics are characterized by a geometric harmonic suppression factor. The construction logic of the geometric harmonic suppression factor is as follows: comprehensively considering the influence of the short-distance effect generated by the pole arc coefficient, the air gap smoothing effect generated by the rotor eccentricity, and the phase interference effect generated by the magnetic pole offset on the air gap magnetic flux density harmonics. Among them, the value of the geometric harmonic suppression factor is positively correlated with the absolute value of the short-distance coefficient of the pole arc coefficient at the target harmonic order, negatively correlated with the waveform distortion suppression capability generated by the rotor eccentricity ratio, and is modulated by the phase offset caused by the magnetic pole offset angle. The smaller the value of the geometric harmonic suppression factor, the better the theoretical waveform quality.

[0009] By adopting the above technical solutions, and comprehensively considering the short-distance effect, air gap smoothing effect, and phase interference effect, a geometric harmonic suppression factor is constructed. This establishes a direct algebraic relationship between the electromagnetic field waveform quality and geometric dimensions, enabling the rapid screening of design spaces with low harmonic potential and avoiding the waste of simulation resources in poor solution regions.

[0010] Preferably, the rotor eccentricity ratio is a dimensionless physical quantity determined by the ratio of the rotor eccentricity distance to the main air gap length; the design variables include the rotor eccentricity ratio, the pole arc coefficient, and the adjacent magnetic pole offset angle.

[0011] By adopting the above technical solution, the rotor eccentricity ratio, pole arc coefficient and adjacent magnetic pole offset angle are selected as design variables and dimensionless processing is performed to transform the specific motor physical structure into a mathematical space that can be identified by the algorithm and is easy to optimize, thus clarifying the boundary conditions for optimization.

[0012] Preferably, in the step of constructing the Kriging proxy model, the energy efficiency boundary risk function is used to construct the energy efficiency risk penalty value, and its construction logic follows: when the predicted efficiency is lower than the energy efficiency limit, the energy efficiency risk penalty value increases exponentially as the difference between the predicted efficiency and the energy efficiency limit increases; at the same time, the energy efficiency risk penalty value is negatively correlated with the prediction uncertainty of the Kriging proxy model, that is, when the prediction efficiency is the same, the higher the prediction uncertainty, the lower the energy efficiency risk penalty value, so as to reduce the penalty intensity in the high uncertainty region.

[0013] By adopting the above technical solution, an energy efficiency risk penalty term is constructed that increases exponentially with the increase of efficiency difference and is negatively correlated with prediction uncertainty. The prediction standard deviation is used as a buffer, which improves the probability of the algorithm finding the global optimal solution.

[0014] Preferably, the energy efficiency boundary risk function aims to guide the optimization direction to explore the critical energy efficiency boundary by reducing the penalty for high uncertainty and potentially non-compliant regions, and to prevent local convergence caused by hard constraints; the energy efficiency limit value is determined according to the national mandatory energy efficiency standard.

[0015] By adopting the above technical solutions, the penalties for high-uncertainty and potentially non-compliant regions are reduced, effectively guiding the optimization process to explore the critical boundary of energy efficiency and avoiding local convergence caused by hard constraints.

[0016] Preferably, in the step of adaptively updating the Kriging proxy model, the torque waveform comprehensive utility function is used to evaluate the simulation value of the sample points. Its construction logic includes a weighted combination of torque gain term, cogging torque utility term, and safety exploration term. The torque gain term is determined by the ratio of the predicted overload torque to the reference torque. The cogging torque utility term is nonlinearly negatively correlated with the predicted cogging torque to amplify the discrimination of low cogging torque regions. The safety exploration term is determined by the product of the torque prediction standard deviation and the energy efficiency safety probability, and is used to preferentially select regions with high prediction uncertainty and low energy efficiency violation risk for sample point supplementation.

[0017] By adopting the above technical solution, a comprehensive torque waveform utility function covering torque gain, cogging torque utility, and safety exploration is constructed, achieving the optimal trade-off under multi-objective conflict and ensuring that the model accuracy adaptively improves with the iteration process.

[0018] Preferably, the cogging torque utility term adopts a logarithmic function form to improve the sensitivity of the score when the cogging torque approaches zero; all terms in the comprehensive utility function are normalized to eliminate the influence of dimensions.

[0019] By adopting the above technical solution, the cogging torque utility term is constructed in the form of a logarithmic function and normalized, which improves the algorithm's sensitivity to optimization in the low cogging torque region and solves the problem of inconsistent dimensions of multiple physical quantities.

[0020] Preferably, the performance response data includes at least average torque, cogging torque, back EMF distortion rate, and motor efficiency; the initial high-quality sample set is generated using the Latin hypercube sampling method.

[0021] By adopting the above technical solution, key performance indicators such as average torque, cogging torque, back EMF distortion rate and motor efficiency are selected, and Latin hypercube sampling is used to generate an initial high-quality sample set, ensuring the uniform distribution of the initial samples in the design space.

[0022] Preferably, the multi-objective optimization algorithm employs a non-dominated sorting genetic algorithm with an elitist strategy.

[0023] By adopting the above technical solution, a non-dominated sorting genetic algorithm with an elitist strategy is used to search for the Pareto front solution set, which improves the search efficiency for finding high-performance design solutions in the multi-objective optimization process.

[0024] Preferably, in the step of adaptively updating the Kriging surrogate model, finite element simulation is performed on the potential sample points selected according to the torque waveform comprehensive utility function, and the simulation results are added to the training set to retrain the Kriging surrogate model until the preset number of iterations or model accuracy requirements are reached.

[0025] By adopting the above technical solution, the simulation results of potential sample points are added to the training set in real time and the Kriging surrogate model is retrained, realizing the closed-loop iterative update of model accuracy and optimization target until the preset accuracy requirement is reached.

[0026] This invention constructs an optimization framework that deeply integrates physical prior driving and data driving, compresses the design space by utilizing the principle of geometric harmonic suppression, and processes energy efficiency hard constraints by using the variance information of Gaussian process regression, thus constructing an efficient and accurate electromagnetic scheme for a high-performance permanent magnet synchronous motor.

[0027] Furthermore, this invention constructs a Kriging proxy model with an energy efficiency boundary risk function and uses the prediction uncertainty to assess the risk of the scheme meeting the energy efficiency standard. This enables the optimization process to be effectively explored in the critical region of energy efficiency compliance, thereby uncovering the ultimate design scheme for the torque performance of high-performance permanent magnet synchronous motors under the premise of meeting the national mandatory energy efficiency standard. Attached Figure Description

[0028] Figure 1 This is a flowchart of a multi-objective optimization method for improving motor torque performance according to the present invention;

[0029] Figure 2 This is a schematic diagram of the three-dimensional response surface of the design variables and geometric harmonic suppression factor in this invention;

[0030] Figure 3 This is a schematic diagram of the multi-objective Pareto front distribution under the energy efficiency boundary risk in this invention;

[0031] Figure 4 This is a schematic diagram comparing the convergence curves of the prediction error of the surrogate model during the optimization process in this invention. Detailed Implementation

[0032] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0033] This invention discloses a multi-objective optimization method for improving the torque performance of a motor, applicable to the electromagnetic scheme design of high-performance permanent magnet synchronous motors. This invention uses the electromagnetic scheme design of a TYL series high-power water-cooled servo motor as an example for detailed explanation. The rated torque of this motor is set at 100 Nm, the number of stator slots is 24, and according to the national standard GB30253, its secondary energy efficiency limit is 96.5%.

[0034] Reference Figure 1 A multi-objective optimization method for improving motor torque performance includes steps S1-S4:

[0035] S1. Establish a parametric model of the motor and select design variables that reflect the rotor geometry based on the motor's structural characteristics.

[0036] In an optional embodiment, technicians first establish a two-dimensional or three-dimensional parametric model of the motor using electromagnetic field finite element simulation software such as Maxwell. It is important to note that, to achieve a deep understanding of the motor's torque performance, the rotor geometric parameters that have the most significant impact on the air gap magnetic field waveform need to be selected as design variables. In an optional embodiment, the three key design variables selected include: rotor eccentricity ratio... Polar arc coefficient and the angle of offset between adjacent magnetic poles .

[0037] Specifically, rotor eccentricity ratio Eccentric distance With the length of the main air gap The ratio of , where eccentricity With the length of the main air gap The units are all mm. The rotor eccentricity ratio is dimensionless through a ratio definition, and its value ranges from 0 to 1, which can intuitively characterize the sinusoidal degree of the air gap; polar arc coefficient. This is the ratio of the actual magnetic pole width to the pole pitch, which is also dimensionless and typically ranges from 0.6 to 0.9; the offset angle between adjacent magnetic poles. Defined as the mechanical offset angle between adjacent magnetic poles in the circumferential direction, in degrees.

[0038] In this way, by using parametric modeling and selecting dimensionless variables, the specific physical structure of the motor is transformed into a mathematical space that the algorithm can recognize and optimize, thus clarifying the boundaries of optimization.

[0039] S2. Based on the harmonic analysis principle of motor air gap magnetic flux density, extract geometric harmonic prior features for evaluating the harmonic suppression capability under various design variable combinations, and use these features as screening criteria to obtain an initial high-quality sample set.

[0040] In an optional embodiment, to avoid wasting a large amount of computational resources on inefficient design schemes, the present invention introduces an analytical calculation step before simulation. Specifically, the present invention uses analytical relationships to calculate the geometric harmonic suppression factor. As a priori feature, the calculation method used to quickly predict waveform quality is as follows:

[0041] ;

[0042] In the formula, This represents the target harmonic order, which is a dimensionless constant. For fractional slot windings, it is typically taken as 5 or 7. This represents the weight of the eccentricity effect, which is a dimensionless empirical constant, and is set to 1.5 based on the historical design experience of the TYL series. This represents the stator cogging pitch angle, in degrees. For a 24-slot motor, ; Pi is the mathematical constant of a circle.

[0043] To more clearly illustrate the role and calculation process of the geometric harmonic suppression factor, the following example will demonstrate its application:

[0044] First, assume that a set of design variables is obtained through Latin hypercube sampling: It is 0.8. It is 0.6. The value is 2.5°. Substituting the above value into the formula for calculating the geometric harmonic suppression factor, we can obtain:

[0045] First, calculate the numerator term characterizing the short-range effect: Next, calculate the denominator term characterizing the air gap smoothing effect: ; Recalculate the cosine term characterizing the phase interference: The final result is: .

[0046] As can be seen from the example above, the final geometric harmonic suppression factor is 0, which indicates that the combination of parameters can theoretically completely eliminate the 5th harmonic and is a high-quality sample, so it should be retained. Conversely, if the calculated geometric harmonic suppression factor is large, it means that the waveform of this design scheme is poor and should be directly rejected.

[0047] Thus, guided by the prior features of geometric harmonics, low-performance regions can be effectively filtered out, ensuring that subsequent finite element simulations are performed only on high-potential samples, thereby significantly improving computational efficiency.

[0048] S3. Obtain performance response data of the initial high-quality sample set through finite element simulation, and construct a Kriging proxy model that reflects the mapping relationship between design variables and performance response. In the construction process, introduce the energy efficiency boundary risk function to evaluate the risk level of the design scheme meeting the energy efficiency standard.

[0049] In an optional embodiment, in order to accurately assess the risk level of a design scheme meeting energy efficiency standards and to solve the technical problem of handling hard constraints of energy efficiency standards, this invention constructs an energy efficiency boundary risk function. This aims to guide optimization by predicting uncertainties, exploring the critical energy efficiency boundary, and preventing local convergence due to rigid constraints. The logic for constructing the energy efficiency boundary risk function is as follows: Selected sample points are imported into finite element simulation software for batch simulation to obtain response data such as efficiency and torque. A Kriging surrogate model reflecting the mapping relationship between design variables and performance response is then trained. The energy efficiency boundary risk function is then constructed. The specific method is as follows:

[0050] ;

[0051] In the formula, This indicates the energy efficiency limit value, which is 0.965 according to the national standard for Level 2 energy efficiency. This represents the model's prediction efficiency, and it is a dimensionless constant. This represents the standard deviation of the forecast, output by the Kriging model, and characterizes uncertainty. This represents the sensitivity coefficient, set to 5.0; To prevent zero constant, take .

[0052] To more clearly illustrate the role and calculation method of the energy efficiency boundary risk function, the following example will demonstrate its application:

[0053] For example, we first assume that the model predicts that the efficiency of a certain scheme is 0.963, which is lower than the limit value.

[0054] In one embodiment of the present invention, if the samples in the region are sparse and the standard deviation of the prediction given by the model is large, The value is 0.01, at which point the exponential term in the energy efficiency boundary risk function calculation formula is... =1, thus obtaining The final calculated energy efficiency boundary risk function is relatively small, which means that the algorithm allows for the retention of potentially non-compliant points even under conditions of high uncertainty.

[0055] In another embodiment of the invention, if the sample density in the region is relatively high, the prediction standard deviation is extremely small. The value is 0.0002, at which point the exponential term in the energy efficiency boundary risk function calculation formula is... If the value is 50, the energy efficiency boundary risk function will explode, forcing the algorithm to avoid the area that is determined to be non-compliant.

[0056] Thus, by introducing the prediction standard deviation as a buffer, the algorithm can approach the physical limit of energy efficiency to the greatest extent possible while ensuring the compliance of the final solution, avoiding the problem of losing the global optimal solution due to "false positives" in traditional methods.

[0057] S4. Based on the Kriging surrogate model, a multi-objective optimization algorithm is used to search for the Pareto front solution set. Potential sample points are selected from the Pareto front solution set by combining the torque waveform comprehensive utility function for simulation verification. Then, the Kriging surrogate model is adaptively updated until the stopping criterion is met, and the target motor design parameters are output to improve the motor torque performance.

[0058] In an optional embodiment, a non-dominated sorting genetic algorithm with an elitist strategy is used to rapidly iterate on the surrogate model. Meanwhile, to further improve the model accuracy and tap potential points, the most valuable sample points need to be selected for realistic finite element simulation.

[0059] Preferably, the present invention utilizes a torque waveform comprehensive utility function. The sample points are scored, and the specific calculation method for the final score meets the following requirements:

[0060] ;

[0061] In the formula, To predict overload torque, As a reference torque, in this embodiment of the invention, the reference torque is set to 100 Nm. The ratio of the predicted overload torque to the reference torque achieves dimensionless representation of the torque term. To predict cogging torque, The rated torque is set to 100 Nm in this embodiment of the invention, and the ratio of the predicted cogging torque to the rated torque achieves the dimensionless representation of the cogging torque term. The standard deviation of torque prediction; All are weighting coefficients, among which In this embodiment of the invention, it is set to 0.6. In this embodiment of the invention, it is set to 0.4. In this embodiment of the invention, it is set to 0.1.

[0062] To more clearly illustrate the role of the final score and the calculation process, the following example will demonstrate this:

[0063] In one embodiment of the present invention, if for a certain candidate sample point, its predicted overload torque... The predicted cogging torque is 250 Nm. The torque prediction standard deviation is 2 Nm. The capacity is 10 Nm, and the energy efficiency compliance risk is extremely low. =0;

[0064] but The high score indicates that this point has high performance potential and exploratory value, and it will be selected as the next simulation verification point.

[0065] Thus, guided by the comprehensive utility function, the optimal trade-off under multi-objective conflict is achieved, and the model accuracy is ensured to adaptively improve with the iteration process, ultimately producing the following output: Figure 3 The optimal trade-off solution is shown.

[0066] Reference Figure 2 This demonstrates how the present invention uses geometric harmonic suppression factor logic to identify the theoretically optimal design interval; (Refer to...) Figure 3 This demonstrates the Pareto front distribution obtained by the optimization algorithm under the energy efficiency boundary risk constraint; (Refer to...) Figure 4 By comparing the prediction root mean square error curves under random point addition without strategy and under the point addition strategy of the present invention, it is confirmed that the strategy of the present invention has a faster convergence speed than the prior art.

[0067] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise expressly and specifically defined.

Claims

1. A multi-objective optimization method for improving the torque performance of a motor, characterized in that, include: Establish a parametric model of the motor and select design variables that reflect the rotor geometry based on the motor's structural characteristics; Based on the harmonic analysis principle of the air gap magnetic flux density of the motor, geometric harmonic prior features are extracted to evaluate the harmonic suppression capability under various combinations of design variables, and these features are used as screening criteria to obtain an initial high-quality sample set; the geometric harmonic prior features are characterized by the geometric harmonic suppression factor. The construction logic of the geometric harmonic suppression factor is as follows: comprehensively consider the influence of the short-distance effect generated by the pole arc coefficient, the air gap smoothing effect generated by the rotor eccentricity ratio, and the phase interference effect generated by the magnetic pole offset on the air gap magnetic flux density harmonics; the value of the geometric harmonic suppression factor is positively correlated with the absolute value of the short-distance coefficient of the pole arc coefficient at the target harmonic order, negatively correlated with the waveform distortion suppression capability generated by the rotor eccentricity ratio, and is modulated by the phase offset caused by the magnetic pole offset angle. The smaller the value of the geometric harmonic suppression factor, the better the theoretical waveform quality. The rotor eccentricity ratio is a dimensionless physical quantity determined by the ratio of the rotor eccentricity distance to the length of the main air gap. Design variables include rotor eccentricity ratio, pole arc coefficient, and adjacent magnetic pole offset angle; The performance response data of the initial high-quality sample set is obtained through finite element simulation, and a Kriging proxy model reflecting the mapping relationship between design variables and performance response is constructed. During the construction process, an energy efficiency boundary risk function is introduced to assess the risk level of the design scheme meeting the energy efficiency standard. The energy efficiency boundary risk function is used to construct the energy efficiency risk penalty value. Its construction logic follows this principle: when the predicted efficiency is lower than the energy efficiency limit, the energy efficiency risk penalty value increases exponentially as the difference between the predicted efficiency and the energy efficiency limit increases. At the same time, the energy efficiency risk penalty value is negatively correlated with the prediction uncertainty of the Kriging proxy model. That is, when the prediction efficiency is the same, the higher the prediction uncertainty, the lower the energy efficiency risk penalty value, so as to reduce the penalty intensity in the high uncertainty region. Based on the Kriging surrogate model, a multi-objective optimization algorithm is used to search for the Pareto front solution set. Potential sample points are selected from the Pareto front solution set by combining the torque waveform comprehensive utility function for simulation verification. Then, the Kriging surrogate model is adaptively updated until the stopping criterion is met, and the target motor design parameters are output to improve the motor torque performance. The torque waveform comprehensive utility function is used to evaluate the simulation value of sample points. Its construction logic includes a weighted combination of torque gain term, cogging torque utility term, and safety exploration term. The torque gain term is determined by the ratio of the predicted overload torque to the reference torque. The cogging torque utility term is nonlinearly negatively correlated with the predicted cogging torque to amplify the discrimination of low cogging torque regions. The safety exploration term is determined by the product of the torque prediction standard deviation and the energy efficiency safety probability, and is used to prioritize the selection of regions with high prediction uncertainty and low energy efficiency violation risk for supplementing sample points.

2. The multi-objective optimization method for improving motor torque performance according to claim 1, characterized in that, The energy efficiency boundary risk function aims to guide the optimization direction to explore the critical energy efficiency boundary by reducing the penalty for high uncertainty and potentially non-compliant regions, and to prevent local convergence caused by hard constraints; the energy efficiency limit value is determined according to the national mandatory energy efficiency standard.

3. The multi-objective optimization method for improving motor torque performance according to claim 1, characterized in that, The cogging torque utility term adopts a logarithmic function form to improve the sensitivity of the score when the cogging torque approaches zero; all terms in the comprehensive utility function have been normalized to eliminate the influence of dimensions.

4. The multi-objective optimization method for improving motor torque performance according to claim 1, characterized in that, The performance response data includes at least average torque, cogging torque, back EMF distortion rate, and motor efficiency; the initial high-quality sample set is generated using the Latin hypercube sampling method.

5. The multi-objective optimization method for improving motor torque performance according to claim 4, characterized in that, The multi-objective optimization algorithm employs a non-dominated sorting genetic algorithm with an elitist strategy.

6. The multi-objective optimization method for improving motor torque performance according to claim 4, characterized in that, In the step of adaptively updating the Kriging surrogate model, finite element simulations are performed on the potential sample points selected based on the torque waveform comprehensive utility function, and the simulation results are added to the training set to retrain the Kriging surrogate model until the preset number of iterations or model accuracy requirements are reached.

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