A motor performance prediction method and system based on an enhanced integrated Kriging surrogate model
By using an enhanced integrated Kriging surrogate model, the problems of multi-scale feature capture and robustness in motor performance prediction of traditional models are solved, achieving high-precision and physically consistent motor performance prediction, which is suitable for the rapid development of high-performance motors.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAQIAO UNIVERSITY
- Filing Date
- 2026-06-11
- Publication Date
- 2026-07-14
Smart Images
Figure CN122389657A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of motor design and optimization technology, specifically a method and system for predicting motor performance based on an enhanced integrated Kriging surrogate model. Background Technology
[0002] As the core power component of electric construction machinery, the performance of the electric motor directly determines the overall efficiency and energy consumption of the machine. Improving motor performance is key to overcoming the technological bottlenecks of electric construction machinery. However, construction machinery operates under complex conditions, and the actual operating performance of the motor is difficult to accurately assess in advance through traditional experience or bench tests. This can easily lead to design redundancy and conservative control. How to predict the actual performance of the motor before it is put into operation has become an urgent problem for motor optimization and overall machine matching.
[0003] Proxy models are widely used in motor design to accelerate performance analysis and optimization. Among them, the Kriging surrogate model is widely used due to its adaptability to nonlinear problems. However, for the complex multiphysics response of high-performance motors, the traditional Kriging model has obvious limitations: it is difficult to capture multi-scale features, its prediction of highly skewed non-negative physical quantities is unstable and may produce non-physical outputs, and its ensemble model has poor aggregation robustness. Therefore, there is an urgent need for a high-fidelity motor performance prediction method that takes into account multi-scale capture, physical consistency, and high robustness to meet the needs of rapid R&D of high-performance motors. Summary of the Invention
[0004] To address the aforementioned technical problems, the present invention aims to provide a method and system for predicting motor performance based on an enhanced integrated Kriging proxy model. This method aims to meet the rapid development needs of high-performance motors by providing a high-fidelity motor performance prediction method that balances multi-scale capture, physical consistency, and high robustness.
[0005] This invention provides a method for predicting motor performance based on an enhanced integrated Kriging surrogate model, comprising the following steps:
[0006] S1: Obtain a sample set of structural parameters of permanent magnet synchronous motors, and obtain the corresponding motor structure and performance data through finite element analysis to construct an initial sample dataset. The motor structure and performance data includes motor structure parameters and motor performance indicators. S2: For motor performance indicators that exhibit a skewed distribution and are physically strictly non-negative, perform a logarithmic shift transformation on the target response values in the initial sample dataset. Map it to an approximate Gaussian distribution, where The target response value in the initial sample dataset; S3: Construct an ensemble Kriging surrogate model and introduce heterogeneous kernel functions into the sub-model library of the ensemble Kriging surrogate model; use the transformed sample dataset to perform cross-validation training on the sub-models with introduced heterogeneous kernel functions, and obtain an enhanced ensemble Kriging surrogate model through weighted fusion; S4: Receive the motor structure parameters to be predicted and input them into the enhanced integrated Kriging proxy model; for performance indicators with drastic fluctuations, use the weighted median statistical method to aggregate the predicted values of each sub-model, restore the physical true value through inverse exponential transformation, and output the motor performance prediction result.
[0007] Preferably, the motor structure parameters in the motor structure and performance data include at least one or more combinations of: stator inner diameter, core length, slot height, slot wedge height, slot body height, slot width, slot wedge width, slot body width, inner permanent magnet width, and outer permanent magnet width; the motor performance indicators in the motor structure and performance data include at least one or more of: average torque, torque pulsation, stator iron loss, rotor iron loss, and permanent magnet loss.
[0008] Preferably, the motor performance indicators that exhibit skewed distribution and are physically strictly non-negative are specifically the motor torque ripple and the motor iron loss, wherein the motor iron loss includes stator iron loss and rotor iron loss.
[0009] Preferably, introducing heterogeneous kernel functions into the sub-model library integrating the Kriging surrogate model specifically includes the following steps: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] The corresponding unknown function can be considered as a superposition of a deterministic regression model and a stochastic process: ,in and These are the deterministic trend term and the stochastic process term, respectively. The deterministic trend term... The expression is: In the formula These are the basis vectors of the regression function. It is the vector of regression coefficients to be determined; the stochastic process term. Used to describe local fluctuations and uncertainties, it is determined by the covariance function, i.e.:
[0010] In the formula, For mathematical expectation, For variance, For covariance, This indicates that the mean of the random process is 0. Let Variance be the variance of the random process. For any two points in the design space, It is a correlation function. A heterogeneous kernel function is introduced into the correlation function to obtain a corresponding correlation function with the introduced heterogeneous kernel function. for:
[0011] in The length scale parameter matrix is specifically a diagonal matrix. Each diagonal element corresponds to a motor geometric parameter. This represents the total number of motor geometric parameters, which include the stator inner diameter and slot width. The scaling mixing parameters are used; after substituting the correlation function of the heterogeneous kernel function into the covariance function, the stochastic process term of the heterogeneous kernel function is obtained, and then the sub-model of the integrated Kriging surrogate model with the heterogeneous kernel function is obtained.
[0012] Preferably, the cross-validation training of the sub-model with the heterogeneous kernel function using the transformed sample dataset specifically includes the following steps: For an unknown point The predicted value of the Kriging model Based on training samples The best linear unbiased estimator for is given by the following formula:
[0013] In the above formula It is the regression basis matrix of the training samples. It is the correlation matrix between training samples. Test point The correlation vector between all training samples, These are the regression coefficients estimated by the generalized least squares method.
[0014] Preferably, the weighted median statistical method for aggregating the predicted values of each sub-model specifically includes the following steps: Assuming the ensemble model contains a total of M sub-models, the predicted value of the m-th model is... The corresponding weight is And normalization satisfies Sort all the predicted values of the sub-models in order of size. The corresponding weights are normalized and adjusted; a sorting index k that satisfies the following conditions is found: and , and its corresponding predicted value As the final output.
[0015] A motor performance prediction system based on an enhanced integrated Kriging surrogate model includes the following modules; Initial sample dataset construction module: Obtain a sample set of structural parameters of permanent magnet synchronous motors, and obtain the corresponding motor structure and performance data through finite element analysis to construct the initial sample dataset. The motor structure and performance data includes motor structural parameters and motor performance indicators. Partial motor performance index processing module: For motor performance indices that exhibit skewed distributions and are physically strictly non-negative, a logarithmic shift transformation is performed on the target response values in the initial sample dataset. Map it to an approximate Gaussian distribution, where The target response value in the initial sample dataset; Integrated Kriging surrogate model building module: Introduces heterogeneous kernel functions into the sub-model library of the integrated model; performs cross-validation training on the sub-models using the transformed sample dataset; and obtains an enhanced integrated Kriging surrogate model through weighted fusion. Motor performance prediction module: Receives the structural parameters of the motor to be predicted and inputs them into the enhanced integrated Kriging proxy model constructed by the integrated Kriging proxy model construction module; for performance indicators with drastic fluctuations, the weighted median statistical method is used to aggregate the predicted values of each sub-model, and the physical true value is restored through inverse exponential transformation, and the motor performance prediction result is output.
[0016] The present invention has the following beneficial effects: The motor performance prediction method and system provided by the present invention introduces logarithmic displacement transformation and inverse transformation mechanisms, eliminating the negative cases that may occur when traditional models predict indicators such as torque ripple or iron loss, and avoiding numerical singularity; through the fusion of heterogeneous kernel functions (Rational Quadratic kernel and Matern kernel), the model can simultaneously take into account the global evolution trend and local high-frequency fluctuations of the motor performance response surface, significantly improving the prediction accuracy of strongly nonlinear indicators such as stator and rotor iron loss; for indicators with drastic fluctuations, a weighted median statistical method is used for aggregation, which has a higher breakdown point than the traditional weighted average method, is insensitive to outliers or poorly performing single sub-models, and provides a more robust central tendency estimate. Attached Figure Description
[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.
[0018] Figure 1A flowchart illustrating a motor performance prediction method based on an enhanced integrated Kriging proxy model, provided in an embodiment of the present invention; Figure 2 This is a schematic cross-sectional view of the geometric model of the permanent magnet synchronous motor involved in an embodiment of the present invention; Figure 3 The following are scatter plots comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values on various key performance indicators in this embodiment of the invention: (a) is a scatter plot comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values (FEA) on average torque in this embodiment of the invention; (b) is a scatter plot comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values (FEA) on torque ripple in this embodiment of the invention; (c) is a scatter plot comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values (FEA) on permanent magnet loss in this embodiment of the invention; (d) is a scatter plot comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values (FEA) on rotor iron loss in this embodiment of the invention; and (e) is a scatter plot comparing the fitting effects of the enhanced integrated Kriging surrogate model's predicted values and finite element calculation values (FEA) on stator iron loss in this embodiment of the invention. Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0020] Example The following are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the following embodiments. All technical solutions that fall within the scope of the present invention are within the scope of protection of the present invention.
[0021] Reference manual attached Figure 1 This invention provides a method for predicting motor performance based on an enhanced integrated Kriging (EEK) surrogate model, the specific steps of which are as follows: S1: Define the design space and construct the initial sample set Reference manual attached Figure 2 In this embodiment, an 8-pole, 48-slot double-V-type internal permanent magnet synchronous motor (IPMSM) is used as the specific application object. Key geometric parameters of the permanent magnet synchronous motor are selected as input variables X, including but not limited to: a multi-dimensional vector consisting of stator inner diameter, core length, slot height, slot wedge height, slot body height, slot width, slot wedge width, slot body width, inner permanent magnet width, and outer permanent magnet width. Core performance indicators are selected as the output response Y, including: average torque, torque ripple, stator iron loss, rotor iron loss, and permanent magnet loss. The Latin hypercube sampling (LHS) method is used to generate samples within the given parameter boundary intervals, and a high-precision sample dataset is obtained through parametric finite element simulation calculations.
[0022] In the above implementation step S1, in order to construct a proxy model that can accurately reflect the electromagnetic characteristics of the motor, this embodiment selects 10 key geometric parameters as input variables. The initial data and value range of each variable are shown in Table 1.
[0023] Table 1 Initial data and value range of various geometric parameters of the motor
[0024] Using the defined input parameter boundaries, 300 finite element calculation schemes are generated within a given interval, thereby obtaining a high-precision sample dataset. These multidimensional vectors, composed of geometric variables with complex and strong coupling relationships, are then used as the high-dimensional input space of the surrogate model.
[0025] S2: Logarithmic displacement transformation based on physical constraints Torque ripple and iron loss, key performance parameters of motors, are physically strictly non-negative and often exhibit skewed distributions. To correct the data distribution and impose physical constraints, a logarithmic shift transformation is performed on the original response value y before model training. , use Instead This transformation is designed to handle cases where the response value may be close to zero, thus avoiding numerical singularity. It maps a skewed distribution to an approximate Gaussian distribution that satisfies the basic assumptions of Gaussian process regression.
[0026] S3: Training of Heterogeneous Kernel Integrated Kriging Proxy Model The traditional Kriging model treats the unknown function as a superposition of a deterministic regression model (trend term) and a stochastic process (error term): , In the above formula and These are the deterministic trend term and the stochastic process term, respectively. The deterministic trend term... The expression used to describe the general trend of function values is: , In the formula These are the basis vectors of the regression function. It is the vector of regression coefficients to be determined.
[0027] stochastic process term This term is used to describe local fluctuations and uncertainties. It is a term with a mean of zero and a variance of... It is a stationary Gaussian random process. Its core characteristic is determined by the covariance function, namely: , In the formula, This indicates that the mean of the random process is 0. Let Variance be the variance of the random process. It is a correlation function that measures any two points in the design space. and The similarity between them.
[0028] For an unknown point The predicted value of the Kriging model Based on training samples The best linear unbiased estimator for is given by the following formula: , In the above formula It is the regression basis matrix of the training samples. It is the correlation matrix between training samples. Test point The correlation vector between all training samples, These are the regression coefficients estimated by the generalized least squares method.
[0029] To enhance the ability to capture multi-scale features, this invention introduces a heterogeneous kernel function strategy in the sub-model library of the integrated model, using a combination of Matern kernel and Rational Quadratic (RQ) kernel.
[0030] The RQ kernel is essentially a scale mixture of infinitely many RBF kernels of different lengths, and its covariance function is defined as: , In the formula It is a scale mixing parameter. When training complex indices with strong nonlinearity and multi-scale characteristics, such as rotor iron loss, the system automatically assigns higher weights to sub-models using RQ kernels to enhance the model's ability to represent multi-scale physical response fields.
[0031] S4: Robust aggregation and inverse transform prediction based on weighted median For performance indicators with high uncertainty, drastic fluctuations, or a tendency to produce outliers (such as torque pulsation and stator / rotor iron loss), a weighted median statistical method is used for aggregation to prevent the output of the integrated model from being skewed by a single sub-model with extremely poor performance.
[0032] The "performance index with drastic fluctuations" refers to motor performance parameters that meet any of the following quantitative statistical characteristics: (1) Fluctuation characteristics based on global sample space: Within the given initial design space of the motor, the coefficient of variation (i.e., the absolute ratio of the sample standard deviation to the mean) of this performance index in the initial sample dataset is greater than or equal to 15%.
[0033] (2) Uncertainty characteristics based on local prediction: In the prediction stage of the integrated surrogate model, for the same set of input motor structural parameters, the maximum relative range (i.e. the difference between the maximum and minimum predicted values, divided by the prediction mean) among the independent predicted values output by the M sub-models exceeds 10%.
[0034] In the motor design of this embodiment, the coefficient of variation of conventional indicators such as average torque is usually within the threshold range. However, due to the influence of nonlinear factors, the coefficient of variation and the predicted range of the sub-model for torque pulsation and stator and rotor iron loss significantly exceed the above-mentioned threshold. Therefore, they are strictly defined as performance indicators with severe fluctuations.
[0035] Assume the ensemble model contains M sub-models, and the predicted value of the m-th model is... The corresponding weight is And normalization satisfies Sort all predicted values in ascending order, and normalization satisfies: Sort all the predicted values of the sub-models in order of size. , The corresponding weights are arranged as follows: , Find a sorted index k that satisfies the following conditions: and , The predicted value corresponding to this index is output as the aggregated central tendency estimate: , Finally, an inverse exponential transform is performed on the aggregated predictions to recover the true physical values: , Since the exponential function is always greater than 0, this inverse transformation process completely eliminates the possibility of negative values in losses or torque pulsations that violate physical laws, thus ensuring the physical consistency of the prediction results.
[0036] Effect verification: To evaluate the predictive performance of the EEK surrogate model proposed in this invention, this embodiment selects the coefficient of determination (R²) and mean absolute percentage error (MAPE) as evaluation metrics, and compares it with the traditional Kriging surrogate model. The closer the R² value is to 1, the better the model fits the data; the smaller the MAPE value, the higher the model's predictive accuracy.
[0037] Table 2 shows the comparison of the prediction performance of the two surrogate models for key motor performance parameters under rated operating conditions, as well as the data in the instruction manual appendix. Figure 3 The scatter plot shows the fitting effect of the EEK proxy model on the predicted values and finite element calculation values of each key performance index in the embodiments of the present invention.
[0038] Table 2 compares the predicted values and fitting effects of the EEK proxy model of this invention on various performance indicators.
[0039] By comparing the evaluation results in Table 2, it can be seen that, under the same sample points, the EEK surrogate model proposed in this invention shows a significantly better predictive ability than the traditional Kriging surrogate model.
[0040] 1. For torque pulsation, a highly nonlinear index with a skewed distribution, the R² of the traditional model is only 0.5979, while the model of this invention improves R² to 0.9934 and reduces MAPE to 0.39% by using logarithmic shift transformation and heterogeneous kernel fusion.
[0041] 2. For rotor iron loss, which is extremely difficult to predict, the R² of the traditional model is as low as 0.1999 (with an error of 16.6%), which completely loses its predictive reference value; while the model of this invention significantly improves its R², stabilizing it at 0.9722, and controls the average absolute percentage error within 0.96%.
[0042] The above data fully demonstrates that the present invention effectively makes up for the shortcomings of traditional methods in handling multi-scale features and strong nonlinear indices, and fully verifies the high reliability of the prediction method in the comprehensive evaluation of multiple motor performance.
[0043] It should be noted that although this embodiment uses an 8-pole 48-slot double V-type built-in permanent magnet synchronous motor as a specific application object for detailed description, the performance prediction method based on enhanced integrated Kriging proposed in this invention is not limited to the specific motor pole-slot combination or rotor topology and motor type mentioned above.
[0044] The core of this invention lies in heterogeneous kernel fusion, physically constrained data transformation, and robust aggregation mechanisms during the proxy model construction process. This method can also be extended to surface-mounted permanent magnet synchronous motors (SPMSM), synchronous reluctance motors (SynRM), and even other types of rotating motors requiring high-dimensional parametric design and multiphysics performance evaluation.
[0045] The above description is merely a preferred embodiment of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention by those skilled in the art within the scope of the technology disclosed in the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.
Claims
1. A method for predicting motor performance based on an enhanced integrated Kriging surrogate model, characterized in that, Includes the following steps: S1: Obtain a sample set of structural parameters of permanent magnet synchronous motors, and obtain the corresponding motor structure and performance data through finite element analysis to construct an initial sample dataset. The motor structure and performance data includes motor structure parameters and motor performance indicators. S2: For motor performance indicators that exhibit a skewed distribution and are physically strictly non-negative, perform a logarithmic shift transformation on the target response values in the initial sample dataset. Map it to an approximate Gaussian distribution, where The target response value in the initial sample dataset; S3: Construct an ensemble Kriging surrogate model and introduce heterogeneous kernel functions into the sub-model library of the ensemble Kriging surrogate model; use the transformed sample dataset to perform cross-validation training on the sub-models with introduced heterogeneous kernel functions, and obtain an enhanced ensemble Kriging surrogate model through weighted fusion; S4: Obtain the motor structure parameters to be predicted and input them into the enhanced integrated Kriging proxy model; for performance indicators with drastic fluctuations, use the weighted median statistical method to aggregate the predicted values of each sub-model, restore the physical true value through exponential inverse transformation, and output the motor performance prediction result.
2. The motor performance prediction method based on the enhanced integrated Kriging surrogate model according to claim 1, characterized in that, The motor structure parameters in the motor structure and performance data include at least one or more combinations of the following: stator inner diameter, core length, slot height, slot wedge height, slot body height, slot width, slot wedge width, slot body width, inner permanent magnet width, and outer permanent magnet width; the motor performance indicators in the motor structure and performance data include at least one or more of the following: average torque, torque pulsation, stator iron loss, rotor iron loss, and permanent magnet loss.
3. The motor performance prediction method based on the enhanced integrated Kriging surrogate model according to claim 1, characterized in that, The motor performance indicators that exhibit skewed distribution and are physically strictly non-negative are specifically the motor's torque ripple and iron loss, wherein the motor's iron loss consists of stator iron loss and rotor iron loss.
4. The motor performance prediction method based on the enhanced integrated Kriging surrogate model according to claim 1, characterized in that, Introducing heterogeneous kernel functions into the sub-model library that integrates the Kriging proxy model specifically includes the following steps: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] The corresponding unknown function can be considered as a superposition of a deterministic regression model and a stochastic process: ,in and These are the deterministic trend term and the stochastic process term, respectively. The deterministic trend term... The expression is: In the formula These are the basis vectors of the regression function. It is the vector of regression coefficients to be determined; the stochastic process term. Used to describe local fluctuations and uncertainties, it is determined by the covariance function, i.e.: In the formula, For mathematical expectation, For variance, For covariance, This indicates that the mean of the random process is 0. Let Variance be the variance of the random process. For any two points in the design space, It is a correlation function. A heterogeneous kernel function is introduced into the correlation function to obtain a corresponding correlation function with the introduced heterogeneous kernel function. for: in The length scale parameter matrix is specifically a diagonal matrix. Each diagonal element corresponds to a motor geometric parameter. This represents the total number of motor geometric parameters, which include the stator inner diameter and slot width. For scale mixing parameters; Substituting the correlation function of the heterogeneous kernel function into the covariance function, we obtain the stochastic process term of the heterogeneous kernel function, and thus obtain the sub-model of the integrated Kriging surrogate model with the heterogeneous kernel function.
5. The motor performance prediction method based on the enhanced integrated Kriging surrogate model according to claim 4, characterized in that, The specific steps for cross-validation training of the sub-model with the introduced heterogeneous kernel function using the transformed sample dataset include the following: For an unknown point The predicted value of the Kriging model Based on training samples The best linear unbiased estimator for is given by the following formula: In the above formula It is the regression basis matrix of the training samples. It is the correlation matrix between training samples. Test point The correlation vector between all training samples, These are the regression coefficients estimated by the generalized least squares method.
6. The method for predicting motor performance based on an enhanced integrated Kriging surrogate model according to claim 1, characterized in that, The weighted median statistical method for aggregating the predicted values of each sub-model includes the following steps: Assuming the ensemble model contains a total of M sub-models, the predicted value of the m-th model is... The corresponding weight is And normalization satisfies Sort all the predicted values of the sub-models in order of size. The corresponding weights are normalized and adjusted; a sorting index k that satisfies the following conditions is found: and , and its corresponding predicted value As the final output.
7. A motor performance prediction system based on an enhanced integrated Kriging surrogate model, characterized in that, Includes the following modules: Initial sample dataset construction module: Obtain a sample set of structural parameters of permanent magnet synchronous motors, and obtain the corresponding motor structure and performance data through finite element analysis to construct the initial sample dataset. The motor structure and performance data includes motor structural parameters and motor performance indicators. Partial motor performance index processing module: For motor performance indices that exhibit skewed distributions and are physically strictly non-negative, a logarithmic shift transformation is performed on the target response values in the initial sample dataset. Map it to an approximate Gaussian distribution, where The target response value in the initial sample dataset; Integrated Kriging surrogate model building module: Introduces heterogeneous kernel functions into the sub-model library of the integrated model; performs cross-validation training on the sub-models using the transformed sample dataset; and obtains an enhanced integrated Kriging surrogate model through weighted fusion. Motor performance prediction module: Receives the structural parameters of the motor to be predicted and inputs them into the enhanced integrated Kriging proxy model constructed by the integrated Kriging proxy model construction module; for performance indicators with drastic fluctuations, the weighted median statistical method is used to aggregate the predicted values of each sub-model, and the physical true value is restored through inverse exponential transformation, and the motor performance prediction result is output.