A method and system for predicting coil parameters of a wireless power transfer system

Abstract

The application discloses a kind of wireless power transmission system coil parameter prediction method and system, it is related to coil electrical parameter calculation technical field, based on the two-dimensional parameterized geometric model of established circular coil carries out finite element simulation, obtains training data, uses training data to train improved Gaussian process regression model, obtains coil parameter prediction model, based on coil parameter prediction model, constructs integrated learning correction model, based on coil parameter prediction model and integrated learning correction model, the coil geometry parameter to be predicted is predicted, obtains including alternating current resistance, self-induction and mutual inductance Coil electrical parameter, to efficiently predict the coil parameter under different working conditions, reduce the time-consuming of traditional finite element simulation, more effectively ensure the accuracy of the coil alternating current resistance, self-induction and mutual inductance predicted, to accurately and efficiently predict the coil parameter of wireless power transmission system.

Description

Technical Field

[0001] This invention relates to the field of coil electrical parameter calculation technology, and in particular to a method and system for predicting coil parameters in a wireless power transmission system. Background Technology

[0002] Wireless power transfer (WPT) technology, as a convenient non-contact energy transfer method, has been widely used in fields such as electric vehicles, consumer electronics, and biomedicine.

[0003] The core objectives of WPT system design (system output power and efficiency) depend on the coupling coefficient. k and quality factor Q ,because k Directly related to mutual inductance and inversely proportional to self-inductance, accurate calculation of coil electrical parameters is crucial. In existing technologies, coil inductance can be determined through finite element analysis (FEA) simulation combined with manual adjustment. While this method achieves the design goal, the complex adjustment process and lengthy simulation time limit its practical application and flexibility. Current coil design and optimization typically rely on FEA simulation, experience, and manual fine-tuning. Although common, this method is time-consuming and cannot reliably determine the optimal design within the theoretically and practically derived self-inductance range.

[0004] Quality Factor Q It is directly related to frequency and inversely proportional to coil resistance. However, since AC resistance increases with frequency, an optimal operating frequency must be determined. f (50~200 (kHz)) to maximize the effect Q The optimal frequency may deviate from the usual 85kHz. Therefore, the accuracy of AC resistance calculations at different operating frequencies is crucial.

[0005] Methods for calculating coil inductance, mutual inductance, and AC resistance fall into three categories: empirical formulas, finite element analysis (2D or 3D), and analytical methods. Empirical formulas involve less computation but are prone to significant errors. FEA software can analyze coil geometry, but 2D simulation models ignore strand transposition, simplifying the coil model to concentric circles. 3D simulation models are accurate but require substantial computation and advanced equipment. Furthermore, the inability to model Litz wire introduces significant errors in AC resistance calculations. Analytical methods parameterize the coil to describe its geometry. To simplify construction and reduce computation, circular coils (CC) are approximated as concentric circles. While these simplifications reduce computational complexity and accelerate inductance calculations in WPT systems, they sacrifice accuracy. Existing AC resistance calculations often assume uniform current distribution; however, at higher resonant frequencies, skin effect losses increase, leading to overheating and incomplete twisting, rendering the uniform current assumption invalid. Moreover, the accuracy of such analytical models decreases when ferrite plates are added. Due to the complex magnetic field distribution in WPT systems, previous analytical models have struggled to accurately analyze the impact of ferrite plates of different sizes on coil inductance. Therefore, there is an urgent need for a precise and efficient method for calculating coil inductance that can be flexibly applied to various coil structures to accelerate the coil design process.

[0006] Machine learning has become a key tool for analyzing nonlinear systems in power electronics research. Feedforward neural networks (FNNs) have been developed to predict the self-inductance of circular coils, while Bayesian neural networks (BNNs) have been proposed to predict self-inductance and mutual inductance over different transmission distances. However, developing specialized prediction models for each coil type is impractical due to the need for extensive data collection and time-consuming training processes. Furthermore, existing research lacks a unified model capable of handling inductance, mutual inductance, and AC resistance. Therefore, developing a generalized coil structure model is crucial for achieving a balance between prediction accuracy and generalization ability in coil modeling. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method and system for predicting the coil parameters of a wireless power transmission system, which can accurately and efficiently predict the coil parameters of the wireless power transmission system.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A method for predicting coil parameters in a wireless power transfer system, comprising the following steps:

[0010] Finite element simulation was performed based on the established two-dimensional parametric geometric model of the circular coil to obtain training data;

[0011] The improved Gaussian process regression model is trained using the training data to obtain a coil parameter prediction model. The improved Gaussian process regression model combines neural processes and Gaussian process regression.

[0012] An integrated learning correction model is constructed based on the coil parameter prediction model.

[0013] Based on the coil parameter prediction model and the integrated learning correction model, the geometric parameters of the coil to be predicted are predicted to obtain the coil electrical parameters, which include AC resistance, self-inductance and mutual inductance.

[0014] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0015] A system for predicting coil parameters of a wireless power transfer system includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the various steps in the method for predicting coil parameters of a wireless power transfer system described above.

[0016] The beneficial effects of this invention are as follows:

[0017] Finite element simulation was performed based on the established two-dimensional parametric geometric model of the circular coil to obtain training data. The improved Gaussian process regression model was trained using the training data to obtain the coil parameter prediction model. The improved Gaussian process regression model combines neural processes and Gaussian process regression. An integrated learning correction model was constructed based on the coil parameter prediction model. The coil geometric parameters to be predicted were predicted based on the coil parameter prediction model and the integrated learning correction model to obtain the coil electrical parameters including AC resistance, self-inductance and mutual inductance. In this way, a two-dimensional finite element model combined with an improved Gaussian process regression model is introduced. Traditional Gaussian process regression models face challenges in computational complexity and expressive power when dealing with high-dimensional, complex structural data. Neural processes, as a model combining neural networks and stochastic processes, can learn efficient representations of data and capture uncertainties in the data. Therefore, the improved Gaussian process regression model combines neural processes and Gaussian process regression. For problems with multiple structures in wireless power transmission coils, the global latent representation learned by the neural process is concatenated with the original input features as the input of the Gaussian process regression model. Such a kernel function is based not only on the original features but also on the abstract features extracted by the neural process, thus making it easier for the Gaussian process regression model to model the relationship between input and output. For data with different structures, the neural process generates different global latent representations. Therefore, even if the distribution of data with different structures is different in the original feature space, they can be better distinguished and modeled in the enhanced feature space, making it more suitable for problems with multiple coil structures. This improves data utilization efficiency and model generalization ability, enabling efficient prediction of coil parameters under different operating conditions and reducing the time consumption of traditional finite element simulation.

[0018] Furthermore, by constructing an integrated learning correction model, the prediction results of the improved Gaussian process regression model can be corrected using the integrated learning correction model, which can more effectively ensure the accuracy of the predicted coil AC resistance, self-inductance and mutual inductance, thereby accurately and efficiently predicting the coil parameters of the wireless power transmission system. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a method for predicting coil parameters in a wireless power transfer system according to an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of a prediction system for coil parameters in a wireless power transfer system according to an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of a two-dimensional parametric geometric model of a circular coil in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0022] Figure 4This is a heatmap of the variables in the correction model of a method for predicting coil parameters in a wireless power transmission system according to an embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram comparing the self-inductance obtained from physical prototype experimental measurement and model prediction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0024] Figure 6 This is a schematic diagram comparing the mutual inductance obtained from physical prototype experimental measurement and model prediction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0025] Figure 7 This is a schematic diagram comparing the resistance obtained from physical prototype experimental measurement and model prediction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0026] Figure 8 This is a schematic diagram of the data distribution before and after self-inductance correction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0027] Figure 9 This is a schematic diagram of the data distribution before and after mutual inductance correction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0028] Figure 10 This is a schematic diagram of the data distribution before and after resistance correction in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0029] Figure 11 This is a comparative schematic diagram of the self-inductance obtained by different methods in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0030] Figure 12 This is a comparative schematic diagram of mutual inductance obtained by different methods in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention.

[0031] Figure 13 This is a schematic diagram comparing the resistances obtained by different methods in a method for predicting coil parameters of a wireless power transfer system according to an embodiment of the present invention.

[0032] Figure 14 This is a schematic diagram of the NGPR model framework in a method for predicting coil parameters of a wireless power transfer system according to an embodiment of the present invention.

[0033] Figure 15 This is a schematic diagram of the overall model data processing in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention;

[0034] Figure 16 This is an integrated learning correction framework diagram in a method for predicting coil parameters of a wireless power transmission system according to an embodiment of the present invention. Detailed Implementation

[0035] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0036] Before detailing the embodiments of this application, some related concepts will first be explained:

[0037] Neurally Guided Gaussian Process Regression (NGPR) Model: This is an improved Gaussian process regression model that combines neural processes and Gaussian process regression. Gaussian process regression is a nonparametric probabilistic regression model based on Bayesian statistics. Its core is to use Gaussian processes to model the distribution of data. It can output regression prediction values ​​and quantify the uncertainty of the prediction (such as confidence intervals). It is a classic method for small sample and nonlinear regression scenarios. Traditional Gaussian process regression models face challenges in computational complexity and expressive power when dealing with high-dimensional and complex structured data. Neural processes can learn efficient representations of data and capture the uncertainty in the data, enhancing the input information of the Gaussian process regression model and enabling it to better model complex data.

[0038] Radial Basis Function (RBF): One of the most commonly used kernel functions, suitable for fitting smooth nonlinear data;

[0039] Matern: A kernel function commonly used in statistics, suitable for non-smooth, noisy data;

[0040] Linear kernel (LIN): corresponds to fitting a linear relationship and is one of the simplest kernel functions;

[0041] Rational Quadratic (RQ): can be viewed as a mixture of multiple RBF kernels of different length scales, adapting to scenarios where data exhibits multiple scale variations.

[0042] In existing technologies, feedforward neural networks have been developed to predict the self-inductance of circular coils, while Bayesian neural networks have been proposed to predict self-inductance and mutual inductance over different transmission distances. However, due to the need for extensive data collection and time-consuming training processes, it is impossible to develop specialized prediction models for each coil type. Furthermore, current research lacks a unified model capable of handling inductance, mutual inductance, and AC resistance. Therefore, developing a general coil structure model is crucial for achieving a balance between prediction accuracy and generalization ability in coil modeling.

[0043] To at least address the aforementioned problems, embodiments of the present invention provide a method and system for predicting coil parameters in a wireless power transfer system. This method and system are applicable to wireless power transfer system coil design scenarios, such as small wireless charging coils for consumer electronic devices (smartphones, wearable devices, etc.) and coil design for biomedical implantable devices. Specific implementation methods are described below:

[0044] Please refer to Figure 1 One embodiment of the present invention is as follows:

[0045] A method for predicting coil parameters in a wireless power transfer system, comprising the following steps:

[0046] S1. Finite element simulation is performed based on the established two-dimensional parametric geometric model of the circular coil to obtain training data.

[0047] The training data includes the number of coil turns, coil outer diameter, wire diameter, transmission distance, and operating frequency.

[0048] Two-dimensional parametric geometric model of a circular coil, as follows Figure 3 As shown, the circular coil consists of two main components: a planar spiral copper conductor (coil winding) and a ferrite plate. A Cartesian coordinate system is established with the coordinate center as the origin, and the parameters... d Indicates the wire diameter of the coil winding. N The number of turns of the coupling coil, parameter gap This indicates the turn spacing of the coil, i.e., the distance between adjacent Litz wires. The coil has a uniform turn spacing. gap Winding, Z offset For the coupling coils Z Axis spacing, i.e., transmission distance. R in The radius of the starting point of the coil winding. R out The radius of the coil winding termination point, i.e., the outer diameter of the coil. R F The magnetic core radius is fixed at 7.5 cm, and the distance from the coil center to the magnetic core surface is fixed at 1 mm. These parameters are related by the following equation:

[0049] ;

[0050] Therefore, each coil can be defined by parameters d , N , gap , R out and R inThe only characteristic is that, in this embodiment, the coil winding method is tight winding, but the finite element simulation cannot set the gap to 0, and too low a gap would require very high mesh accuracy. Therefore, in an alternative implementation, the gap is set to 0.3 mm, and the turn spacing is temporarily excluded from the input layer.

[0051] Finite element simulation was performed based on the established two-dimensional parametric geometric model of the circular coil to obtain training data, specifically:

[0052] A systematic evaluation of the established two-dimensional parametric geometric model of the circular coil was conducted using COMSOL Multiphysics® v6.2. Key electromagnetic parameters (AC resistance, self-inductance, and mutual inductance) were extracted from each finite element analysis. Considering the high cost of physical prototypes and the computational limitations of 3D FEA, a structured parameter space reduction method was adopted. A total of 640 different coil calculation results (10×2×2×4×4) were generated through the combination of all parameter factors, which are the training data, as shown in Table 1. Parameter limits were determined through sensitivity analysis to maximize feature diversity while maintaining physical realizability. The simulated helical coils differed in the values ​​of different parameters, especially under specific operating conditions, where the five input parameters were selected to be uniformly distributed within a specific range. Geometric parameters were determined according to the application scenario. N , R out , d , f and Z offset The range of values ​​for the operating frequency f The kHz setting is above 1kHz to achieve high power density; the parameters of the dataset have an arbitrary range to verify the proposed method and can be extended to a wider range depending on the application; the ferrite material is very important in determining the self-inductance and mutual inductance of the coil, but the potential application scenarios of this invention are mainly small wireless charging applications, such as smart devices. Therefore, the ferrite material is set to TDK PC95, and the ferrite material is temporarily excluded from the input layer of the model.

[0053] Table 1. Parameter Variation of Coupling Mechanism Prediction Model

[0054]

[0055] Finite element simulation based on a two-dimensional parametric geometric model of a circular coil can significantly reduce computational complexity while maintaining accuracy compared to a three-dimensional simulation model.

[0056] S2. The improved Gaussian process regression model is trained using the training data to obtain a coil parameter prediction model. The improved Gaussian process regression model combines neural processes and Gaussian process regression, such as... Figure 14 and Figure 15 As shown.

[0057] Specifically, the number of coil turns, the outer diameter of the coil, the wire diameter, the transmission distance, and the operating frequency are input into an improved Gaussian process regression model for training. The model outputs the AC resistance, self-inductance, and mutual inductance of the coil to obtain a coil parameter prediction model. The selection of input features is crucial during model training. Features need to be ranked through correlation analysis, and features with high correlation are selected as model inputs. The model performance is then evaluated using evaluation metrics to determine if it meets practical requirements.

[0058] In this way, the number of coil turns, outer diameter of the coil, wire diameter, transmission distance, and operating frequency are input into the improved Gaussian process regression model for training, enabling it to accurately output the AC resistance, self-inductance, and mutual inductance of the coil. The resulting coil parameter prediction model has higher accuracy in predicting the self-inductance, mutual inductance, and resistance of the coil than the existing finite element simulation results.

[0059] Among them, such as Figure 14 As shown, the input features selected by the improved Gaussian process regression model are theoretically encoded as m dimensional vector x =[ U 1, U 2, U 3,..., U m Each dimension corresponds to a different physical or geometric parameter. The improved Gaussian process regression model is specifically as follows:

[0060] For a dataset containing n observations, a neural process model is used to learn task assignment:

[0061] ;

[0062] In the formula, The hidden layer representation of the encoder output represents the context representation of the task. This represents the input features of the model. This represents the output features of the model. This represents the mean of the latent variable distribution. The standard deviation of the latent variable distribution. The input feature set represents the context points. The output feature set represents the context points. This represents a deep neural network encoder; the encoder is a multilayer perceptron (...). It maps context points to distribution parameters in the latent space;

[0063] Define task-specific latent variables based on the encoder output:

[0064] ;

[0065] In the formula, Indicates task-specific latent variables, Representing task-specific latent variables The prior distribution, The hidden layer representation of the encoder output is the mean value after further processing, used to define... The distribution, Represents the identity matrix. Represents a multivariate Gaussian distribution; such as Figure 14 As shown, the input and output features of the model are processed by the encoder to obtain corresponding features s1, s2, ..., s n After processing, task-specific latent variables are output.

[0066] By combining the Gaussian process regression model with task priors, the mean function and kernel function are defined:

[0067] ;

[0068] ;

[0069] In the formula, This represents the mean of the task prior obtained from the decoder of the neural process model. Describes the decoder function of a neural process model. This represents the task prior covariance function obtained from the decoder of the neural process model. The covariance decoder function represents the neural process model. Represents the complete mean function. Represents the mean function, Represents the complete covariance function. Represents the kernel function. and It represents any two input feature vectors.

[0070] In this way, to address the problem of unreasonable prior distribution in traditional Gaussian process regression models, a neural-guided probabilistic regression model is used. By combining neural processes with Gaussian process regression, the kernel function and prior distribution are adaptively learned, enhancing the modeling ability of Gaussian processes. Furthermore, for the similar structures between coils in wireless power transmission, the task context is modeled through latent variables, enhancing the ability to capture nonlinear relationships and improving the prediction accuracy under small sample conditions.

[0071] In one alternative implementation, it may further include:

[0072] The mean absolute error of the coil parameter prediction model was evaluated. MAE ), root mean square error ( RMSE ), coefficient of determination ( R 2 ) and mean absolute percentage error ( MAPE Specifically:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] In the formula, Indicates the number of samples. Indicates sample The true value, Indicates sample The model output value, This represents the average value of the model's output.

[0078] Relying on a single evaluation metric can lead to biased model performance assessments, as it may overemphasize the performance of a particular metric while neglecting overall robustness. Therefore, to ensure comprehensiveness, four different evaluation metrics were used. These metrics collectively provide a comprehensive assessment of model performance. Mean absolute error quantifies the average error of the model's predictions; the smaller the value, the higher the accuracy. Root mean square error measures the quadratic mean of the prediction errors, emphasizing the larger errors introduced by squaring, which helps identify outliers and assess model accuracy. Mean absolute percentage error assesses relative accuracy by expressing the error as a percentage, which helps compare model performance at different scales. The coefficient of determination represents the dependent variable explained by the model; a value closer to 1 indicates a better fit between the predictions and the actual data.

[0079] S3. Construct an integrated learning correction model based on the coil parameter prediction model, specifically including S31-S36:

[0080] S31. Use multiple machine learning models as base learners, including random forest (RF), extreme gradient boosting (XGB), lightweight gradient boosting machine (LGBM), and support vector regression (SVR).

[0081] Specifically, to improve the effectiveness of the ensemble, a serial Boosting algorithm and a parallel Bagging (Bootstrap Aggregating) algorithm with weighted instances are used to generate base learners.

[0082] Among them, Boosting is an adaptive ensemble learning method that enhances the performance of the base algorithm by sequential error correction. The process first trains a base learner on the original dataset. Then, an adaptive reweighting mechanism increases attention to mispredicted samples by dynamically adjusting their weights. Subsequent learners are trained on these reweighted samples. This cycle is repeated until a predetermined number of iterations T is reached. Finally, the ensemble prediction is generated by aggregating the outputs of the base learners with optimal weights.

[0083] Complementing the extreme gradient boosting model, the lightweight gradient boosting machine model uses a histogram-based decision tree and a leaf-by-leaf growth strategy, enabling efficient parallel computation and memory optimization. Its gradient-based one-sided sampling (GOSS) and exclusive feature binding (EFB) techniques allow for rapid processing of high-dimensional data. The lightweight gradient boosting machine model also prevents overfitting through early stopping and maximum depth constraints. Both algorithms improve computational efficiency compared to traditional gradient boosting algorithms. The lightweight gradient boosting machine model performs well on large-scale datasets through distributed computing and reduces memory usage through histogram approximation.

[0084] Random forest models employ the Bagging paradigm, using an ensemble of a set of unrelated decision trees. Bagging reduces error through two steps: (1) training multiple base learners in parallel on a perturbed subset of data to minimize variance; and (2) controlling bias by the average of the majority vote or predictions.

[0085] Traditional bagging minimizes error by aggregating models. The decision space combines the judgments of multiple base classifiers, better capturing complex patterns in the data and thus improving overall accuracy and robustness. Bootstrap sampling, also known as replacement sampling, is used, allowing each base model to use a different subset of data, even with a limited sample size. Finally, the results for each base model are calculated. It is assumed that all base learners have the same reliability, and the contributions of all base learners are assigned equal weights. The drawback is that different models have varying predictive abilities, resulting in different performance levels for the trained base learners. Traditional bagging cannot distinguish between these models, and poorly performing models can drag down the overall performance.

[0086] To address the problems of the Bagging algorithm, this invention introduces a weighting mechanism. Instead of assigning equal voting power or averaging weights to all base learners, a weight is assigned to each base learner. The aggregated weights are obtained by aggregating the normalized weights of all base learners. M base The details are as follows.

[0087] S32. Calculate the weights of the base learner based on its performance, and normalize the weights to obtain normalized weights, specifically as follows:

[0088] ;

[0089] ;

[0090] In the formula, Indicates the weights of the base learner. Indicates the first The weights of each base learner This represents the root mean square error of the base learner. This represents a very small positive number to prevent the denominator from being 0. This represents the weights of the normalized base learner. This reflects the reliability of its predictions; the better the base learner's performance, the greater the weight it receives.

[0091] S33. Use the coil parameter prediction model as a meta-learner.

[0092] Among them, the weighted meta-learner features z mata Represented as:

[0093] ;

[0094] In the formula, Indicates the first i Each base learner applies input features The predicted value, Indicates the first The weights of the normalized base learner.

[0095] S34. Generate an ensemble learning correction model based on the base learner with the normalized weights and the meta learner, such as... Figure 16 As shown.

[0096] The ensemble learning correction model addresses the discrepancy between 2D axisymmetric models and high-fidelity simulations, as well as the mismatch between FEA predictions and experimental measurements. The ensemble learning correction model employs a two-layer architecture. In the first stage, base learners (RF, XGB, LGBM, and SVR) extract features using a training subset of K-fold cross-validation. This process first performs normalization to reduce the impact of outliers, then hierarchically divides the dataset into four non-overlapping folds using K-fold cross-validation. Each base learner is trained on three folds and validated on excluded folds, generating out-of-fold predictions that aggregate into a meta-feature matrix. This matrix captures different prediction patterns from the base layer and is used to train a Gaussian process meta-regressor. The regressor uses multiple kernel functions (e.g., RBF, Matern, and polynomial) to model complex nonlinear relationships and uncertainties. During inference, test set predictions from all base learners are concatenated into a meta-test matrix, which is then synthesized by the trained meta-learner into the final prediction.

[0097] The ensemble learning correction model leverages the collective intelligence of different algorithms and compensates for the simulation-reality gap through probability error propagation, enhancing the robustness of independent models. Original data normalization is used to minimize the impact of outliers.

[0098] S35. Establish a calibration dataset based on the training data.

[0099] Actual coil data acquisition involves a lengthy and labor-intensive winding process, making the acquisition of large-scale datasets impractical and detrimental to model training. However, coil electrical parameters exhibit strong correlations with geometric features and material properties, particularly for Litz wire configurations. The choice of Litz wire significantly alters electromagnetic properties. This necessitates the development of a calibration model capable of high-accuracy predictions under extremely scarce data conditions. The calibration dataset contains unique coil configurations derived from the training data. This represents only 12.9% of the original prediction model's training data size, and the corresponding structural parameters are shown in Table 2.

[0100] Table 2. Parameter Variation Table of Integrated Learning Correction Model

[0101]

[0102] In one alternative implementation, it may further include:

[0103] To optimize feature selection and reduce the risk of performance degradation, a multivariate correlation analysis was performed on the FEA output and design parameters using the Pearson correlation coefficient. For example... Figure 4 As shown, the self-induction obtained using experimental measurements L MEA and R out ,d , N and the corresponding results obtained using FEA L FEA The values ​​have a strong dependency relationship, among which... L FEA The correlation was highest. Mutual inductance obtained using experimental measurements... M MEA and R out , N , Z offset and obtained using FEA M FEA Significantly correlated, among which M FEA The correlation coefficient was the strongest, reaching 0.99. The resistance obtained using experimental measurements... R MEA and R out , d , N , f and obtained using FEA R FEA Significantly correlated with simulation results R FEA There is a strong correlation.

[0104] S36. Train the ensemble learning correction model using the correction dataset to obtain the trained ensemble learning correction model, such as... Figure 15 and Figure 16 As shown.

[0105] like Figure 16 As shown, when training an ensemble learning calibration model, the calibration dataset can be divided into multiple validation sets and training sets, which are then input into the model for training to obtain prediction results. Next, test data is used to verify the model performance. If the required performance is not achieved, the model is retrained. If the required performance is achieved, the model can be compared with finite element simulation and experimental measurement for accuracy verification.

[0106] In this way, ensemble learning can reduce variance and bias by combining multiple base learners, effectively compensating for the "simulation-reality" gap. The base learners include random forest models, extreme gradient boosting models, lightweight gradient boosting models, and support vector regression models. The meta-learner is the coil parameter prediction model (NGPR). A weighted aggregation strategy is used to allocate weights according to the performance of the base learners, thereby improving overall robustness.

[0107] S4. Based on the coil parameter prediction model and the integrated learning correction model, predict the geometric parameters of the coil to be predicted to obtain the coil electrical parameters, which include AC resistance, self-inductance, and mutual inductance, such as... Figure 15 As shown, specifically including S41-S42:

[0108] S41. Input the geometric parameters of the coil to be predicted into the coil parameter prediction model, and output the initial coil electrical parameters.

[0109] S42. Input the geometric parameters of the coil to be predicted and the initial electrical parameters of the coil into the integrated learning correction model, and output the electrical parameters of the coil.

[0110] In this way, the coil parameter prediction model is used to make preliminary predictions of the coil electrical parameters, and then the ensemble learning correction model is used to correct the predicted coil electrical parameters, so that the final output coil electrical parameters are more accurate and the coil is designed with high efficiency.

[0111] This study compares several recently developed regression networks with the NGPR model, including Support Vector Regression, Random Forest, Extreme Gradient Boosting, Backpropagation Neural Network (BPNN), and the unmodified GPR model. Model training was performed using the scikit-learn library (a free machine learning library).

[0112] The generalization ability of a regression model to data is primarily determined by its hyperparameters. Even advanced machine learning algorithms can exhibit poor performance if the parameters are poorly chosen. In particular, underfitting or overfitting may occur if a model suitable for a given input data is not fully parameterized. To achieve optimal model performance, Bayesian optimization is used to perform a separate grid search on the hyperparameters of each model to determine its ideal parameters. In this invention, this method ensures that each model achieves optimal performance when using coil data. MAE As the optimization objective of the regression model, MAE The same input test samples were determined using the regression model and COMSOL (finite element simulation software). MAE The parameter selection of the model can be verified.

[0113] Considering the limited initial sample size and potential data imbalance, regression models are prone to overfitting and poor generalization. To address these issues, cross-validation is used to reduce the risk of overfitting and underfitting in the regression model, resolve data insufficiency and imbalance, and ensure the robustness of model training. All datasets are randomly divided into K mutually exclusive subsets of similar size, and K iterations are performed. In each iteration, one fold is used as the test set, and the remaining K-1 folds are used as the training set. The model is trained using the training set and evaluated on the test set to obtain a performance score. After the iterations, K performance scores are obtained, and the final model performance is the average of these K scores. By utilizing the existing limited data more efficiently and reliably, the model's performance and generalization ability are improved. In this embodiment, K is set to 5.

[0114] As shown in Table 3, comparing the mean absolute error (MAE) of the NGPR model with the performance metrics of other regression models, the NGPR model has the best MAE, yielding a more accurate reward closer to the FEA results. The optimized GPR model outperforms all benchmark models in evaluating the objective. High-quality finite element analysis data ensures good fit for all models, but the enhanced GPR model still shows a significant advantage in prediction accuracy, demonstrating the effectiveness of network training.

[0115] Table 3 Comparison of Prediction Model Performance

[0116]

[0117] To verify the generalizability of the model beyond simulation, experiments were conducted on the prototype winding coil under controlled conditions. The coil was tightly wound and coiled. R out and d They are 5cm and 1.08mm respectively. N The values ​​are 15-19. A comparison of self-inductance, mutual inductance, and resistance obtained from physical prototype experimental measurements and model predictions is shown below. Figures 5-7 As shown in the figure, L P1 , M P1 , R P1 These represent the self-inductance, mutual inductance, and resistance predicted using the NGPR model of this invention, respectively. This dual verification framework confirms the robustness of the model across different data domains.

[0118] like Figures 5-7 As shown, the simulation predictions exhibit trends consistent with experimental measurements, but discrepancies arise due to some technical limitations:

[0119] a) Simulation accuracy depends on accurate two-dimensional axisymmetric model design and adaptive mesh refinement;

[0120] b) Calculate the trade-offs to limit model complexity;

[0121] c) The simplified finite element simulation model cannot capture the interstrand proximity effect in the Leeds line;

[0122] d) Incomplete twisting of the Litz wire under high-frequency operating conditions can lead to current redistribution, which is ignored in the simulation.

[0123] Therefore, to address these discrepancies, this invention proposes the aforementioned ensemble learning calibration model. To maximize the advantages of the ensemble learning calibration model, the individual performance of each model is evaluated. This is achieved by determining the ideal settings for the hyperparameters of each model through a separate grid search. In this invention, this method ensures that each model achieves optimal performance when running with calibration data. Based on the statistical data shown in Table 2, the performance of the ensemble learning calibration model, the K-Nearest Neighbors (KNN) algorithm, SVR, and XGB was evaluated respectively. The evaluation results are shown in Table 4, demonstrating that the ensemble learning calibration model of this invention exhibits the best overall performance.

[0124] Table 4 Overall Model Performance Table

[0125]

[0126] Data distribution before and after correction as follows Figures 8-10 As shown, Figures 8-10 middle, y =0.968 x +1.2763 y =0.9066 x +3.182、 y =0.967 x +0.18、 y =0.961 x +5.0144 and y =0.2023 x +41.7087 represents the true value of the corresponding fitted line. y Regarding the predicted value x The linear regression equations are shown in red, representing the coefficient of determination of the corrected fitted line and the linear regression equation, while those in blue represent the coefficient of determination of the finite element simulation fitted line and the linear regression equation. The proposed prediction-correction hybrid model performs well in the optimization objective. The original simulation predictions exhibit significant dispersion, and the simulated values ​​and measured data show the same trend. From... Figures 8-10 As can be seen, the corrected data shows a significant improvement, with the corrected output results clustering closely around the ideal fitting line. It is worth noting that the corrected... R 2The maximum value was improved by 0.55. This calibration method reduced the average relative deviation between targets by more than 30%. Specifically, the consistency of resistance predictions was significantly improved, with the average error reduced to 3.39% and the peak error reduced to 12.17%. These results confirm the effectiveness of the improved model in terms of enhancement.

[0127] To fully verify the accuracy of the proposed self-inductance, mutual inductance, and resistance models, the winding layout was adjusted as follows: Number of turns N The number of turns was increased from 11 to 17, with a step size of 2, and the transmission distance was... Z offset Set to 40mm and 60mm respectively, frequency f Set to 100kHz and 150kHz respectively, diameter d The diameter was set to 1.35 mm. The coil material was 0.1 × 100 Litz wire. The self-inductance, mutual inductance, and resistance of the prototype coil were calculated using FEA, conventional methods, and the methods described above in this invention, and compared with experimental measurements.

[0128] like Figures 11-13 As shown, the self-inductance obtained from the conventional model, the model proposed in this invention, FEA simulation, and experimental measurement are respectively labeled as follows: L CUA , L P , L FEA and L MEA The corresponding mutual inductances are denoted as follows: M CUA , M P , M FEA and M MEA The resistances obtained from the traditional model, the model proposed in this invention, and experimental measurements are respectively denoted as... R CUA , R P and R MEA , Figure 12 The different colored dashed lines in the middle were obtained through different methods. Z offset The mutual inductance values ​​are set at 8cm. The solid lines of different colors represent values ​​obtained through different methods. Z offset Set as the mutual inductance value under the condition of 6cm. Figure 13 The different colored dashed lines in the middle were obtained through different methods. f The resistance values ​​are set at 150kHz; the different colored solid lines represent values ​​obtained through different methods.f Set the resistance value for 100kHz conditions. From Figures 11-13 The results show that the coil prediction correction model proposed in this invention has high accuracy in calculating the three objectives of self-inductance, mutual inductance, and resistance. Finite element simulation also demonstrates high accuracy. However, due to the large prediction error of resistance in finite element simulation, it was not included in the calculations. Figure 13 The annotation is done in the middle. This is because finite element simulation requires very high precision meshing, and finite element simulation software cannot simulate the internal structure of Litz wire. Different numbers of Litz wires will yield the same calculation results, which do not match the actual measured values. L P , L FEA and L MEA The values ​​are very close. M P and M MEA The error between them is very low. This is due to various factors affecting resistance calculations, such as the skin effect and proximity effect. R P and R MEA The error rate of the target is higher than that of the other two targets.

[0129] As shown in Table 5, the proposed coil prediction correction model outperforms finite element simulation under various conditions. The performance of the FEA tool varies with the computer system performance; in this study, the simulation took 92 minutes, while the proposed model and 2D simulation were completed within 2 minutes. Therefore, the proposed model has higher accuracy in calculating self-inductance, mutual inductance, and resistance than traditional methods, and also has a faster computation speed than element simulation.

[0130] Table 5 Comparison of Time Consumption

[0131]

[0132] In summary, the present invention provides a method for predicting coil parameters in a wireless power transmission system. This method utilizes finite element simulation based on a two-dimensional parametric geometric model of a circular coil to obtain training data. The training data is then used to train an improved Gaussian process regression model, resulting in a coil parameter prediction model. This improved Gaussian process regression model combines neural processes and Gaussian process regression. An integrated learning correction model is constructed based on this model. Finally, the coil parameter prediction model and the integrated learning correction model are used to predict the geometric parameters of the coil to be predicted, yielding coil electrical parameters including AC resistance, self-inductance, and mutual inductance. This method introduces a two-dimensional finite element model combined with an improved Gaussian process regression model to efficiently predict coil parameters under different operating conditions. The parameters are improved, reducing the time-consuming nature of traditional finite element simulation. Furthermore, the ensemble learning correction model can be used to correct the prediction results of the improved Gaussian process regression model, more effectively ensuring the accuracy of the predicted coil AC resistance, self-inductance, and mutual inductance, thus accurately and efficiently predicting the coil parameters of the wireless power transmission system. In addition, ensemble learning can reduce variance and bias by combining multiple base learners, effectively compensating for the "simulation-reality" gap. The base learners include random forest model, extreme gradient boosting model, lightweight gradient boosting machine model, and support vector regression model. The meta-learner is the coil parameter prediction model, which uses a weighted aggregation strategy to allocate weights according to the performance of the base learners, thereby improving the overall robustness.

[0133] According to another aspect of the invention, Figure 2 This is a schematic diagram illustrating a system for predicting coil parameters of a wireless power transfer system according to an embodiment of the present invention. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the method for predicting coil parameters of a wireless power transfer system as described above.

[0134] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for predicting coil parameters in a wireless power transfer system, characterized in that, Including the following steps: Finite element simulation was performed based on the established two-dimensional parametric geometric model of the circular coil to obtain training data; The improved Gaussian process regression model is trained using the training data to obtain a coil parameter prediction model. The improved Gaussian process regression model combines neural processes and Gaussian process regression. An integrated learning correction model is constructed based on the coil parameter prediction model. Based on the coil parameter prediction model and the integrated learning correction model, the geometric parameters of the coil to be predicted are predicted to obtain the coil electrical parameters, which include AC resistance, self-inductance and mutual inductance. The improved Gaussian process regression model is specifically as follows: For a dataset containing n observations, a neural process model is used to learn task assignment: ； In the formula, This represents the hidden layer representation of the encoder output. This represents the input features of the model. This represents the output features of the model. This represents the mean of the latent variable distribution. The standard deviation of the latent variable distribution. The input feature set represents the context points. The output feature set represents the context points. This represents a deep neural network encoder; Define task-specific latent variables based on the encoder output: ； In the formula, Indicates task-specific latent variables, Representing task-specific latent variables The prior distribution, The hidden layer representation of the encoder output is the mean value after further processing. Represents the identity matrix. Indicates a multivariate Gaussian distribution; By combining the Gaussian process regression model with task priors, the mean function and kernel function are defined: ； ； In the formula, This represents the mean of the task prior obtained from the decoder of the neural process model. Describes the decoder function of a neural process model. This represents the task prior covariance function obtained from the decoder of the neural process model. The covariance decoder function represents the neural process model. Represents the complete mean function. Represents the mean function, Represents the complete covariance function. Represents the kernel function. and Represents any two input feature vectors; Based on the coil parameter prediction model and the ensemble learning correction model, the geometric parameters of the coil to be predicted are predicted, and the electrical parameters of the coil are obtained, including: Input the geometric parameters of the coil to be predicted into the coil parameter prediction model, and output the initial coil electrical parameters; The geometric parameters of the coil to be predicted and the initial electrical parameters of the coil are input into the integrated learning correction model, and the electrical parameters of the coil are output.

2. The method for predicting coil parameters in a wireless power transfer system according to claim 1, characterized in that, The training data includes the number of coil turns, coil outer diameter, wire diameter, transmission distance, and operating frequency; The improved Gaussian process regression model is trained using the training data to obtain a coil parameter prediction model, including: The improved Gaussian process regression model is trained by inputting the number of coil turns, the outer diameter of the coil, the wire diameter, the transmission distance, and the operating frequency into the output AC resistance, self-inductance, and mutual inductance of the coil to obtain the coil parameter prediction model.

3. The method for predicting coil parameters in a wireless power transfer system according to claim 1, characterized in that, The ensemble learning correction model constructed based on the coil parameter prediction model includes: Multiple machine learning models are used as base learners, including random forest model, extreme gradient boosting model, lightweight gradient boosting machine model and support vector regression model; The weights of the base learner are calculated based on its performance, and the weights are then normalized to obtain normalized weights. The coil parameter prediction model is used as a meta-learner; An ensemble learning correction model is generated based on the base learner and the meta learner with the normalized weights. A calibration dataset is established based on the training data; The ensemble learning correction model is trained using the correction dataset to obtain the trained ensemble learning correction model.

4. A prediction system for coil parameters of a wireless power transfer system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements each step of the method for predicting coil parameters of a wireless power transmission system according to any one of claims 1-3.

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