Deep learning-based magnetic element magnetic core loss prediction and optimization method

Abstract

The invention discloses a method for constructing a magnetic core loss model of a magnetic element based on deep learning, and aims to solve the problem that an existing loss model is insufficient in prediction precision under complex working conditions. A traditional model cannot provide accurate loss evaluation when facing changes of various factors such as temperature, materials, frequency and the like, and magnetic element design and optimization of efficiency of a power converter are limited. Therefore, a high-precision magnetic core loss prediction model is constructed on the basis of a deep learning technology in combination with various key factors such as the temperature, the magnetic core material, the excitation waveform and the working frequency, and the prediction accuracy and universality are remarkably improved. On the basis, a double-target optimization model is further established, an MOEAD algorithm is adopted for solving, and the purposes of minimizing loss and maximizing magnetic energy transmission are achieved by optimizing design variable combinations. The method can be widely applied to the field of magnetic element design and optimization, and theoretical guidance and engineering reference are provided for accurate prediction of magnetic core loss and performance optimization of magnetic elements.

Description

Technical Field

[0001] The present invention relates to technologies related to the performance optimization and loss prediction of magnetic components, in particular to a method of constructing a model through deep learning and combining it with an optimization algorithm to establish a high-precision core loss model that is generally applicable to various working conditions. Background Art

[0002] Power conversion, as one of the cores of modern energy technologies, is a key technology for realizing the conversion between direct current and alternating current, different voltages and frequencies. It is widely used in fields such as communication power supplies, data centers, new energy power conversion, electric vehicles, rail transit, and smart grids. In recent years, with the development of the third-generation power semiconductor technology, power converters are evolving towards high-frequency, high-power density, and high-reliability directions. Magnetic components (such as transformers and inductors), as the core devices in power converters, undertake functions such as magnetic energy transfer, storage, and filtering. Their performance directly affects the volume, weight, efficiency, and cost of power converters. Therefore, achieving the efficient design and optimization of magnetic components has become a key issue in the development of power conversion technology.

[0003] The academic community has carried out a large number of studies in fields such as the loss characteristics of magnetic components, material performance optimization, and loss model construction, and has achieved many results. For example, the research on winding losses has achieved relatively accurate calculations through electromagnetic field finite element simulation technology; in terms of core losses, the classical Steinmetz equation (SE equation) and its modified models provide theoretical support for the loss calculation of sine waveforms. However, there are still many problems to be solved: (1) The existing core loss models are mainly constructed for specific working conditions (such as sine waveforms, constant temperatures, etc.), ignoring the non-linear and complex coupling effects of factors such as working frequency, magnetic flux density, excitation waveform, working temperature, and core material, resulting in insufficient prediction accuracy in practical applications. (2) Due to the complex microstructure of high-frequency magnetic materials (such as ferrites, alloy magnetic powder cores, amorphous / nanocrystalline, etc.), existing research mostly uses empirical formulas for fitting, but fails to fully reveal the physical mechanism of the materials themselves, making it difficult for the models to adapt to new working conditions of high frequency and high power density. (3) Most of the existing literature only conducts loss characteristic analysis based on experimental data, lacking a unified prediction model that can cross different materials and working conditions. In particular, there is less research on loss modeling under non-sine waveform conditions, restricting the scope of application of the models. (4) The existing loss optimization research often focuses on a single goal (such as minimizing losses), and fails to consider comprehensive factors such as power density, transmission efficiency, and material cost at the same time, resulting in limited design optimization space in practical applications. Summary of the Invention

[0004] Objective of the Invention: To solve the above problems, this study starts from the actual working conditions, combines deep learning and mathematical modeling methods, constructs a unified core loss prediction model by collecting the measured data of magnetic components under different temperature, frequency, and magnetic flux density conditions. On this basis, explore the loss optimization strategy under multi-factor coupling, and propose a dual-objective optimization method that takes into account both minimizing core loss and maximizing transmitted magnetic energy, aiming to provide a theoretical basis and technical support for the design and application of high-frequency magnetic components.

[0005] Technical Solution: To achieve the above objective, the technical solution adopted by the present invention is: A method for constructing a core loss model of a magnetic component based on deep learning. By collecting the measured data of magnetic components under different working conditions, combining deep learning technology and mathematical modeling methods, construct a unified core loss prediction model, and on this basis explore the loss optimization strategy under multi-factor coupling, and propose a dual-objective optimization method that takes into account both minimizing core loss and maximizing transmitted magnetic energy. The specific steps are as follows:

[0006] Step 1: Collect the core loss data of magnetic components under different working conditions (such as temperature, frequency, magnetic flux density, etc.); preprocess the collected data, including outlier detection and repair, categorical variable encoding, etc., to ensure data integrity and consistency; extract statistical features, time-domain features, and frequency-domain features, and establish variables that can characterize the distribution characteristics and waveform shape characteristics of magnetic flux density, providing data support for subsequent modeling.

[0007] Step 2: Based on the extracted feature variables, combined with feature importance analysis, screen key variables, and use machine learning algorithms such as gradient boosting trees to construct an excitation waveform classification model. By comparing the performance of different classification algorithms, select the model with the best classification effect to classify and predict the excitation waveform of magnetic components.

[0008] Step 3: Aiming at the problem that the traditional Steinmetz equation has prediction errors under specific conditions (such as sinusoidal waveforms), analyze the loss change law of the same core material at different temperatures; introduce a temperature correction factor into the Steinmetz equation, and combine the interaction terms of temperature and other working condition variables (such as frequency, waveform, material, etc.) to construct a modified core loss model. Further use machine learning technology to optimize the residual part of the model to improve the model prediction accuracy.

[0009] Step 4: Based on the modified core loss model, combined with the frequency equivalence method under different waveform conditions, construct a unified core loss prediction model that can span different core materials and working condition conditions. Use experimental data to train the model using deep learning and various machine learning algorithms, compare the model performance, select the model with the highest prediction accuracy, and verify its generalization ability.

[0010] Step 5: Based on the core loss prediction model constructed in Step 4, a two-objective optimization method is proposed, with the minimization of core loss and the maximization of transmitted magnetic energy as the optimization objectives; temperature, frequency, waveform, peak magnetic flux density, and core material are set as decision variables, an optimization objective function is constructed, and constraint conditions are set. The MOEAD algorithm is used to solve the optimization model to determine the optimal operating condition combination of the magnetic component performance and output the optimal parameter configuration plan.

[0011] Further, the measured data of the magnetic component in Step 1 are from the experimental results of different core materials, and the data corresponding to each material record its performance under different operating conditions. Specifically, there are differences in the data volume of different core materials, and the sample numbers of Material 1 to Material 4 are 3,400, 3,000, 3,200, and 2,800 respectively. Each row of data includes temperature, frequency, type of excitation waveform, core loss, and 1,024 magnetic flux density sampling points, comprehensively reflecting the operating characteristics of the magnetic component under specific operating conditions.

[0012] Specifically, to ensure the accuracy and integrity of the data, detailed preprocessing of the data table is required. First, it is confirmed through screening that there are no missing values in the data; then, the Isolation Forest algorithm is used to detect and repair possible outliers. In addition, to further describe the dynamic characteristics and distribution laws of the magnetic flux density, statistical features such as central tendency, dispersion degree, and distribution shape, as well as indicators such as dynamic changes and frequency distributions, are extracted from the magnetic flux density sampling point data to provide reliable parameter support for the subsequent steps. The specific preprocessing methods are as follows:

[0013] (1) Use the Isolation Forest algorithm to detect outliers. The Isolation Forest is an unsupervised learning algorithm, which is widely used in anomaly detection of structured data due to its linear time complexity and excellent accuracy.

[0014] (2) When there are outliers in the sequence, it will cause great interference to data analysis, not only damaging the continuity of system operation but also violating the principle of "importance of order" of time series. To maintain the integrity and sequentiality of the data, interpolation processing of the abnormal data is considered. The KNN interpolation method is selected for interpolation.

[0015] (3) By observing the measured data, it can be found that the temperature (taking values of 25°C, 50°C, 75°C, and 90°C) is a discrete variable; the core material (taking values of Material 1, Material 2, Material 3, and Material 4) and the excitation waveform (taking values of sine wave, triangular wave, and trapezoidal wave) are both categorical variables. Without encoding, it is difficult to use them for subsequent analysis. Therefore, the present invention first uses the One-hot method to encode the variables and uses the better one of the two for prediction and analysis when establishing the model later.

[0016] Since the temperature data is presented as numerical data, sequence encoding is not performed on it for the time being. Sequence encoding is performed on the core material and excitation waveform, and the specific encoding results are shown in the table:

[0017] Table 1 One-hot Encoding Table for Temperature, Core Material, and Excitation Waveform

[0018]

[0019] Furthermore, in step 2, by classifying the excitation waveforms of magnetic components, the distribution law of magnetic flux density is accurately identified. Different excitation waveforms (such as sine wave, triangular wave, trapezoidal wave) result in different growth, decay, or fluctuation patterns of magnetic flux density. To improve the classification efficiency and accuracy, first, the decision tree algorithm is used to evaluate the importance of feature variables, screen out the key features most relevant to the target variable, reduce the data dimension, and eliminate redundant information. Then, three classification models, namely decision tree, random forest, and XGBoost, are constructed, and the most accurate model is selected for excitation waveform classification to ensure the accuracy and reliability of classification.

[0020] Furthermore, in step 3, aiming at the limitations of the Steinmetz equation in practical applications, a core loss model including a temperature correction factor is constructed. The traditional Steinmetz equation is applicable to sine waveforms and constant operating conditions, but it has poor adaptability to temperature changes. To improve the accuracy of loss prediction, based on the Steinmetz equation, the influence of temperature on loss is analyzed, a temperature correction factor and its cross terms with other factors (such as frequency, magnetic flux density) are added, and a modified equation is constructed to improve the adaptability of the model to different temperature changes.

[0021] After the modified model is constructed, the effectiveness of the temperature correction factor is verified through experimental data, and the model parameters are optimized to improve the prediction accuracy. To enhance the adaptability of the model to complex operating conditions, machine learning methods are introduced to optimize the fitting of the residual loss, make up for the deficiencies of the traditional model, and thus construct a core loss prediction model with higher accuracy and wider application range, laying a foundation for the optimization design of the subsequent unified loss model.

[0022] Furthermore, in step 4, a unified core loss prediction model applicable to different materials and operating conditions is constructed to solve the prediction error of the existing model under non-sine waveform conditions. First, through the equivalent sine wave frequency conversion formula, triangular wave and trapezoidal waveforms are converted into equivalent sine wave frequencies to make them adapt to the Steinmetz correction equation. Then, on this basis, the modified model with the best effect is selected, and machine learning is applied to optimize the residual loss to improve the prediction accuracy under complex operating conditions. Finally, a unified loss prediction model applicable to sine waves and non-sine waves is constructed, significantly improving the generalization ability of the model and providing accurate loss assessment support for the development of power electronics technology.

[0023] Further, in step five, based on the core loss prediction model in step four, the transmitted magnetic energy is introduced as a key performance indicator to construct a bi-objective mixed-integer nonlinear programming model for comprehensive optimization of the performance of magnetic components. The objective of this model is to minimize the core loss and maximize the transmitted magnetic energy. The core loss prediction model takes into account five factors: temperature, frequency, peak magnetic flux density, excitation waveform, and core material, while the transmitted magnetic energy is related to the frequency and peak magnetic flux density. Through frequency equivalent substitution, the core loss prediction model can be applied to all waveform conditions. Corresponding constraint conditions are set in the optimization model, where temperature, waveform, and core material are categorical variables, and frequency and peak magnetic flux density are continuous variables. The MOEAD algorithm is used to solve the bi-objective optimization model to balance the core loss and the transmitted magnetic energy, and finally determine the optimal combination conditions of the five factors to ensure the minimization of the core loss and the maximization of the transmitted magnetic energy, thereby realizing the optimization of the overall performance of magnetic components and providing theoretical support for efficient design and performance improvement.

[0024] The MOEAD algorithm is used to solve the bi-objective optimization model, comprehensively considering the trade-off relationship between the core loss and the transmitted magnetic energy. Finally, the optimal combination conditions of the five influencing factors are determined, achieving the balance of minimizing the core loss and maximizing the transmitted magnetic energy, thereby optimizing the overall performance of magnetic components and providing theoretical support and technical guarantee for the efficient design and performance improvement of magnetic components.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. In the construction process of the excitation waveform classification model of the present invention, 10 key feature variables of magnetic flux density are extracted, covering statistical features, time-domain features, and frequency-domain features, comprehensively describing the distribution characteristics and waveform shape features of magnetic flux density, making the accuracy of the classification model close to 100%, and significantly improving the accuracy and reliability of excitation waveform classification.

[0027] 2. In the process of modifying the Steinmetz equation of the present invention, various forms of temperature functions are fully considered, including linear, quadratic, exponential, and power functions, and the interaction terms between temperature and other influencing factors are introduced. At the same time, the machine learning method is combined to supplement and optimize the residual loss value of the model, significantly improving the prediction accuracy of the modified model and making it more applicable and reliable under complex working conditions.

[0028] 3. The present invention constructs a core loss prediction model based on the Steinmetz modified equation, integrates the interaction of main influencing factors, and selects the model with the best performance for core loss prediction through the training and comparison of various machine learning models. This model has high accuracy and strong generalization ability, and can meet the loss evaluation requirements under different materials and working conditions.

[0029] 4. The core loss prediction model proposed by the present invention can accurately quantify the loss performance of different materials under different working conditions, provide a scientific basis for material selection and magnetic component performance optimization, and contribute to significantly improving the efficiency and stability of magnetic components.

[0030] 5. The core loss prediction model of the present invention takes five main influencing factors, namely temperature, frequency, excitation waveform, peak magnetic flux density, and core material, as the core, has good scalability, can be further optimized by introducing other possible influencing factors, improve the prediction accuracy, and adapt to more complex actual working conditions, supporting the use of magnetic components in more application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Among them:

[0032] Figure 1 For the prediction effect of the XGBOOST model;

[0033] Figure 2 For the results of five-fold cross-validation;

[0034] Figure 3 For the difference in the prediction effect of the Steinmetz equation under different temperatures and materials;

[0035] Figure 4 For the prediction results of the traditional Steinmetz equation and the modified Steinmetz equation;

[0036] Figure 5 For the graph of the prediction results of the core loss BP neural network;

[0037] Figure 6 For the graph of the prediction results of 8 models of core loss;

[0038] Figure 7 For the comparison graph of the prediction results of each model of core loss;

[0039] Figure 8 For the distribution graph of the MOEAD-Pareto front solutions; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and embodiments. However, it should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of the present invention.

[0041] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this invention belongs. The terms used in the description of the present invention herein are for the purpose of describing specific embodiments only and are not intended to limit the present invention.

[0042] 1. Objectives

[0043] How to accurately calculate core loss to solve the problems of insufficient accuracy and limited applicable range of existing models under complex working conditions is a key challenge in the design of magnetic components. Therefore, the present invention combines deep learning technology with optimization algorithms to construct a core loss prediction model with high accuracy and applicable to various working conditions, providing a scientific basis for the optimized design and performance improvement of magnetic components.

[0044] 2. Feature extraction of magnetic flux density data

[0045] The rate of change of magnetic flux density over time directly affects core loss, and the distribution law of magnetic flux density is mainly determined by the excitation waveform. Therefore, accurate classification of the excitation waveform is of great significance for optimizing core design. Different waveforms have significant effects on the growth, decay, and fluctuation characteristics of magnetic flux density. To achieve accurate classification, key variables that can reflect the distribution characteristics of magnetic flux density and the shape characteristics of the waveform need to be extracted.

[0046] The present invention preprocesses the magnetic flux density data, repairs outliers, and encodes categorical variables to ensure data integrity and consistency. Subsequently, variables are extracted from three dimensions: statistical features, time-domain features, and frequency-domain features, including mean, median, variance, rate of change, harmonic factor, etc., to comprehensively describe the dynamic behavior and distribution law of magnetic flux density. To improve the classification efficiency and accuracy, the top 10 key feature variables are selected based on the feature importance ranking, and three models, namely decision tree, random forest, and XGBOOST, are used for classification comparison, and the model with the highest classification accuracy is selected for the final classification.

[0047] 3. Construction of excitation waveform classification model

[0048] The classification of excitation waveforms is a key step in core loss analysis. Different excitation waveforms directly affect the dynamic distribution characteristics of magnetic flux density and have a significant impact on the loss performance of the core. To achieve accurate classification of excitation waveforms, the present invention constructs an excitation waveform classification model based on the extracted magnetic flux density feature variables, reduces redundant information by screening important features, improves the classification efficiency, and conducts a comparative analysis of multiple classification models to select the best model for the classification and recognition of excitation waveforms. The following mainly introduces the classification method of the XGBoost model:

[0049] Gradient Boosting Tree (XGBoost) is an ensemble learning algorithm based on decision trees. Its core idea is to generate a new tree in each iteration to fit the residuals of the previous tree, and continuously iterate to make the predicted value close to the true value. XGBoost is an algorithm that integrates multiple trees, and the algorithm selects CART trees through iteration.

[0050] Let X be the multi-dimensional input variable and Y be the output variable. The corresponding dataset is in the following form: is the j-th input variable of the i-th object, y i is the i-th output variable, and the input-output data form is:

[0051] Suppose the input unit can be divided into N units, O 1 , O 2 , … O N , and there is an output C on each unit n , and the regression tree is expressed as follows:

[0052]

[0053] C n is the average value of y n corresponding to x i within the region O i .

[0054] C n = ave(y i | x i ∈ O n ) (2)

[0055] Next, divide the input features, that is, select the optimal division feature and division point. Select the j-th input variable, that is, the j-th dimension x (j) of the input variable as the splitting variable, and s as the splitting point. The division region can be defined as:

[0056] O 1 (j, s) = {x | x (j) ≤ s}, O 2 (j, s) = {x | x (j) > s} (3)

[0057] Each time, perform binary splitting and solve for the splitting variable j and the splitting point s:

[0058]

[0059] For the fixed input variable j, the optimal splitting point s can be found.

[0060]

[0061] Traversing all input variables can find the optimal input variable j. The input features are divided into two spaces, and the above division steps are continued until the stopping condition is met. The average value of each leaf node can be regarded as the final prediction result. Let j i , s i represent the variable and splitting point of the i-th split, then the formation process of the regression tree can be represented by the following diagram.

[0062] The form of the loss function is:

[0063]

[0064] denote the true value y i and the predicted value The loss function between them is generally represented by the squared difference. is the regularization term of the loss function. There are usually L 1 regularization term and L 2 regularization term, representing the complexity of all t trees. The sum of the complexities of t - 1 trees can also be represented by a constant C.

[0065]

[0066] The residuals generated by the previous tree are fitted by the newly generated tree, and iterated continuously. For the sample x i the predicted value.

[0067]

[0068] The objective function can be updated to:

[0069]

[0070] Performing a Taylor expansion on a function gives:

[0071]

[0072] Let g i be the first derivative of at i.e., Let h i be the second derivative of at i.e.,

[0073] Then the objective function can be written as:

[0074]

[0075] After removing the constant term, the objective function to be optimized can be obtained as follows:

[0076]

[0077] Only by finding the first and second derivatives of the loss function at each step and then optimizing the objective function can the result of the tree f(x) at each step be obtained, and the final model can be obtained according to the addition.

[0078] For the dataset, the set of regression trees is F = {f(x) = w q(x)}, let T be the label set of the leaf tree nodes, q be the function that maps the data to the leaf nodes, and w i be the score of the leaf nodes. Define the complexity of the tree, that is, the regularization term.

[0079]

[0080] where T is the leaf tree of a single tree, and w j is the leaf weight, that is, the model complexity is determined by all the number of leaf nodes and leaf weights. Re-group all the leaf trees, and group all the samples x i belonging to the j-th leaf node into a set, O j = {i | q(x i ) = j}.

[0081] The objective function can finally be rewritten as:

[0082]

[0083] Let be the sum of the first-order partial derivatives of all the samples included in the leaf node j, and be the sum of the second-order partial derivatives of all the samples included in the leaf node j. Taking the derivative of the objective function, the optimal point and optimal value can be obtained as:

[0084]

[0085] When choosing whether to split, it needs to be determined according to the information gain. Assume that the sum of the first-order derivatives and the sum of the second-order derivatives of the left subtree divided by the current node are G L , H L respectively; the sum of the first-order derivatives and the sum of the second-order derivatives of the right subtree divided by the current node are G R , H R respectively. The objective function value of this node before splitting is:

[0086]

[0087] The gain between them is:

[0088] gain = Objbefore -Obj after (19)

[0089] If the gain is positive, a decrease in the loss function indicates that the pivot point can split.

[0090] 4. Construct a correction model for core loss classification

[0091] The accurate calculation of core loss is crucial in the design and optimization of magnetic components. Although the traditional Steinmetz equation is widely used, its prediction effect has certain limitations under complex working conditions, especially under temperature change conditions. To improve the prediction accuracy of core loss, based on the Steinmetz equation, this invention constructs a core loss correction model by introducing a temperature correction factor and interaction terms between temperature and other influencing factors, and combines machine learning methods to supplement and optimize the remaining loss value of the model, further enhancing the applicability and prediction accuracy of the model. The specific correction model method is as follows:

[0092] 4.1 Analysis of the prediction effect of the Steinmetz equation

[0093] The Steinmetz equation (Steinmetz - equation (SE)) is one of the most famous empirical calculation models. Under sinusoidal wave excitation (excitation means that current passes through the coil of the magnetic component to generate a magnetic field), the calculation formula for core loss is as follows:

[0094]

[0095] Where: P core is the core loss; f is the frequency; B m is the peak value of the magnetic flux density; k 1 , α 1 , β 1 are coefficients fitted according to experimental data. Generally, 1 < α 1 < 3, 2 < β 1 < 3. The formula shows that the core loss per unit volume (core loss density) P depends on the power function of the frequency f and the peak value of the magnetic flux density B m . The SE equation is only applicable to sinusoidal wave excitation, and for different core materials and working conditions (working conditions refer to the different working environments of magnetic materials, including temperature, frequency, excitation waveform, etc.), the coefficients k 1 , α 1 , β 1 may not be the same.

[0096] 4.2 Steinmetz correction equation with temperature term introduced

[0097] Assume that the influence of temperature T on core loss is a functional relationship, and its general form is:

[0098]

[0099] When f(T) is in the form of a linear function, i.e., f(T) = k 0 + k 1 T, then there is

[0100]

[0101] where k 0 , k 1 , α 1 , β 1 are parameters to be estimated. k 1 reflects the influence of the temperature factor on the core loss. When this coefficient is greater than 0, it indicates that an increase in temperature will lead to an increase in the degree of core loss; when it is less than 0, it means that a high-temperature environment will instead reduce the core loss.

[0102] When f(T) is in the form of a quadratic function, i.e., f(T) = k 0 + k 1 T + k 2 T 2 , then there is

[0103]

[0104] where k 0 , k 1 , k 2 , α 1 , β 1 are parameters to be estimated. For this problem, the values of T are generally large, so the influence of the temperature factor on the degree of core loss is mainly determined by the coefficient k 2 to be estimated. At the same time, for the sake of illustration, only the quadratic function is used here, and the case of polynomial functions is not considered.

[0105] When f(T) is in the form of an exponential function, i.e., f(T) = k 0 T , then there is

[0106]

[0107] where k 0 , α 1 , β 1 are parameters to be estimated. Since the values of T are all greater than 1, when k 0 > 0, it indicates that the temperature factor has a significant positive influence on the core loss, and vice versa.

[0108] When f(T) is in the form of a power function, i.e., f(T) = T γ , then there is

[0109]

[0110] Among them, γ is the temperature correction coefficient, which is obtained by fitting experimental data. When γ > 0, it indicates that the increase in temperature has an obvious positive effect on the core loss, that is, the high-temperature environment will exacerbate the core loss; γ < 0 indicates that the increase in temperature has a negative effect on the core loss.

[0111] When f(T) reflects the change with the temperature gradient, let f(T) = k 0 +k 1 (T - T 0 ), then the corresponding Steinmetz correction equation is

[0112]

[0113] T 0 is the reference temperature, and here the minimum value of 25 °C is taken. When T takes the same value, this equation degenerates into Equation (20).

[0114] 4.3 Steinmetz Correction Equation with Temperature Cross-Term Introduced

[0115] There are many factors affecting the core loss. Among them, the more important ones are temperature, material, frequency, and peak value of magnetic flux density, etc. As a special variable, temperature not only directly affects the effectiveness of the core loss but also has an impact on other factors. Therefore, the interaction between different influencing factors still needs to be considered in the specific modeling. Considering the availability of data, only the interaction terms of temperature with frequency, excitation waveform, and core material are considered here.

[0116]

[0117] Among them, k 0 , k 1 , k 2 , k 3 , α 1 , β 1 are parameters to be estimated. k 1 , k 2 , k 3 respectively represent the influence coefficients of the interaction terms of temperature with frequency, temperature with excitation waveform, and temperature with core material. When the influence coefficient is not significant, it indicates that this interaction term has no obvious influence on the core loss and can be ignored in subsequent research. When the influence coefficient is significant, it indicates that this interaction term cannot be ignored for the core loss and needs to be considered more in the subsequent modeling process.

[0118] 4.4 Steinmetz Hybrid Correction Model with Machine Learning Introduced

[0119] In addition to introducing correction terms through physical models, a data-driven method is further introduced. By collecting experimental data under different conditions (such as temperature, frequency, waveform, material properties, etc.), a machine learning model is trained to fit the loss function. The output of the machine learning model can be combined with the physical model to form a hybrid model, which not only retains the physical interpretability but also improves the prediction accuracy of the model. Its general form is

[0120] P hybrid = P final + ΔP ML (28)

[0121] where ΔP ML is the residual loss value predicted by the machine learning model (i.e., the error part that cannot be explained by the physical model). In order to improve the prediction accuracy as much as possible, P final uses the model with the highest accuracy and the best prediction result corresponding to the above formulas (22)-(27).

[0122] 5. Construction of Core Loss Prediction Model

[0123] In the research field of core loss, although traditional models have certain applicability under specific conditions, when facing complex working conditions, especially under high-frequency switching and non-sinusoidal excitation conditions, they often show limitations of insufficient accuracy and limited application range. This is mainly because existing models are difficult to comprehensively consider the complex effects of multi-physical field parameters such as electromagnetic effects and thermal effects. Therefore, based on machine learning theory and methods, this invention combines key parameters such as temperature, frequency, magnetic flux density, material, and excitation waveform to construct a core loss prediction model that can span multiple material types and working conditions. On the basis of feature extraction of experimental data, multiple algorithms such as random forest, gradient boosting tree, artificial neural network, linear regression, KNN, decision tree, and Bayesian regression are used to construct prediction models respectively, and with the goal of minimizing the mean square error of weighted prediction, through multiple iterative optimizations and parameter adjustments, the model with the best performance is selected for core loss prediction, significantly improving the prediction accuracy and generalization ability. The specific method for constructing the prediction model is as follows:

[0124] 5.1 Equivalent Sinusoidal Wave Frequency Conversion

[0125] In power electronic power converters, magnetic components are usually excited by non-sinusoidal waveforms. If only the SE equation is used to evaluate the core loss under non-sinusoidal wave excitation, significant errors may occur. To solve this problem, without introducing additional parameters, an improved model based on the Steinmetz equation, namely the Modified Steinmetz-Equation (MSE), is proposed. MSE is based on the physical assumption of the relationship between core loss and the rate of change of magnetic flux density. By weighted averaging the rate of change of magnetic flux density at different time points, a weighted average rate of change of magnetic flux is obtained. This model assumes that the core loss depends on this weighted average value. Through this method, the equivalent sine wave frequency corresponding to any waveform excitation can be calculated.

[0126]

[0127] 5.2 Regression Model Considering Interaction Terms

[0128] For non-sinusoidal waveforms, the equivalent sine wave frequency can be used to calculate the core loss under non-sinusoidal wave excitation, as shown in the following equation:

[0129]

[0130] It can be seen that there are significant similarities between Equation (30) and the Steinmetz equation Equation (20). To make them consistent in form, it is transformed to obtain Equation (31):

[0131]

[0132] In terms of form, Equation (31) is consistent with Equation (20). The corresponding prediction model can be constructed with reference to the relevant results of Question 2. Considering the heterogeneity of the core material, the following prediction model can be constructed:

[0133]

[0134] Among them, k 0 、k 1 、k 2 、k 3 、α 1 、β 1 are parameters to be estimated. k 1 、k 2 、k 3 represent the influence coefficients of the interaction terms between temperature and frequency, temperature and excitation waveform, and temperature and core material, respectively.

[0135] 5.3 Construction of Core Loss Prediction Model Based on Machine Learning

[0136] (1) KNN regression

[0137] KNN regression is a non - parametric regression method based on instances. Its basic idea is to find the k closest observations of the sample to be predicted in the training set and use the target values of these observations in the neighborhood for prediction.

[0138] Given a training data set \(T=\{(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x N ,y N )\}, where \(x i \) is the independent variable of the instance, \(y i \) is the dependent variable of the instance, \(i = 1,2,\cdots,N\). According to the given distance metric, find the k samples in training \(T\) that are closest to \(x\), and calculate the predicted value through the mean method or the weighted mean method based on the target values of the k nearest neighbors.

[0139] The key of KNN regression is to determine the neighborhood through the distance metric. Common distance metric methods include Manhattan distance, Minkowski distance, Chebyshev distance, and cosine distance, etc.

[0140] The formula in the n - dimensional space is:

[0141] d(a,b)=\max i (|x ai -x bi |) (33)

[0142] where \(x ia \) and \(x ib \) represent the coordinates of points \(a\) and \(b\) in the \(i\) - th dimension.

[0143] The performance of KNN regression is very sensitive to the number of neighbors \(K\). Usually, cross - validation is used to select the optimal \(K\) value. Too small \(K\) is likely to lead to overfitting, while too large \(K\) may lead to underfitting. The increase of the \(K\) value means that the overall model becomes simpler. If \(K\) is too large, the nearest neighbor classifier may misclassify the test example because the k nearest neighbors may include data points that are far away and not of the same class. In applications, the \(K\) value is generally selected as a relatively small number, and usually cross - validation is used to select the optimal \(K\) value.

[0144] (2) Multivariate LASSO regression

[0145] Multivariate LASSO regression adds an L1 regularization term to the original multiple linear regression equation. Suppose there is data \((x i ,y i), i = 1, 2, …, N, where x i =(x i1 , … x ip ) T are the predictor variables and y i is the response. As in the usual regression setting, it is assumed that the observations are independent, or that given x ij , y i is conditionally independent. If x ij is standardized, then ∑ i x ij / N = 0,

[0146] Let β=(β 1 ,..., β p ). The LASSO estimate is defined as:

[0147]

[0148] where t ≥ 0 is a tuning parameter. For all t, the solution for α is The parameter t ≥ 0 controls the amount of shrinkage applied to the estimate. Let be the full least squares estimate and let When t < t 0 , the solution will shrink towards 0 and some coefficients may be exactly equal to 0. For example, when t = t 0 / 2, the effect is roughly similar to finding the best subset of size p / 2.

[0149] The LASSO model is derived from the non - negative lasso minimization of Breiman (1993):

[0150]

[0151] The lasso starts with the OLS (ordinary least squares) estimate, shrinks by non - negative factors, and the sum of these factors is constrained. In a wide range of simulation studies, Breiman showed that this method performs more stably in terms of prediction error compared to subset selection methods and can rival ridge regression in most cases, only performing slightly worse when the true model contains a large number of small non - zero coefficients.

[0152] (4) BP neural network

[0153] The BP neural network is a feedback of a multi-layer neural network, with the ability of arbitrary complex pattern classification and excellent non-linear function mapping. Structurally, the BP neural network has an input layer, a hidden layer, and an output layer. In different cases, the number of layers and the number of neurons in each layer can be set arbitrarily, and its performance will also vary with the change of the structure. During the transfer process, the input signal enters from the input layer and is processed layer by layer through the hidden layer until the output layer. The state of each layer of neurons will directly affect the state of the next layer of neurons. If the output layer cannot meet the actual expected data, it is converted to backpropagation, and the weights and thresholds are changed according to the prediction error to approach the expected output result.

[0154] After each input quantity in the BP neural network passes through the hidden layer, the corresponding weights and thresholds will change to a certain extent, and after being weighted in the hidden layer, it reaches the output layer for output. According to the principle of the BP neural network, for each layer:

[0155] Output layer:

[0156] h k =f(net k ), k = 1, 2, …, m (36)

[0157]

[0158] Hidden layer:

[0159] y j =f(net j ), j = 1, 2, …, m (38)

[0160]

[0161] Where:

[0162]

[0163] The BP neural network model has learning and memory functions, and its steps are as follows:

[0164] Step 1: Initialization. Assign random numbers to the weight matrices W and V, set the sample pattern counter p and the number of training times q to 1, set the error E to 0, set the learning rate η to a decimal within 0 to 1, and set the accuracy E min reached after training to a positive number.

[0165] Step 2: Input the training samples and calculate the outputs of each layer.

[0166] Step 3: Calculate the network output error.

[0167]

[0168] Root Mean Square (Total Output) Error:

[0169]

[0170] Step 4: Calculate the error of each layer using the expected output and the actual output of the network.

[0171]

[0172] Step 5: Adjust the weights of each layer. The weight adjustment amount is:

[0173]

[0174] Step 6: Check whether one round of training for all samples is completed. If pq < 4, then increment the counters p and q, and return to Step 2; otherwise, proceed to the next step.

[0175] Step 7: Check whether the root mean square (total output) error of the network meets the accuracy requirement. If E RME < E min then the training ends; otherwise, set E to 0, set p to 1, and thus return to Step 2.

[0176] 6. Construction of the Magnetic Component Performance Optimization Model

[0177] The design and optimization of magnetic components not only need to focus on core loss, but also need to comprehensively consider key performance indicators such as transmitted magnetic energy to achieve the optimal balance of overall performance. Reducing core loss can improve the efficiency of magnetic components, while optimizing transmitted magnetic energy can enhance its energy transfer ability. Therefore, it is of great significance to optimize these two indicators simultaneously in the design. Based on the core loss prediction model constructed above, combined with the calculation formula of transmitted magnetic energy, a two-objective optimization model aiming at minimizing core loss and maximizing transmitted magnetic energy is constructed. This model takes temperature, frequency, excitation waveform, peak magnetic flux density, and core material as core variables, sets corresponding constraint conditions, and solves it by using the MOEAD algorithm. Finally, the parameter configuration and operating condition combination with the optimal performance of magnetic components are obtained. The specific method for constructing the optimization model is as follows:

[0178] 6.1 Objective Function

[0179] To achieve the excellence and optimization of the overall performance of magnetic components, it is necessary to consider both core loss and transmitted magnetic energy indicators. Therefore, based on the core loss prediction model established in Section 5, considering the influence of the transmitted magnetic energy indicator, a two-objective optimization model aiming at minimizing core loss and maximizing transmitted magnetic energy is constructed. The specific form of the objective function is as follows:

[0180]

[0181] Among them, i represents the samples, with a total of 12,400, and j represents the influencing factor variables, with a total of 5 types. is the core loss target of the i-th sample, and x factor is the influencing factor variable, including temperature, frequency, waveform, peak magnetic flux density, and core material. knn(x factor , x ij ) is the core loss KNN prediction function. P mcpt (i) is the magnetic energy transmission function, measured by the product of the sample frequency f and the sample density peak B m .

[0182] 6.2 Constraints

[0183] The decision variables of this model correspond to the important influencing factors of core loss and magnetic energy transmission, including the frequency f 1 , the peak magnetic flux density B m , the temperature T, the material M, and the excitation waveform W. Among them, the frequency f 1 and the peak magnetic flux density B m are continuous variables, and the corresponding constraints are respectively:

[0184] f 1 min <f 1 <f 1 max (49)

[0185]

[0186] According to the description of the problem data and the summary results of the attachment data, the values of f 1 min and f 1 max are 500,000 and 500,000 respectively, and are -1.52 and -1.18 respectively.

[0187] Since the material M and the excitation waveform W are discrete variables, in order to simplify the problem as much as possible, the data of the core material and excitation waveform sequence coding table shown in Table 2 are used, and the corresponding constraints are respectively:

[0188] M = 1, 2, 3, 4 (51)

[0189] W = 1, 2, 3 (52)

[0190] In this study, the temperature variable is discretized into four fixed values: 25 °C, 50 °C, 70 °C, and 90 °C, and is treated as a categorical variable. Corresponding constraints are set for each temperature value to ensure the accuracy of the optimization model.

[0191] T = 25, 50, 70, 90 (53)

[0192] 6.3. MOEAD Algorithm

[0193] MOEAD decomposes the multi-objective problem into multiple single-objective sub-problems, and through information sharing among sub-problems, these single-objective sub-problems are optimized simultaneously, thereby obtaining the Pareto solution set. The specific implementation details of the algorithm are as follows:

[0194] Step 1: Randomly generate an initial population P with N individuals in the decision space, calculate the objective function values corresponding to each individual in the population P; generate uniformly distributed weight vectors λ 1 , λ 2 , …, λ N , and calculate the TN weight vectors that are closest to the i-th weight vector in Euclidean distance, and denote its neighborhood as B(i) = (i 1 , i 2 , …, i TN ), where represents the TN weight vectors closest to λ i ; initialize the reference points of m objectives to be optimized

[0195] Step 2: Randomly select two numbers k and l from B(i), and then determine the individuals x k and x l in the population P, use simulated binary crossover and polynomial mutation to generate a new individual y, and calculate the objective function value corresponding to the new individual y.

[0196] Step 3: Compare the objective function value of the new individual y with the original reference points and update the reference points.

[0197] Step 4: Compare the scalar functions of each individual in the neighborhood of the individual x i and the new individual y, and update the neighborhood of x i .

[0198] Step 5: Judge the termination condition. If it is satisfied, terminate the program, obtain the Pareto solution set and Pareto front, and output the results; otherwise, go to Step 2.

[0199] The complex problem of searching for the Pareto front is transformed into several simple scalar optimization problems through the corresponding aggregation function. In this paper, the Chebyshev method is adopted. The scalar function corresponding to the Chebyshev method is as follows:

[0200]

[0201] where, z *Denote the set of reference points, that is, the set composed of the minimum values of each objective component. For each objective component f i (x),

[0202] 6.4 Algorithm Performance Evaluation

[0203] Through the continuous evolutionary iteration of the population, MOEAD can obtain an approximate Pareto front. By evaluating the approximate Pareto front, the advantages and disadvantages of MOEAD can be judged. Currently, the commonly used evaluation index is the Inverted Generational Distance (IGD), which can represent the distance between the actual Pareto front and the estimated Pareto front obtained by the algorithm. The lower the IGD value, the better the convergence and diversity of the estimated approximate Pareto front obtained by the algorithm, and the closer it is to the true Pareto front. Its calculation formula is shown in Equation (109).

[0204]

[0205] Among them, PV represents a set of uniform samples on the actual PF, PV * is the PF obtained by the multi-objective optimization algorithm, |PV| is the scale of PV, and d(PV i -PV * ) is the minimum Euclidean distance between PV i and PV * , where i = 1, 2, …, |PV|.

[0206] To further select an objective and unique Pareto optimal solution from the Pareto solution set and thus guide practical applications, a multi-attribute decision-making method is adopted. Let the solution set of the multi-attribute optimization problem be S = {s 1 , s 2 , …, s n}, and the attribute set be Q = {q 1 , q 2 , …, q j}. The solution set S is the Pareto solution set obtained by the multi-objective optimization algorithm, and the attribute set Q is the set of objectives to be optimized. For the solution s i , measure it according to the attribute q j , and obtain the attribute value of s i with respect to q j as av ij , where i = 1, 2, …, n, i = 1, 2, …, n, j = 1, 2, …, m. The matrix AV = (av ij ) n×mIt is called the decision matrix of the solution set S with respect to the attribute set Q. Usually, the dimensions of different attributes are also different. For unified calculation, the decision matrix is normalized as shown in Equation (8-11).

[0207]

[0208] The normalized decision matrix is RV = (rv ij ) n×m , and let the attribute weight vector be AW = {aw 1 , aw 2 , …, aw m}, where the sum of aw j is 1 and aw j > 0. The attribute weights can be directly given by establishing a model with historical data. After the attribute weight vector is known, the calculation method of the comprehensive utility value of each solution is as follows:

[0209]

[0210] Among them, the solution with the largest comprehensive utility value Ui is the ideal solution, that is, the ideal Pareto optimal solution.

[0211] 7. Case Analysis

[0212] The purpose of this study is to solve the problems of accurate prediction of core loss and performance optimization. By constructing a high-precision loss prediction model and a two-objective optimization method, the efficient design and optimization of magnetic components under various materials and complex working conditions are realized. For the problem of exciting waveform classification, the statistical features, time-domain features, and frequency-domain features of the magnetic flux density are extracted, the key variables are screened, and the XGBoost model is used to achieve accurate classification of sine waves, triangular waves, and trapezoidal waves. In the prediction of core loss, based on the Steinmetz correction equation, the temperature correction factor and its interaction with other parameters are introduced, and at the same time, machine learning methods are combined to optimize the residual loss value, thus significantly improving the prediction accuracy and applicability of the model. For the problem of non-sinusoidal waveform adaptation, the equivalent sine wave frequency method is adopted to construct a cross-working-condition core loss prediction model, and the high-precision prediction of losses under different materials and complex working conditions is realized. In terms of performance optimization, with the goal of minimizing core loss and maximizing transmitted magnetic energy, a two-objective optimization model is constructed, and the MOEAD algorithm is combined to solve multi-parameter combinations to obtain the optimal working condition configuration solution with the best performance, providing a scientific basis and technical support for the design and optimization of magnetic components.

[0213] Based on the method in Section 2 of the specific implementation method, the characteristics of the magnetic flux density data were extracted, and 25 characteristic variables were obtained. Since different materials may have a greater impact on the magnetic flux density, in order to avoid the possible impact of the core material, characteristic variables were extracted for the four materials respectively. For ease of display, Table 2 only shows the characteristic variables corresponding to the magnetic flux density data under the first five working conditions of material 1.

[0214] Table 2 Some characteristic variables corresponding to different working conditions of material 1

[0215]

[0216] In order to simplify the data set, reduce computational complexity and storage requirements, and further improve data quality, we need to remove irrelevant or erroneous information to effectively improve the performance of the machine learning model. By using a decision tree to calculate the importance of the feature vectors extracted above, we finally extracted 10 more important indicators such as kurtosis, sample entropy, and total harmonic distortion.

[0217] According to the extracted feature variables, predictions are made based on the three tree classification models constructed in Section 3. The comparison results show that the XGBOOST model has the best classification effect, with an accuracy of 100% in both the training set, validation set and test set. Figure 1 As shown in the figure. The first row shows the ROC curves on the three data sets, and it can be found that their AUC values ​​are all 1; the second row shows the corresponding confusion matrix, and it can be seen that the probability of each type of data being correct is 100%; the third row draws the curves corresponding to the true value and the predicted value, and it is found that the two completely overlap. Therefore, it can be considered that the prediction effect of this model is relatively good.

[0218] In order to evaluate the generalization ability of the model, the K-fold cross validation method is used for evaluation. Here, 5-fold cross validation is used to evaluate the generalization ability of the model. Figure 2 The results shown show that the accuracy of the five-fold cross-validation results is 1, which indicates that the model has good generalization ability.

[0219] Based on the above results, the XGBOOST model is used to identify the waveform of the sample, and the classification results are shown in the second column, where 1 represents a sine wave, 2 represents a triangle wave, and 3 represents a trapezoidal wave. The classification results of 10 samples are randomly selected, as shown in Table 3:

[0220] Table 3 Partial results of excitation waveform classification in Appendix II

[0221]

[0222] On the basis of classifying the excitation waveforms, a core loss model is further constructed. In the traditional core loss model, the Steinmetz equation is widely used as a classic model. However, this equation is mainly designed for sinusoidal waveforms, and for different types of core materials and changes in operating temperature, the SE equation will cause large errors, which brings many inconveniences and complexities in practical engineering applications. Therefore, it is necessary to correct the core loss model under non-sinusoidal waveforms.

[0223] For the same core material and sinusoidal waveform, explore the differences in the prediction effect of core loss under different temperature changes. First, extract the core loss, frequency, and magnetic flux density data corresponding to the sinusoidal waveform in the attachment, and perform fitting for different materials and different temperatures respectively. The results shown in Table 4 can be obtained.

[0224] Table 4 Prediction effect of Steinmetz equation under different temperatures and materials

[0225]

[0226]

[0227] To more intuitively reflect the differences shown in Table 7, plot them as Figure 3 the graph shown in. The graph shows the changes in R 2 , MSE, AIC, and BIC corresponding to Material 1, Material 2, Material 3, and Material 4. From the fitting effect of the model, there are large fluctuations in R 2 of different materials at different temperatures. For Material 1 and Material 2, the fitting effect is the best at 50 °C, followed by 25 °C, then 70 °C, and the worst at 90 °C; for Material 3, the fitting effect at 90 °C is better than that at 70 °C; for Material 4, the higher the temperature, the better the fitting effect. From the fitting effect of the model, for different materials, the prediction effect at 25 °C is the worst, manifested as the largest value of MSE; for Material 1, Material 2, and Material 4, the working environment at 90 °C can achieve the best prediction effect, and for Material 3, the working environment at 70 °C can achieve the best prediction effect. Overall, the higher the temperature, the better the prediction effect.

[0228] By fitting the parameters to be estimated of the model, the results shown in Table 5 can be obtained. k 0 , k 1 , k 2 , k 3 , α 1 , β 1 correspond to the parameters to be estimated of different models respectively. Substituting these parameters into the original equation can obtain the corresponding estimation equation.

[0229] Table 5 Model parameter estimation results

[0230]

[0231] Furthermore, the estimation results of each model and the Steinmetz equation can be compared, as shown in Table 6. The specific values of R 2 , MSE, AIC, and BIC corresponding to the original equation and the above six models are presented here. From the perspective of the fitting effect of the models, the fitting effect of Model 6 is better than that of other models, and the fitting effect of the original equation is the worst. From the perspective of the prediction effect of the models, it also shows that the prediction effect of Model 6 is the best, and the prediction effect of the original equation is the worst. In order to find a balance between the fitting degree and complexity of the models to avoid overfitting and improve the generalization ability of the models, the AIC and BIC corresponding to different models are calculated. It can be found through comparison that although the AIC value of Model 3 is the smallest, it is not much different from other models except the original equation. The BIC values of Models 1 - 5 are almost the same. Considering comprehensively, Model 6 is selected as the optimal estimation equation.

[0232] Table 6 Comparison of the Estimation Effects between the Modified Steinmetz Equation and the Original Equation

[0233]

[0234] Through the above comparison, it can be found that the estimation effect of the modified Steinmetz equation has been significantly improved, specifically manifested as the continuous decrease in the value of the mean square error. At the same time, the estimation effect of Model 6 is better. Next, the machine learning method is further introduced. Substitute Model 6 into Equation (28) to further improve the estimation accuracy. By using the data in Annex 3 for training, the prediction results of the traditional Steinmetz equation and the modified Steinmetz equation can be obtained, as Figure 4 shown. It can be found that the prediction effect of the modified Steinmetz equation is significantly better, and the absolute error of the fitting also decreases significantly.

[0235] For this problem, use Equation (29) to convert the frequencies corresponding to triangular waves and trapezoidal waves into equivalent sine wave frequencies. Some conversion results are shown in Tables 7 and 8:

[0236] Table 7 Equivalent Sine Wave Frequencies of Triangular Waves

[0237]

[0238]

[0239] Table 8 Equivalent Sine Wave Frequencies of Trapezoidal Waves

[0240]

[0241] According to the experimental data in Material 1, feature extraction is carried out on the data of magnetic flux density. On this basis, temperature, frequency, material, waveform, and peak magnetic flux density are used as independent variables, and core loss is used as the dependent variable to construct a multiple regression model. Since the data set is complex and the amount of data is large, 80% of the data is used as the training set, 10% of the data is used as the validation set, and 10% of the data is used as the test set in this paper. In order to minimize the prediction error of the model as much as possible, this paper selects multiple machine learning methods such as random forest, linear regression, gradient boosting tree, artificial neural network, KNN, decision tree, Bayesian regression and other models for comparison, and takes the minimization of the mean square error of weighted prediction as the objective function. After multiple iterations of optimization, the parameters of the prediction model are continuously adjusted to strive for the best prediction effect.

[0242] Based on the above different machine learning models, a multiple regression model is constructed. Among them, the relevant prediction results of the neural network model are as Figure 5 shown. The leftmost part in the figure reflects the structural framework of the neural network. The four scatter plots in the middle respectively show the comparison between the predicted values and the actual values of different models when predicting core loss. The horizontal axis is the actual value, and the vertical axis is the predicted value. The R 2 value in the figure represents the goodness of fit of the model, which is used to evaluate the quality of the model's prediction effect.

[0243] The four scatter plots in the middle part show the prediction performance of the model on the training set, validation set, test set and the whole data set. The horizontal axis is the actual value, and the vertical axis is the predicted value. The R 2 value marked in each figure reflects the goodness of fit of the model. Among them, the R 2 values of the training set and the test set are 0.17959 and 0.16007 respectively, the R 2 value of the validation set is 0.21702, and the R 2 value of the whole data set is 0.18233. These R 2 values are relatively low, indicating that the fitting effect of the model on each data set is poor, and it is difficult to fully capture the non-linear relationship between complex features and core loss, resulting in a large prediction error.

[0244] The loss function convergence curve in the upper right corner shows the change trend of the loss value during the model training process. As the training progresses, the loss value gradually decreases, indicating that the model is gradually converging. However, the convergence speed is relatively slow, suggesting that the model may not reach the ideal optimization state and there may be certain overfitting or underfitting phenomena.

[0245] The error distribution histogram in the lower right corner reveals the prediction error distribution of each data set. Most of the errors are concentrated in a small range, indicating that the model performs relatively stably on most samples, but there are still relatively large prediction errors for some samples, which is consistent with the low R 2This corresponds to the poor fitting effect reflected by the value, further indicating that the model fails to accurately capture the loss characteristics for some samples and there is a lack of prediction accuracy. Generally speaking, the model's prediction ability for core loss is still insufficient. In the future, it is necessary to further optimize the network structure or adjust the model parameters to improve the prediction effect and the generalization ability of the model.

[0246] Therefore, it is very necessary to compare multiple models to find the optimal prediction model. The changes in the core loss prediction results of 8 models are shown as Figure 6 follows. The horizontal axis in the figure is the sample number, and the vertical axis is the predicted core loss value of each model under each sample number. Specifically, the eight subgraphs respectively correspond to the core loss prediction values of the LASSO regression, linear regression, optimized weighted average model, gradient boosting tree (GBDT), artificial neural network (ANN), K-nearest neighbor (KNN), decision tree, and Bayesian regression models.

[0247] To more accurately evaluate the prediction quality of the models, the minimized weighted mean squared error of each model is calculated, and the specific results are shown in Table 9.

[0248] Table 9 Comparison of the minimized weighted mean squared error of prediction

[0249]

[0250] It can be seen from the table that the machine learning models have greatly improved in prediction accuracy compared to the general linear models. In contrast, the prediction effect of KNN is slightly better among all models. Therefore, the subsequent core loss prediction results will be given by the KNN model.

[0251] To more clearly and intuitively reflect the core loss prediction results of each model, the prediction results of all models are plotted in one figure for comparison, as Figure 7 shown.

[0252] Finally, the KNN model with the best prediction effect is used to predict the core loss. To ensure the wide applicability of the prediction results, typical samples (serial numbers 16, 76, 98, 126, 168, 230, 271, 338, 348, 379) under different temperature conditions are selected, and the core loss prediction results are shown in Table 10.

[0253] Table 10 Core loss prediction results

[0254]

[0255] The above-mentioned bi-objective optimization model and the decomposition-based multi-objective evolutionary algorithm (MOEAD) are used for solution to obtain the optimal magnetic component performance optimization scheme for each sample. Since the objectives need to simultaneously satisfy the minimization of core loss and the maximization of transmitted magnetic energy, the form of the solution is the Pareto non-dominated solution set. That is, while satisfying the minimum possible core loss, it is necessary to reduce the transmitted magnetic energy to a certain extent as the cost, so as to achieve the optimal performance. Specifically, as shown in Figure 8 shown.

[0256] To more clearly show the optimal values of influencing factors such as temperature, frequency, waveform, peak magnetic flux density, and core material, as well as the corresponding core loss and transmitted magnetic energy values, 20 of the schemes are listed in Table 11 as follows:

[0257] Table 11 Optimal Schemes

[0258]

[0259] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, or improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing a core loss model of a magnetic component based on deep learning, characterized in that The deep learning model is used to analyze the factors affecting the core loss and achieve accurate prediction. The method includes the following steps: Step 1: Collect the core loss data of the magnetic components under different working conditions (temperature, frequency, and magnetic flux density), analyze the distribution characteristics of the magnetic flux density and the shape characteristics of different waveforms, and extract variables that can reflect the waveform characteristics; based on the extracted characteristic variables, construct an excitation waveform classification model, and perform excitation waveform classification prediction on the sample data. Step 2: Based on the application of the Steinmetz equation under sinusoidal wave excitation conditions, the loss prediction effect of the same core material at different temperatures is analyzed to study the influence of temperature on the core loss. Further, a temperature correction factor is added to the Steinmetz equation to construct a core loss correction equation, and the prediction effects of the original equation and the corrected equation are compared. Step three, based on experimental data, study the independent effects of the three core influencing factors of temperature, excitation waveform and core material on core loss; further analyze the impact of the synergistic effect between each factor on core loss, and explore the optimal configuration of these three factors under different combination conditions to minimize core loss. Step 4: Use experimental data to build a core loss prediction model that can span different core material types and operating conditions, and analyze the model's prediction accuracy and generalization ability; based on the constructed model, predict the core loss of sample data and verify the application effect of the model. Step five, based on the core loss prediction model and combined with the transmitted magnetic energy as the objective function, an optimization model with the dual objectives of minimizing core loss and maximizing transmitted magnetic energy is established; based on experimental data, the combined effects of the five influencing factors of temperature, frequency, excitation waveform, magnetic flux density peak and core material under different conditions are analyzed, and the operating conditions with the optimal performance of the magnetic component are determined.

2. The method for constructing a core loss model of a magnetic component according to claim 1, characterized in that: The core loss data described in step 1 include measured data at different temperatures, frequencies and magnetic flux densities; specifically, it includes data preprocessing, feature extraction and classification model construction: (1) Data preprocessing part, by detecting and repairing missing values ​​and outliers, ensuring data integrity and encoding classification variables; (2) Feature extraction part, extracting feature variables from three dimensions of statistical features, time domain features and frequency domain features to describe the distribution law and waveform shape characteristics of magnetic flux density; (3) In the classification model construction part, the key feature variables are screened by combining feature importance analysis, and the classification model is established using machine learning algorithms such as gradient boosting tree. After the optimal classification model is determined, the excitation waveform of the sample data is classified.

3. The method for constructing a magnetic component core loss model according to claim 2, characterized in that: In step 2, the prediction effect of the core loss is analyzed and corrected based on the Steinmetz equation. First, the core loss data under sinusoidal excitation conditions is screened, and the influence of different temperatures on the prediction effect of the Steinmetz equation under the same core material is studied, and the error change law is quantified; then, by introducing the temperature correction factor and its interaction terms with frequency, waveform and core material, a correction equation is constructed; finally, the machine learning model is combined to optimize the residual error in the correction equation to further improve the prediction accuracy of the model.

4. The method for analyzing core loss of a magnetic component according to claim 3, characterized in that: In step 3, the independent and synergistic effects of core loss are studied by analyzing the three core influencing factors of temperature, excitation waveform and core material. The independent effect uses descriptive statistics and regression analysis methods to quantify the direction and degree of influence; the synergistic effect is verified by multi-factor variance analysis, and the specific impact of the interaction is quantified by combining the regression equation. Based on the analysis results, the combination conditions of different influencing factors are predicted to determine the optimal configuration when the core loss is minimized.

5. The method for predicting core loss of a magnetic component according to claim 4, characterized in that: In step 4, a core loss prediction model that can span different core materials and working conditions is constructed by combining the modified Steinmetz equation. In order to meet the calculation requirements of non-sinusoidal waveforms, the triangle wave and trapezoidal wave are processed equivalently and converted into sinusoidal wave frequency data; the deep learning and other machine learning algorithms are further trained and optimized using experimental data, and the prediction effects of multiple algorithms are compared to determine the optimal model, and based on this, the core loss is predicted for the sample data to verify the generalization ability of the model.

6. The method for optimizing magnetic component performance according to claim 5, characterized in that: The dual-objective optimization model described in step 5 takes minimizing core loss and maximizing transmitted magnetic energy as the optimization objectives. The process includes the following: (1) Constructing an optimization objective function, in which the core loss is based on the calculation results of the optimal prediction model in step 4, and the transmitted magnetic energy is measured by the product of frequency and peak magnetic flux density, while ensuring that the optimization target can cover the actual needs under different working conditions. (2) Setting temperature, frequency, waveform, peak magnetic flux density and core material as decision variables, and the constraints include the value range of each variable and the physical working condition restrictions, to ensure that the optimization model is operational in actual engineering. (3) Using the MOEAD algorithm to solve the dual-objective optimization model, comprehensively considering the trade-off between core loss and transmitted magnetic energy, determine the optimal working condition combination for the performance of the magnetic component, and output the corresponding optimal parameter configuration scheme to meet engineering design and application requirements.

Images