Nanocrystalline high-frequency transformer robust design method considering magnetic core uncertainty

Abstract

The invention discloses a nanocrystalline high-frequency transformer robust design method considering magnetic core uncertainty, and belongs to the technical field of high-frequency transformers, and the method comprises the steps: S1, carrying out the initial design of a nanocrystalline high-frequency transformer based on multiple physical fields; s2, defining an optimization target of the nanocrystalline high-frequency transformer and constructing a corresponding robust optimization design model; s3, after the robust optimization design model is determined, representative sample points are generated through orthogonal experimental design; s4, constructing a support vector regression agent model; s5, evaluating the uncertainty of the design through Monte Carlo analysis; and S6, obtaining a Pareto frontier through a non-dominated genetic algorithm-III, and then carrying out multi-objective optimization. According to the nanocrystalline high-frequency transformer robust design method considering the magnetic core uncertainty, the requirements of the fields of new energy, electric automobiles and the like are met by reducing energy loss, optimizing heat management and improving the structural stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of high-frequency transformers, and in particular to a robust design method for nanocrystalline high-frequency transformers considering core uncertainties. BACKGROUND

[0002] With the rapid development of power electronics technology, high-frequency transformers, as the core components of power conversion and transmission systems, have been widely used in new energy generation, electric vehicle charging, aerospace power supply, and industrial power supply. Nanocrystalline materials, due to their high magnetic permeability, low loss, and high saturation magnetic flux density, have become the preferred material for high-frequency transformer cores. However, in actual production and application, nanocrystalline high-frequency transformers face challenges brought by material property and manufacturing process uncertainties, which have a significant impact on the electromagnetic performance, thermal performance, and long-term stability of the transformer.

[0003] Traditional high-frequency transformer design methods are usually based on deterministic optimization models, assuming fixed material properties and geometric dimensions. However, in actual production, parameters such as the saturation magnetic flux density of the core material, the lamination factor, and the distance between the winding and the core may change randomly due to manufacturing tolerances, material non-uniformity, or environmental factors. For example, the saturation magnetic flux density of nanocrystalline cores may deviate due to material batch differences, the distance between the winding and the core may change due to assembly errors, and the lamination factor may deviate from the design value due to insufficient processing precision. These uncertainty factors may lead to increased loss, excessive temperature rise, or reduced efficiency of the transformer in actual operation, thereby affecting the reliability and service life of the system.

[0004] To address these issues, some research attempts to increase design margins or use conservative design parameters to improve the robustness of the transformer. However, this approach often sacrifices power density or increases material cost, making it difficult to achieve the best balance between efficiency, cost, and performance. In addition, traditional design methods usually rely on finite element analysis for performance verification, which is computationally expensive and time-consuming. Especially when considering multi-objective optimization and uncertainty factors, the computational complexity further increases, limiting the design efficiency and optimization depth.

[0005] In recent years, the concept of robust optimization design has been gradually introduced into the field of engineering design. By modeling uncertainty factors as random variables and combining statistical methods and surrogate models, the robustness and performance stability of the design can be effectively improved. In the design of high-frequency transformers, some research attempts to introduce Monte Carlo analysis or surrogate models to evaluate the impact of uncertainty on performance, but these methods often only focus on a single objective (such as loss or temperature rise), lacking comprehensive optimization of multiple objectives (such as efficiency, thermal resistance, and cost).

[0006] In view of the above problems, a high-frequency transformer robust optimization design method considering material and geometric uncertainties is urgently needed to achieve multi-objective optimization while ensuring performance. SUMMARY

[0007] The purpose of the present application is to provide a nanocrystalline high-frequency transformer robust design method considering core uncertainty, aiming to solve the design optimization problem caused by material and geometric uncertainty in the prior art. By introducing a robust optimization design method, the manufacturing errors and material property changes of design variables, as well as the performance targets such as transformer loss, thermal resistance, temperature rise, etc. are considered comprehensively to improve the overall performance and robustness of the transformer under different working conditions.

[0008] To achieve the above purpose, the present application provides a nanocrystalline high-frequency transformer robust design method considering core uncertainty, comprising the following steps: S1, initial design of nanocrystalline high-frequency transformer based on multi-physical field; S2, defining the optimization target of nanocrystalline high-frequency transformer and constructing the corresponding robust optimization design model; S3, after determining the robust optimization design model, generating representative sample points using orthogonal experimental design; S4, constructing a support vector regression surrogate model; S5, evaluating the uncertainty of the design through Monte Carlo analysis; S6, obtaining the Pareto front by non-dominated genetic algorithm-III, and then performing multi-objective optimization.

[0009] Preferably, step S1 is specifically: The design indicators of nanocrystalline high-frequency transformer based on multi-physical field, selecting appropriate core material and structure, specifically, selecting nanocrystalline core material suitable for high-frequency application according to design requirements, considering its high saturation magnetic flux density, low loss and other characteristics; Determine the magnetic flux density and current density according to design experience; According to the working frequency, rated power, magnetic flux density and current density, calculate the area product value and determine the core type; determine the number of turns and cross-sectional area of the winding; Calculate the loss and efficiency and evaluate, if it meets the requirements, the design is completed, if it does not meet the requirements, reselect the core until it meets the requirements.

[0010] Preferably, the calculation formula of the area product value is as follows: ; Wherein, represents the area product value, S T represents the rated power, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, B s Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, A e Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, A w Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, k w Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, k f Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, k j Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core,

[0011] Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core,

[0012] Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, B s Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, , Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, B s Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, d wcg Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, , , p Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, ta Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, , , p Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, d wcg Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, S ta Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, Bs is the saturation magnetic flux density of the nanocrystalline magnetic core, pdenotes the correlation coefficient; The fillet size of the nanocrystalline magnetic core follows a bivariate normal distribution, denoted as Δ F inner_c ~bivariateNormal( , , p ) and Δ F outer_c ~bivariateNormal( , , p ), where Δ F inner_c and Δ F outer_c each denote the fillet size of the nanocrystalline magnetic core, and are the mean values of the inner and outer fillet radii of the magnetic core, respectively, and are the standard deviations of the inner and outer fillet radii of the magnetic core, respectively, p is the correlation coefficient, and its standard deviation is set to 1 / 3 of the corresponding manufacturing tolerance.

[0013] Preferably, the formula of the robust optimization design model is as follows: ; wherein, f Lσ , f total_loss and f Thotspot denote the leakage inductance value, total loss, and hotspot temperature of the nanocrystalline high-frequency transformer, respectively, and w inner , h inner , w c , d ct , F outer_c and F inner_c are the size parameters of the nanocrystalline high-frequency transformer, Δ d wcg , Δ B s and Δ S ta are the winding and magnetic core spacing error, saturation magnetic flux density deviation, and lamination coefficient deviation, respectively, , , p denote the mean value, standard deviation, and correlation coefficient in sample statistics, respectively.

[0014] Preferably, S3 comprises the following steps: S31, considering 6 control factors and setting 6 control factors to different levels; S32, based on the above control factors, 18 groups of representative samples are generated by orthogonal experiment table to ensure the uniform distribution of each control factor; S33, finite element simulation is performed on each group of representative samples to obtain the corresponding performance response data.

[0015] Preferably, S4 comprises the following steps: S41, data preprocessing is needed, specifically, sample data generated by orthogonal experiment is standardized by Z-score to ensure that variables are trained on a unified scale; The Z-score standardization formula is: ; Where, is the original data, m is the mean of the data, s is the standard deviation of the data; S42, after completing the data preprocessing, support vector regression is selected as the surrogate model, and the parameters of the support vector regression surrogate model are selected; S43, the prediction accuracy of the support vector regression model is evaluated by calculating the root mean square error, which is expressed as: ; Where, represents the root mean square error, y i and represent the calculated value and the predicted value of the test sample respectively.

[0016] Preferably, S5 comprises the following steps: S51, based on the probability distribution of each noise factor defined in S2, a large number of random samples are generated to simulate the uncertainty of each design variable; S52, each sample is input into the support vector regression surrogate model constructed in step four to calculate the corresponding performance response, and the mean and standard deviation of the response performance are calculated; S53, the statistical characteristics of the performance response are analyzed to evaluate the influence of uncertainty on the optimization objective, and the robustness of the optimization result in actual production is ensured.

[0017] Preferably, S6 comprises the following steps: S61, based on the random samples generated by Monte Carlo analysis, the population is initialized, which is composed of random samples obtained in S5, and the corresponding performance response is calculated by the support vector regression surrogate model constructed in S4; S62, evaluate the fitness of each individual by non-dominated sorting and crowding distance, so as to select which individuals will be parents, and then generate new offspring individuals; S63, generate new individuals through selection, crossover and mutation operations, and the mutation probability is controlled between 0.1 and 0.2; S64, when generating a new generation population, the parents and offspring are combined, and then the best individuals are screened out by non-dominated sorting and crowding distance; S65, after multiple generations of evolution, a set of Pareto optimal solution set is generated, representing the best balance between different objectives.

[0018] Therefore, the application adopts the above-mentioned nanocrystalline high-frequency transformer robust design method considering the uncertainty of the magnetic core, which has the following beneficial effects: (1) The application models the uncertainty of the magnetic core material (such as saturation magnetic flux density deviation, lamination coefficient deviation) and geometric error as random variables through robust optimization design, combines Monte Carlo analysis and support vector regression (SVR) model, and significantly enhances the performance stability of nanocrystalline high-frequency transformer under complex working conditions; the optimization design effectively deals with manufacturing errors and material property changes, ensures the efficient operation of the transformer in high-frequency and high-power scenarios, significantly improves long-term reliability, and adapts to the needs of new energy, power electronics and other fields.

[0019] (2) The application fully considers the influence of manufacturing errors and material property changes on transformer performance through orthogonal experimental design and random variable modeling.

[0020] (3) The application uses a support vector regression (SVR) surrogate model to replace traditional finite element analysis, which greatly reduces the computational cost and time in the optimization process; the SVR model is trained through orthogonal experimental data, efficiently handles high-dimensional and multi-variable problems, and ensures prediction accuracy; fast iterative design scheme, shortens the development cycle, provides efficient support for high-frequency transformer design, especially suitable for engineering scenarios that need to quickly verify multiple design schemes.

[0021] (4) Using non-dominated genetic algorithm-III (NSGA-III), the application realizes multi-objective optimization of total loss, thermal resistance and hot spot temperature, and generates a set of Pareto optimal solutions; designers can find the best balance between efficiency, thermal stability and reliability according to the requirements, meet the diversified application requirements of large-capacity high-frequency transformers, and ensure that the equipment has both performance and economy in high-power scenarios.

[0022] (5) The robust optimization method provided by the application provides innovative guidance for nanocrystalline high-frequency transformer design, reduces energy loss, optimizes heat management and improves structural stability to meet the needs of new energy, electric vehicles and other fields; the method is flexible, and the optimization target can be adjusted according to the application, has high popularization potential, and provides a reliable solution for high-performance transformer engineering design.

[0023] The technical solutions of the embodiments of the application will be further described in detail below with reference to the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 A flowchart of a nanocrystalline high-frequency transformer robust design method considering core uncertainty of an embodiment of the application; Figure 2 A high-frequency transformer topology diagram; Figure 3 A schematic diagram of the uncertainty of nanocrystalline magnetic core material and nanocrystalline high-frequency transformer design size; Figure 4 A schematic diagram of the Pareto frontier in the performance target. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the embodiments of the application clearer, the technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. The components of the embodiments of the application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the application provided in the drawings is not intended to limit the scope of the claimed application, but only represents selected embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the protection of the application.

[0026] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0027] EMBODIMENT

[0028] As shown in Figure 1 , the application provides a nanocrystalline high-frequency transformer robust design method considering core uncertainty, comprising the following steps: S1, initial design of nanocrystalline high-frequency transformer based on multi-physical field.

[0029] In the initial design stage, the nanocrystalline high-frequency transformer is designed by using the area product (AP) method, which is based on the current density and magnetic flux density limits specified by multi-physical field to determine the size of the magnetic core and winding.

[0030] The flow of the AP method is as follows: according to the design index, the appropriate magnetic core material and structure are selected, specifically, the nanocrystalline magnetic core material suitable for high-frequency application is selected according to the design requirement, considering its high saturation magnetic flux density, low loss and other characteristics; then, the magnetic flux density and current density are determined according to the design experience; then, according to the working frequency (f) f s ), rated power (P S T ), magnetic flux density (B B s ) and current density (J J ) and other parameters, the area product value is calculated and the magnetic core type is determined; then, the number of turns and cross-sectional area of the winding are determined; finally, the loss and efficiency are calculated and evaluated, specifically, the copper loss and iron loss of the transformer are calculated, and whether the design meets the efficiency and loss requirements is evaluated, if it meets the requirements, the design is completed, if it does not meet the requirements, the magnetic core is reselected (repeat the above steps) until the requirements are met. The calculation formula of the area product value is as follows: ; wherein, represents the area product value, S T represents the rated power, f s f is the working frequency of the nanocrystalline high-frequency transformer, B s represents the working magnetic flux density, A e and A w are the effective cross-sectional area of the magnetic core and the window area, respectively, k w , k f , k j are the magnetic core window utilization coefficient, voltage waveform factor and current density ratio coefficient, respectively, represents the magnetic core shape constant.

[0031] The AP method considers the relevant design variables: the magnetic core window area and the magnetic cross-sectional area. According to the given maximum magnetic flux density (B B max ) and winding current density (J J) to meet the power handling requirements. This method considers copper and iron losses, limiting current density can reduce winding losses, while limiting magnetic flux density constrains core losses and prevents saturation. The basic design specifications and initial parameter ranges determine this preliminary design process, generating a transformer design that complies with the nanocrystalline high-frequency transformer standard AP method, as shown in Table 1: Table 1. Nanocrystalline high-frequency transformer topology design parameters ;

[0032] S2, define the optimization objectives of the nanocrystalline high-frequency transformer and build the corresponding robust optimization design model.

[0033] For nanocrystalline high-frequency transformers, optimization objectives include minimizing total losses (L) P total_loss ), thermal resistance (Rth) R cond ) and hot spot temperature (Thot) T hotspot , which directly affect the efficiency and thermal stability of high-frequency transformers. The specific form of the traditional deterministic optimization design model is as follows: ; wherein, f Lσ , f total_loss and f Thotspot represent the leakage inductance value, total loss and hot spot temperature of the nanocrystalline high-frequency transformer, X min and X max are the boundary values of the design parameters, and h represent the leakage inductance target value and transformer efficiency, w inner , h inner , w c , d ct , F outer_c and F inner_c are the size parameters of the nanocrystalline high-frequency transformer, as shown in detail in Figure 2 , Δ d wcg , Δ B s and Δ S ta are the winding and core spacing error, saturation magnetic flux density deviation and lamination coefficient deviation, respectively.

[0034] Magnetic core window size (W w inner , h inner ) affects winding space and magnetic flux path, which in turn affects the efficiency and thermal performance of high-frequency transformers. Magnetic core leg width (L w c ) affects the distribution of magnetic flux, with narrower leg widths potentially increasing the risk of saturation, and wider leg widths potentially leading to material waste. Magnetic core thickness (T d ct ) determines the reluctance, which in turn affects magnetic coupling and efficiency, but can also increase core loss at high frequencies. Inner and outer radii of the magnetic core (R F inner_c , F outer_c ) affect the distribution of magnetic flux, with variations in size potentially leading to crowding of magnetic flux and the creation of hotspots. Optimizing these variables ensures efficient operation of the transformer, reducing losses and maintaining thermal stability while considering manufacturing uncertainties and material variations. This holistic approach improves the performance, robustness, and reliability of the transformer, ensuring stable operation under different conditions.

[0035] To address the uncertainties arising from material properties and geometric variations, the traditional deterministic optimization design model is converted into a robust optimization design model. In the robust optimization design model, the saturation flux density deviation (Δ B s ), winding-to-core distance error (Δ d wcg ), lamination factor deviation (Δ S ta ), and magnetic core fillet size error (Δ F inner_c , Δ F outer_c ) are treated as random variables, and specific statistical distributions (including Weibull, normal, and binormal) are used to consider their variations. The objective function is expressed through the mean and standard deviation of the performance response.

[0036] For the saturation flux density deviation of nanocrystalline magnetic cores, Δ B s , it is assumed to follow a Weibull distribution, i.e., Δ B s ~Weibull ( , ), where is the size parameter of the saturation flux density deviation, and is the shape parameter of the saturation flux density deviation, and the size parameter and shape parameter are set to 1 / 3 of the manufacturing tolerance of the magnetic core material.

[0037] Referring toFigure 3 For the winding-to-core distance error (Δ d wcg ) and the lamination factor deviation (Δ S ta ), considering that the manufacturing accuracy of the core material is lower than that of the nanometer high-frequency transformer winding, the geometric uncertainty of the nanocrystalline core and the copper foil winding needs to be discussed in detail. The gap that may occur during manufacturing and assembly will affect the thermal and electrical performance. It is assumed that the winding-to-core distance error and the lamination factor deviation caused by manufacturing and assembly defects follow a normal distribution, i.e. Δ d wcg ~N( , , p ), ΔS ta ~N( , , p ), where represents the mean of the winding-to-core distance error, represents the standard deviation of the winding-to-core distance error, p represents the correlation coefficient. The core thickness is adjusted according to the nominal value minus the winding-to-core distance.

[0038] For the corner size of the nanocrystalline core (Δ F inner_c , Δ F outer_c ), the uncertainty mainly comes from the non-uniformity of the material and the difference in the manufacturing process. It is assumed that the corner size of the nanocrystalline core follows a bivariate normal distribution, i.e. Δ F inner_c ~bivariateNormal( , , p ), Δ F outer_c ~bivariateNormal( , , p ). Wherein and are the mean of the inner and outer corner radii of the core, and are the standard deviation of the inner and outer corner radii of the core, p is the correlation coefficient, and its standard deviation is set to 1 / 3 of the corresponding manufacturing tolerance.

[0039] This uncertainty distribution contains five noise factors: saturation flux density deviation (Δ B s ), winding-to-core distance error (Δ dwcg ), lamination factor deviation (Δ S ta ), and inner-outer corner radius deviation (Δ F inner_c and Δ F outer_c In the robust optimization design model, the target is expressed by the mean (μ m ) and standard deviation (σ s ) of the design performance, so that the expected performance can be calculated under uncertainty. The formula of the robust optimization design model is as follows: ; wherein, μ , σ , and ρ p represent the mean, standard deviation, and correlation coefficient in sample statistics, respectively.

[0040] S3, generating representative sample points by orthogonal experimental design.

[0041] After determining the robust optimization design model, the model needs to be solved to search for the optimal high-frequency transformer structure. The greatest advantage of orthogonal experimental design is that it can select a small number of highly representative tests from a large number of tests to obtain reliable results, which is convenient for analysis and calculation.

[0042] In this embodiment, the specific steps of S3 include: S31, considering 6 control factors: w inner , h inner , w c , d ct , F outer_c , F inner_c , and setting the 6 control factors to different levels, wherein, w inner contains 6 levels, h inner , w c , d ct , F outer_c , F inner_c contains 3 levels.

[0043] S32, based on the above control factors, generating 18 groups of representative samples by an orthogonal experimental table (such as an L18 table), ensuring that the levels of each control factor are evenly distributed. Specifically, in the 18 experiments,w inner Each level appears 18 ÷ 6 = 3 times, h inner 、 w c 、 d ct 、 F outer_c 、 F inner_c Each level appears 18 ÷ 3 = 6 times, as shown in Tables 2 and 3: Table 2 Distribution of levels of control factors ;

[0044] Table 3 Orthogonal experiment table ;

[0045] S33, finite element simulation is performed on each group of representative samples to obtain the corresponding performance response data (total loss, thermal resistance, hot spot temperature).

[0046] S4, a support vector regression proxy model is constructed.

[0047] Directly using finite element analysis and evolutionary algorithm for model optimization will result in significant computational cost. To alleviate this problem, a support vector regression proxy model is used to replace finite element analysis, thereby reducing the computational burden.

[0048] In this embodiment, the specific steps of S4 include: S41, data preprocessing is needed, specifically, the sample data generated by the orthogonal experiment is standardized by Z-score to ensure that the variables are trained on a unified scale.

[0049] In S3, 18 experimental combinations are obtained by orthogonal experimental design, each experimental combination corresponds to a specific value of a design variable, and finite element analysis is used to simulate these experimental combinations to obtain the corresponding performance response (loss, thermal resistance, temperature rise). These experimental data will be used as input data for the proxy model. Since the experimental design involves variables of different dimensions and ranges (such as size, temperature, etc.), in order to ensure that all input features are trained on the same scale, data standardization is needed.

[0050] This embodiment uses Z-score standardization to convert the data to a distribution with a mean of 0 and a standard deviation of 1. The Z-score standardization formula is: ; where, is the original data, m is the mean of the data, s is the standard deviation of the data.

[0051] S42、After completing the data preprocessing, support vector regression (SVR) is selected as the surrogate model. SVR is a regression method based on the principle of support vector machine (SVM), which can efficiently fit complex nonlinear relationships, especially suitable for cases with multiple input variables and data with nonlinear characteristics. The radial basis function (RBF) kernel is selected as the kernel function of the support vector regression surrogate model. The parameters of the support vector regression surrogate model also need to be selected: C (the regularization parameter), e (the tolerance), g (the kernel function parameter).

[0052] C : Regularization parameter, used to balance the training error and model complexity. C When the value of is larger, the model will pay more attention to the fitting of the training set, but may cause overfitting.

[0053] e : Tolerance, controls the number of support vectors. Smaller

[0054] g : Parameter of the kernel function, determines the range of data point influence. Larger

[0055] Using the design variables and performance responses from the orthogonal experimental design, the support vector regression surrogate model is trained by selecting appropriate C , e and g parameters, so that the surrogate model can fit the data as accurately as possible.

[0056] S43, the prediction accuracy of the support vector regression model is evaluated by calculating the root mean square error (RMSE), which is expressed as: ; where represents the root mean square error, y i and represent the calculated value and predicted value of the test sample, respectively.

[0057] S5, the uncertainty of the design is evaluated by Monte Carlo analysis (MAC).

[0058] In this embodiment, the specific steps of S5 include: S51, based on the probability distribution of each noise factor defined in S2, a large number of random samples are generated to simulate the uncertainty of each design variable. In step two, five noise factors are determined: saturation magnetic flux density deviation (ΔB s ), the distance error between the winding and the core (Δ d wcg ), stacking coefficient deviation (Δ S ta ), and the deviation of the inner and outer corner radii (Δ F inner_c and Δ F outer_c ), and defines the probability distribution followed by each noise factor.

[0059] S52, input each sample into the support vector regression agent model constructed in step 4, calculate the corresponding performance response (total loss, thermal resistance and hot spot temperature), and calculate the mean of the response performance ( m ) and standard deviation ( s ).

[0060] S53. Analyze the statistical characteristics of performance responses, evaluate the impact of uncertainty on optimization objectives, and ensure the robustness of optimization results in actual production.

[0061] S6. Obtain the Pareto front by non-dominated genetic algorithm-III (NSGA-III), and then perform multi-objective optimization.

[0062] The optimization targets of this embodiment include thermal resistance ( R cond ), hotspot temperature ( T hotspot ) and total loss ( P total_loss ) are key factors in evaluating the performance of nanocrystalline high-frequency transformer systems. NSGA-III is an improved multi-objective optimization genetic algorithm designed to obtain a set of Pareto optimal solutions by maintaining and optimizing the balance of multiple objectives. The core concept of NSGA-III is to use non-dominated sorting and congestion calculation to guide the search process, and to utilize the concept of reference points to help find a more evenly distributed Pareto front.

[0063] In this embodiment, the specific step S6 includes: S61. Initialize the population based on the random samples generated by Monte Carlo analysis. The population is composed of the random samples obtained in S5. The corresponding performance responses are calculated using the support vector regression surrogate model constructed in S4. These performance responses are used to measure the fitness of each individual.

[0064] S62. Evaluate the fitness of each individual through non-dominated sorting and crowding distance in order to select which individuals will become parents and generate new offspring individuals.

[0065] Non-dominated sorting is one of the core operations of NSGA-III, which sorts the individuals in the population according to the dominance relationship between objectives. In multi-objective optimization, individual A is said to dominate individual B if A is not worse than B in all objectives and better than B in at least one objective. Dominated individuals have higher priority and are therefore considered first in selection. Crowding distance is used to measure the distance between an individual and its neighbors. A larger crowding distance means that the individual occupies a larger area in the objective space and can represent more design choices in the Pareto front.

[0066] S63, new individuals are generated through selection, crossover, and mutation operations, with a mutation probability controlled between 0.1 and 0.2. These operations help to pass on the good genes of parent individuals to the next generation while introducing new diversity.

[0067] Selection operation: two individuals are randomly selected from the population each time, and the non-dominated sorting level and crowding distance are compared to determine which individual is suitable as a parent. Individuals with higher non-dominated levels and larger crowding distances are preferred.

[0068] Crossover operation: new individuals are generated by exchanging the genes of parent individuals. The purpose of crossover is to combine the good characteristics of parent individuals into new individuals to improve the fitness of offspring.

[0069] Mutation operation: mutation operation increases the diversity of the population by making small random changes to individual genes. The mutation probability of mutation operation is generally small, usually set between 0.1 and 0.2.

[0070] S64, when generating a new generation of population, the parents and offspring are combined, and then the best individuals are selected through non-dominated sorting and crowding distance. This process ensures the diversity and quality of the population and makes the solutions of the Pareto front more uniform.

[0071] S65, after multiple generations of evolution, a set of Pareto optimal solutions is generated, representing the best balance between different objectives, as described in Figure 4 These solutions represent the optimal trade-offs between multiple objectives, with each solution being better than others in some objectives but possibly worse in others.

[0072] The final optimized design is selected based on the Pareto optimal solution set, and Table 2 compares the results of the design objectives before and after optimization. The results show that the multi-objective optimization method effectively improves the performance of nanocrystalline high-frequency transformers, ensuring robustness and thermal stability under uncertain operating conditions.

[0073] Table 2 Comparison of optimization results of nanocrystalline high-frequency transformers ;

[0074] Therefore, the application adopts the above-mentioned nanocrystalline high-frequency transformer robust design method considering the uncertainty of the magnetic core, and the designer can find the best balance among efficiency, thermal stability and reliability according to the requirements, meet the diversified application requirements of large-capacity high-frequency transformers, and ensure that the equipment considers performance and economy in high-power scenarios.

[0075] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A robust design method for nanocrystalline high-frequency transformers considering core uncertainty, characterized in that: The following steps are involved: S1. Initial design of nanocrystalline high-frequency transformer based on multi-physics field; S2. Define the optimization objectives of nanocrystalline high-frequency transformers and build a corresponding robust optimization design model; S3. After determining the robust optimization design model, an orthogonal experimental design is used to generate representative sample points; S4, constructing a support vector regression agent model; S5. Assess design uncertainty through Monte Carlo analysis; S6. Obtain the Pareto front using the non-dominated genetic algorithm-III and then perform multi-objective optimization.

2. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 1, characterized in that: Step S1 is specifically as follows: Based on the multi-physics field nanocrystalline high-frequency transformer design indicators, the core material and structure are selected. Specifically, nanocrystalline core materials suitable for high-frequency applications are selected according to the design requirements, taking into account their high saturation flux density and low loss. Determine the magnetic flux density and current density based on design experience; Calculate the area product value and determine the core model based on the operating frequency, rated power, magnetic flux density and current density; Determine the number of turns and cross-sectional area of ​​the winding; Calculate the loss and efficiency and evaluate them. If they meet the requirements, the design is completed. If not, reselect the magnetic core until they meet the requirements.

3. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 2, characterized in that: The area product value is calculated as follows: ； in, represents the area product value, S T Indicates rated power, is the operating frequency of the nanocrystalline high-frequency transformer, B s represents the working magnetic flux density, A e and A w are the effective cross-sectional area of ​​the core and the window area, k w 、 k f 、 k j They are the core window utilization coefficient, voltage shape factor and current density ratio coefficient, x Represents the core shape constant.

4. The robust design method for nanocrystalline high-frequency transformers considering core uncertainty according to claim 1, characterized in that: Optimization objectives include minimizing total losses, thermal resistance, and hotspot temperature; In the robust optimization design model, the noise factor is treated as a random variable, and a specific statistical distribution is used to consider its variation. The objective function is expressed by the mean and standard deviation of the performance response. Noise factors include saturation flux density deviation, winding-core distance error, lamination factor deviation, and core fillet size error.

5. The robust design method for nanocrystalline high-frequency transformers considering core uncertainty according to claim 4, characterized in that: The saturation flux density deviation of the nanocrystalline core follows the Weibull distribution, which is expressed as Δ B s ~Weibull( , ), where Δ B s represents the saturation flux density deviation of the nanocrystalline core, is the dimensional parameter of the saturation flux density deviation, is the shape parameter of the saturation magnetic flux density deviation, and the size parameter and shape parameter are set to 1 / 3 of the manufacturing tolerance of the core material; The winding-core distance error and the lamination coefficient deviation follow a normal distribution, which is represented by Δ d wcg ~N( , , ρ ), ΔS ta ~N( , , ρ ), where Δ d wcg Indicates the distance error between the winding and the core, Δ S ta Indicates the lamination coefficient deviation, Represents the mean value of the distance error between the winding and the core, Indicates the standard deviation of the distance error between the winding and the core, ρ represents the correlation coefficient; The fillet size of the nanocrystalline core follows a bivariate normal distribution, expressed as Δ F inner_c ~bivariateNormal( , , ρ ) and Δ F outer_c ~bivariateNormal( , , ρ ), where Δ F inner_c and Δ F outer_c Both represent the fillet size of the nanocrystalline core. and are the mean values ​​of the inner and outer corner radii of the core, and are the standard deviations of the inner and outer corner radii of the core, ρ is the correlation coefficient, and its standard deviation is set to 1 / 3 of the corresponding manufacturing tolerance.

6. The robust design method for nanocrystalline high-frequency transformers considering core uncertainty according to claim 5, characterized in that: The formula of the robust optimization design model is as follows: ； in, f Lσ 、 f total_loss and f Thotspot They represent the leakage inductance, total loss and hot spot temperature of the nanocrystalline high-frequency transformer respectively. and represent the leakage inductance target value, w inner 、 h inner 、 w c 、 d ct 、 F outer_c and F inner_c are the size parameters of the nanocrystalline high-frequency transformer, Δ d wcg , Δ B s and Δ S ta They are the winding and core spacing error, saturation flux density deviation and lamination factor deviation, 、 、 ρ They represent the mean, standard deviation and correlation coefficient in sample statistics respectively.

7. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 1, characterized in that: The S3 specific steps include: S31. Consider 6 control factors and set them to different levels; S32. Based on the above control factors, 18 groups of representative samples were generated through the orthogonal experimental table to ensure that the levels of each control factor were evenly distributed; S33. Perform finite element simulation on each group of representative samples to obtain corresponding performance response data.

8. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 1, characterized in that: The specific steps of S4 include: S41. Data preprocessing is required. Specifically, Z-score standardization is performed on the sample data generated by the orthogonal experiment to ensure that the variables are trained on a uniform scale. The Z-score normalization formula is: ； in, is the original data, μ is the mean of the data, σ is the standard deviation of the data; S42. After completing data preprocessing, select support vector regression as the proxy model, and select parameters of the support vector regression proxy model; S43. Evaluate the prediction accuracy of the support vector regression model by calculating the root mean square error, which is expressed as: ； in, represents the root mean square error, y i and They represent the calculated value and predicted value of the test sample respectively.

9. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 1, characterized in that: The specific steps of S5 include: S51, based on the probability distribution of each noise factor defined in S2, simulate the uncertainty of each design variable by generating a large number of random samples; S52, input each sample into the support vector regression proxy model constructed in step 4, calculate the corresponding performance response, and calculate the mean and standard deviation of the response performance; S53. Analyze the statistical characteristics of performance responses, evaluate the impact of uncertainty on optimization objectives, and ensure the robustness of optimization results in actual production.

10. The robust design method for nanocrystalline high-frequency transformer considering core uncertainty according to claim 1, characterized in that: The specific steps of S6 include: S61. Initialize a population based on random samples generated by Monte Carlo analysis, where the population is composed of the random samples obtained in S5, and calculate the corresponding performance response using the support vector regression surrogate model constructed in S4. S62, evaluate the fitness of each individual through non-dominated sorting and crowding distance, so as to select which individuals will become parents and generate new offspring individuals; S63. Generate new individuals through selection, crossover and mutation operations, and control the mutation probability between 0.1 and 0.2; S64. When generating a new generation of population, merge the parent and offspring generations, and then select the best individuals through non-dominated sorting and crowding distance; S65. After multiple generations of evolution, a set of Pareto optimal solutions is generated, representing the best balance between different objectives.

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