A robust design method for nanocrystalline high-frequency transformer considering core uncertainty

Abstract

The application discloses a kind of nanocrystalline high-frequency transformer robust design method considering magnetic core uncertainty, belong to high-frequency transformer technical field, S1, based on multi-physical field, initial design of nanocrystalline high-frequency transformer is carried out;S2, the optimization target of nanocrystalline high-frequency transformer is defined and the corresponding robust optimization design model is constructed;S3, after determining the robust optimization design model, representative sample points are generated using orthogonal experimental design;S4, support vector regression surrogate model is constructed;S5, the uncertainty of design is evaluated by Monte Carlo analysis;S6, the Pareto front is obtained by non-dominated genetic algorithm-III, and then multi-objective optimization is carried out.The application uses the above-mentioned nanocrystalline high-frequency transformer robust design method considering magnetic core uncertainty, reduces energy loss, optimizes heat management and improves structural stability, meets the demand of new energy, electric vehicle and other fields.

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, there is an urgent need for a high-frequency transformer robust optimization design method that comprehensively considers material and geometric uncertainties 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 comprehensively considered 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:

[0009] S1, initial design of nanocrystalline high-frequency transformer based on multi-physical field;

[0010] S2, defining the optimization target of nanocrystalline high-frequency transformer and constructing the corresponding robust optimization design model;

[0011] S3, after determining the robust optimization design model, generating representative sample points using orthogonal experimental design;

[0012] S4, constructing a support vector regression surrogate model;

[0013] S5, evaluating the uncertainty of the design through Monte Carlo analysis;

[0014] S6, obtaining the Pareto front by using non-dominated genetic algorithm-III, and then performing multi-objective optimization.

[0015] Preferably, step S1 is specifically:

[0016] Based on the design indicators of nanocrystalline high-frequency transformer, select appropriate core material and structure, specifically, select nanocrystalline core material suitable for high-frequency application according to design requirements, considering its high saturation magnetic flux density, low loss and other characteristics;

[0017] Determine the magnetic flux density and current density according to design experience;

[0018] 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;

[0019] 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.

[0020] Preferably, the area product value is calculated according to the following formula:

[0021] ;

[0022] wherein, represents the area product value, S T represents the rated power, 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 window utilization coefficient of the magnetic core, the voltage waveform factor and the current density ratio coefficient, respectively, represents the magnetic core shape constant.

[0023] Preferably, the optimization objectives include minimizing the total loss, thermal resistance and hot spot temperature;

[0024] In the robust optimization design model, the noise factors are taken as random variables, and specific statistical distributions are used to consider their variations, and the objective function is expressed by the mean and standard deviation of the performance response;

[0025] The noise factors include the saturation magnetic flux density deviation, the winding and magnetic core distance error, the lamination coefficient deviation and the magnetic core round corner size error.

[0026] Preferably, the saturation magnetic flux density deviation of the nanocrystalline magnetic core follows the Weibull distribution, and is represented as Δ B s ~Weibull( , ), wherein Δ B s represents the saturation magnetic flux density deviation of the nanocrystalline magnetic core, is the size parameter of the saturation magnetic flux density deviation, is the shape parameter of the saturation magnetic flux density deviation, and the size parameter and the shape parameter are set to 1 / 3 of the manufacturing tolerance of the magnetic core material;

[0027] The winding and magnetic core distance error and the lamination coefficient deviation follow the normal distribution, and are represented as Δ d wcg ~N( , , p ), ΔS ta ~N( , , p ), wherein Δ d wcg represents the winding and core distance error, Δ S ta represents the lamination coefficient deviation, represents the mean value of the winding and core distance error, represents the standard deviation of the winding and core distance error, p represents the correlation coefficient;

[0028] The fillet size of the nanocrystalline core follows a bivariate normal distribution, denoted as Δ F inner_c ~bivariateNormal( , , p ) and Δ F outer_c ~bivariateNormal( , , p ), wherein 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 fillet radii of the core, respectively, and are the standard deviations of the inner and outer fillet radii of the core, respectively, p is the correlation coefficient, and its standard deviation is set to 1 / 3 of the corresponding manufacturing tolerance.

[0029] Preferably, the formula of the robust optimization design model is as follows:

[0030] ;

[0031] wherein, f Lσ , f total_loss and f Thotspot represent 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 Finner_c are the size parameters of nanocrystalline high-frequency transformer, respectively 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 represent the mean, standard deviation and correlation coefficient in sample statistics, respectively.

[0032] Preferably, the S3 specific steps include:

[0033] S31, considering 6 control factors, and setting 6 control factors to different levels;

[0034] S32, based on the above control factors, 18 groups of representative samples are generated through orthogonal experiment table to ensure the uniform distribution of each control factor;

[0035] S33, finite element simulation is performed on each representative sample to obtain the corresponding performance response data.

[0036] Preferably, the S4 specific steps include:

[0037] S41, data preprocessing is needed, specifically, the sample data generated by orthogonal experiment is standardized by Z-score to ensure that the variables are trained on a unified scale;

[0038] The Z-score standardization formula is:

[0039] ;

[0040] wherein, is the original data, m is the mean of the data, s is the standard deviation of the data;

[0041] 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;

[0042] S43, the prediction accuracy of the support vector regression model is evaluated by calculating the root mean square error, and the expression is:

[0043] ;

[0044] wherein, represents the root mean square error, y i and respectively represent the calculated value and the predicted value of the test sample.

[0045] Preferably, the S5 specific steps include:

[0046] 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;

[0047] S52, input each sample into the support vector regression surrogate model constructed in step four, calculate the corresponding performance response, and calculate the mean and standard deviation of the response performance;

[0048] S53, analyze the statistical characteristics of the performance response, evaluate the influence of uncertainty on the optimization target, and ensure the robustness of the optimization result in actual production.

[0049] Preferably, the S6 specific steps include:

[0050] S61, initialize the population based on the random samples generated by the Monte Carlo analysis, the population is composed of random samples obtained in S5, and the corresponding performance response is calculated through the support vector regression surrogate model constructed in S4;

[0051] S62, evaluate the fitness of each individual by non-dominated sorting and crowding distance, so as to select which individuals will become parents, and then generate new offspring individuals;

[0052] S63, generate new individuals by selection, crossover and mutation operations, and the mutation probability is controlled between 0.1 and 0.2;

[0053] S64, when generating a new generation of population, combine the parents and offspring, and then screen out the best individuals by non-dominated sorting and crowding distance;

[0054] S65, after multiple generations of evolution, a set of Pareto optimal solutions is generated, representing the best balance between different objectives.

[0055] Therefore, the nanocrystalline high-frequency transformer robust design method considering the uncertainty of the magnetic core has the following beneficial effects:

[0056] (1) The present application models the uncertainty of the magnetic core material (such as saturation 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.

[0057] (2) The application fully considers the influence of manufacturing errors and material property changes on the performance of the transformer through orthogonal experimental design and random variable modeling.

[0058] (3) The application uses a support vector regression (SVR) surrogate model to replace traditional finite element analysis, significantly reducing 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, ensures prediction accuracy, quickly iterates design schemes, shortens development cycles, provides efficient support for high-frequency transformer design, and is particularly suitable for engineering scenarios that require rapid verification of multiple design schemes.

[0059] (4) The application uses non-dominated genetic algorithm-III (NSGA-III) to realize multi-objective optimization of total loss, thermal resistance and hot spot temperature, and generates a Pareto optimal solution set; designers can find the best balance between efficiency, thermal stability and reliability according to 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.

[0060] (5) The robust optimization method proposed by the application provides innovative guidance for nanocrystalline high-frequency transformer design, reduces energy loss, optimizes thermal management and improves structural stability to meet the needs of new energy, electric vehicles and other fields; the method is flexible and can adjust the optimization target according to the application, has high promotion potential, and provides a reliable solution for high-performance transformer engineering design.

[0061] The technical solutions of the application will be further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is a flowchart of a nanocrystalline high-frequency transformer robust design method considering magnetic core uncertainty according to an embodiment of the application;

[0063] Figure 2 is a high-frequency transformer topology diagram;

[0064] Figure 3 is a schematic diagram of the uncertainty of nanocrystalline magnetic core material and nanocrystalline high-frequency transformer design size;

[0065] Figure 4 is a schematic diagram of the Pareto front in the performance target. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0067] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0068] Example

[0069] like Figure 1 As shown, this invention provides a robust design method for nanocrystalline high-frequency transformers that considers core uncertainties, comprising the following steps:

[0070] S1. Initial design of nanocrystalline high-frequency transformer based on multiphysics field.

[0071] In the initial design phase, the nanocrystalline high-frequency transformer is designed using the area product (AP) method, which determines the core and winding dimensions based on the current density and flux density constraints specified by the multiphysics field.

[0072] The AP method process is as follows: Based on design specifications, select appropriate core materials and structures. Specifically, select nanocrystalline core materials suitable for high-frequency applications based on design requirements, considering their high saturation flux density, low loss, and other characteristics; then, determine the flux density and current density based on design experience; finally, based on the operating frequency (… f s ), rated power ( S T ), magnetic flux density ( B s ) and current density ( J Parameters such as area and cross-sectional area are used to calculate the area product and determine the core type. Then, the number of turns and cross-sectional area of ​​the winding are determined. Finally, losses and efficiency are calculated and evaluated. Specifically, the copper and iron losses of the transformer are calculated, and the design is evaluated to see if it meets the efficiency and loss requirements. If it meets the requirements, the design is completed; if not, a new core is selected (repeating the above steps) until the requirements are met. The formula for calculating the area product is as follows:

[0073] ;

[0074] wherein, represents the area product value, S T represents the rated power, f s is the operating frequency of the nanocrystalline high-frequency transformer, B s represents the operating 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, the voltage waveform factor and the current density ratio coefficient, respectively, represents the magnetic core shape constant.

[0075] The AP method takes into account the relevant design variables: the magnetic core window area and the magnetic cross-sectional area. According to the constraints selected according to the given maximum magnetic flux density ( B max ) and winding current density ( J ), the power handling requirements are met. This method takes into account copper loss and iron loss, limiting current density can reduce winding loss, and limiting magnetic flux density can constrain core loss and prevent saturation. The basic design specifications and initial parameter range determine this preliminary design process, generating a transformer design that meets the AP method of nanocrystalline high-frequency transformer standards, as shown in Table 1:

[0076] Table 1 Nanocrystalline high-frequency transformer topology design parameters

[0077] ;

[0078] S2, define the optimization objective of the nanocrystalline high-frequency transformer and build the corresponding robust optimization design model.

[0079] For nanocrystalline high-frequency transformers, the optimization objectives include minimizing total loss ( P total_loss ), thermal resistance ( R cond ) and hot spot temperature ( T hotspot ), which directly affect the efficiency and thermal stability of the high-frequency transformer. The specific form of the traditional deterministic optimization design model is as follows:

[0080] ;

[0081] 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, respectively, X min and X max are the boundary values of the design parameters, and h represent the leakage inductance target value and transformer efficiency, respectively, 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, specifically as shown in Figure 2 Δ d wcg Δ B s and Δ S ta are the winding-to-core spacing error, saturation flux density deviation, and lamination coefficient deviation, respectively.

[0082] The core window size ( w inner 、 h inner ) affects the winding space and magnetic flux path, which in turn affects the efficiency and thermal performance of the high-frequency transformer. The core leg width ( w c ) affects the distribution of magnetic flux, and a narrower leg width may increase the risk of saturation, while a wider leg width may result in material waste. The core thickness ( d ct ) determines the magnetic resistance, which in turn affects magnetic coupling and efficiency, but may also increase core loss at high frequencies. The inner and outer radii of the core ( F inner_c , F outer_c ) affect the distribution of magnetic flux, and changes in size may cause crowding of magnetic flux and the generation of hot spots. Optimizing these variables ensures efficient operation of the transformer, reducing losses and maintaining thermal stability while considering manufacturing uncertainties and material differences. This overall approach improves the performance, robustness, and reliability of the transformer, ensuring stable operation under different conditions.

[0083] To address the uncertainty caused by 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 and core distance error (Δ d wcg ), lamination coefficient deviation (Δ S ta ) and core fillet size error (Δ F inner_c , Δ F outer_c ) are taken as random variables, and specific statistical distributions (including Weibull distribution, normal distribution and binary normal distribution) are used to consider their variations, and the objective function is expressed by the mean and standard deviation of the performance response.

[0084] For the saturation flux density deviation Δ B s of the nanocrystalline core, it is assumed to follow the Weibull distribution, i.e. Δ B s ~Weibull (B , ), where B is the size parameter of the saturation flux density deviation, B is the shape parameter of the saturation flux density deviation, and the size parameter and the shape parameter are set to 1 / 3 of the manufacturing tolerance of the core material.

[0085] Referring to Figure 3 , for the winding and core distance error (Δ d wcg ) and the lamination coefficient deviation (Δ S ta ), considering that the manufacturing precision 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 and core distance error and the lamination coefficient deviation caused by manufacturing and assembly defects follow the normal distribution, i.e. Δ d wcg ~N (B , , p ), ΔS ta ~N (B , , p ), where B represents the mean of the winding and core distance error, represents the standard deviation of the winding and core distance error, pThe correlation coefficient is denoted by. The core thickness is then adjusted according to the nominal value minus the winding-to-core distance.

[0086] For the fillet size of nanocrystalline core (Δ F inner_c , Δ F outer_c ), its uncertainty mainly comes from the material inhomogeneity and the difference in manufacturing process. Assuming that the fillet size of nanocrystalline core follows a bivariate normal distribution, i.e., Δ F inner_c ~bivariateNormal( , , p ), Δ F outer_c ~bivariateNormal( , , p ). Here, and are the mean of inner and outer fillet radius, and are the standard deviation of inner and outer fillet radius, p is the correlation coefficient, and its standard deviation is set to 1 / 3 of the corresponding manufacturing tolerance.

[0087] This uncertainty distribution contains five noise factors: the saturation flux density bias (Δ B s ), the winding-to-core distance error (Δ d wcg ), the lamination coefficient bias (Δ S ta ), and the inner and outer fillet radius bias (Δ F inner_c and Δ F outer_c ). In the robust optimization design model, the objective is to express 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:

[0088] ;

[0089] where, , , p represent the mean, standard deviation, and correlation coefficient in sample statistics, respectively.

[0090] S3, generating representative sample points using orthogonal experimental design.

[0091] After the robust optimization design model is determined, the model needs to be solved to search for the optimal high-frequency transformer structure. The maximum advantage of orthogonal test design is that a small number of highly representative tests can be selected from a large number of tests to obtain reliable results, which is convenient for analysis and calculation.

[0092] In this embodiment, the specific steps of S3 include:

[0093] 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.

[0094] S32, based on the above control factors, 18 representative samples are generated through an orthogonal experiment table (such as an L18 table), to ensure that each control factor is 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:

[0095] Table 2 Level distribution of control factors

[0096] ;

[0097] Table 3 Orthogonal experiment table

[0098] ;

[0099] S33, perform finite element simulation on each group of representative samples to obtain corresponding performance response data (total loss, thermal resistance, hot spot temperature).

[0100] S4, construct a support vector regression proxy model.

[0101] 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.

[0102] In this embodiment, the specific steps of S4 include:

[0103] 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.

[0104] 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.

[0105] 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:

[0106] ;

[0107] where, is the original data, m is the mean of the data, s is the standard deviation of the data.

[0108] S42, after completing data preprocessing, support vector regression (SVR) is selected as the proxy 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. Select the radial basis function (RBF) kernel as the kernel function of the support vector regression proxy model. The parameters of the support vector regression proxy model also need to be selected: C (regularization parameter), e (tolerance), g (kernel function parameter).

[0109] C: regularization parameter, used to balance the training error and the model complexity. C When the value of C is large, the model will pay more attention to the fitting of the training set, but it may lead to overfitting.

[0110] e : tolerance, controls the number of support vectors, smaller ε will make more data points become support vectors, thus increasing the model complexity.

[0111] g : parameter of kernel function, determines the range of data points influence. Larger γ value may lead to overfitting.

[0112] Using the design variables and performance responses from the orthogonal experimental design, train the support vector regression surrogate model by selecting appropriate C , e and g parameters, so that the surrogate model can fit the data as accurately as possible.

[0113] S43, evaluate the prediction accuracy of the support vector regression model by calculating the root mean square error (RMSE), which is expressed as:

[0114] ;

[0115] Where, RMSE represents the root mean square error, y i and represent the calculated value and predicted value of the test sample respectively.

[0116] S5, evaluate the uncertainty of the design by Monte Carlo analysis (MAC).

[0117] In this embodiment, the specific steps of S5 include:

[0118] 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. In step two, five noise factors are determined: saturation magnetic flux density deviation (Δ B s ), winding and magnetic core distance error (Δ d wcg ), lamination coefficient deviation (Δ S ta ), and the deviation of inner and outer angular radius (Δ F inner_c and Δ F outer_c ), and the probability distribution followed by each noise factor is defined.

[0119] S52, input each sample into the support vector regression surrogate model constructed in step four, calculate the corresponding performance responses (total loss, thermal resistance and hotspot temperature), calculate the mean ( m ) and standard deviation ( s ) of the response performance.

[0120] S53, analyze the statistical properties of the performance responses, evaluate the impact of uncertainty on the optimization objectives, and ensure the robustness of the optimization results in actual production.

[0121] S6, obtain the Pareto front by non-dominated genetic algorithm-III (NSGA-III), and then perform multi-objective optimization.

[0122] The optimization objectives of this embodiment include the mean and standard deviation of thermal resistance ( R cond ), hotspot temperature ( T hotspot ) and total loss ( P total_loss ), which are key factors for evaluating the performance of nanocrystalline high-frequency transformer system. NSGA-III is an improved multi-objective optimization genetic algorithm, which aims to obtain a set of Pareto optimal solutions by maintaining and optimizing the balance of multi-objectives. The core idea of NSGA-III is to use non-dominated sorting and crowding distance calculation to guide the search process, and use the concept of reference point to help find a more uniformly distributed Pareto front.

[0123] In this embodiment, the specific steps of S6 include:

[0124] S61, initialize the population based on the random samples generated by Monte Carlo analysis, the population is composed of random samples obtained in S5, and the corresponding performance responses are calculated by the support vector regression surrogate model constructed in S4. These performance responses are used as the basis for measuring the fitness of each individual.

[0125] S62, evaluate the fitness of each individual by non-dominated sorting and crowding distance, so as to select which individuals will become parents and then generate new offspring individuals.

[0126] 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 the objectives. In multi-objective optimization, if individual A is not worse than individual B in all objectives, and is better than B in at least one objective, A is said to dominate B. Dominated individuals have higher priority, so non-dominated individuals are considered first in selection. Crowding distance is used to measure the distance between individuals and adjacent individuals. 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.

[0127] S63, new individuals are generated by selection, crossover and mutation operations, with mutation probability controlled between 0.1 and 0.2, these operations help to pass the good genes of parent individuals to the next generation, while introducing new diversity.

[0128] Selection operation: two individuals are randomly selected from the population each time, and it is determined which individual is suitable to be the parent by comparing their non-dominated ranking and crowding distance. The individual with higher non-dominated ranking and larger crowding distance is preferentially selected.

[0129] 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.

[0130] 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.

[0131] S64, when generating a new generation of population, the parents and offspring are combined, and then the best individuals are screened out by 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.

[0132] S65, after multiple generations of evolution, a set of Pareto optimal solutions is generated, representing the best balance between different objectives, referring to Figure 4 These solutions represent the optimal trade-off between multiple objectives, with each solution being superior to other solutions in some objectives, but possibly inferior in some objectives.

[0133] The final optimization design is based on the selection of 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 transformer, ensuring the robustness and thermal stability under uncertain operating conditions.

[0134] Table 2 Comparison of optimization results of nanocrystalline high-frequency transformer

[0135] ;

[0136] Therefore, the present 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 transformer, and ensure that the equipment can balance performance and economy in high-power scenarios.

[0137] It should be pointed out finally that the above examples are only used to illustrate the technical solutions of the present application but not to limit it, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can still be modified or replaced equivalently, and these modifications or equivalent replacements should not 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 uncertainties, characterized in that, Includes the following steps: S1. Initial design of nanocrystalline high-frequency transformer based on multiphysics field; S2. Define the optimization objective of the nanocrystalline high-frequency transformer and construct the corresponding robust optimization design model; Optimization objectives include minimizing total losses, thermal resistance, and hot spot temperatures; In the robust optimization design model, the noise factor is treated as a random variable, and its variation is considered using a specific statistical distribution. 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 coefficient deviation, and core fillet size error; The saturation flux density deviation of the nanocrystalline magnetic core follows a Weber distribution, denoted as Δ. B s ~Weibull( , ), where Δ B s This indicates the deviation in saturation magnetic flux density of the nanocrystalline magnetic core. The dimensional parameter representing the deviation of the saturation magnetic flux density. The shape parameter is the deviation of the saturation magnetic flux density, and the size parameter and shape parameter are set to 1 / 3 of the manufacturing tolerance of the magnetic core material; The winding-to-core distance error and lamination factor deviation follow a normal distribution, representing Δ d wcg ~N( , , ρ ), ΔS ta ~N( , , ρ ), where Δ d wcg Δ represents the distance error between the winding and the magnetic core. S ta Indicates the deviation of the stacking coefficient. This represents the mean value of the distance error between the winding and the magnetic core. This represents the standard deviation of the distance error between the winding and the magnetic core. ρ Represents the correlation coefficient; The fillet dimensions of nanocrystalline magnetic cores follow a binary normal distribution, denoted 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 refer to the fillet radius of the nanocrystalline magnetic core. and These are the average radii of the inner and outer fillet radii of the magnetic core, respectively. and These are the standard deviations of the inner and outer corner radii of the magnetic core, respectively. ρ The correlation coefficient is set to 1 / 3 of the corresponding manufacturing tolerance. The formula for the robust optimization design model is as follows: ； in, and These represent the leakage inductance, total loss, and hot spot temperature of the nanocrystalline high-frequency transformer, respectively. and represent the target value for leakage sensing, , , , , and These are the dimensional parameters of the nanocrystalline high-frequency transformer. , and These are the winding-to-core spacing error, saturation flux density deviation, and lamination coefficient deviation, respectively. These represent the mean, standard deviation, and correlation coefficient in sample statistics, respectively. S3. After determining the robust optimization design model, orthogonal experimental design is used to generate representative sample points; S4. Construct a support vector regression surrogate model; S5. Evaluate design uncertainties 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 transformers considering core uncertainties according to claim 1, characterized in that, Step S1 is as follows: Design parameters for nanocrystalline high-frequency transformers based on multiphysics fields, selection of core materials and structures, specifically, selection of nanocrystalline core materials suitable for high-frequency applications based on design requirements, considering their high saturation magnetic 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 and evaluate the losses and efficiency. If they meet the requirements, complete the design. If they do not meet the requirements, select a new magnetic core until the requirements are met.

3. The robust design method for nanocrystalline high-frequency transformers considering core uncertainties according to claim 2, characterized in that, The formula for calculating the product of areas is as follows: ； in, Represents the product of areas. Indicates rated power. This refers to the operating frequency of the nanocrystalline high-frequency transformer. Indicates the working magnetic flux density. and These are the effective cross-sectional area of ​​the magnetic core and the window area, respectively. These are the core window utilization factor, voltage waveform factor, and current density ratio factor, respectively. This represents the core shape constant.

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

5. The robust design method for nanocrystalline high-frequency transformers considering core uncertainties according to claim 1, characterized in that, The specific steps of S4 include: S41. Data preprocessing is required, specifically, Z-score standardization of the sample data generated by the orthogonal experiment is performed to ensure that the variables are trained on a uniform scale. The Z-score standardization formula is: ； in, It is the raw data. It is the mean of the data. It is the standard deviation of the data; S42. After completing the data preprocessing, select support vector regression as the surrogate model and select the parameters of the support vector regression surrogate model. S43. The prediction accuracy of the support vector regression model is evaluated by calculating the root mean square error, the expression of which is: ； in, This represents the root mean square error. and These represent the calculated and predicted values ​​for the test sample, respectively.

6. The robust design method for nanocrystalline high-frequency transformers considering core uncertainties 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, the uncertainty of each design variable is simulated by generating a large number of random samples; S52. Input each sample into the support vector regression surrogate model constructed in step four, calculate the corresponding performance response, and calculate the mean and standard deviation of the response performance. S53. Analyze the statistical characteristics of the performance response, assess the impact of uncertainty on the optimization objective, and ensure the robustness of the optimization results in actual production.

7. A robust design method for nanocrystalline high-frequency transformers considering core uncertainties according to claim 1, characterized in that, The specific steps of S6 include: S61. Initialize the population based on random samples generated by Monte Carlo analysis. The population consists of random samples obtained in S5, and calculate the corresponding performance response through the support vector regression surrogate model constructed in S4. S62. The fitness of each individual is assessed by non-dominated ranking and crowding distance in order to select which individuals will become parents and thus generate new offspring individuals; S63. New individuals are generated through selection, crossover, and mutation operations, with the mutation probability controlled between 0.1 and 0.2; S64. When generating a new generation of population, the parent and offspring generations are merged, and then the best individuals are selected 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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