A multi-physical field multi-objective robust optimization design method and system for nanocrystalline high-frequency transformers

Abstract

The application discloses a kind of nanocrystalline high-frequency transformer multi-physics field multi-objective robust optimization design method and system, belong to high-frequency transformer technical field, method includes: constructing multi-objective optimization function;Introduce the coupling calculation model of core loss and winding loss;Establish multidimensional constraint condition;Identify the high sensitivity parameter and low sensitivity parameter that optimization target is significantly influenced, simplify optimization dimension;Construct Kriging surrogate model, generate sample point using Latin hypercube sampling;Determine the optimization of Kriging surrogate model, obtain Pareto optimal solution set;Divide control factor and noise factor, use Taguchi method to design orthogonal experiment;Introduce support vector regression to construct robust optimization surrogate model, optimize control factor in combination with NSWOA algorithm.The application uses the above method and system, improves the anti-interference ability of equipment, solves the performance dispersion problem under high-frequency working condition, guarantees the stability of nanocrystalline high-frequency transformer long-term operation.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer technology, and in particular to a robust optimization design method and system for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives. Background Technology

[0002] As power electronic devices iterate and upgrade towards higher power density and higher conversion efficiency, nanocrystalline high-frequency transformers (nanoHFTs) are becoming increasingly critical in fields such as new energy grid connection, energy storage conversion, rail transit traction, and ship power systems. To meet the stringent requirements of modern power systems for high frequency, miniaturization, and long lifespan, the design of nanocrystalline high-frequency transformers is shifting from optimizing single performance indicators to robust designs that incorporate multi-physics coordination and resistance to manufacturing deviations. How to achieve low-loss operation under high-frequency conditions while improving the equipment's tolerance to fluctuations in material properties and manufacturing tolerances has become a core issue for the industrial application of nanocrystalline high-frequency transformers.

[0003] Under the influence of high-frequency alternating magnetic fields, the performance of nanocrystalline high-frequency transformers is severely constrained by the coupling effects of multiple physical fields, including electric, magnetic, and thermal fields. Core hysteresis losses, winding eddy current losses, and proximity effect losses are all converted into heat. The localized temperature rise caused by this accumulated heat not only reduces the permeability of the nanocrystalline material but also accelerates winding insulation aging, placing extremely high demands on the equipment's heat dissipation performance and structural reliability. Especially in high-capacity, high-frequency applications, the positive feedback effect of electromagnetic losses and temperature rise, as well as the performance dispersion caused by manufacturing deviations, significantly affect the long-term operational stability of the equipment. Therefore, robust optimization design through multi-physical field coupling is urgently needed to ensure the efficient and reliable operation of nanocrystalline high-frequency transformers under complex operating conditions.

[0004] The properties of the core material are the core factors determining the high-frequency performance of nanocrystalline high-frequency transformers. Compared to traditional silicon steel, nanocrystalline alloys have become the preferred material for high-frequency transformer cores due to their advantages of high saturation magnetic flux density and low high-frequency losses. However, under high-frequency heavy-load conditions, the losses of nanocrystalline cores still increase with increasing frequency. Furthermore, compositional fluctuations and lamination process deviations during material preparation can further lead to the dispersion of core losses. How to reduce core losses while suppressing performance fluctuations caused by material uncertainties has become a prominent challenge in the design.

[0005] The winding structure design also needs to consider both high-frequency effects and manufacturing compatibility. Under high-frequency, high-power conditions, the skin effect and proximity effect significantly increase the AC resistance loss of the winding. While using multi-strand stranded Litz wire can alleviate this problem, manufacturing tolerances in parameters such as the winding arrangement and conductor cross-sectional area still affect the loss distribution and heat conduction path. By combining multiphysics simulation with robust optimization methods, precise design of core dimensions, winding parameters, and material properties can be achieved. This improves the power density and efficiency of nanocrystalline high-frequency transformers while enhancing the equipment's adaptability to manufacturing deviations and controlling the total life-cycle cost.

[0006] Current traditional design methods for nanocrystalline high-frequency transformers are mostly based on deterministic operating conditions, neglecting the impact of material property fluctuations and manufacturing tolerances, and lacking in-depth analysis of multi-physics coupling effects. This results in difficulties in precisely controlling electromagnetic losses and temperature rise during actual operation, leading to insufficient performance stability and making it difficult to simultaneously meet the application requirements of high power density, high efficiency, and high reliability. Summary of the Invention

[0007] The purpose of this invention is to provide a robust optimization design method and system for nanocrystalline high-frequency transformers with multiple physics fields and multiple objectives, in order to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, this invention provides a robust optimization design method for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives, comprising the following steps: S1. Based on the application requirements of high power density and high thermal stability of nanocrystalline high-frequency transformers, multi-objective optimization functions for core loss, conduction thermal resistance and hot spot temperature are constructed respectively. S2. Based on the magnetic properties and high-frequency operating characteristics of nanocrystalline materials, a coupled calculation model of core loss and winding loss is introduced, and combined with temperature coefficient correction, the total loss and heat generation distribution of the transformer are obtained. S3. Based on the geometric constraints, electromagnetic performance constraints, thermal stability constraints and manufacturing tolerance range of nanocrystalline iron core, establish multi-dimensional constraints, including dimensional constraints, electromagnetic constraints, thermal constraints and manufacturing tolerance constraints. S4. Based on Sobel sensitivity analysis, identify high-sensitivity and low-sensitivity parameters that have a significant impact on the optimization target, thus simplifying the optimization dimensions. S5. Based on high-sensitivity parameters, a Kriging surrogate model is constructed, and sample points are generated using Latin hypercube sampling. S6. Based on the non-dominated sorting whale optimization algorithm, deterministic optimization of the Kriging surrogate model is performed to obtain the Pareto optimal solution set and verify the model accuracy and optimization effectiveness. S7. Divide the control factor and noise factor, design an orthogonal experiment using the Taguchi method, and improve the design's anti-interference capability through signal-to-noise ratio analysis; S8. Introduce support vector regression to construct a robust optimization surrogate model, combine it with the NSWOA algorithm to optimize the control factor, and select the optimal robust design scheme through comprehensive performance indicators.

[0009] Preferably, the multi-objective optimization function in S1 includes a deterministic optimization objective function and a robust optimization objective function; The deterministic optimization objective function and constraints are as follows: ; ; ; ; in, , , These represent the core loss, thermal resistance, and hot spot temperature rise of the nanocrystalline high-frequency transformer, respectively. These are design variables, encompassing winding geometry parameters, core dimensions, and material properties. Window width , Window height , For the width of the iron core , For conductor thickness , inner corner radius , outer corner radius ; For hot spot temperature, Hotspot temperature threshold; For transformer efficiency; , These are the boundary values ​​for each design parameter; The robust optimization objective function and constraints are as follows: ; ; ; In the formula, This is a mean function of the performance metrics; This is the variance function of the performance index, representing the degree of performance fluctuation; Noise factor; The maximum permissible fluctuation range for each noise factor is specified, and the maximum fluctuation range shall not exceed [specified value]. Noise factors include core air gap deviation. saturation flux density deviation wait.

[0010] Preferably, the core loss model in S2 adopts a modified model that considers the temperature coefficient, and the calculation formula is as follows: ; In the formula, For the core loss model; For switching cycles; and These are the operating frequency and the equivalent frequency, respectively. Peak magnetic flux density; All are core loss coefficients; Temperature coefficient; This refers to the core temperature. The ambient temperature; This is the effective cross-sectional area of ​​the iron core; This represents the magnetic flux path length. The resistivity of nanocrystalline iron core; This refers to the input voltage amplitude. Duty cycle; and These represent the number of turns on the primary side and the total number of turns, respectively. The winding loss model takes into account the skin effect and proximity effect, and the calculation formula is as follows: ; In the formula, For winding loss model; The winding conductivity; This represents the average turn length of the winding. This represents the cross-sectional area of ​​the winding. It is a dimensionless parameter; For the first The effective value current of the subharmonic; AC resistance considering skin effect and proximity effect; It is a DC resistance; This is the skin effect correction factor; This is the neighborhood effect correction coefficient; A coupled calculation model covering core loss and winding loss is constructed, and the thermal resistance and hot spot temperature rise are calculated as follows: ; ; ; ; ; ; ; In the formula, For the thermal resistance of the iron core; The thermal resistance of the iron core temperature gradient; For the thermal resistance of the winding; Thermal resistance of the medium surrounding the winding; This represents the total thermal resistance of the winding. The total thermal resistance of the transformer; , , These are the lengths of the heat conduction path for the core, windings, and surrounding medium, respectively. , , These are the thermal conductivity coefficients of the iron core, windings, and surrounding medium, respectively. , , These are the cross-sectional areas of the corresponding heat conduction paths; The topic is gaining traction.

[0011] Preferably, the Sobel sensitivity coefficient in S4 is calculated as follows: ; ; In the formula, This represents the single-target sensitivity index calculated based on the Sobol method. This represents the multi-objective weighted overall sensitivity coefficient. For parameters Fixed objective function The conditional expected variance; The total variance of the objective function; As a weighting factor; , , These are the sensitivity coefficients corresponding to core loss, thermal resistance, and hot spot temperature, respectively.

[0012] Preferably, the Kriging surrogate model in S5 is constructed based on Gaussian process regression, and the sample matrix and related model calculations are as follows: ; ; ; ; ; In the formula, Represents the sample matrix, This represents the mean function of the Kriging proxy model. Represents the covariance matrix between training samples. and Let represent the values ​​of two different sample points in the i-th dimension of the design variable. , These are the lower and upper bounds of the design variable, respectively. This is the normalized Latin hypercube sampling matrix; The number of samples; For high-sensitivity parameter dimensions; Represent a Gaussian process; The variance of the signal; The relevant length scale for each parameter; For new input variables; It is the cross covariance vector; The inverse matrix of the covariance matrix of the training data; Output the training data; This is for predicting the output.

[0013] Preferably, S6 specifically involves: initializing the whale population size, variables, and maximum number of iterations, and generating a random initial population; calculating the fitness and position vectors of all whales and prey; performing a non-dominated sort on the initial population and calculating the crowding distance of each individual; performing pairwise comparisons on individuals and selecting individuals with higher dominance or greater crowding distance; iteratively updating the population; repeating the sorting, selection, and updating process until the maximum number of iterations is reached; and finally obtaining the optimal solution of the Pareto front.

[0014] Preferably, the position update formula for the non-dominated sorting whale optimization algorithm in S6 is as follows: ; In the formula, Number of iterations The whale's location at that time; This is the current optimal solution position; This represents the position vector of the current individual whale at the t-th iteration, which is the combination of design variables corresponding to the current candidate design scheme; , For coefficient vectors; The switching threshold; ; It is the logarithmic spiral shape constant; It is a random number in the interval [-1, 1].

[0015] Preferably, the signal-to-noise ratio analysis in S7 includes: Calculate the signal-to-noise ratio, data standardization index, and overall performance index of orthogonal experiments in robust optimization: ; ; ; In the formula, These are the hotspot temperatures from the orthogonal experiment. The number of samples; Standardize the indicators for the data; This represents the maximum signal-to-noise ratio among all orthogonal experimental schemes; This represents the minimum signal-to-noise ratio among all orthogonal experimental schemes; For comprehensive performance indicators; , , All are weighted coefficients, highlighting the priority of hotspot temperatures; , , These are the standardized indicators corresponding to total loss, thermal resistance, and hot spot temperature, respectively.

[0016] Preferably, the robust optimization agent model constructed in S8 includes: The optimal decision surface for the robust surrogate model based on support vector regression is calculated as follows: ; In the formula, For Gaussian kernel function mapping; This is the weight vector; For bias terms; The optimization problem of a robust surrogate model for support vector regression is calculated by mapping the sample data using a Gaussian kernel function. ; ; In the formula, As a penalty factor; For insensitive loss parameters; , All are slack variables; , These are the input and output of the training samples, respectively. .

[0017] This invention also provides a robust optimization design system for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives, comprising: The optimized target building module is configured to: preset based on the application scenario of nanocrystalline high-frequency transformers. The default operating parameters can be customized by the user, and the objective functions and constraints for deterministic and robust optimization can be constructed to clarify the range of design variables. The loss and thermal network modeling module is configured to: establish a core loss model considering the temperature coefficient, a winding loss model considering the skin / proximity effect, construct a core-winding coupled thermal network model, and obtain the total loss and heat distribution characteristics. The constraint establishment module is configured to integrate dimensional constraints, electromagnetic constraints, thermal constraints, and manufacturing tolerance constraints to establish a multi-dimensional set of constraint conditions. The sensitivity analysis module is configured to use the Sobel sensitivity analysis method to classify high / low sensitivity parameters and simplify the optimization dimensions. The surrogate model construction module is configured to: construct deterministic and robustly optimized surrogate models based on Latin hypercube sampling and Kriging model and support vector regression model, respectively. The optimization algorithm execution module is configured to: solve Pareto fronts for deterministic optimization using NSWOA, achieve robust optimization by combining Taguchi method and NSWOA-SVR, and select the optimal solution through comprehensive performance indicators; The verification module is configured to: conduct electromagnetic-thermal bidirectional coupling simulation verification and prototype experimental testing, compare simulation and measured data, and verify the effectiveness and robustness of the design scheme.

[0018] Therefore, the present invention employs the above-mentioned robust optimization design method and system for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives, which has the following beneficial effects: (1) This invention integrates a dual framework of deterministic optimization and robust optimization, breaking through the limitations of traditional design that ignores material property fluctuations and manufacturing tolerances; by simultaneously optimizing the average performance and the degree of fluctuation, it can improve the anti-interference capability of the equipment while achieving a coordinated reduction in core loss, thermal resistance, and hot spot temperature, thus solving the performance dispersion problem under high-frequency operating conditions and ensuring the long-term stability of nanocrystalline high-frequency transformers.

[0019] (2) This invention introduces Sobel sensitivity analysis to accurately identify high-sensitivity design parameters and constructs a Kriging proxy model by combining Latin hypercube sampling. This method greatly reduces the computational cost of multiphysics simulation, realizes efficient exploration of complex design space, lays the foundation for rapid iteration of subsequent optimization algorithms, and improves the efficiency and accuracy of the overall design process.

[0020] (3) This invention uses the Non-Dominated Sorting Whale Optimization Algorithm (NSWOA) combined with Taguchi method and Support Vector Regression (SVR) to construct a multi-objective robust optimization system; by using signal-to-noise ratio analysis and comprehensive performance index (MPCI) to screen the optimal solution, it achieves a balance between electromagnetic performance, thermal stability and resistance to manufacturing deviations, effectively reducing the hot spot temperature fluctuation range by 32%-41%, and taking into account the high performance and high reliability of the equipment.

[0021] (4) This invention relies on electromagnetic-thermal bidirectional coupling simulation analysis and prototype experimental testing to complete the full-process verification from theoretical model to practical application; the high degree of agreement between simulation and measured data proves the prediction accuracy of the optimized model and ensures the feasibility of the design scheme in high-capacity, high-frequency application scenarios.

[0022] (5) The multi-physics robust optimization design method constructed in this invention has universality and can be adapted to the design requirements of nanocrystalline high-frequency transformers in multiple fields such as new energy grid connection, energy storage converter, and rail transit traction. This method gets rid of the limitations of single physical field or single target optimization and achieves synergistic improvement of electromagnetic, thermal and mechanical properties.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a robust optimization design method for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives, according to an embodiment of the present invention. Figure 2 This is a three-dimensional topology of a transformer according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the hierarchical optimization framework process that integrates deterministic design and robust design in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the specific steps of the non-dominated sorting whale optimization algorithm in an embodiment of the present invention; Figure 5 This is a schematic diagram of the correlation analysis results of control factors in an embodiment of the present invention; Figure 6 This is the Pareto front of the NSWOA algorithm in robust design according to an embodiment of the present invention; Figure 7 The graphs show the performance of deterministic and robust designs in the embodiments of the present invention on three targets: thermal resistance, hot spot temperature, and total loss. Detailed Implementation

[0025] 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.

[0026] 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.

[0027] Example like Figure 1 As shown, this invention provides a robust optimization design method for nanocrystalline high-frequency transformers using multi-physics and multi-objective approaches. The method focuses on a 20kW, 10kHz nanocrystalline high-frequency transformer used in a new energy grid-connected scenario, referencing... Figure 2 In combination with the core requirements of high power density and high thermal stability, the following steps are included: S1. Based on the application requirements of high power density and high thermal stability of nanocrystalline high-frequency transformers, multi-objective optimization functions for core loss, conduction thermal resistance, and hot spot temperature are constructed respectively, while taking into account the dual objectives of minimizing the average performance and the degree of fluctuation.

[0028] Focusing on the four core requirements of "low loss, low thermal resistance, low hot spot temperature, and high robustness", we have identified a multi-objective optimization direction: on the one hand, to reduce the average value of core loss, conduction thermal resistance and hot spot temperature, and on the other hand, to suppress performance fluctuations caused by manufacturing deviations.

[0029] refer to Figure 3 The deterministic optimization objective function and constraints are as follows: ; ; ; ; in, , , These represent the core loss, thermal resistance, and hot spot temperature rise of the nanocrystalline high-frequency transformer, respectively. These are design variables, encompassing winding geometry parameters, core dimensions, and material properties. Window width , Window height , For the width of the iron core , For conductor thickness , inner corner radius , outer corner radius ; For hot spot temperature, Hotspot temperature threshold; For transformer efficiency; , These are the boundary values ​​for each design parameter.

[0030] For example, core width for conductor thickness for .

[0031] The robust optimization objective function and constraints are as follows: ; ; ; In the formula, This is a mean function of the performance metrics; This is the variance function of the performance index, representing the degree of performance fluctuation; noise factor ( , , , , ); The maximum permissible fluctuation range for each noise factor is specified, and the maximum fluctuation range shall not exceed [specified value]. Noise factors include core air gap deviation. saturation flux density deviation wait.

[0032] For example, the constraints for deterministic and robust optimization objective functions are as follows: Electromagnetic confinement: peak magnetic flux density Operating frequency Transformer efficiency ; Thermal constraint: Hot spot temperature threshold ; Size constraints: For example, the core width is The conductor thickness is ; Robust constraint: Noise factor The maximum fluctuation range does not exceed Noise factors include core air gap deviation. saturation flux density deviation wait.

[0033] S2. Based on the magnetic properties and high-frequency operating characteristics of nanocrystalline materials, a coupled calculation model of core loss and winding loss is introduced, and combined with temperature coefficient correction, the total loss and heat generation distribution of the transformer are obtained.

[0034] The core loss model is associated with the switching cycle, operating frequency, equivalent frequency, peak magnetic flux density, core loss coefficient, temperature coefficient, core temperature, ambient temperature, effective cross-sectional area of ​​the core, magnetic flux path length, resistivity of the nanocrystalline core, input voltage amplitude, duty cycle, number of primary turns, and total number of turns.

[0035] The core loss model uses a modified model that considers the temperature coefficient, as follows: ; In the formula, For the core loss model; For switching cycles; and These are the operating frequency and the equivalent frequency, respectively. Peak magnetic flux density; All are core loss coefficients; Temperature coefficient; This refers to the core temperature. The ambient temperature; This is the effective cross-sectional area of ​​the iron core; This represents the magnetic flux path length. The resistivity of nanocrystalline iron core; This refers to the input voltage amplitude. Duty cycle; and These represent the number of turns on the primary side and the total number of turns, respectively.

[0036] The winding loss model takes into account the skin effect and proximity effect, and the relevant calculations are as follows: ; In the formula, For winding loss model; The winding conductivity; This represents the average turn length of the winding. This represents the cross-sectional area of ​​the winding. It is a dimensionless parameter; For the first The effective value current of the subharmonic; AC resistance considering skin effect and proximity effect; It is a DC resistance; This is the skin effect correction factor; This is the neighborhood effect correction coefficient.

[0037] A coupled calculation model (i.e., a thermal network model) covering core loss and winding loss is constructed. The calculations for each thermal resistance and hot spot temperature rise are as follows: ; ; ; ; ; ; ; In the formula, For the thermal resistance of the iron core; The thermal resistance of the iron core temperature gradient; For the thermal resistance of the winding; Thermal resistance of the medium surrounding the winding; This represents the total thermal resistance of the winding. The total thermal resistance of the transformer; , , These are the lengths of the heat conduction path for the core, windings, and surrounding medium, respectively. , , These are the thermal conductivity coefficients of the iron core, windings, and surrounding medium, respectively. , , These are the cross-sectional areas of the corresponding heat conduction paths; The topic is gaining traction.

[0038] S3. Based on the geometric constraints, electromagnetic performance constraints (magnetic flux density, frequency), thermal stability constraints (hot spot temperature threshold), and manufacturing tolerance range of the nanocrystalline iron core, establish multi-dimensional constraints, including dimensional constraints (…). Electromagnetic confinement (peak magnetic flux density ≤ 0.88T, operating frequency 10kHz), thermal confinement (hot spot temperature) ) and manufacturing tolerance constraints ( ).

[0039] S4. Based on Sobel sensitivity analysis, identify high-sensitivity parameters (core width, conductor thickness, etc.) and low-sensitivity parameters that have a significant impact on the optimization target, thus simplifying the optimization dimensions.

[0040] Sobel sensitivity coefficient is calculated as follows: ; ; In the formula, This represents the single-objective sensitivity index calculated using the Sobol method, used to measure the contribution of a single design parameter to the variance of the objective function output. This represents the multi-objective weighted comprehensive sensitivity coefficient, which is obtained by weighting the sensitivity coefficients corresponding to three objectives: core loss, thermal resistance, and hot spot temperature. It is used to comprehensively characterize the overall influence of design parameters on the three objectives of core loss, thermal resistance, and hot spot temperature. For parameters Fixed objective function The conditional expected variance; The total variance of the objective function; As a weighting factor; , , These are the sensitivity coefficients corresponding to core loss, thermal resistance, and hot spot temperature, respectively.

[0041] Analysis results: Core width With conductor thickness These are high-sensitivity parameters, contributing over 60%; window size and corner radius are low-sensitivity parameters. The optimization dimension was reduced from 6 dimensions to 2 dimensions.

[0042] S5. Based on high-sensitivity parameters, a Kriging proxy model is constructed, and sample points are generated using Latin hypercube sampling to achieve an efficient alternative to multiphysics simulation.

[0043] The Kriging surrogate model is based on Gaussian process regression. The sample matrix and related model calculations are as follows: ; ; ; ; ; In the formula, Represents the sample matrix, This represents the mean function of the Kriging proxy model; in this embodiment, we take... This indicates that, after standardization or normalization, the model residuals or response changes are described using a zero-mean Gaussian process. This represents the covariance matrix among training samples, used to describe the correlation between different sample points. and Indicates two different sample points x and x ′ in the The values ​​of each design variable dimension , These are the lower and upper bounds of the design variable, respectively. This is the normalized Latin hypercube sampling matrix; The number of samples; For high-sensitivity parameter dimensions; Represent a Gaussian process; The variance of the signal; The relevant length scale for each parameter; For new input variables; It is the cross covariance vector; The inverse matrix of the covariance matrix of the training data; Output the training data; To predict the output, the Kriging surrogate model's prediction error is controlled to within 3%.

[0044] S6. Based on the Non-Dominated Sorting Whale Optimization Algorithm (NSWOA), perform deterministic optimization on the Kriging surrogate model to obtain the Pareto optimal solution set, and verify the model accuracy and optimization effectiveness, such as... Figure 4 As shown, the specific steps are as follows: Initialize the whale population size, variables, and maximum number of iterations, and generate a random initial population; calculate the fitness and position vectors of all whales and prey; perform a non-dominated sort on the initial population and calculate the crowding distance of each individual; perform pairwise comparisons on individuals and select individuals with higher dominance or larger crowding distances; iteratively update the population; repeat the sorting, selection, and updating process until the maximum number of iterations is reached; finally, obtain the optimal solution of the Pareto front.

[0045] The position update formula for the Non-Dominated Sorting Whale Optimization Algorithm (NSWOA) is as follows: ; In the formula, Number of iterations The whale's location at that time; This is the current optimal solution position; This represents the position vector of the current individual whale at the t-th iteration, which is the combination of design variables corresponding to the current candidate design scheme; , For coefficient vectors; For switching threshold ( ); ; It is the logarithmic spiral shape constant; It is a random number in the interval [-1, 1].

[0046] Optimization result: The total loss corresponding to the optimal parameter combination under ideal operating conditions is The hotspot temperature is .

[0047] S7. Divide control factors (window size, core width, etc.) and noise factors (material property fluctuations, manufacturing tolerances, etc.), and design orthogonal experiments using the Taguchi method. Improve the design's anti-interference capability through signal-to-noise ratio (S / N) analysis.

[0048] Orthogonal experiment: using Orthogonal arrays are used to perform full factorial experiments. The next reduction to Second-rate.

[0049] The signal-to-noise ratio, data standardization index, and overall performance index of the robustly optimized orthogonal experiment are calculated as follows: ; ; ; In the formula, These are the hotspot temperatures from the orthogonal experiment. The number of samples; Standardize the indicators for the data; This represents the maximum signal-to-noise ratio among all orthogonal experimental schemes; This represents the minimum signal-to-noise ratio among all orthogonal experimental schemes; For comprehensive performance indicators; , , All are weighted coefficients, highlighting the priority of hotspot temperatures; , , These are the standardized indicators corresponding to total loss, thermal resistance, and hot spot temperature, respectively.

[0050] like Figure 5 As shown in the figure, this diagram presents the correlation analysis results of various control factors during the robust optimization stage of the nanocrystalline high-frequency transformer. The figure reflects the strength and trend of correlations among design parameters such as window size, core width, conductor thickness, and fillet radius, helping to identify the coupling relationships and independence characteristics between parameters. Parameter pairs with larger absolute values ​​of correlation coefficients indicate a strong correlation in their structural or performance impact, while parameter pairs with correlation coefficients close to zero indicate a weaker coupling. This correlation analysis provides a basis for the rational selection of control factors, the configuration of orthogonal experimental factors, and the subsequent construction of robust surrogate models, thereby reducing the interference of redundant design variables on the optimization results and improving the targeting and efficiency of robust optimization.

[0051] S8. Introduce Support Vector Regression (SVR) to construct a robust optimization surrogate model, combine it with the NSWOA algorithm to optimize the control factor, and select the optimal robust design scheme through the comprehensive performance index (MPCI).

[0052] The optimal decision surface of the SVR robustly optimized agent model is: ; In the formula, For Gaussian kernel function mapping; This is the weight vector; For bias terms; The optimization problem of the SVR robust surrogate model, which maps sample data using a Gaussian kernel function, is as follows: ; ; In the formula, As a penalty factor; For insensitive loss parameters; , All are slack variables; , These are the input and output of the training samples, respectively. .

[0053] like Figure 6 As shown in the figure, this diagram illustrates the Pareto front distribution obtained by the Non-Dominated Sorting Whale Optimization Algorithm (NSWOA) in the robust design of nanocrystalline high-frequency transformers. Each front point in the diagram corresponds to a set of feasible design schemes, reflecting the competition and coordination among performance indicators such as total loss, conductive thermal resistance, and hot spot temperature. As the performance of one objective is further improved, other objectives are usually sacrificed to varying degrees. Therefore, this diagram can intuitively reveal the trade-offs between various indicators in multi-objective optimization problems. By analyzing the Pareto front solution set, candidate schemes that balance low loss, low thermal resistance, low hot spot temperature, and strong resistance to manufacturing deviations can be screened, providing support for subsequent comprehensive performance evaluation and determination of the optimal robust design scheme.

[0054] S9. Perform multi-physics bidirectional coupling simulation analysis on the optimal design scheme, compare the electromagnetic performance and thermal distribution characteristics of the deterministic design and the robust design, and verify the stability of the scheme under manufacturing deviations; also includes Monte Carlo analysis on the optimal robust design scheme to verify the performance fluctuation range under manufacturing deviations, ensure that the probability of failure (POF) meets the design requirements, and reduce the hot spot temperature fluctuation amplitude by 32%-41% compared with the deterministic design.

[0055] Multiphysics bidirectional coupling simulation analysis: Electromagnetic performance: Peak flux density of a robust design Improved compared to deterministic design ; Thermal properties: Maximum temperature of the iron core Maximum winding temperature The temperature fluctuation range of hotspots has decreased. ; Monte Carlo analysis: The probability of failure (POF) meets the design requirements.

[0056] S10. Through prototype testing, voltage, current, and temperature data are collected to verify the prediction accuracy and actual operational reliability of the optimized model.

[0057] Prototype prototype testing includes: Electrical performance: Actual measured effective values ​​of primary and secondary voltages RMS current value ,efficiency ; Thermal performance: Maximum steady-state temperature after 9 hours of continuous operation The deviation from the simulated value is less than .

[0058] like Figure 7 As shown in the figure, this comparison illustrates the performance differences between deterministic and robust design schemes for nanocrystalline high-frequency transformers in three core indicators: total loss, conductive thermal resistance, and hot spot temperature. Compared to the deterministic design, which optimizes only for ideal operating conditions, the robust design, while considering the optimization of the target mean, further takes into account the disturbances caused by material property fluctuations and manufacturing tolerances. Therefore, it performs better in terms of hot spot temperature control, thermal resistance suppression, and overall performance stability. Especially under the condition of manufacturing deviations, the robust design scheme can effectively reduce performance dispersion and hot spot temperature fluctuation amplitude, indicating that the proposed method can not only improve the overall performance of nanocrystalline high-frequency transformers but also enhance their long-term operational reliability under complex operating conditions.

[0059] This invention also provides a robust optimization design system for nanocrystalline high-frequency transformers using multiple physics fields and multiple objectives, comprising: The optimized target building module is configured to: preset based on the application scenario of nanocrystalline high-frequency transformers. Default operating parameters ( , It supports user-defined adjustments, constructs objective functions and constraints for deterministic and robust optimization, and clarifies design variables (window width). Window height Core width Conductor thickness Inner corner radius outer corner radius )scope; The loss and thermal network modeling module is configured to: establish a core loss model considering the temperature coefficient, a winding loss model considering the skin / proximity effect, construct a core-winding coupled thermal network model, and obtain the total loss and heat distribution characteristics. The constraint creation module is configured to integrate dimensional constraints. Electromagnetic confinement (peak magnetic flux density ≤ 0.88T, operating frequency 10kHz), thermal confinement (hot spot temperature) ) and manufacturing tolerance constraints ( Establish a multi-dimensional set of constraints; The sensitivity analysis module is configured to use the Sobel sensitivity analysis method to classify high / low sensitivity parameters and simplify the optimization dimensions. The surrogate model construction module is configured to: construct deterministic and robustly optimized surrogate models based on Latin hypercube sampling and Kriging model and support vector regression model, respectively. The optimization algorithm execution module is configured to: solve Pareto fronts for deterministic optimization using NSWOA, achieve robust optimization by combining Taguchi method and NSWOA-SVR, and select the optimal solution through comprehensive performance indicators; The verification module is configured to: conduct electromagnetic-thermal bidirectional coupling simulation verification and prototype experimental testing, compare simulation and measured data (total loss, hot spot temperature, magnetic flux density, voltage, current data, etc.) to verify the effectiveness and robustness of the design scheme.

[0060] Therefore, the present invention adopts the above-mentioned robust optimization design method and system for nanocrystalline high-frequency transformers with multiple physics fields and multiple objectives, which overcomes the limitations of single physics field or single objective optimization and achieves synergistic improvement of electromagnetic, thermal and mechanical properties.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches, characterized in that, Includes the following steps: S1. Based on the application requirements of high power density and high thermal stability of nanocrystalline high-frequency transformers, multi-objective optimization functions for core loss, conduction thermal resistance and hot spot temperature are constructed respectively. S2. Based on the magnetic properties and high-frequency operating characteristics of nanocrystalline materials, a coupled calculation model of core loss and winding loss is introduced, and combined with temperature coefficient correction, the total loss and heat generation distribution of the transformer are obtained. S3. Based on the geometric constraints, electromagnetic performance constraints, thermal stability constraints and manufacturing tolerance range of nanocrystalline iron core, establish multi-dimensional constraints, including dimensional constraints, electromagnetic constraints, thermal constraints and manufacturing tolerance constraints. S4. Based on Sobel sensitivity analysis, identify high-sensitivity and low-sensitivity parameters that have a significant impact on the optimization target, thus simplifying the optimization dimensions. S5. Based on high-sensitivity parameters, a Kriging surrogate model is constructed, and sample points are generated using Latin hypercube sampling. S6. Based on the non-dominated sorting whale optimization algorithm, deterministic optimization of the Kriging surrogate model is performed to obtain the Pareto optimal solution set and verify the model accuracy and optimization effectiveness. S7. Divide the control factor and noise factor, design an orthogonal experiment using the Taguchi method, and improve the design's anti-interference capability through signal-to-noise ratio analysis; S8. Introduce support vector regression to build a robust optimization surrogate model, combine it with the NSWOA algorithm to optimize the control factor, and select the optimal robust design scheme through comprehensive performance indicators. The Sobel sensitivity coefficient in S4 is calculated as follows: ； ； In the formula, This represents the single-target sensitivity index calculated based on the Sobol method. This represents the multi-objective weighted comprehensive sensitivity coefficient, which is obtained by weighting the sensitivity coefficients corresponding to three objectives: core loss, thermal resistance, and hotspot temperature. For parameters Fixed objective function The conditional expected variance; These are design variables, encompassing winding geometry parameters, core dimensions, and material properties. Window width , Window height , For the width of the iron core , For conductor thickness , inner corner radius , outer corner radius ; The total variance of the objective function; As a weighting factor; , , These are the sensitivity coefficients corresponding to core loss, thermal resistance, and hot spot temperature, respectively.

2. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 1, characterized in that: The multi-objective optimization function in S1 includes deterministic optimization objective function and robust optimization objective function; The deterministic optimization objective function and constraints are as follows: ； ； ； ； in, , , These represent the core loss, thermal resistance, and hot spot temperature rise of the nanocrystalline high-frequency transformer, respectively. For hot spot temperature, Hotspot temperature threshold; For transformer efficiency; , These are the boundary values ​​for each design parameter; The robust optimization objective function and constraints are as follows: ； ； ； In the formula, This is a mean function of the performance metrics; This is the variance function of the performance index, representing the degree of performance fluctuation; Noise factor; The maximum permissible fluctuation range for each noise factor is specified, and the maximum fluctuation range shall not exceed [specified value]. Noise factors include core air gap deviation. saturation flux density deviation .

3. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 2, characterized in that: The core loss model in S2 uses a modified model that considers the temperature coefficient, and the calculation formula is as follows: ； In the formula, For the core loss model; For switching cycles; and These are the operating frequency and the equivalent frequency, respectively. Peak magnetic flux density; All are core loss coefficients; Temperature coefficient; This refers to the core temperature. The ambient temperature; This is the effective cross-sectional area of ​​the iron core; This represents the magnetic flux path length. The resistivity of nanocrystalline iron core; This refers to the input voltage amplitude. Duty cycle; and These represent the number of turns on the primary side and the total number of turns, respectively. The winding loss model takes into account the skin effect and proximity effect, and the calculation formula is as follows: ； In the formula, For winding loss model; The winding conductivity; This represents the average turn length of the winding. This represents the cross-sectional area of ​​the winding. It is a dimensionless parameter; For the first The effective value current of the subharmonic; AC resistance considering skin effect and proximity effect; It is a DC resistance; This is the skin effect correction factor; This is the proximity effect correction coefficient; A coupled calculation model covering core loss and winding loss is constructed, and the thermal resistance and hot spot temperature rise are calculated as follows: ； ； ； ； ； ； ； In the formula, For the thermal resistance of the iron core; The thermal resistance of the iron core temperature gradient; For the thermal resistance of the winding; Thermal resistance of the medium surrounding the winding; This represents the total thermal resistance of the winding. The total thermal resistance of the transformer; , , These are the lengths of the heat conduction path for the core, windings, and surrounding medium, respectively. , , These are the thermal conductivity coefficients of the iron core, windings, and surrounding medium, respectively. , , These are the cross-sectional areas of the corresponding heat conduction paths; The topic is gaining traction.

4. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 3, characterized in that: The Kriging surrogate model in S5 is constructed based on Gaussian process regression. The sample matrix and related model calculations are as follows: ； ； ； ； ； In the formula, Represents the sample matrix, This represents the mean function in the Kriging proxy model. This represents the covariance matrix between the input variables of the training samples. Indicates that another sample point x′ is at the th... The values ​​of each design variable dimension , These are the lower and upper bounds of the design variable, respectively. This is the normalized Latin hypercube sampling matrix; The number of samples; For high-sensitivity parameter dimensions; Represent a Gaussian process; The variance of the signal; The relevant length scale for each parameter; For new input variables; It is the cross covariance vector; The inverse matrix of the covariance matrix of the training data; Output the training data; This is for predicting the output.

5. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 4, characterized in that: S6 specifically involves: initializing the whale population size, variables, and maximum number of iterations, and generating a random initial population; calculating the fitness and position vectors of all whales and prey; performing a non-dominated sort on the initial population and calculating the crowding distance of each individual; and performing pairwise comparisons on individuals to select those with higher dominance or greater crowding distance. The population is iteratively updated; the process of sorting, selecting and updating is repeated until the maximum number of iterations is reached; finally, the optimal solution of the Pareto front is obtained.

6. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 5, characterized in that: The position update formula for the non-dominated sorting whale optimization algorithm in S6 is as follows: ； In the formula, Number of iterations The whale's location at that time; This is the current optimal solution position; This represents the position vector of the current individual whale at the t-th iteration, which is the combination of design variables corresponding to the current candidate design scheme; , For coefficient vectors; The switching threshold; ; It is the logarithmic spiral shape constant; It is a random number in the interval [-1, 1].

7. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective approaches according to claim 6, characterized in that: The signal-to-noise ratio analysis in S7 includes: Calculate the signal-to-noise ratio, data standardization index, and overall performance index of orthogonal experiments in robust optimization: ； ； ； In the formula, These are the hotspot temperatures from the orthogonal experiment. The number of samples; Standardize the indicators for the data; This represents the maximum signal-to-noise ratio (RSN) among all orthogonal experimental schemes; This represents the minimum signal-to-noise ratio (RSN) among all orthogonal experimental schemes; For comprehensive performance indicators; , , All are weighted coefficients, highlighting the priority of hotspot temperatures; , , These are the standardized indicators corresponding to total loss, thermal resistance, and hot spot temperature, respectively.

8. The robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective methods according to claim 7, characterized in that: Building a robust and optimized proxy model in S8 includes: The optimal decision surface for the robust surrogate model based on support vector regression is calculated as follows: ； In the formula, For Gaussian kernel function mapping; This is the weight vector; For bias terms; The optimization problem of a robust surrogate model for support vector regression is calculated by mapping the sample data using a Gaussian kernel function. ； ； In the formula, As a penalty factor; For insensitive loss parameters; , All are slack variables; , These are the input and output of the training samples, respectively. .

9. A robust optimization design system for nanocrystalline high-frequency transformers using multiphysics and multi-objective methods, applied to the robust optimization design method for nanocrystalline high-frequency transformers using multiphysics and multi-objective methods as described in any one of claims 1-8, characterized in that... include: The optimized target building module is configured to: preset based on the application scenario of nanocrystalline high-frequency transformers. The default operating parameters can be customized by the user, and the objective functions and constraints for deterministic and robust optimization can be constructed to clarify the range of design variables. The loss and thermal network modeling module is configured to: establish a core loss model considering the temperature coefficient, a winding loss model considering the skin / proximity effect, construct a core-winding coupled thermal network model, and obtain the total loss and heat distribution characteristics. The constraint establishment module is configured to integrate dimensional constraints, electromagnetic constraints, thermal constraints, and manufacturing tolerance constraints to establish a multi-dimensional set of constraint conditions. The sensitivity analysis module is configured to use the Sobel sensitivity analysis method to classify high / low sensitivity parameters and simplify the optimization dimensions. The surrogate model construction module is configured to: construct deterministic and robustly optimized surrogate models based on Latin hypercube sampling and Kriging model and support vector regression model, respectively. The optimization algorithm execution module is configured to: solve Pareto fronts for deterministic optimization using NSWOA, achieve robust optimization by combining Taguchi method and NSWOA-SVR, and select the optimal solution through comprehensive performance indicators; The verification module is configured to: conduct electromagnetic-thermal bidirectional coupling simulation verification and prototype experimental testing, compare simulation and measured data, and verify the effectiveness and robustness of the design scheme.

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