A multi-objective optimization method for nanocrystalline high-frequency transformer based on three-dimensional thermal network fast temperature rise prediction

Abstract

The application discloses a kind of nanocrystalline high-frequency transformer multi-objective optimization methods based on three-dimensional thermal network rapid temperature rise prediction, belong to transformer temperature rise prediction technical field, including: constructing three-dimensional thermal network model;Through nanocrystalline high-frequency transformer temperature rise analysis, verify the correctness of three-dimensional thermal network model;Nanocrystalline high-frequency transformer design variable is optimized by using improved taguchi method;Variable classification mechanism is introduced to analyze electrothermal coupling, and the design variable of nanocrystalline high-frequency transformer is reduced in dimension and guided optimization;Proxy model is constructed and combined with Kepler optimization algorithm, and nanocrystalline high-frequency transformer is further optimized, and the optimal design scheme satisfying multi-objective constraint condition is obtained.The application uses the above method, by constructing high-precision three-dimensional thermal network model, the accurate characterization of nanocrystalline high-frequency transformer complex three-dimensional heat conduction process is realized, and the calculation cost is significantly reduced while ensuring the accuracy close to finite element analysis.

Description

Technical Field

[0001] This invention relates to the field of transformer temperature rise prediction technology, and in particular to a multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network. Background Technology

[0002] With the increasing demand for high power density and energy conversion efficiency, high-frequency transformers are being used more and more widely in power electronics fields such as smart grid architectures and renewable energy grid-connected systems. Among various magnetic components, high-frequency transformers based on nanocrystalline materials are gaining attention due to their excellent magnetic properties, such as high saturation flux density and low high-frequency core losses. Although these characteristics help to significantly reduce device size, the substantial reduction in core size also brings prominent thermal management problems. Studies have found that local heat accumulation can create temperature gradients exceeding the safety threshold, thereby reducing the permeability of nanomaterials and threatening long-term insulation reliability. Therefore, overcoming this thermal management bottleneck under high power density conditions has become a core challenge restricting the development of this technology.

[0003] Efficient temperature rise prediction models are fundamental to solving the aforementioned problems. While numerical methods such as finite element analysis and computational fluid dynamics offer high accuracy, their computational costs are significant, making direct integration into multi-round optimization iterations difficult. Therefore, lumped-parameter thermal network methods, due to their favorable trade-off between accuracy and efficiency, are widely used in the thermal analysis of electromagnetic devices. However, in the field of electric motors, existing methods suffer from topological mismatches in rotating motor models, and hybrid methods incur high computational costs. Furthermore, lumped-parameter thermal network models for two-dimensional transformers neglect longitudinal heat conduction, and their reliance on empirical parameters and general boundary conditions limits their modeling accuracy in complex-encapsulated nano-frequency transformers.

[0004] The fundamental challenge in solving thermal management problems lies in the fact that the design of nano-frequency transformers is not a simple thermal issue, but a multi-physics trade-off problem constrained by strong coupling mechanisms. Traditional single-objective optimization strategies are insufficient to meet the requirements. Therefore, it is necessary to construct an electromagnetic-thermal synergistic multi-objective optimization framework to identify the optimal design equilibrium point. However, directly employing multi-physics coupling methods is often computationally expensive and difficult to apply to rapid, multi-round optimization iteration processes. Therefore, a multi-physics multi-objective optimization strategy is urgently needed to overcome the limitations of single objectives, quantify the coupling relationships between variables, efficiently handle the trade-offs between various physics objectives, and possess rapid thermal prediction capabilities. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, in order to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, this invention provides a multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, comprising the following steps: S1. Construct a three-dimensional thermal network model based on the actual structural parameters of the nanocrystalline high-frequency transformer; S2. The correctness of the three-dimensional thermal network model is verified by analyzing the temperature rise of the nanocrystalline high-frequency transformer. S3. Based on a three-dimensional thermal network model, the design variables of nanocrystalline high-frequency transformers are optimized using an improved Taguchi method. S4. Based on the results of multi-objective optimization, a variable classification mechanism is introduced to analyze electrothermal coupling, thereby reducing the dimensionality of the design variables of the nanocrystalline high-frequency transformer and guiding the optimization. S5. Construct a proxy model and combine it with the Kepler optimization algorithm to further optimize the nanocrystalline high-frequency transformer and obtain the optimal design scheme that satisfies the multi-objective constraints.

[0007] Preferably, the three-dimensional thermal network model is composed of heat flow sources, thermal conduction resistance, convective heat transfer resistance, radiative heat transfer resistance, heat capacity, and ambient node temperature, forming an equivalent thermal network for accurately predicting the steady-state temperature distribution of the transformer.

[0008] Preferably, S2 specifically involves: calculating the temperature rise characteristics of the nanocrystalline high-frequency transformer and comparing the calculation results with the finite element results.

[0009] Preferably, S3 includes: S31. Select seven geometric parameters as the main design variables; S32. The L18 orthogonal array was used for the experiment. S33. Using signal-to-noise ratio as a unified evaluation standard, select the maximum power density. Leakage inductance and minimizing hotspot temperature As an optimization target; S34. To address the differences in signal-to-noise ratio, units, and dimensions among different optimization objectives, the fuzzy logic method is combined with the Taguchi method to transform multi-objective optimization problems into single-objective optimization problems.

[0010] Preferably, S34 includes: The calculated signal-to-noise ratio is normalized to a dimensionless DSI value in the range of 0 to 1 to ensure the comparability of different indicators. The DSI value is processed by fuzzy membership function to cover the uncertainties in the design process; Calculate the multi-performance characteristic index for each sample.

[0011] Preferably, S4 includes: S41. Sensitivity analysis was performed using the Pearson correlation coefficient to identify several parameters with significant univariate sensitivity. S42. Multivariate analysis of variance reveals the non-negligible coupling characteristics between variables, while combining univariate sensitivity analysis and multivariate interaction analysis. S43. Based on the results of sensitivity and interaction analysis, the design variables are divided into three categories, and the search range of each variable is adjusted through differentiation and refinement. S44. Based on the optimal solution obtained in the previous round of optimization, the range of values ​​for the design variables is gradually narrowed according to the interval adjustment strategy, and an improved orthogonal array is constructed and iteratively optimized.

[0012] Preferably, the design variables are: low-impact parameters are simplified to a two-level configuration, high-sensitivity weak interaction variables maintain a four-level structure and strengthen constraints, and high-sensitivity strong interaction variables adopt a four-level strategy to capture nonlinear coupling.

[0013] Preferably, S5 includes: S51. A convolutional neural network-long short-term memory network predictor is used as a surrogate model. The range of design variables is gradually refined through an iterative optimization process. Based on the optimal solution obtained in the previous optimization, the search is focused on the high-performance region until the change in the results of two adjacent optimizations is within the preset tolerance range. S52. Compare and analyze the impact of different dataset sizes and different numbers of hidden layer neurons on the prediction error of the surrogate model; S53. A pre-trained high-precision surrogate model is used to replace finite element simulation. The surrogate model is then embedded into the iterative process of the Kepler optimization algorithm. In each iteration, the target value is quickly calculated through the surrogate model. S54. Output the Pareto optimal solution set and select the optimal design scheme.

[0014] Therefore, the present invention employs the above-mentioned multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, which has the following beneficial effects: (1) A three-dimensional thermal network model was constructed. Compared with the traditional two-dimensional thermal network model, it can accurately simulate heat transfer in multiple directions. This model achieves the characterization of anisotropic heat conduction by setting independent equivalent thermal resistances along orthogonal directions. Finite element analysis verified that the model can effectively capture non-uniform loss distribution while having significant computational efficiency, and can be used as a high-fidelity prediction tool.

[0015] (2) A systematic variable classification mechanism is proposed to analyze the electrothermal coupling problem. This mechanism uses Pearson correlation coefficient and variance analysis to rigorously quantify the interaction between nonlinear parameters, and achieves dimensionality reduction and optimization guidance by designing variable hierarchies, effectively handling the balance between multi-physics objectives and solving the limitations of traditional single objectives.

[0016] (3) An improved robust optimization strategy with dynamic variable range adjustment function is proposed. Essentially, it is an alternative optimization method based on CNN-LSTM and intelligent optimization algorithm. Compared with traditional finite element analysis, driven by the variable classification results, it achieves accurate positioning of high-performance regions by iteratively refining the search range, thereby achieving an effective balance between global search capability and local development accuracy, and significantly improving optimization efficiency while ensuring accuracy.

[0017] 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

[0018] Figure 1 This is a flowchart of a multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, according to an embodiment of the present invention. Figure 2 This is a topology diagram of the high-frequency transformer model established in an embodiment of the present invention; Figure 3 This is a node distribution diagram of the three-dimensional thermal network model in an embodiment of the present invention; Figure 4 This is a temperature rise characteristic diagram of different nanotransformer nodes in an embodiment of the present invention, wherein, Figure 4 (a) is a comparison diagram of the temperature rise characteristics of the iron core nodes. Figure 4 (b) is a comparison diagram of the temperature rise characteristics of the winding nodes; Figure 5 This is a half-heat network model of a nano-frequency transformer according to an embodiment of the present invention; Figure 6 This is a steady-state temperature distribution diagram of the nano-frequency transformer according to an embodiment of the present invention; Figure 7 This is a radial bar chart of multiple performance characteristic indices for different design variables in embodiments of the present invention; Figure 8 This is a sensitivity analysis diagram of an embodiment of the present invention, wherein, Figure 8 (a) is a univariate sensitivity analysis plot based on Pearson correlation coefficient. Figure 8 (b) is a graph showing the interaction of variables based on multifactor ANOVA; Figure 9 This is a schematic diagram of variable adjustment according to an embodiment of the present invention, wherein, Figure 9(a) is a schematic diagram of the shrinkage of the low-impact parameter interval and the simplification of the two levels. Figure 9 (b) is a schematic diagram of the refinement of the high-sensitivity parameter range; Figure 10 This is a schematic diagram of a convolutional neural network-long short-term memory network according to an embodiment of the present invention; Figure 11 This describes the performance of the CNN-LSTM model under different dataset sizes and different numbers of hidden layer neurons in the embodiments of the present invention. Figure 12 This describes the performance of the CNN-LSTM model under different dataset sizes in the embodiments of the present invention. Figure 13 This is a scatter-edge distribution map of a nanoscale high-frequency transformer (nanoHFT) based on the CNN-LSTM algorithm in an embodiment of the present invention, wherein... Figure 13 (a) represents the scatter plot relationship between the predicted power density and the simulated actual power density. Figure 13 (b) represents the scatter plot relationship between the predicted leakage inductance and the actual simulation value. Figure 13 (c) represents the scatter plot fitting relationship between the predicted hotspot temperature and the simulated actual value; Figure 14 This is a Pareto scatter plot of the KOA-CNN-LSTM algorithm in an embodiment of the present invention. Detailed Implementation

[0019] 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.

[0020] 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.

[0021] Example like Figure 1 As shown, this invention provides a multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, comprising: S1. Based on the actual structural parameters of the nanocrystalline high-frequency transformer, a three-dimensional thermal network (3DTN) model is constructed to capture the non-uniform loss distribution and serve as a high-fidelity predictor. The design specifications of the modeled nanocrystalline high-frequency transformer are shown in Table 1.

[0022] Table 1 Design Specifications of Nano High Frequency Transformers

[0023] To construct a high-precision three-dimensional thermal network model, the iron core was divided into 7 sub-regions based on its geometric structure, and the primary and secondary windings were each divided into 4 sub-regions radially to reflect the spatial distribution characteristics of losses and temperature. The loss density of each sub-region was calculated separately, and the specific results are shown in Table 2.

[0024] Table 2 Loss density of each sub-region in the 3D thermal network model

[0025] Traditional two-dimensional heat transfer networks cannot accurately simulate the heat transfer of nanocrystals in three directions. Therefore, a three-dimensional heat transfer model of nanocrystals encapsulated in epoxy resin was established, such as... Figure 2-3 As shown, this three-dimensional thermal network model consists of heat flow sources, thermal conduction resistance, convective heat transfer resistance, radiative heat transfer resistance, heat capacity, and ambient node temperatures, forming an equivalent thermal network used to accurately predict the steady-state temperature distribution of the transformer. To accurately capture the anisotropic thermal characteristics and local hot spots present in the three-dimensional temperature field, this embodiment employs a refined node division method for the core and windings when constructing the three-dimensional thermal network model.

[0026] The losses of the core and windings are injected into the corresponding nodes of the model through the heat flow source module in Simulink, and the heat flow source values ​​are taken from the loss values ​​of each region. There are a total of 8 nodes for the primary and secondary windings, and the total winding loss is distributed to each node according to the volume ratio to reflect the spatial distribution characteristics of the winding loss. At the same time, considering the high hysteresis loss and eddy current loss of the nano-frequency transformer core at the corners, the core thermal network model is divided into rectangular elements (corresponding to the yoke) and arc-shaped elements (corresponding to the corners) to accurately capture the spatial characteristics of the loss.

[0027] To account for heat dissipation on the inner surface of the yoke, a half-steady-state thermal network model of the nano-frequency transformer was established, such as... Figure 5 As shown, the nodal heat balance equations are as follows: ; ; ; ; ; ; ; ; In the formula, Corresponding to the The loss of each node, , , These represent the iron core in the X, Y, and Z directions, respectively. The thermal resistance of each node. , These represent the first and second arcs of the iron core in the outer and inner diameter directions, respectively. Thermal resistance of each node , This indicates the winding in the X and Z directions. The thermal resistance of each node , These represent the epoxy resin in the X, Y, and Z directions, respectively. Thermal resistance of each node , These represent the epoxy resin surface in the X, Y, and Z directions, respectively. Convection heat transfer thermal resistance of each node , , Indicates ambient temperature. Indicates the heat capacity of the iron core and windings. .

[0028] S2. To verify the correctness of the three-dimensional thermal network model, a temperature rise analysis of the nanocrystalline high-frequency transformer was performed. Specifically, the temperature rise characteristics of the nanocrystalline high-frequency transformer were calculated, and the calculation results were compared with the finite element results.

[0029] like Figure 4 As shown, Figure 4 (a) shows a comparison of the predicted temperature rise results for each node of the iron core, including the three-dimensional thermal network model (3DTN) proposed in this invention, the traditional two-dimensional thermal network model (2DTN), and the finite element analysis results; Figure 4 (b) shows a comparison of the predicted temperature rise at each node of the winding, also used to compare the consistency of predictions in the winding region between 3DTN, 2DTN, and finite element analysis. Figure 4 (a) shows that at the core node, because the two-dimensional model ignores the heat dissipation channel in the Z direction, its prediction error in the region near the winding increases significantly; Figure 4(b) It can be seen that at the winding nodes, the two-dimensional model generally overestimates the temperature because it does not consider axial heat transfer, while the three-dimensional thermal network model is in high agreement with the finite element analysis results. This comparison result shows that the 3DTN model constructed in this invention can more accurately characterize the multidimensional heat conduction process inside the nanocrystalline high-frequency transformer and has higher temperature rise prediction accuracy.

[0030] like Figure 4 As shown in (a), at the core node, the prediction error increases to 16% because the two-dimensional model ignores heat dissipation in the Z-axis direction. Figure 4 (b) shows that the two-dimensional model of the winding node does not consider axial heat transfer and lacks accuracy, while the three-dimensional model can fully consider the anisotropic thermal properties of the material and has good accuracy. In summary, it can be seen that the three-dimensional thermal network model proposed in this invention can effectively characterize the multi-dimensional heat conduction process and achieve high-precision temperature prediction.

[0031] like Figure 6 As shown, the steady-state temperature distribution of the epoxy resin nanocrystalline high-frequency transformer is illustrated through an overall three-dimensional temperature cloud map and layered temperature distribution curves of five characteristic sections along the vertical direction (z=12.5mm to z=197.5mm). The simulation results reveal a significant thermal asymmetry, with the temperature of the lower core yoke (80℃) lower than that of the upper core yoke (88℃), forming a temperature gradient along the vertical direction. This phenomenon is mainly due to the coupling effect of two heat transfer mechanisms: firstly, the bottom surface of the high-frequency transformer (z=12.5mm) is in direct contact with the metal mounting base, forming an effective conductive heat dissipation path; secondly, under natural convection conditions, the hot air surrounding the epoxy resin surface moves upward under the action of buoyancy, intensifying heat accumulation in the upper region (z=197.5mm).

[0032] As can be seen from the cross-sectional views, the temperature gradually increases from the bottom to the top, with the winding region consistently experiencing the highest thermal stress, reaching a maximum temperature of 104.83℃, which occurs in the winding area. In the intermediate cross-sections (z=80mm and z=112.5mm), it is clearly evident that the temperature of the core column enclosed by the winding is significantly higher than that of the exposed yoke. If the boundary conditions for convection and radiation heat transfer are ignored or oversimplified, it will be difficult to accurately reflect this temperature distribution difference caused by convection, further verifying the necessity of the refined node division method used for the core and winding in this embodiment.

[0033] S3. Multi-objective optimization of design variables for nanocrystalline high-frequency transformers is performed using the improved Taguchi method. The Taguchi method is a statistically based experimental design and robust optimization method. Its core idea is to identify the optimal parameter combination among numerous influencing factors through a small number of orthogonal experiments, and to make the product performance insensitive to noise factors, i.e., to improve robustness.

[0034] S31. Seven geometric parameters were selected as the main design variables, covering core and window dimensions, high-frequency characteristic parameters, and angular radius, respectively, to balance magnetic flux and current density, control leakage inductance and heat conduction path, and ensure geometric feasibility. The selected parameters are shown in Table 3.

[0035] Table 3 Main Design Variables

[0036] S32, Select L18 ( × An orthogonal array was used for the experiment. This orthogonal array can accommodate one 6-level control factor and up to six 3-level control factors. The level refers to the number of values ​​selected for each design variable to be optimized. In this way, only 18 sets of experiments are required, which greatly reduces the workload of simulation. The orthogonal experimental scheme and optimization performance results are shown in Table 4.

[0037] Table 4. Orthogonal experimental design and optimized performance results

[0038] S33. In order to combat various interference factors during the optimization process, the signal-to-noise ratio is used as a unified evaluation standard, and the maximum power density is selected. Leakage inductance and minimizing hotspot temperature As the optimization objective, the maximum power density is... Taking signal-to-noise ratio as an example, the calculation formula is: ; In the formula, The total number of samples, This is the sample number.

[0039] Based on the signal-to-noise ratio calculation results, a data standardization index is introduced for cross-index comparison. The formula is as follows: ; In the formula, max with min These represent the maximum and minimum signal-to-noise ratios of all samples, respectively. This formula normalizes the signal-to-noise ratios of all samples.

[0040] S34. To address the differences in signal-to-noise ratio, units, and dimensions among different optimization objectives, the fuzzy logic method is combined with the Taguchi method to transform the multi-objective optimization problem into a single-objective optimization problem. The specific process is as follows: The calculated signal-to-noise ratio is normalized to a dimensionless DSI value in the range of 0 to 1 to ensure the comparability of different indicators. The DSI value is processed by fuzzy membership function to cover the uncertainties in the design process; Calculate the Multiple Performance Feature Index (MPCI) for each sample, which is the weighted aggregation result of each individual optimization objective. The calculation formula is as follows: ; in, Indicates the first The multi-performance characteristic index of each test sample is used to comprehensively evaluate the overall performance of the sample under multiple optimization objectives. , and They represent the first The first, second, and third optimization objective function values ​​corresponding to each test sample are, in this paper, power density, leakage inductance deviation, and hot spot temperature, respectively. This represents a data standardization index function, used to normalize objective function values ​​with different dimensions and ranges to a unified evaluation interval. , and Let represent the weight coefficients of the three optimization objectives, used to characterize the relative importance of different objectives in the comprehensive evaluation, and satisfy . . The larger the value, the more significant the number. The better the overall optimization performance of each sample, the better. Figure 7 As shown in Table 5, the final levels of each design variable and their impact on the overall performance of the transformer can be determined. The performance results at each level of the design variables are shown in Table 5. Table 5 Performance results at each level of design variables

[0041] The optimal combination of design variable levels can be determined using the Multi-Performance Characteristic Index (MPCI) corresponding to different levels of each design variable in Table 5. The specific method is as follows: for each design variable, the MPCI values ​​at each level are compared, and the level with the highest MPCI is selected as the preferred level for that variable. Based on this principle, the window width is 157 mm, the window height is 165 mm, the core column width is 24 mm, the core thickness is 56 mm, the core outer corner radius is 30 mm, and the winding height is 132 mm. For the core inner corner radius, the MPCI values ​​corresponding to 5.0 mm and 5.5 mm are similar. Considering manufacturing feasibility, structural continuity, and the stability of subsequent optimization iterations, 5.0 mm is ultimately selected as the preferred level. Therefore, the optimal combination of design variable levels in the Taguchi method stage is: 157 mm, 165 mm, 24 mm, 56 mm, 30 mm, 5.0 mm, and 132 mm.

[0042] S4. Based on the results of multi-objective optimization, a variable classification mechanism is introduced to analyze electrothermal coupling, reduce the dimensionality of the design variables of nanocrystalline high-frequency transformers and guide optimization. The variable classification mechanism uses Pearson correlation coefficient and variance analysis to strictly quantify the interaction between nonlinear parameters, and achieves dimensionality reduction and optimization guidance through hierarchical design variables.

[0043] In this embodiment, S4 specifically refers to: S41. Sensitivity analysis was performed using the Pearson correlation coefficient to identify several parameters with significant univariate sensitivity.

[0044] In multi-objective optimization design, reasonable sensitivity analysis is a core step in ensuring optimization results. In this embodiment, Pearson correlation coefficient is used for sensitivity analysis, and the calculation formula is as follows: ; In the formula, Representing variables and variables The correlation coefficient, Indicates the first Design variables for each sample Indicates the first The optimization objective for each sample The total number of samples.

[0045] S42. Multivariate analysis of variance revealed the non-negligible coupling characteristics among variables, especially the moderate correlation, while combining univariate sensitivity analysis and multivariate interaction analysis.

[0046] like Figure 8 As shown in (a), Figure 8 (a) represents the univariate sensitivity analysis results obtained based on the Pearson correlation coefficient, used to evaluate the strength of the independent influence of each design variable on the optimization objective; Figure 8 (b) represents the results of variable interaction analysis based on multifactor ANOVA, used to reveal the degree of coupling between different design variables on the overall performance. Figure 8 (a) It can be seen that variables such as winding height, core outer corner radius, and core thickness are highly sensitive to the optimization objective, and more refined horizontal settings should be given in subsequent optimizations; Figure 8 (b) It is evident that there are significant interaction effects among some design variables, indicating that relying solely on the traditional Taguchi method's single-factor analysis is insufficient to fully reflect the design patterns under electrothermal coupling conditions. Therefore, this invention combines univariate sensitivity analysis with multivariate interaction analysis to provide a basis for subsequent variable selection, interval narrowing, and hierarchical optimization.

[0047] S43. Based on the results of sensitivity and interaction analysis, the design variables are systematically divided into three categories: low-impact parameters simplified to a two-level configuration, high-sensitivity, weak-interaction variables maintaining a four-level structure with strengthened constraints, and high-sensitivity, strong-interaction variables employing a four-level strategy to capture nonlinear coupling. By adjusting the search range of each variable in a differentiated and refined manner, the optimization efficiency is significantly improved, thereby achieving variable stratification to reduce dimensionality and guide subsequent optimization. A schematic diagram of variable adjustment is shown below. Figure 9 As shown, Figure 9 (a) shows a schematic diagram of the interval contraction and two-level simplification strategy for low-impact parameters, that is, narrowing the range of values ​​around the optimal value obtained in the previous round of optimization, and using a two-level configuration to reduce redundant search; Figure 9 (b) illustrates the interval refinement and multi-level retention strategy for highly sensitive variables. Specifically, it retains a four-level structure for variables with significant sensitivity and potential interactions to improve local optimization resolution and capture nonlinear coupling effects. Figure 9 The hierarchical adjustment mechanism shown in this invention enables differentiated processing of different types of design variables, thereby reducing the search dimension and improving the efficiency of subsequent iterations while ensuring optimization accuracy.

[0048] S44. To further improve the efficiency of iterative optimization, based on the optimal solution obtained in the previous round of optimization, and following the interval adjustment strategy described above, the range of values ​​for the design variables is gradually narrowed, an improved orthogonal array is constructed, and iterative optimization is performed. The horizontal intervals of each variable are adaptively determined. A more adaptable L16(4) was constructed. 3 ,2 4 Orthogonal arrays are used for subsequent optimization. After each iteration, the variable range is narrowed to focus the search on the high-performance region of the design space. Iteration continues until the difference between the target values ​​obtained from two consecutive iterations (e.g., the j-th and j+1-th iterations) falls within a preset tolerance threshold, at which point the iteration terminates. The final optimized complete design scheme for the nanocrystalline high-frequency transformer is obtained, and the design parameters and performance indicators are shown in Table 6. Table 6 Design Variables for Nanocrystalline High-Frequency Transformers

[0049] S5. Construct a proxy model and combine it with the Kepler optimization algorithm to further optimize the nanocrystalline high-frequency transformer and obtain the optimal design scheme that satisfies the multi-objective constraints.

[0050] In this embodiment, S5 includes: S51. A convolutional neural network-long short-term memory network (CNN-LSTM) predictor is used as a surrogate model. The range of design variables is gradually refined through an iterative optimization process. Based on the optimal solution obtained in the previous optimization, the search is focused on the high-performance region until the change between two adjacent optimization results is within the preset tolerance range, thereby achieving an effective balance between global search capability and local development accuracy.

[0051] A Convolutional Neural Network-Long Short-Term Memory Network (CNN-LSTM) predictor is used as a surrogate model. CNN excels at extracting spatial geometric features, while LSTM excels at capturing strong nonlinear dependencies between parameters. This hybrid model perfectly suits the high-dimensional, strongly nonlinear mapping problem between transformer structure and performance. Optimization is carried out on the seven variables proposed in this invention, with the core optimization objective being to maximize power density. Minimize hotspot temperature Leakage inductance Constrained to the design target value, the neural network diagram used is shown below. Figure 10 As shown.

[0052] S52. To find the optimal parameters, the impact of different dataset sizes and different numbers of hidden layer neurons on the prediction error of the surrogate model was compared and analyzed. The results are as follows: Figure 11 As shown, a dataset of 800 samples was ultimately selected, with a hidden layer neuron count of 100. The iterative convergence stability of this model for each optimization objective is as follows: Figure 12 As shown, this ensures that the optimization process does not oscillate and can stably converge to the optimal solution. Furthermore, this embodiment uses... Figure 13 The scatter-margin distribution plot shown verifies the high prediction fidelity of the model. This plot consists of three scatter-margin distribution subplots, used to verify the prediction accuracy of the CNN-LSTM surrogate model on the three optimization objectives. The closer the scatter points in each subplot are to the diagonal, the higher the consistency between the surrogate model's predicted values ​​and the simulated true values; the margin distribution reflects the numerical distribution characteristics of the samples on the corresponding objectives. Since the coefficients of determination for all three objectives are greater than 0.995, it indicates that the CNN-LSTM surrogate model constructed in this invention has extremely high prediction accuracy for power density, leakage inductance, and hotspot temperature, and can effectively replace time-consuming finite element simulations and support subsequent optimization iterations. Therefore, the optimization function is constructed as follows: ; ; ; In the formula, F 1. F 2. F 3 represents power density. Leakage inductance and hot spot temperature The corresponding optimization objective function; This represents the absolute deviation between the actual leakage inductance and the target leakage inductance; where the power density target is the maximization target, the hot spot temperature target is the minimization target, and the leakage inductance participates in the optimization as a constraint or target coordination term. X This represents a design vector consisting of seven design variables. By constructing the above multi-objective optimization function, the prediction results of the surrogate model can be embedded into the Kepler optimization algorithm to achieve rapid optimization of the overall performance of nanocrystalline high-frequency transformers.

[0053] S53. A pre-trained high-precision surrogate model is used to replace finite element simulation. The surrogate model is then embedded in the iterative process of the Kepler (KOA) optimization algorithm. Each iteration calculates the target value quickly through the surrogate model instead of calling time-consuming simulation, which greatly improves the optimization efficiency.

[0054] S54. Output the Pareto optimal solution set and select the optimal design scheme.

[0055] The optimization results are presented in the form of a Pareto scatter plot, such as... Figure 14 As shown, in multi-objective optimization, multiple objectives often conflict with each other, and no single solution can simultaneously optimize all objectives. The spatial distribution of candidate solutions intuitively reflects the trade-offs between conflicting objectives, resulting in a set of Pareto optimal solutions. The power density of the optimal design sample selected by this invention can reach [a certain value]. The leakage inductance is 63.63. The hotspot temperature is 100.55. This verified its effectiveness in selecting high-performance design solutions.

[0056] Therefore, this invention adopts the above-mentioned multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction of three-dimensional thermal network. By iteratively refining the search range, it achieves accurate positioning of high-performance regions, thereby achieving an effective balance between global search capability and local development accuracy, and significantly improving optimization efficiency while ensuring accuracy.

[0057] 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 multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network, characterized in that, Includes the following steps: S1. Construct a three-dimensional thermal network model based on the actual structural parameters of the nanocrystalline high-frequency transformer; S2. The correctness of the three-dimensional thermal network model is verified by analyzing the temperature rise of the nanocrystalline high-frequency transformer. S3. Based on a three-dimensional thermal network model, the design variables of nanocrystalline high-frequency transformers are optimized using an improved Taguchi method. S4. Based on the results of multi-objective optimization, a variable classification mechanism is introduced to analyze electrothermal coupling, thereby reducing the dimensionality of the design variables of the nanocrystalline high-frequency transformer and guiding the optimization. S5. Construct a proxy model and combine it with the Kepler optimization algorithm to further optimize the nanocrystalline high-frequency transformer and obtain the optimal design scheme that satisfies the multi-objective constraints. S3 includes: S31. Select seven geometric parameters as the main design variables; S32. The L18 orthogonal array was used for the experiment. S33. Using signal-to-noise ratio as a unified evaluation standard, select the maximum power density. leakage inductance and minimizing hotspot temperature As an optimization target; S34. To address the differences in signal-to-noise ratio, units, and dimensions among different optimization objectives, the fuzzy logic method is combined with the Taguchi method to transform multi-objective optimization problems into single-objective optimization problems. S34 includes: The calculated signal-to-noise ratio is normalized to a dimensionless DSI value in the range of 0 to 1 to ensure the comparability of different indicators. The DSI value is processed by fuzzy membership function to cover the uncertainties in the design process; Calculate the multi-performance characteristic index for each sample; S4 includes: S41. Sensitivity analysis was performed using the Pearson correlation coefficient to identify several parameters with significant univariate sensitivity. S42. Multivariate analysis of variance reveals the non-negligible coupling characteristics between variables, while combining univariate sensitivity analysis and multivariate interaction analysis. S43. Based on the results of sensitivity and interaction analysis, the design variables are divided into three categories, and the search range of each variable is adjusted through differentiation and refinement. S44. Based on the optimal solution obtained in the previous round of optimization, the range of values ​​for design variables is gradually narrowed according to the interval adjustment strategy. An improved orthogonal array is constructed and iteratively optimized. S5 includes: S51. A convolutional neural network-long short-term memory network predictor is used as a surrogate model. The range of design variables is gradually refined through an iterative optimization process. Based on the optimal solution obtained in the previous optimization, the search is focused on the high-performance region until the change in the results of two adjacent optimizations is within the preset tolerance range. S52. Compare and analyze the impact of different dataset sizes and different numbers of hidden layer neurons on the prediction error of the surrogate model; S53. A pre-trained high-precision surrogate model is used to replace finite element simulation. The surrogate model is then embedded into the iterative process of the Kepler optimization algorithm. In each iteration, the target value is quickly calculated through the surrogate model. S54. Output the Pareto optimal solution set and select the optimal design scheme.

2. The multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network as described in claim 1, characterized in that: The three-dimensional thermal network model is composed of heat flow sources, thermal conduction resistance, convective heat transfer resistance, radiative heat transfer resistance, heat capacity, and ambient node temperature, forming an equivalent thermal network for accurately predicting the steady-state temperature distribution of transformers.

3. The multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network as described in claim 1, characterized in that: S2 specifically involves calculating the temperature rise characteristics of a nanocrystalline high-frequency transformer and comparing the calculation results with the finite element results.

4. The multi-objective optimization method for nanocrystalline high-frequency transformers based on rapid temperature rise prediction using a three-dimensional thermal network as described in claim 1, characterized in that: The design variables are: low-impact parameters are simplified to a two-level configuration; high-sensitivity weak interaction variables maintain a four-level structure and have stronger constraints; and high-sensitivity strong interaction variables adopt a four-level strategy to capture nonlinear coupling.

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