A large current lead magnetic field calculation and optimization method based on response surface method

Abstract

This application discloses a method for calculating and optimizing the magnetic field of high-current lead wires based on the response surface methodology, comprising: constructing a parameterized three-dimensional nonlinear electromagnetic-thermal bidirectional coupled finite element model; selecting representative sample points in the design space using the optimal Latin hypercube sampling method, training a surrogate model based on the sample points and dynamically adding points, and outputting a set of representative sample points; performing finite element calculations on each output representative sample point, extracting the performance indicators corresponding to each sample point, and then constructing a Kriging gradient-enhanced hybrid response surface model; establishing an optimization objective function to guide the optimization direction, and then using a multi-objective optimization algorithm to quickly optimize the high-precision hybrid response surface model, generating a Pareto optimal solution set; selecting the optimal design scheme from the Pareto optimal solution set based on the entropy weight-TOPSIS dynamic decision method and performing double verification, and outputting optimization parameters and a performance report after successful verification. This application achieves synergistic optimization of performance, cost, and reliability.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic design and optimization technology for high-voltage, high-current power equipment, specifically to a method for calculating and optimizing the magnetic field of high-current leads based on the response surface methodology. Background Technology

[0002] Flexible direct current (DC) transmission systems are key technological equipment for building new power systems. The valve-side winding of the converter transformer, its core component, needs to be connected to the bridge valve via a high-current lead. This lead typically carries thousands of amperes of power frequency or harmonic current, exciting a strong alternating leakage magnetic field in the surrounding space. This magnetic field causes significant eddy current losses in the steel structural components of the transformer tank walls, clamps, tie plates, and pressure plates, leading to abnormally high local temperatures, forming hot spots, and seriously threatening the transformer's insulation life and operational reliability.

[0003] Traditional design methods heavily rely on engineers' experience, employing a cyclical trial-and-error model of "modeling-calculation-analysis-manual modification-recalculation," which has inherent flaws. Secondly, they consume enormous computational resources; calculations of three-dimensional nonlinear time-harmonic fields or transient fields are extremely time-consuming, often requiring several to tens of hours for a single complete calculation. Furthermore, optimization efficiency is extremely low. Due to the large number and strong coupling of design variables, manual adjustments are highly unpredictable and difficult to traverse the entire design space. Simultaneously, traditional single-response models have limited fitting capabilities for strongly nonlinear problems, resulting in insufficient accuracy of surrogate models. Moreover, multi-objective trade-offs are incomplete, typically considering only two objectives and neglecting temperature and robustness, as well as uncertainties such as dimensional tolerances, current fluctuations, and material deviations that can lead to performance drift in real-world engineering. For multiple optimization objectives, such as NSGA-II, the solution set degenerates significantly when there are more than three objectives. Decision-making relies on manually selecting Pareto solutions, lacking quantitative basis, and only performing nominal value verification without robustness and uncertainty verification, resulting in insufficient stability.

[0004] Therefore, developing a high-precision, multi-objective optimization, and robust electromagnetic-thermal-cost optimization design method for high-current leads is of great significance for improving the reliability of my country's high-end power equipment. Summary of the Invention

[0005] In order to solve the above-mentioned technical problems, this application proposes the following technical solution: This application provides a method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology, including: The bi-level optimization variables and their distribution characteristics are determined, and a parameterized three-dimensional nonlinear electromagnetic-thermal bi-directional coupled finite element model is constructed based on the deterministic design variables in the bi-level optimization variables. The deterministic design variables are mapped to a standardized design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points in the standardized design space. A surrogate model is trained based on the representative sample points. Points are dynamically added according to the surrogate model error and the filling distance, and a set of representative sample points is output. For each representative sample point in the output, perform a three-dimensional nonlinear transient electromagnetic-thermal bidirectional coupled finite element calculation to extract the performance index corresponding to each sample point. Based on the representative sample point set and the corresponding performance indicators, a Kriging gradient-enhanced hybrid response surface model is constructed, and the model is validated to output a high-precision hybrid response surface model. After establishing the optimization objective function to guide the optimization direction, the improved NSGA-III multi-objective optimization algorithm is used to quickly optimize the high-precision mixed response surface model and generate the Pareto optimal solution set. The optimal design scheme is selected from the Pareto optimal solution set based on the entropy weight-TOPSIS dynamic decision method, and then verified by finite element method and Monte Carlo uncertainty. After the verification is passed, the final optimization parameters and performance report are output.

[0006] In one possible implementation, determining the bi-level optimization variables and their distribution characteristics, and constructing a parametric three-dimensional nonlinear electromagnetic-thermal bi-directional coupled finite element model based on the deterministic design variables in the bi-level optimization variables, includes: Determine the two-level optimization variables and their distribution characteristics, including deterministic design variables and uncertain random variables. The deterministic design variables include geometric parameters, material properties and shielding measures, while the uncertain random variables include geometric dimensional tolerances, operating current fluctuations and material permeability deviations. A three-dimensional finite element model was established based on actual engineering drawings, including valve side leads, oil tank, oil tank cover, riser seat, clamps, pull plate and iron core, and an excitation source and nonlinear magnetic material were introduced. The geometric parameters and shielding parameters in the deterministic design variables are defined as parameter variables, and a parameter-driven relationship is established. At the same time, in combination with the actual operating conditions, an infinite magnetic field boundary, a natural convection heat dissipation boundary, and a thermal radiation boundary are applied. Using the valve-side lead conductor as the excitation object, a preset power frequency sinusoidal current is applied to simulate the actual operating conditions of the high-current lead, providing input conditions for the leakage magnetic field distribution and structural component loss calculation; For nonlinear magnetic components, BH magnetization curves and BP iron loss curves were set, and the effect of material conductivity on temperature was determined. An electromagnetic-thermal bidirectional coupling iterative calculation process was established, and the electromagnetic field was solved by Maxwell to obtain eddy current loss, hysteresis loss and additional loss. The loss is imported into the thermal field model in the form of volumetric loss density to calculate the temperature distribution; The material's electrical conductivity and magnetic permeability are then corrected based on the temperature results and fed back to the electromagnetic field model for recalculation. Through iterative iterations, until the loss and temperature results meet the convergence requirements, the parameterized three-dimensional nonlinear electromagnetic-thermal coupled finite element model is established.

[0007] In one possible implementation, the deterministic design variables are mapped to a standardized design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points within the standardized design space. A surrogate model is trained based on these representative sample points, and points are dynamically added according to the surrogate model error and the filling distance. The result is an output set of representative sample points, including: Deterministic design variables such as geometric parameters, material properties, and shielding parameters are normalized and mapped to a preset standard hypercube space to construct a unified high-dimensional design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points in the high-dimensional design space, so that each dimension is uniformly layered and the sample spacing is maximized. Train a Kriging-gradient augmentation hybrid agent model based on the representative sample points; The global model error and the local model error are calculated by combining the coefficient of determination, root mean square error and Kriging prediction variance. Calculate the Euclidean distance from any candidate point in the high-dimensional design space to the nearest existing sample point, and use the Euclidean distance as the fill distance. The calculation formula is as follows: in, For target sample points The Euclidean distance to the nearest sample in the dataset. For the target sample point whose nearest neighbor distance needs to be calculated, To iterate through all other samples in the dataset Take the minimum distance. For index variables of other sample points in the dataset, To sum over all feature dimensions of the sample, Here, d represents the feature dimension index, and d is the total number of feature dimensions for the sample. For target sample points In the The values ​​taken on each feature dimension For the first The sample point at the th th The values ​​taken on each feature dimension For two sample points at the th The square of the difference across each feature dimension; Based on the coupling criterion between local model error and filling distance, new sample points are added in high error regions and large filling distance regions. At the same time, the stopping condition is judged based on the global model error. After each round of point addition, the Kriging-gradient enhancement hybrid surrogate model is retrained. Iteratively perform point addition and training until all output metrics meet the preset accuracy requirements, and output a representative sample point set.

[0008] In one possible implementation, the formula for calculating the global model error and the local model error, which combines the coefficient of determination, root mean square error, and Kriging prediction variance, is as follows: in, The values ​​represent the actual response values ​​in the finite element simulation. For the surrogate model's predicted values, The mean of the true responses is given, and n is the total number of samples. As the coefficient of determination, This is the root mean square error.

[0009] In one possible implementation, for each representative sample point in the output, a three-dimensional nonlinear transient electromagnetic-thermal bidirectional coupled finite element calculation is performed to extract the performance indicators corresponding to each sample point, including: For each representative sample point in the output, the geometric parameters, material properties, and shielding measures of the parametric three-dimensional finite element model are updated based on the design variable values. By performing three-dimensional nonlinear transient electromagnetic field calculations, the leakage magnetic field distribution is obtained, and the magnetic flux density distribution and loss density distribution of each structural component are extracted. The loss obtained from electromagnetic field calculation is imported into the thermal field model in the form of volumetric loss density. Temperature field calculation is performed to obtain the temperature distribution of each structural component and the temperature of local hot spots. The electrical conductivity and magnetic permeability of the material are corrected based on the temperature field calculation results and fed back to the electromagnetic field model for recalculation. The process is iterated until the electromagnetic field and temperature field results meet the convergence conditions. The maximum magnetic flux density, maximum loss density, leakage flux, hysteresis loss, eddy current loss, total loss density, local hotspot temperature, temperature gradient, material cost, and robustness index are extracted from the converged calculation results. The calculation formulas are as follows: in, Let B be the leakage flux, B be the leakage magnetic induction intensity, and S be the integral surface. For hysteresis loss, This is the hysteresis loss coefficient. f For frequency, For the maximum magnetic flux density, Where is the Steinmetz coefficient, and V is the material volume. For eddy current losses, The eddy current loss coefficient is... Total loss density, For local hotspot temperatures, For ambient temperature, For thermal resistance, For total material costs, These are the unit prices for fuel tank materials, riser base materials, and shielding materials, respectively. These are the volumes of the fuel tank and the riser, respectively. This refers to the shielding area.

[0010] In one possible implementation, based on the representative sample point set and corresponding performance indicators, a Kriging gradient-enhanced hybrid response surface model is constructed, and the model is validated to output a high-precision hybrid response surface model, including: The design variable data and corresponding performance index data in the representative sample point set are normalized to obtain the normalized sample dataset. Based on the normalized sample dataset, a hybrid response surface model is constructed using a hybrid structure of the Kriging model as the main model and the gradient-enhanced response surface as the auxiliary model. The Kriging model is used to output the predicted value and the prediction error, and the gradient-enhanced response surface is used to capture nonlinearity and local peaks. The hybrid response surface model is trained using a generalized least squares loss function, and the output value and output gradient are fitted simultaneously. The accuracy of the trained mixed response surface model was verified by using the coefficient of determination, root mean square error, maximum relative error, and residual normality test. If the verification result does not meet the preset accuracy requirements, the system returns dynamically supplemented sample points and retrains; if the accuracy requirements are met, a high-precision hybrid response surface model is output.

[0011] In one possible implementation, the optimization objective function aims to minimize the maximum magnetic flux density, the maximum loss density, the local hot spot temperature, the material cost, and the robustness, while introducing magnetic saturation constraints, temperature safety constraints, size and process constraints, and uncertainty fluctuation constraints.

[0012] In one possible implementation, the step of using an improved NSGA-III multi-objective optimization algorithm to quickly optimize the high-precision mixed response surface model and generate a Pareto optimal solution set includes: Using the normalized design variables as individual codes, an initial population is generated within the range of design variable values ​​and constraints, and the high-precision hybrid response surface model is used to calculate the objective function value corresponding to each individual. Based on the number of iterations and the distribution of individuals, the crossover and mutation probabilities are adjusted, and crossover and mutation operations are performed on the individuals in the population to obtain the offspring population. Perform boundary correction and constraint judgment on individuals in the parent and offspring populations, and remove or correct individuals that do not meet the design requirements; Based on the optimization objective function, the candidate population is non-dominated and sorted to obtain multiple non-dominated layers; Using reference points, individuals within the same non-dominated layer are selected based on their distribution, prioritizing the retention of individuals with higher non-dominated levels and more even distribution. The next generation of the population is formed according to the elite preservation strategy, and the above process is repeated until the termination condition is met, and the Pareto optimal solution set is output.

[0013] In one possible implementation, the entropy-weighted TOPSIS dynamic decision-making method selects the optimal design scheme from the Pareto optimal solution set and performs dual verification using finite element analysis and Monte Carlo uncertainty testing. After successful verification, the final optimization parameters and performance report are output, including: Using each solution in the Pareto optimal solution set as the scheme to be evaluated and the performance index as the evaluation index, an original evaluation matrix is ​​constructed. After positiveizing the indicators in the original evaluation matrix, the positiveized indicator data is then standardized. The objective weights of each evaluation index are calculated using the entropy weight method; A weighted standardized matrix is ​​constructed based on the objective weights, and the positive and negative ideal solutions are determined. Calculate the Euclidean distance from each evaluated scheme to the positive and negative ideal solutions, and then calculate the proximity coefficient of the samples based on the calculated Euclidean distances. The calculation formulas are as follows: in, For the first The proximity coefficient of each sample. For the first The Euclidean distance from each sample to the positive ideal solution. For the first The Euclidean distance from each sample to the negative ideal solution. For the first The sample at the th The weighted standardized index value under each indicator, The first positive ideal solution vector One portion, The first of the negative ideal solution vectors One portion, The vector is the positive ideal solution. The negative ideal solution vector. This represents the total number of indicators involved in the evaluation. For the first The objective weight of each indicator For the first The sample at the th Standardized indicator values ​​under each indicator For the first The standardized value of each sample in the first feature dimension For the first The standardized value of each sample in the second feature dimension. For the first The standardized value of a sample on the m-th feature dimension To obtain the minimum value of all samples in the first feature dimension, and use this as the value of the negative ideal point in that dimension, To obtain the minimum value of all samples in the second feature dimension, and use this as the value of the negative ideal point in that dimension, To find the minimum value of all samples in the m-th feature dimension, and use it as the value of the negative ideal point in that dimension, To obtain the maximum value of all samples in the first feature dimension, and use it as the value of the positive ideal point in that dimension, To obtain the maximum value of all samples in the second feature dimension, and use it as the value of the positive ideal point in that dimension, The maximum value of all samples in the m-th feature dimension is taken as the value of the positive ideal point in that dimension. The scheme with the highest proximity coefficient is selected as the optimal compromise design scheme; The optimal compromise design scheme is substituted into the original finite element model for conventional finite element verification. The prediction error of each performance index is calculated. If the prediction error of all indicators is within the preset threshold range, the finite element verification is passed. Based on the distribution characteristics of the uncertainty variables, Monte Carlo simulation is performed on the optimal compromise design scheme to statistically analyze the fluctuation range of each performance index. If the fluctuation of all indicators is within the preset fluctuation threshold range, then the Monte Carlo uncertainty verification is passed. When both the finite element verification and the Monte Carlo uncertainty verification are passed, the final optimization parameters and performance report are output.

[0014] In one possible implementation, the entropy weight method is used to calculate the objective weights of each evaluation index. The calculation formula is as follows: in, For the first The objective weight of each indicator For the first The coefficient of difference of the indicators For the first The entropy value of the indicator, The adjustment coefficient is calculated for the entropy value, where n is the total number of samples. For the first The sample at the th Sample proportion under each indicator For the first The sample at the th The original indicator values ​​under each indicator For the first The sample at the th The minimum value of all original values ​​of all samples under the item indicator. For the first The sample at the th The maximum value of the original values ​​of all samples under this indicator.

[0015] Compared with the prior art, the beneficial effects of this application are as follows: This application comprehensively utilizes finite element simulation, experimental design, adaptive sampling, hybrid response surface surrogate models, improved NSGA-III multi-objective optimization, entropy-weighted TOPSIS decision-making, and uncertainty robustness verification to efficiently, cost-effectively, and robustly solve the problem of local overheating of structural components caused by lead leakage magnetic fields, achieving synergistic optimization of performance, cost, and reliability. By employing response surface surrogate models, the time for a single optimization evaluation is reduced from hours to minutes, significantly improving efficiency and making global optimization possible.

[0016] This application improves prediction accuracy by constructing a Kriging model based on real finite element data, ensuring the correct optimization direction. Combined with the DOE and NSGA-III algorithms, it can effectively explore the entire design space and find a set of globally optimal or near-optimal solutions. This methodology is highly versatile and can be extended to any scenario with high-current electromagnetic-thermal optimization problems, such as generator outgoing lines and GIS busbars. By considering manufacturing and operational uncertainties, the optimization results are less susceptible to fluctuations in operating conditions, exhibiting strong robustness. It eliminates the need for subjective manual selection and can automatically output optimal compromise solutions to a certain extent, leading to more scientific decision-making. Attached Figure Description

[0017] Figure 1 A flowchart illustrating a method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology, provided in an embodiment of this application; Figure 2 A schematic diagram of a parametric three-dimensional finite element model provided in an embodiment of this application; Figure 3 A schematic diagram of the two-dimensional projection distribution of Latin hypercube sampling in the design space, provided for an embodiment of this application; Figure 4 Example of a finite element calculation result cloud diagram provided for an embodiment of this application; Figure 5 A schematic diagram illustrating the Pareto front and final scheme selection obtained through multi-objective optimization as provided in the embodiments of this application.

[0018] Figure 2 The symbols are: 1-valve side lead wire, 2-tank cover, 3-lift seat, 4-iron core, 5-tank wall, 6-clamp, 7-shield, 8-pull plate. Detailed Implementation

[0019] The present solution will now be described in conjunction with the accompanying drawings and specific embodiments.

[0020] Figure 1 A flowchart illustrating a method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology, provided in this application embodiment, is shown below. Figure 1 This embodiment presents a method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology, comprising: S101, determine the two-layer optimization variables and their distribution characteristics, and construct a parameterized three-dimensional nonlinear electromagnetic-thermal bidirectional coupled finite element model based on the deterministic design variables in the two-layer optimization variables.

[0021] In this embodiment, a two-layer design variable and optimization space are determined, and key variables affecting magnetic field distribution, temperature rise, cost, and robustness are identified. These variables are divided into deterministic design variables and uncertain random variables. The deterministic design variables include geometric parameters, material properties, and shielding measures. Geometric parameters include the minimum distance from the center of the lead conductor to the mailbox wall, the mailbox cover opening diameter, and the riser seat opening diameter. Material properties include the mailbox material type and riser seat material type, such as low-carbon steel, stainless steel, and low-magnetic steel. Shielding measures include whether to add electromagnetic shielding, the number of shielding layers, and the shielding thickness. Uncertain random variables include dimensional tolerances, operating current fluctuations, and material permeability deviations.

[0022] See Figure 2 Based on actual engineering drawings, a three-dimensional finite element model with the same structure as the product was constructed in the ANSYS Maxwell platform, including valve side lead 1, oil tank, oil tank cover 2, riser 3, clamp 6, pull plate 8 and iron core 4. An excitation source and nonlinear magnetic material were introduced to provide a model basis for electromagnetic field calculation and electromagnetic-thermal coupling analysis.

[0023] Parametric modeling was performed on key structural components such as the fuel tank, fuel tank cover 2, and riser 3. Dimensions such as the distance from the lead wire center to the fuel tank wall, the opening diameter of the fuel tank cover, the opening diameter of the riser, the shielding thickness, and the number of layers were defined as parameter variables, establishing a parameter-driven relationship to achieve rapid adjustment and automatic updating of model dimensions. Simultaneously, considering actual operating conditions, infinitely far magnetic field boundaries, natural convection heat dissipation boundaries, and thermal radiation boundaries were applied to improve the realism of the simulation boundary conditions.

[0024] Using the valve-side lead conductor as the excitation object, a 3200A power frequency sinusoidal current is applied to simulate the actual operating conditions of the high-current lead, providing input conditions for the calculation of leakage magnetic field distribution and structural component losses.

[0025] For nonlinear magnetically conductive components such as iron cores, clamps, and pull plates, BH magnetization curves and BP iron loss curves are set, and the influence of material conductivity on temperature changes is determined, providing a basis for material parameter correction in electromagnetic-thermal coupling calculations.

[0026] An iterative calculation process for electromagnetic-thermal bidirectional coupling was established. The electromagnetic field was solved by Maxwell to obtain eddy current loss, hysteresis loss and additional loss. The loss was imported into the thermal field model in the form of volumetric loss density to calculate the temperature distribution. The material conductivity and permeability were then corrected based on the temperature results and fed back to the electromagnetic field model for recalculation. Through iterative iteration, the loss and temperature results met the convergence requirements, thus completing the establishment of a parameterized three-dimensional nonlinear electromagnetic-thermal coupled finite element model.

[0027] S102 maps deterministic design variables to a standardized design space, uses an adaptive optimal Latin hypercube sampling method to select representative sample points in the standardized design space, trains a surrogate model based on the representative sample points, and dynamically adds points according to the surrogate model error and filling distance, outputting a set of representative sample points.

[0028] See Figure 3 In this embodiment, the deterministic design variables of geometric parameters, material properties, and shielding parameters are normalized and mapped to a preset standard hypercube space of [0,1] to construct a unified high-dimensional design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points in the high-dimensional design space, so that each dimension is uniformly layered and the sample spacing is maximized, ensuring that the initial sample distribution is uniform and highly representative.

[0029] A Kriging-gradient enhancement hybrid surrogate model is trained based on representative sample points. This model is used for error assessment, dynamic point addition, and rapid calculation of subsequent optimization. It takes design variables as input and finite element calculation results as output, and employs a joint training method using the negative log-likelihood function and the generalized least squares loss function. Simultaneously, it fits response values ​​and gradient information. The global and local model errors are calculated comprehensively using the coefficient of determination, root mean square error, and Kriging prediction variance. The calculation formula is as follows: in, The values ​​represent the actual response values ​​in the finite element simulation. For the surrogate model's predicted values, The mean of the true responses is given, and n is the total number of samples. As the coefficient of determination, This is the root mean square error.

[0030] Calculate the Euclidean distance from any candidate point in the high-dimensional design space to the nearest existing sample point, and use the Euclidean distance as the padding distance to identify sparse regions of the sample. The calculation formula is as follows: in, For target sample points The Euclidean distance to the nearest sample in the dataset. For the target sample point whose nearest neighbor distance needs to be calculated, To iterate through all other samples in the dataset Take the minimum distance. For index variables of other sample points in the dataset, To sum over all feature dimensions of the sample, Here, d represents the feature dimension index, and d is the total number of feature dimensions for the sample. For target sample points In the The values ​​taken on each feature dimension For the first The sample point at the th th The values ​​taken on each feature dimension For two sample points at the th The square of the difference across each feature dimension; Based on the coupling criterion between local model error and filling distance, new sample points are added in high error regions and large filling distance regions. At the same time, the stopping condition is judged based on the global model error. After each round of point addition, the Kriging-gradient enhancement hybrid surrogate model is retrained. The point addition and training are iteratively executed until all output indicators meet the preset accuracy requirements of a determination coefficient greater than or equal to 0.99 and a root mean square error less than or equal to 0.01, and a representative sample point set is output.

[0031] S103 performs a three-dimensional nonlinear transient electromagnetic-thermal bidirectional coupled finite element calculation on each representative sample point in the output, and extracts the performance index corresponding to each sample point.

[0032] In this embodiment, for each representative sample point output, the geometric parameters, material properties, and shielding measures of the parameterized three-dimensional finite element model are updated based on the design variable values. By performing three-dimensional nonlinear transient electromagnetic field calculations, the leakage magnetic field distribution is obtained, and the magnetic flux density distribution and loss density distribution of each structural component are extracted. The loss obtained from the electromagnetic field calculation is imported into the thermal field model in the form of volumetric loss density. Temperature field calculations are performed to obtain the temperature distribution and local hot spot temperatures of each structural component. The material conductivity and permeability are corrected based on the temperature field calculation results and fed back to the electromagnetic field model for recalculation. This iteration continues until the electromagnetic field and temperature field results meet the convergence condition. From the converged calculation results, the maximum magnetic flux density, maximum loss density, leakage flux, hysteresis loss, eddy current loss, total loss density, local hot spot temperature, temperature gradient, material cost, and robustness indicators are extracted. The calculation formulas are as follows: in, Let B be the leakage flux, B be the leakage magnetic induction intensity, and S be the integral surface. For hysteresis loss, This is the hysteresis loss coefficient. f For frequency, For the maximum magnetic flux density, Where is the Steinmetz coefficient, and V is the material volume. For eddy current losses, The eddy current loss coefficient is... Total loss density, For local hotspot temperatures, For ambient temperature, For thermal resistance, For total material costs, These are the unit prices for fuel tank materials, riser base materials, and shielding materials, respectively. These are the volumes of the fuel tank and the riser, respectively. This refers to the shielding area.

[0033] Figure 4 The example cloud diagram of the finite element analysis results shows the magnetic flux density distribution on the tank wall. Through electromagnetic-thermal coupled finite element analysis, the magnetic flux density, loss, and temperature distribution of key structural components can be obtained, which can be used to identify high magnetic flux density, high loss, and high temperature regions, and provide simulation basis for objective function evaluation and optimization scheme comparison.

[0034] S104, based on a representative sample point set and corresponding performance indicators, constructs a Kriging gradient-enhanced hybrid response surface model, performs model validation, and outputs a high-precision hybrid response surface model.

[0035] In this embodiment, the design variable data in the representative sample point set and the output indicators such as magnetic flux density, loss, temperature, cost, and robustness obtained from finite element calculation are normalized to eliminate dimensional differences, resulting in a normalized sample dataset. Based on the normalized sample dataset, a hybrid response surface model is constructed using a hybrid structure of the Kriging model as the main model and the gradient-enhanced response surface as the auxiliary model. This model simultaneously outputs predicted values ​​and prediction errors, adapting to highly nonlinear, multi-peak, and strongly coupled characteristics. The Kriging model is used to output predicted values ​​and prediction errors, while the gradient-enhanced response surface is used to capture nonlinearity and local peaks.

[0036] A generalized least squares loss function is used to train the hybrid response surface model, and the output value and output gradient are fitted simultaneously. The accuracy of the trained hybrid response surface model is verified by the coefficient of determination, root mean square error, maximum relative error, and residual normality test. If the verification result does not meet the preset accuracy requirements, the model is dynamically supplemented with sample points and retrained. If the accuracy requirements are met, a high-precision hybrid response surface model is output for quickly evaluating targets such as magnetic flux density, loss, temperature, cost, and robustness, providing support for subsequent multi-objective optimization.

[0037] S105. After establishing the objective function to guide the optimization direction, the improved NSGA-III multi-objective optimization algorithm is used to quickly optimize the high-precision mixed response surface model and generate the Pareto optimal solution set.

[0038] Figure 5 This diagram illustrates the Pareto front obtained through multi-objective optimization and the final solution selection. Multi-objective optimization yields a non-dominated solution set, forming the Pareto front. The entropy weight method is then used to determine the weights of each objective, and the TOPSIS method is combined to calculate the closeness of each solution. From this, the compromise solution with the best overall performance is selected, achieving optimal decision-making for structural parameters. In this embodiment, the optimization objective function aims to minimize the maximum magnetic flux density, the maximum loss density, the local hotspot temperature, the material cost, and maximize robustness. Simultaneously, magnetic saturation constraints, temperature safety constraints, dimensional and process constraints, and uncertainty fluctuation constraints are introduced. Minimizing the maximum magnetic flux density prevents magnetic saturation; minimizing the maximum loss density reduces structural losses; minimizing the local hotspot temperature prevents local overheating of structural components; minimizing material cost controls and optimizes costs; and maximizing robustness enhances robustness. The constraints include a peak leakage magnetic flux density constraint of less than or equal to 1.5T, a local hotspot temperature constraint of less than or equal to 118℃ or a temperature rise to ambient temperature of less than or equal to 78K, with an ambient temperature maximum of 40℃; dimensions satisfying the processing technology; uncertainty performance fluctuation less than or equal to 5%; and the assemblability constraint of the shielding structure.

[0039] An improved NSGA-III multi-objective optimization algorithm is employed to perform rapid optimization on a mixed response surface model. Adaptive crossover and mutation, elite preservation, and boundary repair mechanisms are introduced to obtain a Pareto optimal solution set with stronger uniformity and coverage, including: Using normalized design variables as individual codes, an initial population is generated within the range of design variable values ​​and constraints. A high-precision mixed response surface model is then used to calculate the objective function value for each individual. Crossover and mutation probabilities are adjusted based on the number of iterations and individual distribution, and crossover and mutation operations are performed on the individuals in the population to obtain the offspring population. Boundary corrections and constraint checks are performed on individuals in both the parent and offspring populations, eliminating or correcting individuals that do not meet the design requirements. Based on five optimization objective functions, the candidate populations are non-dominated, resulting in multiple non-dominated layers. Individuals within the same non-dominated layer are selected using reference points, prioritizing the retention of individuals with higher and more evenly distributed non-dominated levels. An elite retention strategy is used to form the next generation population, and the above process is repeated until the termination condition is met, outputting the Pareto optimal solution set.

[0040] S106 selects the optimal design scheme from the Pareto optimal solution set based on the entropy weight-TOPSIS dynamic decision method and performs dual verification of finite element method and Monte Carlo uncertainty. After the verification is passed, the final optimization parameters and performance report are output.

[0041] In this embodiment, each solution in the Pareto optimal solution set is used as the scheme to be evaluated, and the performance index is used as the evaluation index. An original evaluation matrix is ​​constructed. After the indexes in the original evaluation matrix are positively oriented, the positively oriented index data is standardized. The objective weight of each evaluation index is calculated using the entropy weight method. The calculation formula is as follows: in, For the first The objective weight of each indicator For the first The coefficient of variation of an indicator reflects the degree of its information contribution. For the first The entropy value of the indicator, This is an adjustment coefficient calculated for the entropy value, which standardizes the entropy value to the interval [0, 1], where n is the total number of samples. For the first The sample at the th Sample proportion under each indicator For the first The sample at the th The original indicator values ​​under each indicator For the first The sample at the th The minimum value of all original values ​​of all samples under the item indicator. For the first The sample at the th The maximum value of the original values ​​of all samples under this indicator.

[0042] A weighted standardized matrix is ​​constructed based on objective weights, and positive and negative ideal solutions are determined. The Euclidean distance from each evaluated solution to the positive and negative ideal solutions is calculated. The proximity coefficient of the samples is then calculated based on the calculated Euclidean distances. The calculation formulas are as follows: in, For the first The proximity coefficient of each sample. For the first The Euclidean distance from each sample to the positive ideal solution. For the first The Euclidean distance from each sample to the negative ideal solution. For the first The sample at the th The weighted standardized index value under each indicator, The first positive ideal solution vector One portion, The first of the negative ideal solution vectors One portion, The positive ideal solution vector is the vector formed by the maximum weighted values ​​of all samples under each indicator. The negative ideal solution vector is the vector formed by the minimum weighted values ​​of all samples under each indicator. This represents the total number of indicators involved in the evaluation. For the first The objective weight of each indicator For the first The sample at the th Standardized indicator values ​​under each indicator For the first The standardized value of each sample in the first feature dimension For the first The standardized value of each sample in the second feature dimension. For the first The standardized value of a sample on the m-th feature dimension To obtain the minimum value of all samples in the first feature dimension, and use this as the value of the negative ideal point in that dimension, To obtain the minimum value of all samples in the second feature dimension, and use this as the value of the negative ideal point in that dimension, To find the minimum value of all samples in the m-th feature dimension, and use it as the value of the negative ideal point in that dimension, To obtain the maximum value of all samples in the first feature dimension, and use it as the value of the positive ideal point in that dimension, To obtain the maximum value of all samples in the second feature dimension, and use it as the value of the positive ideal point in that dimension, The maximum value of all samples in the m-th feature dimension is taken as the value of the positive ideal point in that dimension.

[0043] The scheme with the highest closeness coefficient is selected as the optimal compromise design scheme. This optimal compromise design scheme is then substituted into the original finite element model for conventional finite element verification. The prediction errors of each performance index are calculated. If the prediction errors of all indices are within a preset threshold range, the finite element verification is passed. Based on the distribution characteristics of the uncertainty variables, Monte Carlo simulation is performed on the optimal compromise design scheme to statistically analyze the fluctuation range of each performance index. If the fluctuations of all indices are within a preset fluctuation threshold range, the Monte Carlo uncertainty verification is passed. When both the finite element verification and the Monte Carlo uncertainty verification are passed, the final optimized parameters and performance report are output.

[0044] Furthermore, this embodiment is described in detail using a complete design example of the valve leads of a 3200A flexible DC converter transformer: the distance from the lead center to the tank wall is defined as 260mm, the tank cover aperture is 450mm, the riser aperture is 550mm, and both the tank and riser materials are low-carbon steel. Electromagnetic shielding is added to the shielding measures, with two shielding layers and a shielding thickness of 2mm. Uncertainty random variables include dimensional tolerance ±2%, current ±5%, and magnetic permeability ±5%.

[0045] A parametric electromagnetic-thermal bidirectional coupling model was established in ANSYS Workbench. A Python script was used to call the ANSYS API to achieve parametric and automated modeling, coupling calculations, and data extraction. An initial 100 samples were generated using the adaptive optimal Latin hypercube method, and 42 samples were dynamically added after error assessment, for a total of 142 samples, satisfying that all output coefficients of determination are greater than or equal to 0.99.

[0046] In the automated calculation phase, a batch processing script was written to run 142 calculation tasks sequentially, automatically extracting maximum magnetic flux density, maximum loss density, hysteresis loss, eddy current loss, total loss density, hotspot temperature, temperature gradient, cost, and robustness metrics. In the coupled calculation, the electromagnetic field maps the loss to the thermal field with each iteration, and the thermal field updates the temperature and feeds back to correct the electromagnetic parameters until the two fields converge.

[0047] After importing the sample data into MATLAB, a Kriging surrogate model was established based on fitrgp, and gradient enhancement polynomial terms were superimposed to improve the surrogate model's ability to fit nonlinear responses and its local prediction accuracy. Accuracy tests showed that the determination coefficients of the loss model, temperature model, and cost model reached 0.994, 0.991, and 0.998, respectively, indicating that the constructed hybrid surrogate model has high prediction accuracy and can meet the needs of subsequent multi-objective optimization calculations.

[0048] In the optimization and solution stage, the improved NSGA-III algorithm is called, with a population size of 200 and an iteration number of 300. Based on the hybrid surrogate model, the algorithm quickly finds the optimal solution set for the five objectives, which is uniformly distributed, non-degenerate, and fully covered.

[0049] The optimal compromise solution was automatically selected using the entropy weight-TOPSIS method. The final solution is as follows: the distance from the center to the tank wall is 265mm, the tank cap aperture is 445mm, the riser aperture is 545mm, the tank and riser materials are both low-carbon steel, the shielding layer has two layers, and the shielding thickness is 2mm. Finite element analysis and Monte Carlo uncertainty verification were performed on this solution. The finite element prediction error is about 2.7%, the uncertainty drift is about 3.2%, the maximum loss density is reduced by 57%, the hot spot temperature is reduced to 42℃, the cost only increases by 7%, and the robustness coefficient is η=0.96; the optimization effect is significant and meets the actual engineering needs.

[0050] In this embodiment, "multiple" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0051] The above description is merely a specific embodiment of this application. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. The protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology, characterized in that, include: The bi-level optimization variables and their distribution characteristics are determined, and a parameterized three-dimensional nonlinear electromagnetic-thermal bi-directional coupled finite element model is constructed based on the deterministic design variables in the bi-level optimization variables. The deterministic design variables are mapped to a standardized design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points in the standardized design space. A surrogate model is trained based on the representative sample points. Points are dynamically added according to the surrogate model error and the filling distance to output a set of representative sample points. For each representative sample point in the output, perform a three-dimensional nonlinear transient electromagnetic-thermal bidirectional coupled finite element calculation to extract the performance index corresponding to each sample point. Based on the representative sample point set and the corresponding performance indicators, a Kriging gradient-enhanced hybrid response surface model is constructed, and the model is validated to output a high-precision hybrid response surface model. After establishing the optimization objective function to guide the optimization direction, the improved NSGA-III multi-objective optimization algorithm is used to quickly optimize the high-precision mixed response surface model and generate the Pareto optimal solution set. The optimal design scheme is selected from the Pareto optimal solution set based on the entropy weight-TOPSIS dynamic decision method and then verified by finite element method and Monte Carlo uncertainty. After the verification is passed, the final optimization parameters and performance report are output.

2. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, The process of determining the two-layer optimization variables and their distribution characteristics, and constructing a parametric three-dimensional nonlinear electromagnetic-thermal bidirectional coupled finite element model based on the deterministic design variables in the two-layer optimization variables, includes: Determine the two-level optimization variables and their distribution characteristics, including deterministic design variables and uncertain random variables. The deterministic design variables include geometric parameters, material properties and shielding measures, while the uncertain random variables include geometric dimensional tolerances, operating current fluctuations and material permeability deviations. A three-dimensional finite element model was established based on actual engineering drawings, including valve side leads, oil tank, oil tank cover, riser seat, clamps, pull plate and iron core, and an excitation source and nonlinear magnetic material were introduced. The geometric parameters and shielding parameters in the deterministic design variables are defined as parameter variables, and a parameter-driven relationship is established. At the same time, in combination with the actual operating conditions, an infinite magnetic field boundary, a natural convection heat dissipation boundary, and a thermal radiation boundary are applied. Using the valve-side lead conductor as the excitation object, a preset power frequency sinusoidal current is applied to simulate the actual operating conditions of the high-current lead, providing input conditions for the leakage magnetic field distribution and structural component loss calculation; For nonlinear magnetic components, BH magnetization curves and BP iron loss curves were set, and the effect of material conductivity on temperature was determined. An electromagnetic-thermal bidirectional coupling iterative calculation process was established, and the electromagnetic field was solved by Maxwell to obtain eddy current loss, hysteresis loss and additional loss. The loss is imported into the thermal field model in the form of volumetric loss density to calculate the temperature distribution; The material's electrical conductivity and magnetic permeability are then corrected based on the temperature results and fed back to the electromagnetic field model for recalculation. Through iterative iterations, until the loss and temperature results meet the convergence requirements, the parameterized three-dimensional nonlinear electromagnetic-thermal coupled finite element model is established.

3. The method for calculating and optimizing the magnetic field of high-current leads based on the response surface methodology according to claim 1, characterized in that, The deterministic design variables are mapped to a standardized design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points within the standardized design space. A surrogate model is trained based on these representative sample points, and points are dynamically added according to the surrogate model error and the filling distance. The resulting set of representative sample points includes: Deterministic design variables such as geometric parameters, material properties, and shielding parameters are normalized and mapped to a preset standard hypercube space to construct a unified high-dimensional design space. An adaptive optimal Latin hypercube sampling method is used to select representative sample points in the high-dimensional design space, so that each dimension is uniformly layered and the sample spacing is maximized. Train a Kriging-gradient augmentation hybrid agent model based on the representative sample points; The global model error and the local model error are calculated by combining the coefficient of determination, root mean square error and Kriging prediction variance. Calculate the Euclidean distance from any candidate point in the high-dimensional design space to the nearest existing sample point, and use the Euclidean distance as the fill distance. The calculation formula is as follows: in, For target sample points The Euclidean distance to the nearest sample in the dataset. For the target sample point whose nearest neighbor distance needs to be calculated, To iterate through all other samples in the dataset Take the minimum distance. For index variables of other sample points in the dataset, To sum over all feature dimensions of the sample, Here, d represents the feature dimension index, and d is the total number of feature dimensions for the sample. For target sample points In the The values ​​taken on each feature dimension For the first The sample point at the th th The values ​​taken on each feature dimension For two sample points at the th The square of the difference across each feature dimension; Based on the coupling criterion between local model error and filling distance, new sample points are added in high error regions and large filling distance regions. At the same time, the stopping condition is judged based on the global model error. After each round of point addition, the Kriging-gradient enhancement hybrid surrogate model is retrained. Iteratively perform point addition and training until all output metrics meet the preset accuracy requirements, and output a representative sample point set.

4. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 3, characterized in that, The formula for calculating the global model error and the local model error by combining the coefficient of determination, root mean square error, and Kriging prediction variance is as follows: in, The values ​​represent the actual response values ​​in the finite element simulation. For the surrogate model's predicted values, The true mean response is given, and n is the total number of samples. As the coefficient of determination, This is the root mean square error.

5. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, For each representative sample point in the output, a three-dimensional nonlinear transient electromagnetic-thermal bidirectional coupled finite element calculation is performed to extract the performance indicators corresponding to each sample point, including: For each representative sample point in the output, the geometric parameters, material properties, and shielding measures of the parametric three-dimensional finite element model are updated based on the design variable values. By performing three-dimensional nonlinear transient electromagnetic field calculations, the leakage magnetic field distribution is obtained, and the magnetic flux density distribution and loss density distribution of each structural component are extracted. The loss obtained from electromagnetic field calculation is imported into the thermal field model in the form of volumetric loss density. Temperature field calculation is performed to obtain the temperature distribution of each structural component and the temperature of local hot spots. The electrical conductivity and magnetic permeability of the material are corrected based on the temperature field calculation results and fed back to the electromagnetic field model for recalculation. The process is iterated until the electromagnetic field and temperature field results meet the convergence conditions. The maximum magnetic flux density, maximum loss density, leakage flux, hysteresis loss, eddy current loss, total loss density, local hotspot temperature, temperature gradient, material cost, and robustness index are extracted from the converged calculation results. The calculation formulas are as follows: in, Let B be the leakage flux, B be the leakage magnetic induction intensity, and S be the integral surface. For hysteresis loss, This is the hysteresis loss coefficient. f For frequency, For the maximum magnetic flux density, Where is the Steinmetz coefficient, and V is the material volume. For eddy current losses, This is the eddy current loss coefficient. Total loss density, For local hotspot temperatures, For ambient temperature, For thermal resistance, For total material costs, These are the unit prices for fuel tank materials, riser base materials, and shielding materials, respectively. These are the volumes of the fuel tank and the riser, respectively. This refers to the shielding area.

6. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, Based on the representative sample point set and corresponding performance indicators, a Kriging gradient-enhanced hybrid response surface model is constructed, and the model is validated to output a high-precision hybrid response surface model, including: The design variable data and corresponding performance index data in the representative sample point set are normalized to obtain the normalized sample dataset. Based on the normalized sample dataset, a hybrid response surface model is constructed using a hybrid structure of the Kriging model as the main model and the gradient-enhanced response surface as the auxiliary model. The Kriging model is used to output the predicted value and the prediction error, and the gradient-enhanced response surface is used to capture nonlinearity and local peaks. The hybrid response surface model is trained using a generalized least squares loss function, and the output value and output gradient are fitted simultaneously. The accuracy of the trained mixed response surface model was verified by using the coefficient of determination, root mean square error, maximum relative error, and residual normality test. If the verification result does not meet the preset accuracy requirements, the system returns dynamically supplemented sample points and retrains; if the accuracy requirements are met, a high-precision hybrid response surface model is output.

7. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, The optimization objective function aims to minimize the maximum magnetic flux density, the maximum loss density, the local hot spot temperature, the material cost, and the robustness, while also incorporating magnetic saturation constraints, temperature safety constraints, size and process constraints, and uncertainty fluctuation constraints.

8. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, The improved NSGA-III multi-objective optimization algorithm is used to quickly optimize the high-precision mixed response surface model and generate a Pareto optimal solution set, including: Using the normalized design variables as individual codes, an initial population is generated within the range of design variable values ​​and constraints, and the objective function value corresponding to each individual is calculated using the high-precision hybrid response surface model. Based on the number of iterations and the distribution of individuals, the crossover and mutation probabilities are adjusted, and crossover and mutation operations are performed on the individuals in the population to obtain the offspring population. Perform boundary correction and constraint judgment on individuals in the parent and offspring populations, and remove or correct individuals that do not meet the design requirements; Based on the optimization objective function, the candidate population is non-dominated and sorted to obtain multiple non-dominated layers; Using reference points, individuals within the same non-dominated layer are selected based on their distribution, prioritizing the retention of individuals with higher non-dominated levels and more even distribution. The next generation of the population is formed according to the elite preservation strategy, and the above process is repeated until the termination condition is met, and the Pareto optimal solution set is output.

9. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 1, characterized in that, The entropy-weighted TOPSIS dynamic decision-making method selects the optimal design scheme from the Pareto optimal solution set and performs dual verification using finite element analysis and Monte Carlo uncertainty testing. After successful verification, the final optimization parameters and performance report are output, including: Using each solution in the Pareto optimal solution set as the scheme to be evaluated and the performance index as the evaluation index, an original evaluation matrix is ​​constructed. After positiveizing the indicators in the original evaluation matrix, the positiveized indicator data is then standardized. The objective weights of each evaluation index are calculated using the entropy weight method; A weighted standardized matrix is ​​constructed based on the objective weights, and the positive and negative ideal solutions are determined. Calculate the Euclidean distance from each evaluated scheme to the positive and negative ideal solutions, and then calculate the proximity coefficient of the samples based on the calculated Euclidean distances. The calculation formulas are as follows: in, For the first The proximity coefficient of each sample. For the first The Euclidean distance from each sample to the positive ideal solution. For the first The Euclidean distance from each sample to the negative ideal solution. For the first The sample at the th The weighted standardized index value under each indicator, The first positive ideal solution vector One portion, The first of the negative ideal solution vectors One portion, The vector is the positive ideal solution. The negative ideal solution vector. This represents the total number of indicators involved in the evaluation. For the first The objective weight of each indicator For the first The sample at the th Standardized indicator values ​​under each indicator For the first The standardized value of each sample in the first feature dimension For the first The standardized value of each sample in the second feature dimension. For the first The standardized value of a sample on the m-th feature dimension To obtain the minimum value of all samples in the first feature dimension, and use this as the value of the negative ideal point in that dimension, To obtain the minimum value of all samples in the second feature dimension, and use this as the value of the negative ideal point in that dimension, To find the minimum value of all samples in the m-th feature dimension, and use it as the value of the negative ideal point in that dimension, To obtain the maximum value of all samples in the first feature dimension, and use it as the value of the positive ideal point in that dimension, To obtain the maximum value of all samples in the second feature dimension, and use it as the value of the positive ideal point in that dimension, The maximum value of all samples in the m-th feature dimension is taken as the value of the positive ideal point in that dimension. The scheme with the highest proximity coefficient is selected as the optimal compromise design scheme; The optimal compromise design scheme is substituted into the original finite element model for conventional finite element verification. The prediction error of each performance index is calculated. If the prediction error of all indicators is within the preset threshold range, the finite element verification is passed. Based on the distribution characteristics of the uncertainty variables, Monte Carlo simulation is performed on the optimal compromise design scheme to statistically analyze the fluctuation range of each performance index. If the fluctuation of all indicators is within the preset fluctuation threshold range, then the Monte Carlo uncertainty verification is passed. When both the finite element verification and the Monte Carlo uncertainty verification are passed, the final optimization parameters and performance report are output.

10. The method for calculating and optimizing the magnetic field of a high-current lead based on the response surface methodology according to claim 9, characterized in that, The objective weights of each evaluation index are calculated using the entropy weight method. The calculation formula is as follows: in, For the first The objective weight of each indicator For the first The coefficient of difference of the indicators For the first The entropy value of the indicator, The adjustment coefficient is calculated for the entropy value, where n is the total number of samples. For the first The sample at the th Sample proportion under each indicator For the first The sample at the th The original indicator values ​​under each indicator For the first The sample at the th The minimum value of all original values ​​of all samples under the item indicator. For the first The sample at the th The maximum value of the original values ​​of all samples under this indicator.

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