An intelligent global multi-objective optimization method for core reactor facing electromagnetic thermal multi-field coupling

Abstract

The application discloses an intelligent global multi-objective optimization method for electromagnetic thermal multi-field coupling of a core reactor, which comprises the following steps: a three-dimensional geometric model of the core reactor is established; a circuit-magnetic field simulation model is established to obtain electromagnetic field distribution; a flow field-temperature field two-way coupling model is established according to the loss distribution to obtain a temperature field; a magnetic field-structure force field coupling model is established according to the electromagnetic field to obtain vibration displacement; a sample library is constructed by combining optimal Latin hypercube experimental design and finite element simulation, and key parameters are screened through sensitivity analysis; an FT-Transformer proxy model is constructed based on the key parameters, and a Pareto optimal solution set is solved by combining an NSGA-III algorithm; and the optimal solution is obtained through comprehensive decision-making by introducing an entropy weight-TOPSIS method and is verified. The application comprehensively covers three physical fields of electromagnetism, heat and force through multi-physical field coupling simulation, realizes high-precision nonlinear mapping by adopting an FT-Transformer proxy model, realizes multi-objective trade-off decision-making by combining NSGA-III and entropy weight-TOPSIS, and effectively reduces the quality, loss, temperature rise and vibration displacement of the reactor.

Description

Technical Field

[0001] This invention relates to the field of electrical equipment optimization technology, and in particular to an intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal-field coupling. Background Technology

[0002] As a core electrical device in a power system, the operating performance of iron-core reactors directly determines the stability and reliability of the power system. In actual service conditions, complex electromagnetic-thermal-mechanical multi-physics coupling effects exist within iron-core reactors. These coupling characteristics have a critical impact on the reactor's loss control accuracy, temperature rise limit compliance rate, mechanical vibration suppression effect, and service life stability, and are directly related to the equipment's operational quality and the power system's energy efficiency level. Currently, the optimization design of iron-core reactors is mostly limited to single physical fields or isolated performance indicators, lacking a systematic consideration of the electromagnetic, thermal, and mechanical multi-field coupling mechanisms. This makes it difficult for optimization schemes to simultaneously meet the synergistic requirements of quality control, loss suppression, and temperature and vibration performance. While some multi-objective optimization methods attempt to consider multiple performance indicators, they still rely on traditional optimization algorithms and have inherent defects such as weak global optimization ability, slow convergence speed, and easy getting trapped in local optima. They are difficult to adapt to the multi-objective collaborative optimization requirements of iron-core reactors under mass, loss, temperature and vibration, and cannot achieve dynamic balance and comprehensive improvement of various performance indicators. Therefore, it is necessary to design an intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic thermodynamic multi-field coupling to solve the above problems. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide an intelligent global multi-objective optimization method for iron-core reactors with electromagnetic-thermal-field coupling, which aims to solve the multi-objective optimization problem of iron-core reactors by finding the optimal parameter design of the iron-core reactor.

[0004] To achieve the above technical solution, the technical solution adopted by the present invention is as follows: A smart global multi-objective optimization method for iron-core reactors with electromagnetic-thermal multi-field coupling includes the following steps: Based on the electrical and structural parameters of the dry-type iron-core reactor, a three-dimensional geometric model of the iron-core reactor was established using finite element simulation software. A circuit-magnetic field simulation model of an iron-core reactor was established, and the electromagnetic field distribution characteristics of the reactor were obtained through simulation calculations. The loss distribution of each part of the iron core reactor is obtained by the circuit-magnetic field simulation results. Based on this, a two-way coupled simulation model of flow field and temperature field is established to obtain the temperature field simulation results of the iron core reactor. A coupled magnetic field-structural force field model of the iron-core reactor was established based on the circuit-magnetic field simulation results, and the vibration displacement of the reactor was obtained. By selecting the optimal parameters of the iron-core reactor, the optimal Latin hypercube experimental design and finite element simulation were combined to obtain the mass, loss, temperature and vibration results of the iron-core reactor under different parameters. The key optimization parameters were screened out through sensitivity analysis. Based on key parameters, an FT-Transformer agent model is constructed. A multi-objective optimization function is established in conjunction with this model. The NSGA-Ⅲ algorithm is used to solve the problem and output the Pareto optimal solution set. The entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set, determine the optimal solution for multi-objective joint optimization, and reset the optimized parameters into the model for verification.

[0005] Furthermore, the three-dimensional geometric model includes an iron core, an iron yoke, windings, and clamps; the following equivalent simplification scheme is adopted in the modeling: the laminated iron core is equivalent to a homogeneous integral magnetic conductor, and the internal lamination gaps are ignored; the multi-layer windings are modeled in a partitioned equivalent manner, the winding structure is unified and merged and the equivalent number of turns is configured; the mechanical clamping structure of the fastening screw is replaced by boundary fixed constraint conditions.

[0006] Furthermore, when establishing the circuit-magnetic field simulation model, the Epstein square test method was used to conduct magnetic property experiments on the silicon steel sheet material used in the reactor core, and the hysteresis parameters of the silicon steel sheet under different excitation conditions were obtained, which were used as the experimental basis for assigning the core material properties in the finite element simulation.

[0007] Preferably, the material properties of each component in the model are defined by combining the experimentally measured magnetic property curves of silicon steel sheets. A power frequency alternating current excitation is applied to the end of the coil, and the electromagnetic field control differential equation is numerically solved within the finite element magnetic field solution module. The electromagnetic field control differential equation is: ; in, For vector magnetic potential, The magnetic permeability of the material, For the electrical conductivity of the material, For time, This represents the winding excitation current density.

[0008] Furthermore, in step S2, when solving the magnetic field using the finite element method, local mesh refinement is applied to the air gap region of the iron core, and the mesh element size in the air gap region does not exceed half the element size of the other regions.

[0009] Preferably, the non-uniform losses of each component of the reactor are extracted as heat sources based on the circuit-magnetic field simulation results. A two-way coupled flow field-temperature field model is established, considering the dynamic characteristics of fluid properties changing with temperature. The overall temperature field distribution law of the reactor is obtained through iterative solution. The core loss consists of hysteresis loss, eddy current loss, and abnormal loss, which is calculated using the Steinmetz loss formula. ; in, Loss per unit volume For frequency, Peak magnetic flux density , , The Steinmetz coefficient; Reactor winding losses are calculated using the Joule heating formula: ; in, For winding losses, To excite the current, For winding resistance; Heat is transferred via convection on the surface of the reactor core, the surface of the windings, and the winding air passages, as shown below: ; in, For heat flux density, The convective heat transfer coefficient is... The wall temperature, The fluid temperature.

[0010] Furthermore, the Steinmetz coefficient , , The parameters were determined by analyzing the hysteresis loop experimental data of the iron-core silicon steel sheet material. The value range is 1.0 to 2.0. The value range is 1.5 to 3.0. The range of values ​​is .

[0011] Furthermore, loss data of key components such as the core, windings, and clamps are extracted, taking into account the non-uniformity of spatial distribution of losses caused by differences in electromagnetic structure, material properties, and uneven magnetic field distribution. This includes loss concentration caused by local magnetic saturation of the core, loss differences caused by skin effect and proximity effect of winding conductors, and discrete distribution characteristics of eddy current loss of clamps.

[0012] Furthermore, when establishing a two-way coupled simulation model of flow field and temperature field, the non-uniform loss distribution of each component is transmitted to the temperature field in real time as a heat source. At the same time, the characteristics of air fluid density, thermal conductivity, viscosity and other properties as a function of temperature, as well as the effect of temperature rise on the heat dissipation efficiency of the components are considered. Through the interaction and iterative solution of flow field and temperature field, the temperature distribution cloud map of each component is obtained.

[0013] Furthermore, the convergence criterion for the bidirectional coupled iterative solution of the flow field and temperature field is that the maximum relative change in the temperature field between two adjacent iterations is less than... .

[0014] Preferably, when establishing the magnetic field-structural force field coupling model, the magnetostrictive constitutive model of the iron core silicon steel sheet is embedded into the finite element simulation system, and the parameter values ​​are assigned by combining the material magnetostrictive characteristic equation; the iron core is subjected to force under the action of the magnetic field. By Maxwell and magnetostrictive force Composition, namely: ; The iron core vibrates under stress, which can be represented by the following equation in the structural field: ; in, For the iron core to bear the force, For Maxwell, It is magnetostrictive force. The mass matrix of the iron core, The damping coefficient of the iron core, The mechanical stiffness matrix of the iron core. The vibration displacement to be determined is denoted as .

[0015] Preferably, the coupling relationship between the core magnetic field and the structural field is expressed by the following equation: ; in, Here is the magnetic field stiffness matrix. For vector magnetic potential, For winding excitation current density, The mechanical stiffness matrix of the iron core. For vibration displacement, The iron core is subjected to force.

[0016] Furthermore, in the multiphysics coupled simulation of magnetic field and structural force field, the temperature field distribution results are used as the basis for correcting the mechanical properties of the insulating material. A correlation mapping between temperature and the mechanical properties of the insulating material is established to update the material properties of each region. The mechanical properties include the elastic modulus and the coefficient of thermal expansion. The correlation mapping between temperature and the mechanical properties of the insulating material is established based on the thermodynamic experimental data of the material, and the elastic modulus is constructed using linear interpolation or polynomial fitting methods. and coefficient of thermal expansion Regarding temperature The functional relationship.

[0017] Preferably, the core size and winding structure are selected as design variables. The optimal Latin hypercube experimental design method is used to uniformly sample each design variable. Simulation models of circuit-magnetic field, flow-temperature field, and magnetic field-structural force field are called to perform simulation calculations on each set of parameter samples. Data on reactor mass, loss, temperature, and vibration response under different combinations of structural parameters are obtained, and a sample database corresponding to design parameters and performance responses is established. The design variables include winding height. airway width Air gap height Width of the first layer winding Second layer winding width Third layer winding width Height of the iron yoke Discus height and core radius .

[0018] Preferably, based on the design parameter-performance response multidimensional simulation sample dataset, Pearson correlation coefficient is used for parameter sensitivity analysis: ; in, For the first One optimization parameter, For the first One optimization objective response value, To optimize the mean of the parameters, To optimize the mean of the target response, This represents the number of samples.

[0019] Furthermore, the key optimization parameters screened through sensitivity analysis include air passage width, air gap height, winding height, winding width of each layer, and yoke height.

[0020] Preferably, key design parameters are used as model inputs, and reactor mass, loss, temperature rise, and vibration displacement are selected as optimized output responses to construct an FT-Transformer surrogate model. This model completes the unified dimensional mapping of input parameters through feature word embedding, and relies on the multi-head self-attention mechanism of the Transformer encoder to mine the nonlinear coupling correlation and high-order interaction characteristics between key parameters. The AdamW optimizer is used to complete the iterative update of all model parameters, with the minimization of mean squared error as the training objective, and the goodness of fit is utilized. Error verification was conducted on the indicators.

[0021] Furthermore, the FT-Transformer proxy model has 2 to 4 encoder layers, 4 to 8 heads in the multi-head self-attention mechanism, and 32 to 128 feature embedding dimensions.

[0022] Furthermore, a multi-objective optimization function was established with mass, loss, temperature rise and vibration displacement as optimization objectives, and the inductance value variation was limited to no more than 5%. The non-dominated sorting genetic algorithm NSGA-Ⅲ was used to solve the optimization problem in combination with the FT-Transformer surrogate model. The population size was set to 12, the number of generations was 30 and the crossover probability was 0.9. After iterative calculation to the termination condition, the Pareto solution set was output.

[0023] Furthermore, the population size of the NSGA-Ⅲ algorithm ranges from 10 to 50, the number of generations ranges from 20 to 100, and the crossover probability ranges from 0.7 to 0.95.

[0024] Preferably, the entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set. Weights are automatically assigned according to the dispersion of each optimization objective data, and all non-dominated solutions are ranked in order of merit to select the optimal compromise parameter scheme. Then, the optimal structural parameters are re-imported into the original multiphysics simulation model for electromagnetic, temperature field and vibration simulation verification, and the performance parameters before and after optimization are compared.

[0025] Preferably, the entropy weight-TOPSIS method includes the following steps: Construct the original decision matrix ,in Let be the number of non-dominated solutions in the Pareto solution set. To optimize the number of targets, Indicates the first The solution of the first... One target value; For each optimization objective, negative indicators are standardized: ; in, These are the standardized values; Calculate the first Under the first goal The proportion of each solution ,in Specific gravity; Calculate the first Information entropy of a target The normalization constant , For information entropy, This is the normalization constant; Calculate the first Entropy weight of each target ,in Entropy weight; Construct a weighted decision matrix ,in , For a weighted decision matrix, For elements of a weighted decision matrix; Determine the ideal solution and negative ideal solution ,in For the positive ideal solution, It is a negative ideal solution; Calculate the Euclidean distance between each solution and the positive and negative ideal solutions: ; ; in, For the first The Euclidean distance from each solution to the ideal solution. For the first The Euclidean distance from each solution to the negative ideal solution; Calculate relative fit ,in For the first The relative fit of each solution; Select The solution corresponding to the maximum value is taken as the optimal solution.

[0026] The beneficial effects of this invention are as follows: 1. To address the technical problems of large computational load and lengthy design cycle in the existing multi-parameter and multi-objective optimization process of iron-core reactors, which relies on repeated simulation iterations of finite element methods, this invention conducts parameter sensitivity analysis based on Pearson correlation coefficient, selects key design parameters that have a significant impact on each performance objective, reduces the dimensionality of optimization variables, and simplifies the solution complexity; at the same time, it constructs an FT-Transformer surrogate model to replace multi-physics finite element simulation calculations, which significantly improves the overall optimization design efficiency.

[0027] 2. The invention adopts the entropy weight-TOPSIS integrated decision-making method, which relies on the entropy weight method to automatically allocate weights according to the discrete characteristics of the target data, effectively eliminating the errors caused by manual subjective weighting; combined with the TOPSIS method to calculate the closeness between each Pareto non-dominated solution and the positive and negative ideal solutions, it realizes the objective quantitative selection of the optimal compromise solution, and greatly improves the reliability of multi-objective optimization results.

[0028] 3. This invention integrates multi-physics field coupled simulation, parameter sensitivity screening, neural network surrogate model, NSGA-II multi-objective optimization and objective comprehensive decision-making method to obtain the optimal combination of structural parameters of iron core reactor. It can coordinate and balance mass, loss, temperature rise and vibration performance, solve the defects of traditional single-objective optimization that is incomplete and has low simulation iteration efficiency, and comprehensively improve the overall performance and engineering practicality of reactor structural optimization design. Attached Figure Description

[0029] Figure 1This is an overall optimized flowchart of the present invention; Figure 2 The hysteresis loop and magnetostrictive property curves were measured experimentally. Figure 3 This is a three-dimensional model diagram of the iron core reactor in this invention; Figure 4 The results are simulations of the magnetic field of the iron-core reactor in this invention. Figure 5 The results are simulations of the temperature field of the iron core reactor in this invention. Figure 6 The simulation results of the vibration displacement of the iron core reactor in this invention; Figure 7 This is a diagram illustrating the optimized parameters of the iron core reactor in this invention. Figure 8 The results of sensitivity analysis of the structural parameters of the iron core reactor in this invention; Figure 9 This is the model architecture of the FT-Transformer in this invention; Figure 10 This refers to the proxy model constructed in this invention; Figure 11 This is the Pareto solution set graph of the non-dominated sorting genetic algorithm used in this invention. Detailed Implementation

[0030] Example 1: like Figure 1 As shown, a smart global multi-objective optimization method for iron-core reactors with electromagnetic-thermal multi-field coupling includes the following steps: Based on the electrical and structural parameters of the dry-type iron-core reactor, a three-dimensional geometric model of the iron-core reactor was established using finite element simulation software. A circuit-magnetic field simulation model of an iron-core reactor was established, and the electromagnetic field distribution characteristics of the reactor were obtained through simulation calculations. The loss distribution of each part of the iron core reactor is obtained by the circuit-magnetic field simulation results. Based on this, a two-way coupled simulation model of flow field and temperature field is established to obtain the temperature field simulation results of the iron core reactor. A coupled magnetic field-structural force field model of the iron-core reactor was established based on the circuit-magnetic field simulation results, and the vibration displacement of the reactor was obtained. By selecting the optimal parameters of the iron-core reactor, the optimal Latin hypercube experimental design and finite element simulation were combined to obtain the mass, loss, temperature and vibration results of the iron-core reactor under different parameters. The key optimization parameters were screened out through sensitivity analysis. Based on key parameters, an FT-Transformer agent model is constructed. A multi-objective optimization function is established in conjunction with this model. The NSGA-Ⅲ algorithm is used to solve the problem and output the Pareto optimal solution set. The entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set, determine the optimal solution for multi-objective joint optimization, and reset the optimized parameters into the model for verification.

[0031] like Figure 3 As shown, the three-dimensional geometric model further includes an iron core, an iron yoke, windings, and clamps; the following equivalent simplification scheme is adopted in the modeling: the laminated iron core is equivalent to a homogeneous integral magnetic conductor, and the internal lamination gaps are ignored; the multi-layer windings are modeled in a partitioned equivalent manner, the winding structure is unified and merged and the equivalent number of turns is configured; the mechanical clamping structure of the fastening screw is replaced by boundary fixed constraint conditions.

[0032] Furthermore, when establishing the circuit-magnetic field simulation model, the Epstein square test method was used to conduct magnetic property experiments on the silicon steel sheet material used in the reactor core, and the hysteresis parameters of the silicon steel sheet under different excitation conditions were obtained, which were used as the experimental basis for assigning the core material properties in the finite element simulation.

[0033] like Figure 2 As shown, preferably, the material properties of each component in the model are defined by combining the experimentally measured magnetic property curves of silicon steel sheets. A power frequency alternating current excitation is applied to the end of the coil, and the electromagnetic field control differential equation is numerically solved in the finite element magnetic field solution module. The electromagnetic field control differential equation is: ; in, For vector magnetic potential, The magnetic permeability of the material, For the electrical conductivity of the material, For time, This represents the winding excitation current density.

[0034] Furthermore, in step S2, when solving the magnetic field using the finite element method, local mesh refinement is applied to the air gap region of the iron core, and the mesh element size in the air gap region does not exceed half the element size of the other regions.

[0035] Preferably, the non-uniform losses of each component of the reactor are extracted as heat sources based on the circuit-magnetic field simulation results. A two-way coupled flow field-temperature field model is established, considering the dynamic characteristics of fluid properties changing with temperature. The overall temperature field distribution law of the reactor is obtained through iterative solution. The core loss consists of hysteresis loss, eddy current loss, and abnormal loss, which is calculated using the Steinmetz loss formula. ; in, Loss per unit volume For frequency, Peak magnetic flux density , , The Steinmetz coefficient; Reactor winding losses are calculated using the Joule heating formula: ; in, For winding losses, To excite the current, For winding resistance; Heat is transferred via convection on the surface of the reactor core, the surface of the windings, and the winding air passages, as shown below: ; in, For heat flux density, The convective heat transfer coefficient is... The wall temperature, The fluid temperature.

[0036] Furthermore, the Steinmetz coefficient , , The parameters were determined by analyzing the hysteresis loop experimental data of the iron-core silicon steel sheet material. The value range is 1.0 to 2.0. The value range is 1.5 to 3.0. The range of values ​​is .

[0037] Furthermore, loss data of key components such as the core, windings, and clamps are extracted, taking into account the non-uniformity of spatial distribution of losses caused by differences in electromagnetic structure, material properties, and uneven magnetic field distribution. This includes loss concentration caused by local magnetic saturation of the core, loss differences caused by skin effect and proximity effect of winding conductors, and discrete distribution characteristics of eddy current loss of clamps.

[0038] Furthermore, when establishing a two-way coupled simulation model of flow field and temperature field, the non-uniform loss distribution of each component is transmitted to the temperature field in real time as a heat source. At the same time, the characteristics of air fluid density, thermal conductivity, viscosity and other properties as a function of temperature, as well as the effect of temperature rise on the heat dissipation efficiency of the components are considered. Through the interaction and iterative solution of flow field and temperature field, the temperature distribution cloud map of each component is obtained.

[0039] Furthermore, the convergence criterion for the bidirectional coupled iterative solution of the flow field and temperature field is that the maximum relative change in the temperature field between two adjacent iterations is less than... .

[0040] Preferably, when establishing the magnetic field-structural force field coupling model, the magnetostrictive constitutive model of the iron core silicon steel sheet is embedded into the finite element simulation system, and the parameter values ​​are assigned by combining the material magnetostrictive characteristic equation; the iron core is subjected to force under the action of the magnetic field. By Maxwell and magnetostrictive force Composition, namely: ; The iron core vibrates under stress, which can be represented by the following equation in the structural field: ; in, For the iron core to bear the force, For Maxwell, It is magnetostrictive force. The mass matrix of the iron core, The damping coefficient of the iron core, The mechanical stiffness matrix of the iron core. The vibration displacement to be determined is denoted as .

[0041] Preferably, the coupling relationship between the core magnetic field and the structural field is expressed by the following equation: ; in, Here is the magnetic field stiffness matrix. For vector magnetic potential, For winding excitation current density, The mechanical stiffness matrix of the iron core. For vibration displacement, The iron core is subjected to force.

[0042] Furthermore, in the multiphysics coupled simulation of magnetic field and structural force field, the temperature field distribution results are used as the basis for correcting the mechanical properties of the insulating material. A correlation mapping between temperature and the mechanical properties of the insulating material is established to update the material properties of each region. The mechanical properties include the elastic modulus and the coefficient of thermal expansion. The correlation mapping between temperature and the mechanical properties of the insulating material is established based on the thermodynamic experimental data of the material, and the elastic modulus is constructed using linear interpolation or polynomial fitting methods. and coefficient of thermal expansion Regarding temperature The functional relationship.

[0043] Preferably, the core size and winding structure are selected as design variables. The optimal Latin hypercube experimental design method is used to uniformly sample each design variable. Simulation models of circuit-magnetic field, flow-temperature field, and magnetic field-structural force field are called to perform simulation calculations on each set of parameter samples. Data on reactor mass, loss, temperature, and vibration response under different combinations of structural parameters are obtained, and a sample database corresponding to design parameters and performance responses is established. The design variables include winding height. airway width Air gap height Width of the first layer winding Second layer winding width Third layer winding width Height of the iron yoke Discus height and core radius .

[0044] Preferably, based on the design parameter-performance response multidimensional simulation sample dataset, Pearson correlation coefficient is used for parameter sensitivity analysis: ; in, For the first One optimization parameter, For the first One optimization objective response value, To optimize the mean of the parameters, To optimize the mean of the target response, This represents the number of samples.

[0045] Furthermore, the key optimization parameters screened through sensitivity analysis include air passage width, air gap height, winding height, winding width of each layer, and yoke height.

[0046] Preferably, key design parameters are used as model inputs, and reactor mass, loss, temperature rise, and vibration displacement are selected as optimized output responses to construct an FT-Transformer surrogate model. This model completes the unified dimensional mapping of input parameters through feature word embedding, and relies on the multi-head self-attention mechanism of the Transformer encoder to mine the nonlinear coupling correlation and high-order interaction characteristics between key parameters. The AdamW optimizer is used to complete the iterative update of all model parameters, with the minimization of mean squared error as the training objective, and the goodness of fit is utilized. Error verification was conducted on the indicators.

[0047] Furthermore, the FT-Transformer proxy model has 2 to 4 encoder layers, 4 to 8 heads in the multi-head self-attention mechanism, and 32 to 128 feature embedding dimensions.

[0048] Furthermore, a multi-objective optimization function was established with mass, loss, temperature rise and vibration displacement as optimization objectives, and the inductance value variation was limited to no more than 5%. The non-dominated sorting genetic algorithm NSGA-Ⅲ was used to solve the optimization problem in combination with the FT-Transformer surrogate model. The population size was set to 12, the number of generations was 30 and the crossover probability was 0.9. After iterative calculation to the termination condition, the Pareto solution set was output.

[0049] Furthermore, the population size of the NSGA-Ⅲ algorithm ranges from 10 to 50, the number of generations ranges from 20 to 100, and the crossover probability ranges from 0.7 to 0.95.

[0050] Preferably, the entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set. Weights are automatically assigned according to the dispersion of each optimization objective data, and all non-dominated solutions are ranked in order of merit to select the optimal compromise parameter scheme. Then, the optimal structural parameters are re-imported into the original multiphysics simulation model for electromagnetic, temperature field and vibration simulation verification, and the performance parameters before and after optimization are compared.

[0051] Preferably, the entropy weight-TOPSIS method includes the following steps: Construct the original decision matrix ,in Let be the number of non-dominated solutions in the Pareto solution set. To optimize the number of targets, Indicates the first The solution of the first... One target value; For each optimization objective, negative indicators are standardized: ; in, These are the standardized values; Calculate the first Under the first goal The proportion of each solution ,in Specific gravity; Calculate the first Information entropy of a target The normalization constant , For information entropy, This is the normalization constant; Calculate the first Entropy weight of each target ,in Entropy weight; Construct a weighted decision matrix ,in , For a weighted decision matrix, For elements of a weighted decision matrix; Determine the ideal solution and negative ideal solution ,in For the positive ideal solution, It is a negative ideal solution; Calculate the Euclidean distance between each solution and the positive and negative ideal solutions: ; ; in, For the first The Euclidean distance from each solution to the ideal solution. For the first The Euclidean distance from each solution to the negative ideal solution; Calculate relative fit ,in For the first The relative fit of each solution; Select The solution corresponding to the maximum value is taken as the optimal solution.

[0052] Example 2: Using a dry-type iron-core reactor with a rated voltage of 10kV, a rated current of 1000A, and a rated capacity of 17.32Mvar as the implementation object, this reactor is used in the reactive power compensation system of a substation, and is required to simultaneously meet four indicators: lightweight, low loss, low temperature rise, and low vibration. A three-dimensional multiphysics coupled model of the reactor was constructed based on COMSOL Multiphysics 6.2 finite element simulation software. The hardware platform consisted of a workstation equipped with dual Intel Xeon Gold 6348 CPUs and 512GB of memory, and a single full-order multiphysics simulation took approximately 45 minutes.

[0053] Initial structural parameter settings: winding height mm, airway width mm, air gap height mm, width of the first layer winding mm, second layer winding width mm, third layer winding width mm, yoke height mm, discus height mm, core radius mm. The silicon steel sheet grade is B35A270, and the Steinmetz coefficient was measured using the Epstein square test method. , , .

[0054] Initial performance: The reactor has a total mass of 1268 kg and a total loss of 4515 W, including core loss of 825 W, winding loss of 3640 W, clamp loss of 50 W, winding hot spot temperature rise of 72.6℃, and core vibration displacement of 38.5 μm.

[0055] Optimized parameter settings: An initial sample of 120 groups was extracted using the optimal Latin hypercube design, and a parameter-performance sample library was constructed using multiphysics simulation. The FT-Transformer surrogate model has a 3-layer encoder, 6 attention heads, and 64 embedding dimensions, and was trained for 500 rounds using AdamW. The NSGA-Ⅲ population size is 12, the number of generations is 30, the crossover probability is 0.9, and the inductance constraint deviation does not exceed 5%.

[0056] Comparison method settings: Comparison Method 1: A second-order response surface is used as a surrogate model, and the NSGA-II algorithm is used to solve it. The population size is 12, the number of generations is 30, the crossover probability is 0.9, and the other conditions are the same.

[0057] Comparison Method 2: The optimization is based solely on the electromagnetic field simulation results, without introducing temperature field and structural force field coupling. The surrogate model and optimization algorithm parameters are the same as those in this method. Specific data are shown in Tables 1 and 2 below.

[0058] Table 1: Comparison of structural parameters and performance before and after optimization using this method;

[0059] Table 2: Comparison of performance improvement magnitudes of different optimization methods;

[0060] As shown in Table 1, after optimization using this method, the reactor mass decreased from 1268 kg to 1195 kg, the total loss decreased from 4515 W to 4075 W, the winding hot spot temperature rise decreased from 72.6℃ to 64.3℃, and the core vibration displacement decreased from 38.5 μm to 31.1 μm. All four indicators showed significant improvement. Among them, the improvement in vibration displacement was the most prominent. This is because this method introduces a magnetostrictive constitutive model into the magnetic field-structural force field coupling model, and at the same time corrects the insulation material properties with the temperature field, which greatly improves the accuracy of the structural force field solution. Consequently, the accuracy and optimization range of vibration optimization are superior to traditional methods.

[0061] As shown in Table 2, our proposed method outperforms both the RSM+NSGA-II and single-physics optimization methods in terms of overall improvement across all four performance indicators. The RSM+NSGA-II method achieves lower optimization rates for loss (7.5%), temperature rise (8.3%), and vibration (12.6%) compared to our proposed method. This is primarily because the second-order response surface model has limited accuracy in fitting the strong nonlinear coupling relationships between multiple physics fields, leading to accumulated prediction biases in the surrogate model during the optimization process. While the single-physics optimization method achieves a similar 6.2% improvement in mass as our proposed method, its improvements in temperature rise and vibration are only 2.8% and 3.5%, respectively, significantly lower. This indicates that neglecting the multi-physics coupling effect severely limits the optimization space for the temperature field and structural force field related performance. Furthermore, the Pareto solution efficiency rate of this method is 91.7%, which is significantly higher than that of RSM+NSGA-Ⅱ (75.0%) and single-physics optimization (66.7%). This indicates that the Pareto front solution set generated by this method has better diversity and convergence, providing decision-makers with a richer set of effective candidate solutions.

[0062] like Figure 4 As shown in the figure, the magnetic flux density is highest in the core column region, with its peak value occurring inside the central section of the core column. The yoke region shows the next highest magnetic flux density, while the winding region exhibits a significant decrease. A noticeable edge flux diffusion effect is observed near the air gap, with the magnetic field partially entering the winding end space from the core column through the air gap. These simulation results verify the correctness of the established circuit-magnetic field coupling model, confirming that the maximum magnetic flux density of the core is below the material saturation threshold, thus providing accurate electromagnetic load input for subsequent loss calculations and structural force field analysis.

[0063] like Figure 5 As shown, the winding region is the highest temperature area, with the hot spot located in the upper middle part of the winding. This location has the worst heat dissipation conditions and is closest to the core heat source. The core temperature is the next highest because the core loss density is much lower than the winding loss density and the core surface has a larger heat dissipation area. Air rises from the winding duct due to heating, creating natural convection, and the duct wall temperature gradually increases along the height. This result reflects the accuracy of the two-way coupled flow-temperature field simulation and verifies that the established temperature-fluid property feedback mechanism can effectively capture the true location and temperature rise of the hot spot.

[0064] Figure 6 The figure shows the simulation results of the vibration displacement of the iron-core reactor in this invention. It can be seen that the vibration displacement amplitude of the iron core column is the largest, followed by the iron yoke, while the winding vibration displacement is relatively small. The iron core vibration is dominated by the fundamental frequency of 100Hz, and the displacement distribution exhibits a characteristic of being larger in the middle and smaller at both ends along the height of the iron core column, which is consistent with the fixed-support boundary conditions of the iron core structure. This result verifies the vibration prediction capability of the magnetic field-structural force field coupling model combined with the magnetostrictive constitutive model, providing a benchmark reference for vibration control in subsequent multi-objective optimization.

[0065] Figure 7 This is a diagram illustrating the optimized parameters of the core reactor in this invention. Based on a schematic diagram of the core reactor's geometry, it marks the key optimized parameters identified through sensitivity analysis and their locations: winding height. airway width Air gap height Width of the first layer winding Second layer winding width Third layer winding width Height of the iron yoke Discus height and core radius The spatial location of each parameter is clearly marked in the figure, providing an intuitive geometric correspondence for determining the parameter value range and interpreting the optimization results in the experimental design.

[0066] Figure 8 This paper presents a bar chart showing the sensitivity of each structural parameter, calculated using the Pearson correlation coefficient after optimal Latin hypercube sampling and multiphysics simulation, to four performance indicators: reactor mass, losses, temperature rise, and vibration displacement. The chart clearly reflects the primary and secondary influence relationships of each parameter: air passage width... It has a strong negative impact on temperature rise, air gap height It has the highest sensitivity to vibration displacement, and the winding height is... Its contribution to quality and loss is most significant. This result provides a quantitative basis for screening out five key optimization parameters from nine initial variables.

[0067] like Figure 9 and Figure 10 The diagram shows the architecture of the FT-Transformer proxy model and the constructed proxy model in this invention. Figure 9 The complete network structure of FT-Transformer is presented, which includes three main components: a feature segmentation embedding layer, a multi-layer Transformer encoder, and an output regression layer. The input multi-dimensional optimization parameters are mapped into a sequence of embedding vectors of uniform dimension through feature segmentation embedding. After the high-order interaction and nonlinear coupling relationship between the parameters are modeled by the self-attention mechanism of the multi-layer encoder, the output layer maps them to four performance prediction values: mass, loss, temperature rise, and vibration displacement. Figure 10 This shows a regression scatter plot of the surrogate model's predicted values ​​on the test set versus the actual values ​​from the finite element simulation. The scatter points are closely distributed along the diagonal. Nearby, goodness of fit The value reached 0.975, verifying that the FT-Transformer surrogate model has high accuracy and good generalization ability in multiphysics performance prediction.

[0068] Figure 11 This is a Pareto solution set obtained using the non-dominated sorting genetic algorithm NSGA-Ⅲ in this invention. The figure, presented as a three-dimensional scatter plot, illustrates the distribution of non-dominated solutions in the four objective spaces of mass, loss, temperature rise, and vibration displacement, under the condition that the inductance constraint deviation does not exceed 5%. The solution points in the figure form a clear three-dimensional Pareto front surface. There are no dominance relationships between solutions on the front surface, reflecting the mutual constraints among the four optimization objectives of mass, loss, temperature rise, and vibration. The optimal compromise solution determined by the entropy-weighted TOPSIS method is highlighted in the figure; this solution achieves the best balance among multiple objectives.

Claims

1. A smart global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal-field coupling, characterized in that, Includes the following steps: Based on the electrical and structural parameters of the dry-type iron-core reactor, a three-dimensional geometric model of the iron-core reactor was established using finite element simulation software. A circuit-magnetic field simulation model of an iron-core reactor was established, and the electromagnetic field distribution characteristics of the reactor were obtained through simulation calculations. The loss distribution of each part of the iron core reactor is obtained by the circuit-magnetic field simulation results. Based on this, a two-way coupled simulation model of flow field and temperature field is established to obtain the temperature field simulation results of the iron core reactor. A coupled magnetic field-structural force field model of the iron-core reactor was established based on the circuit-magnetic field simulation results, and the vibration displacement of the reactor was obtained. By selecting the optimal parameters of the iron-core reactor, the optimal Latin hypercube experimental design and finite element simulation were combined to obtain the mass, loss, temperature and vibration results of the iron-core reactor under different parameters. The key optimization parameters were screened out through sensitivity analysis. Based on key parameters, an FT-Transformer agent model is constructed. A multi-objective optimization function is established in conjunction with this model. The NSGA-Ⅲ algorithm is used to solve the problem and output the Pareto optimal solution set. The entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set, determine the optimal solution for multi-objective joint optimization, and reset the optimized parameters into the model for verification.

2. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, Based on the experimentally measured magnetic property curves of silicon steel sheets, the material properties of each component in the model are defined. A power frequency alternating current excitation is applied to the coil end. The electromagnetic field control differential equation is numerically solved within the finite element magnetic field solution module. The electromagnetic field control differential equation is as follows: ； in, For vector magnetic potential, The magnetic permeability of the material, For the electrical conductivity of the material, For time, This represents the winding excitation current density.

3. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, Based on the circuit-magnetic field simulation results, the non-uniform losses of each component of the reactor are extracted as heat sources. A two-way coupled flow field-temperature field model is established, considering the dynamic characteristics of fluid properties changing with temperature. The overall temperature field distribution law of the reactor is obtained through iterative solution. The core loss consists of hysteresis loss, eddy current loss, and abnormal loss, which is calculated using the Steinmetz loss formula. ； in, Loss per unit volume For frequency, Peak magnetic flux density , , The Steinmetz coefficient; Reactor winding losses are calculated using the Joule heating formula: ； in, For winding losses, To excite the current, For winding resistance; Heat is transferred via convection on the surface of the reactor core, the surface of the windings, and the winding air passages, as shown below: ； in, For heat flux density, The convective heat transfer coefficient is... The wall temperature, The fluid temperature.

4. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, When establishing the magnetic field-structural force field coupling model, the magnetostrictive constitutive model of the iron core silicon steel sheet is embedded into the finite element simulation system, and the parameter values ​​are assigned by combining the material magnetostrictive characteristic equation; the iron core is subjected to force under the action of the magnetic field. By Maxwell and magnetostrictive force Composition, namely: ； The iron core vibrates under stress, which can be represented by the following equation in the structural field: ； in, For the iron core to bear the force, For Maxwell, It is magnetostrictive force. The mass matrix of the iron core, The damping coefficient of the iron core, The mechanical stiffness matrix of the iron core. The vibration displacement to be determined is denoted as .

5. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 4, characterized in that, The coupling relationship between the core magnetic field and the structure field is expressed by the following equation: ； in, Here is the magnetic field stiffness matrix. For vector magnetic potential, For winding excitation current density, The mechanical stiffness matrix of the iron core. For vibration displacement, The iron core is subjected to force.

6. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, Core dimensions and winding structure were selected as design variables. The optimal Latin hypercube experimental design method was used to uniformly sample each design variable. Simulation models of circuit-magnetic field, flow-temperature field, and magnetic field-structural force field were called to perform simulation calculations on each set of parameter samples. Data on reactor mass, losses, temperature, and vibration response under different combinations of structural parameters were obtained, and a sample database corresponding to design parameters and performance responses was established. The design variables include winding height. airway width Air gap height First layer winding width Second layer winding width Third layer winding width Height of the iron yoke Discus height and core radius .

7. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 6, characterized in that, Based on the multidimensional simulation sample dataset of design parameters and performance response, parameter sensitivity analysis was performed using the Pearson correlation coefficient: ； in, For the first One optimization parameter, For the first One optimization objective response value, To optimize the mean of the parameters, To optimize the mean of the target response, This represents the number of samples.

8. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, Using key design parameters as model inputs, and selecting reactor mass, loss, temperature rise, and vibration displacement as optimized output responses, an FT-Transformer surrogate model is constructed. This model achieves unified dimensional mapping of input parameters through feature word segmentation embedding, and leverages the multi-head self-attention mechanism of the Transformer encoder to mine the nonlinear coupling correlation and high-order interaction characteristics between key parameters. The AdamW optimizer is used to complete the iterative update of all model parameters, with minimizing the mean squared error as the training objective, and goodness-of-fit is utilized. Error verification was conducted on the indicators.

9. The intelligent global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling as described in claim 1, characterized in that, The entropy-weighted TOPSIS method is introduced to make comprehensive decisions on the Pareto solution set. Weights are automatically assigned according to the dispersion of each optimization objective data, and all non-dominated solutions are ranked in order of merit to select the optimal compromise parameter scheme. Then, the optimal structural parameters are re-imported into the original multiphysics simulation model for electromagnetic, temperature field and vibration simulation verification, and the performance parameters before and after optimization are compared.

10. A smart global multi-objective optimization method for iron-core reactors oriented towards electromagnetic-thermal multi-field coupling, as described in claim 9, is characterized in that... The entropy weight-TOPSIS method includes the following steps: Construct the original decision matrix ,in Let be the number of non-dominated solutions in the Pareto solution set. To optimize the number of targets, Indicates the first The solution of the first... One target value; For each optimization objective, negative indicators are standardized: ； in, These are the standardized values; Calculate the first Under the first goal The proportion of each solution ,in Specific gravity; Calculate the first Information entropy of a target The normalization constant is , , For information entropy, This is the normalization constant; Calculate the first Entropy weight of a target ,in Entropy weight; Construct a weighted decision matrix ,in , For a weighted decision matrix, For elements of a weighted decision matrix; Determine the ideal solution and negative ideal solution ,in For the positive ideal solution, It is a negative ideal solution; Calculate the Euclidean distance between each solution and the positive and negative ideal solutions: ； ； in, For the first The Euclidean distance from each solution to the ideal solution. For the first The Euclidean distance from each solution to the negative ideal solution; Calculate relative fit ,in For the first The relative fit of each solution; Select The solution corresponding to the maximum value is taken as the optimal solution.

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