Method and device for simulating hysteresis loop of soft magnetic material

Abstract

The application discloses a hysteresis loop simulation method and device of a soft magnetic material, and the method comprises the following steps: determining various to-be-optimized parameters of the soft magnetic material through a target hysteresis model, wherein the to-be-optimized parameters meet a preset value interval according to material data of the soft magnetic material; sampling the various to-be-optimized parameters at least twice, and obtaining an initial data set each time; constructing a target function according to a magnetic field intensity prediction value and a magnetic field intensity measured value; iteratively processing the to-be-optimized parameters of different dimensions in the initial data set, and obtaining individual optimal values and global optimal values of the output minimum of the target function; and substituting the global optimal values into the target hysteresis model to generate a hysteresis loop of the soft magnetic material under a corresponding working condition. The application effectively decouples the strong coupling relationship of the parameters through collaborative iteration, avoids local optimization, supports various hysteresis models, adapts to simulation requirements in multiple scenes, and has high parameter extraction precision and strong universality.

Description

Technical Field

[0001] This application relates to the technical field, and in particular to a method and apparatus for simulating the hysteresis loop of soft magnetic materials. Background Technology

[0002] As core materials for electrical equipment such as motors and transformers, soft magnetic materials have a direct and crucial impact on the magnetic field distribution, excitation current response, and iron loss characteristics of electromagnetic devices due to their hysteresis properties. Therefore, constructing an accurate hysteresis model is a core prerequisite for achieving quantitative evaluation of the high-performance electromagnetic design and operating characteristics of electrical equipment.

[0003] Among numerous hysteresis models, hysteresis models are inherently characterized by a large number of parameters and strong coupling between them. The accuracy and efficiency of parameter extraction directly determine the reliability of the model simulation results. Existing techniques for hysteresis model parameter extraction mainly fall into two categories: one is based on direct calculation using traditional formulas. This method requires solving complex transcendental equations or relying on empirical approximation formulas to estimate parameters, failing to effectively decouple the strong correlations between parameters. The accumulation of numerical solution errors and approximation calculation errors easily leads to insufficient accuracy of the extracted model parameters, making it difficult to meet the actual needs of high-precision electromagnetic simulation and equipment design. The other category is based on fitting methods using a single optimization algorithm (such as simulated annealing and particle swarm optimization). These methods are prone to getting trapped in local optima or cannot adapt to complex multi-peak solution domains, limiting the accuracy and stability of parameter extraction under complex conditions such as unsaturation and DC bias. Summary of the Invention

[0004] This application provides a method and apparatus for simulating the hysteresis loop of soft magnetic materials, in order to solve the technical problems of insufficient parameter extraction accuracy, low convergence efficiency, easy getting trapped in local optima, and poor adaptability to operating conditions in existing hysteresis models.

[0005] To achieve the above objectives, this application adopts the following technical solution: In a first aspect, this application provides a method for simulating the hysteresis loop of soft magnetic materials, including: The various parameters to be optimized for the soft magnetic material are determined by the target hysteresis model. The parameters to be optimized are based on the material data of the soft magnetic material and meet the preset value range. Each parameter to be optimized is sampled at least twice, and each sampling yields an initial dataset. The initial dataset of each sampling is input into the target hysteresis model to obtain the corresponding predicted magnetic field strength. Based on the hysteresis properties of the soft magnetic material, the measured magnetic field strength of the soft magnetic material is determined. The objective function is constructed based on the predicted magnetic field strength and the measured magnetic field strength. The optimization parameters of different dimensions in the initial dataset are iterated, and different optimization parameters are extracted from different initial datasets to form learning vectors. The learning vectors are subtracted from the optimization parameters in a set of initial datasets one by one to obtain the dimension bias vector. The current iteration speed of the objective function is determined based on the dimension bias vector, and the current iteration speed is superimposed with the set of initial datasets to obtain the iterated target dataset. The target dataset and the initial dataset are input into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized. Substituting the global optimum into the target hysteresis model generates the hysteresis loop of the soft magnetic material under the corresponding working conditions.

[0006] Furthermore, the current iteration rate of the objective function is determined based on the dimensionality deviation vector. The formula for the current iteration rate is as follows: ; In the formula: Let be the inertia weight for the t-th iteration; For the target dataset i The velocity in the t-th iteration; C r The learning factor is a constant. For the target dataset i The learning vector; For the target dataset i The optimal value for an individual in the t-th iteration.

[0007] Furthermore, the inertia weight decreases linearly from the preset maximum inertia weight to the preset minimum inertia weight with the number of iterations.

[0008] Furthermore, by inputting the target dataset and the initial dataset into the objective function, the individual optimal value and the global optimal value are obtained when the output of the objective function is minimized, including: By inputting the target dataset and the initial dataset into the objective function, the initial individual optimal value and the initial global optimal value are obtained when the output of the objective function is minimized. Cluster analysis was performed on all the initial individual optimal values ​​to obtain each cluster category and its corresponding cluster center; A cluster center is weighted and merged with any cluster center that is different from it to obtain the candidate data value corresponding to the cluster center. The optimal difference is obtained by subtracting the optimal values ​​of any two different initial individuals. Each optimal difference is scaled to obtain a scaled difference. The candidate data value is superimposed with at least one scaled difference to obtain the variant data value corresponding to the cluster center. The parameters to be optimized in the initial individual optimal value are cross-dimensionally compared with the parameters to be optimized in the corresponding mutated data values ​​to obtain the cross-data values; Input the cross-data values ​​and the initial individual optimal values ​​into the objective function to obtain the individual optimal value when the output of the objective function is minimized. Then, determine the global optimal value with the smallest output of the objective function from all individual optimal values.

[0009] Furthermore, before performing cluster analysis on the optimal values ​​of all initial individuals to obtain each cluster category and its corresponding cluster center, the following steps are also included: Determine whether the value of each parameter to be optimized in the initial individual optimal value exceeds the corresponding value range. If it does, adjust the value of the parameter to be optimized in the initial individual optimal value to the boundary value of the value range.

[0010] Furthermore, the parameters to be optimized in the initial individual optimal values ​​are cross-referenced with the parameters to be optimized in the corresponding mutated data values ​​to obtain cross-referenced data values, including: Set crossover probability constraints, including a first constraint and a second constraint. The first constraint is that the random number is less than a preset crossover probability value, and the random number is less than 0. The value of 1 is generated within its range; the second constraint is that the dimension of the parameter to be optimized during the dimension cross is consistent with the random dimension, and the random dimension is selected from the dimension of the parameter to be optimized in the initial individual optimal value; Sequentially determine whether each parameter to be optimized in the initial individual optimal value satisfies the first constraint or the second constraint. If it does, update the corresponding parameter to be optimized in the initial individual optimal value to the parameter to be optimized corresponding to the mutated data value; otherwise, leave the corresponding parameter to be optimized in the initial individual optimal value unchanged. Update all parameters to be optimized in the initial individual optimal values ​​to obtain cross data values.

[0011] Furthermore, the parameters to be optimized include at least one of the following: demagnetization factor, adaptive geometry of magnetic domains or grains, proportional constant related to saturated magnetic field, material anisotropy related constant, and pinning point density related constant.

[0012] Secondly, this application also provides a hysteresis loop simulation device for soft magnetic materials, comprising: The sampling module is used to determine various parameters to be optimized for the soft magnetic material through the target hysteresis model. The parameters to be optimized meet the preset value range based on the material data of the soft magnetic material. The processing module is used to sample each parameter to be optimized at least twice, with each sampling yielding an initial dataset. The initial dataset from each sampling is input into the target hysteresis model to obtain the corresponding predicted magnetic field strength. Based on the hysteresis properties of the soft magnetic material, the measured magnetic field strength of the soft magnetic material is determined. An objective function is constructed based on the predicted and measured magnetic field strength values. The module iterates over the parameters to be optimized in different dimensions of the initial dataset, extracting different parameters from each initial dataset to form a learning vector. The learning vector is subtracted step-by-step from the parameters to be optimized in the initial dataset to obtain a dimension bias vector. The current iteration speed of the objective function is determined based on the dimension bias vector, and the current iteration speed is superimposed on the initial dataset to obtain the iterated target dataset. The target dataset and the initial dataset are input into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized. The execution module is used to substitute the global optimal value into the target hysteresis model to generate the hysteresis loop of the soft magnetic material under the corresponding working conditions.

[0013] Thirdly, this application also provides an electronic device, including at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the program is executed by the processing unit, the processing unit performs the above-mentioned hysteresis loop simulation method for soft magnetic materials.

[0014] Fourthly, this application also provides a readable storage medium storing a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the aforementioned hysteresis loop simulation method for soft magnetic materials.

[0015] This application effectively decouples the strong coupling relationship between the parameters of the target hysteresis model through an iterative mechanism of learning vector construction, dimension deviation vector generation, and dynamic updating of velocity vector, avoiding the defect of traditional single optimization algorithms being prone to getting trapped in local optima; the construction of the objective function solves the problem of insufficient parameter accuracy caused by error accumulation in the direct calculation method; the target hysteresis model supports multiple hysteresis models such as the Energetic hysteresis model, the Preisach hysteresis model, and the Jiles–Atherton hysteresis model, solving the problems of poor versatility and limited adaptability of existing methods, and meeting the needs of hysteresis loop simulation in multiple scenarios. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the hysteresis loop simulation method for soft magnetic materials provided in this application; Figure 2 A flowchart illustrating the global optimal parameter vector in the hysteresis loop simulation method for soft magnetic materials provided in this application; Figure 3A schematic diagram of the experimental testing platform for the soft magnetic material nanocrystal 1K107 provided in this application; Figure 4 A schematic diagram of the hysteresis model measurement results at different Bm / Bs values ​​provided in this application; Figure 5 A schematic diagram comparing the hysteresis loops calculated by the five optimization algorithms provided in this application with experimentally measured loops of different Bm / Bs. Figure 6 A schematic diagram comparing the objective function values ​​of five optimization algorithms for simulating hysteresis loops under different Bm / Bs conditions provided in this application; Figure 7 A schematic diagram comparing the model prediction accuracy of five optimization algorithms for simulating hysteresis loops under different Bm / Bs ratios provided in this application; Figure 8 A schematic diagram comparing the solution diversity of five optimization algorithms for simulating hysteresis loops under different Bm / Bs conditions provided in this application; Figure 9 A schematic diagram comparing the relative errors of five key parameters of the hysteresis loop simulated by five optimization algorithms under different Bm / Bs conditions provided in this application; Figure 10 A schematic diagram showing the measurement results of the hysteresis model under different DC bias voltages provided in this application; Figure 11 A schematic diagram comparing the hysteresis loops calculated by the five optimization algorithms provided in this application with the experimentally measured loops under different DC bias voltages; Figure 12 A schematic diagram comparing the objective function values ​​of five optimization algorithms for simulating hysteresis loops under different DC bias voltages provided in this application; Figure 13 A schematic diagram comparing the model prediction accuracy of five optimized algorithms for simulating hysteresis loops under different DC bias voltages provided in this application; Figure 14 A schematic diagram comparing the solution diversity of five optimized algorithms for simulating hysteresis loops under different DC bias voltages provided in this application; Figure 15 A schematic diagram comparing the relative errors of five key parameters of the hysteresis loop simulated by five optimized algorithms under different DC bias voltages provided in this application; Figure 16 A schematic diagram of the framework of the hysteresis loop simulation device provided in this application; Figure 17 A schematic diagram of the communication framework of the electronic device provided in this application. Detailed Implementation

[0017] The present application will be described in detail below with reference to the specific embodiments shown in the accompanying drawings. However, these embodiments do not limit the present application. Any structural, methodological, or functional modifications made by those skilled in the art based on these embodiments are included within the protection scope of the present application.

[0018] It should be noted that the terms "first," "second," and similar terms used in this application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "a" or "one," etc., do not indicate a quantity limitation, but rather indicate the presence of at least one. "A plurality" or "several" indicates at least two, unless otherwise specified. Terms such as "front and back," "left and right," "up and down," etc., are for ease of explanation only and are not limited to a single location or spatial orientation. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0019] like Figure 1 As shown, this application provides a method for simulating the hysteresis loop of soft magnetic materials. The method for simulating the hysteresis loop of soft magnetic materials includes the following steps: S101: Determine the various parameters to be optimized for the soft magnetic material through the target hysteresis model. The parameters to be optimized meet the preset value range based on the material data of the soft magnetic material. As one approach, the target hysteresis model can be the Energetic hysteresis model, the Preisach hysteresis model, the Jiles–Atherton hysteresis model, or other hysteresis models with well-defined physical foundations. Based on the mathematical expression corresponding to each target hysteresis model, parameters are screened and analyzed to determine the parameters to be optimized for the soft magnetic material.

[0020] For example, the target hysteresis model is the Energetic hysteresis model, and its mathematical expression can be as follows: ; in, H , H d , H r and H i These are magnetic field strength, magnetic field strength before demagnetization, reversible magnetic field strength, and irreversible magnetic field strength, respectively. m Magnetization M With saturation magnetization M s The ratio of the two, i.e., the relative magnetization; m 0 corresponds to the previous magnetic field reversal point value; Nε It is the demagnetizing factor; k This is the hysteresis loss coefficient; μ 0 represents the permeability of free space; C R Adaptive geometry for magnetic domains or grains; q An adaptive constant related to the pinning point density; κ This is the reversal function, representing the influence of the total magnetization state on the magnetic field reversal point; h This is a proportionality constant related to the saturation magnetic field; g This is an adaptive constant related to the anisotropy of the material. H d , These are used to describe the linear and nonlinear characteristics of materials, respectively. Used to express hysteresis characteristics, such as residual magnetic flux density, coercivity, and hysteresis loss in the quasi-static condition.

[0021] According to the inversion function κ The update rule for the magnetization curve of the Energetic hysteresis model is shown in the following formula: ; When using this Energetic hysteresis model to solve for the hysteresis loop, the starting point of the hysteresis loop is located at the origin of the initial magnetization curve. m 0 corresponds to the previous magnetic field reversal point value, initial m The value of 0 is zero. κ 0 corresponds to the previous magnetic field reversal point κ value, initial κ 0 has a value of 1.

[0022] Furthermore, the saturation magnetization of the Energetic hysteresis model M s This can be determined by measuring the vertex of the limiting hysteresis loop. Below the limiting hysteresis loop, the hysteresis loss energy per unit volume is equal to the area of ​​the hysteresis loop. W h For soft magnetic materials, the limiting hysteresis loop is approximately a symmetrical rectangular loop, and the formula for calculating the area of ​​the hysteresis loop is as follows: ; In the formula: μ 0 represents the permeability of free space; M s The saturation magnetization; H c Coercivity, in physical terms, is the strength of the reverse magnetic field required to bring the magnetization back to zero. It directly determines the width of the hysteresis loop. The smaller the coercivity, the lower the hysteresis loss of the material and the better its soft magnetic properties.

[0023] Irreversible magnetic field energy density and parameters of the Energetic hysteresis model k Directly related, and since the hysteresis loss energy of the limiting hysteresis loop is equivalent to the integral result of the irreversible energy density, the following derivation is obtained: ; As can be seen from the above derivation, some parameters of soft magnetic materials in the mathematical expression of the Energetic hysteresis model can be obtained by testing or deducing the magnetization curve of the Energetic hysteresis model. The parameters of soft magnetic materials that cannot be obtained by testing or deducing the magnetization curve of the Energetic hysteresis model are the parameters to be optimized. These parameters to be optimized include the demagnetization factor, the adaptive geometric size of magnetic domains or grains, the proportional constant related to the saturation magnetic field, the material anisotropy-related constant, and the pinning point density-related constant.

[0024] Furthermore, the material data of soft magnetic materials includes inherent properties, microstructure, and experimental test data. The inherent properties of soft magnetic materials refer to the inherent characteristics of the material itself that do not change significantly with external working conditions. The microstructure of soft magnetic materials refers to the internal structural morphology of the material at the micrometer to nanometer scale, which is the core factor determining its magnetic performance. Inherent properties, microstructure, and experimental test data can all be obtained by consulting material handbooks, technical specifications, academic papers, and other texts.

[0025] For example, taking the parameters to be optimized in the Energetic hysteresis model as an example, and combining the specific material data of the soft magnetic material, the steps for preset value ranges are as follows: Considering the inherent magnetic circuit characteristics of soft magnetic materials, the absolute physical limit of the demagnetization factor is 10. 6 10 1 If the soft magnetic material is a toroidal core, such as a 1K107B nanocrystalline core, based on the geometric parameters of the core's microstructure (inner diameter 40mm, outer diameter 70mm, cross-sectional area 2.81cm²), the theoretical range of the demagnetization factor for this geometric structure, calculated using the magnetic circuit calculation formula, is approximately 10. 3 10 2 Preliminary experiments were conducted on the 1K107B nanocrystalline magnetic core. The measured approximate value of the demagnetization factor, obtained through hysteresis loop fitting, was 5 × 10⁻⁶. 3 A review of relevant literature on nanocrystalline toroidal magnetic cores revealed that the demagnetization factor values ​​are concentrated around 10. 4 5×10 2Substituting the aforementioned value range into the Energetic hysteresis model, a hysteresis loop was simulated to verify whether the output of the Energetic hysteresis model conforms to the basic characteristics of soft magnetic materials, such as saturation flux density, coercivity, and hysteresis loss, and whether the deviations from the measured values ​​are within acceptable ranges. Simulations were performed for multiple operating conditions to ensure that the demagnetizing factor parameters within the range can adapt to changes in operating conditions without distortion. Finally, the value range was set to 10. 6 10 1 .

[0026] The adaptive geometry of magnetic domains or grains is positively correlated with the domain size and grain size of soft magnetic materials. The physical limit of grain size for nanocrystalline soft magnetic materials is 0.01–0.1 μm. In the Energetic hysteresis model, the adaptive geometry of magnetic domains or grains must match the material's microstructure; it cannot be less than the domain wall thickness (approximately 0.01 μm) or greater than the upper limit of grain size (0.1 μm). Microstructural observation of the 1K107B nanocrystalline magnetic core using transmission electron microscopy revealed a grain size of 0.03–0.08 μm, corresponding to an adaptive geometry of approximately 0.03–0.07 μm for the domains or grains. A literature search of Energetic hysteresis model parameters for nanocrystalline materials showed fitted values ​​for the adaptive geometry of magnetic domains or grains ranging from 0.02 to 0.09 μm. With the microscopic observation value of 0.03~0.07μm as the core range, combined with the physical limit of 0.01~0.1μm and the literature value of 0.02~0.09μm, the value range is set to 0.01~0.1μm, which not only covers the actual microscopic size, but also reserves search space for optimization algorithms.

[0027] The proportionality constant related to the saturation magnetic field is positively correlated with the saturation magnetic field strength of the material, controlling the nonlinearity of reversible magnetization. Considering the typical range of saturation magnetic field strength for soft magnetic materials (10–100 kA / m), the theoretical proportionality constant is derived to be 0.1–1.0. If the saturation magnetic field strength is below 10 kA / m, and the proportionality constant is less than 0.1, the reversible magnetization part of the Energetic hysteresis model shows almost no nonlinear change, which does not match the actual characteristics of soft magnetic materials. If the saturation magnetic field strength is above 100 kA / m, and the proportionality constant is greater than 1.0, the Energetic hysteresis model exhibits excessive nonlinearity, leading to hysteresis loop distortion. Saturation magnetization tests were performed on a 1K107B magnetic core, and the measured saturation magnetic field strength was approximately 30 kA / m. Substituting this into the proportional relationship of the Energetic hysteresis model, the approximate value of the proportionality constant related to the saturation magnetic field was found to be 0.3. A review of literature on model parameters for similar soft magnetic materials revealed that the fitted values ​​of the proportionality constant related to the saturation magnetic field range from 0.2 to 0.8. Combining theoretical proportional range, experimental predictions, and literature values, the value range was set to 0.1~1.0 to ensure coverage of the variation range of the proportional constant related to the saturated magnetic field under different saturation conditions.

[0028] The anisotropy-related constants of materials are based on the physical nature of magnetic anisotropy. Soft magnetic materials exhibit weak magnetic anisotropy, and their typical range for anisotropy constants is 10³. Based on the mapping relationship between the material anisotropy correlation constant and the physical anisotropy constant in the Energetic hysteresis model, the theoretical range of the material anisotropy correlation constant is derived to be 10~50. If the material anisotropy correlation constant is less than 10, the Energetic hysteresis model cannot reflect the influence of magnetic anisotropy on hysteresis characteristics; if the material anisotropy correlation constant is greater than 50, the Energetic hysteresis model will exhibit strong anisotropy, which contradicts the core characteristic of low anisotropy of soft magnetic materials. The magnetic anisotropy of a 1K107B magnetic core was measured using a vibrating sample magnetometer, and the physical anisotropy constant was calculated to be approximately 3×10⁴ J / m³. Substituting this into the mapping relationship of the Energetic hysteresis model, the approximate value of the material anisotropy correlation constant is 30. A search of relevant research on nanocrystalline soft magnetic materials revealed that the fitted values ​​of the material anisotropy correlation constant are between 20 and 40. The final range was determined based on theoretical range, experimental predictions, and literature values. The range was set to 10~50, which not only conforms to the low anisotropy of soft magnetic materials, but also covers the anisotropic fluctuations caused by different preparation processes.

[0029] The pinning density correlation constant is determined based on the physical nature of pinning points. Soft magnetic materials control pinning density to reduce hysteresis loss, with a typical range corresponding to the theoretical limit of 20-50 in the Energetic hysteresis model. If the pinning density correlation constant is less than 20, the coercivity and remanence of the hysteresis loop will be lower than the actual material properties. If the pinning density correlation constant is greater than 50, the pinning effect is too strong, and the coercivity and remanence will exceed the normal range of soft magnetic materials. Through hysteresis loop fitting, the coercivity of the 1K107B core is approximately 20 A / m. Substituting this into the correlation formula between the pinning density correlation constant and coercivity in the Energetic hysteresis model, an approximate value of 35 is calculated for the pinning density correlation constant. A review of model parameters for similar materials in the literature reveals that the fitted value of the pinning density correlation constant is between 30 and 45. Combining the theoretical limit, experimental predictions, and literature values, a value range of 20-50 is set to ensure coverage of pinning density variations under DC bias conditions.

[0030] As discussed above, the parameters to be optimized in the Energetic hysteresis model can be set to a fixed value under certain specific scenarios through theoretical limits, experimental predictions, or literature values. For example, for a soft magnetic material like the 1K107B core, the saturation magnetic field related proportionality constant can be set to 0.3. Therefore, this saturation magnetic field related proportionality constant does not require iterative optimization. Thus, the parameters to be optimized through iterative optimization can be at least one of the following: demagnetization factor, adaptive geometry of magnetic domains or grains, saturation magnetic field related proportionality constant, material anisotropy related constant, and pinning point density related constant.

[0031] S102: Sample each parameter to be optimized at least twice, and obtain an initial dataset each time; As one implementation method, sampling is performed within the value range of each parameter to be optimized, and the sampled values ​​are combined to form an initial dataset. The sampling is repeated to obtain a pre-set number of initial datasets.

[0032] Furthermore, the value ranges of each parameter to be optimized are evenly divided into multiple equally spaced sub-intervals. During repeated sampling, the sub-intervals within the value ranges of each parameter to be optimized are sampled evenly, ensuring that the initial dataset covers all possible ranges of the value ranges of each parameter to be optimized. This avoids homogenization of the initial dataset due to sampling bias and ensures that the initial dataset can comprehensively explore the value ranges, providing a rich search starting point for subsequent iterative optimization and reducing the risk of getting trapped in local optima. By combining multiple sets of initial datasets, various possible combinations under parameter coupling can be covered, avoiding the omission of effective search regions due to strong parameter coupling. This provides the prerequisite for subsequent decoupling of parameters through operations such as dimensionality bias, clustering, and mutation.

[0033] S103: Input the initial dataset of each sampling into the target hysteresis model to obtain the corresponding predicted magnetic field strength value. Based on the hysteresis properties of the soft magnetic material, determine the measured magnetic field strength value of the soft magnetic material. Construct the objective function based on the predicted magnetic field strength value and the measured magnetic field strength value. One approach involves inputting the measured magnetic field strength value into the parameter vector to be optimized and substituting it into the target hysteresis model to output the predicted magnetic flux density value. Then, the predicted magnetic field strength value is derived by reverse engineering the target hysteresis model. Finally, an objective function is constructed based on the deviation between the measured and predicted magnetic field strength values. The deviation can be measured using indicators such as root mean square error, absolute error, or relative error.

[0034] For example, the objective function is constructed using the root mean square error as an example, and the formula is as follows: ; Wherein, RMSE is the root mean square error value; H meas This is the measured value of the magnetic field strength; H cal The predicted value is obtained by substituting the parameter vector to be optimized into the mathematical expression of the hysteresis model; N This represents the number of measured data points.

[0035] The measured magnetic field strength can be obtained using the Chroma programmable soft magnetic material AC testing system to experimentally measure the hysteresis characteristics of the 1K107B nanocrystalline toroidal core. The experiment utilizes Ampere's law and Faraday's law of electromagnetic induction, combined with the hardware acquisition capabilities of the testing system, to eliminate phase difference errors and ensure the synchronization and accuracy of the magnetic field strength H and magnetic flux density B.

[0036] Specifically, according to Ampere's law, the magnetic field strength is proportional to the excitation current. The excitation current of the primary coil is measured using the Chroma programmable soft magnetic material AC testing system. i 1. Combined with the number of coil turns N Equivalent magnetic circuit length l m The formula for calculating the magnetic field strength is as follows: ; According to Faraday's law of electromagnetic induction, the rate of change of magnetic flux is proportional to the induced voltage. The open-circuit voltage u2 of the secondary coil was measured using a Chroma programmable soft magnetic material AC testing system, combined with the number of coil turns. N Given the equivalent cross-sectional area A, the magnetic flux density formula is as follows: .

[0037] Furthermore, by adjusting the test conditions, the applicability of the hysteresis model under multiple operating conditions was verified. These conditions included operating conditions with different saturation levels and different DC biases.

[0038] By changing the secondary coil voltage under operating conditions with different saturation levels, the maximum magnetic flux density can be altered. B m saturation magnetic flux density B s It is an inherent property of the material and is a fixed value. By adjusting the ratio between the two, we can obtain the hysteresis loop under different saturation levels, such as unsaturated, half-saturated, and saturated.

[0039] Applying DC excitation current under different DC bias conditions I When using a 1K107B nanocrystalline toroidal magnetic core sample, the DC bias magnetic field can be directly calculated according to Ampere's law. H b The calculation formula is as follows: .

[0040] DC bias changes the degree of hysteresis loop offset, which is determined by the initial magnetization curve. H b The DC bias magnetic flux density is derived. B b This allows us to obtain hysteresis loops under different DC bias voltages.

[0041] As can be seen from the above, by verifying the applicability of the target hysteresis model under multiple operating conditions, obtaining complete hysteresis characteristic data covering different saturation levels and different DC biases, and comparing the hysteresis loops calculated for the parameters to be optimized in the target hysteresis model with these experimental data, the accuracy and efficiency of the parameters to be optimized can be verified.

[0042] S104: Iterate through the parameters to be optimized in different dimensions of the initial dataset, extract different parameters to be optimized from different initial datasets to form learning vectors; subtract the learning vectors from the parameters to be optimized in a set of initial datasets step by step to obtain the dimension bias vector; determine the current iteration speed of the objective function based on the dimension bias vector, and superimpose the current iteration speed with the set of initial datasets to obtain the iterated target dataset; input the target dataset and the initial dataset into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized; One implementation approach involves an initial dataset composed of multiple parameters to be optimized, with a fixed order in which each parameter occupies a position corresponding to its dimension. This ensures that the parameters for each dimension in each initial dataset are identical. Iterative optimization is then performed on the parameters for each dimension in the initial dataset. For each dimension of each initial dataset, a parameter value is randomly selected from all initial datasets for that dimension and combined according to the parameter order to form a learning vector. The parameter values ​​in the learning vector are then subtracted from the corresponding parameter values ​​in the initial dataset, one by one, according to the parameter order, to obtain a dimension bias vector. The current iteration speed of the objective function is determined based on the dimension bias vector, with the iteration speed of the initial dataset set to zero. The current iteration speed is then superimposed with the initial dataset to obtain the iterated target dataset. Minimizing the objective function yields the individual optimal value and the global optimal value corresponding to the initial dataset. This setup ensures that the individual optimal value always moves closer to its historical optimal value, avoiding aimless random searches and accelerating the convergence speed of the optimization process.

[0043] As discussed above, the learning vector selects values ​​from all initial datasets, essentially fusing the features of the parameters to be optimized from multiple high-quality initial datasets. This ensures that the current iteration speed update of each initial dataset incorporates different high-quality information, maintaining the diversity of the parameters to be optimized and improving the comprehensiveness of the search. The dimensionality bias vector breaks down the correlation limitations between the parameters to be optimized, allowing the algorithm to explore more combinations of parameters that were previously difficult to cover, effectively preventing the algorithm from getting trapped in local optima. This diversity setting ensures that the algorithm can search within a larger space of parameters to be optimized during iteration, making it easier to find the true global optimum rather than a local optimum.

[0044] Furthermore, the current iteration rate of the objective function is determined based on the dimensionality deviation vector, and the formula can be as follows: ; In the formula: Let be the inertia weight for the t-th iteration; For the target dataset i The velocity in the t-th iteration; Cr is the learning factor, which is a constant; For the target dataset i The learning vector; For the target dataset i The optimal value for an individual in the t-th iteration.

[0045] Furthermore, the inertia weight decreases linearly from a preset maximum inertia weight to a preset minimum inertia weight with each iteration. This setup results in a high inertia weight in the early stages of iteration, where the previous iteration's velocity accounts for a large proportion of the current iteration's velocity formula. Combined with the random exploration of the dimension deviation vector, this allows for rapid coverage of a wide range of parameter values ​​to be optimized. In the later stages of iteration, the inertia weight decreases, relatively increasing the proportion of the dimension deviation vector in the current iteration's velocity formula, narrowing the search range, and achieving refined convergence.

[0046] For example, the linear formula for inertia weight can be as follows: ; In the formula: T max The maximum number of iterations is preset. t This represents the current iteration number; Let be the inertia weight for the t-th iteration; The maximum inertia weight; This represents the minimum inertia weight. The inertia weight formula iterates from zero.

[0047] For example, the linear formula for inertia weight can be as follows: ; In the formula: T This represents the maximum number of iterations. t This represents the current iteration number; For the first t The inertia weight of the next iteration; The maximum inertia weight; This is the minimum inertia weight. The inertia weight formula iterates starting from 1.

[0048] In the embodiments of this application, after obtaining the individual optimal value, it is necessary to determine whether each parameter to be optimized in the individual optimal value exceeds the corresponding value range. If it does, the parameter to be optimized in the individual optimal value is adjusted to be close to the range boundary on one side.

[0049] For example, the individual optimal value is guaranteed by a projection constraint mechanism that each parameter to be optimized in the individual optimal value is located within its corresponding value interval. The projection constraint formula can be as follows: ; In the formula: This is a projection operator used to restrict the parameter to be optimized to a corresponding range of values.

[0050] Furthermore, the global optimum can be verified using two evaluation metrics: prediction accuracy and global search effectiveness.

[0051] For example, the prediction accuracy improvement percentage can be used as a validation evaluation metric, and the formula for the prediction accuracy improvement percentage can be as follows: ; In the formula: The root mean square error corresponding to the global optimum; is the root mean square error corresponding to the reference value, which can be obtained through genetic algorithm (GA), simulated annealing algorithm (SA), particle swarm optimization algorithm (PSO), or brainstorming algorithm (BSO); n is the number of measurement frequency points, which refers to the total number of times the response is measured at different frequencies.

[0052] From the above formula, we can see that if η A value greater than 0 indicates that the root mean square error of the global optimum is smaller than that of the reference value, meaning the global optimum has better accuracy; and η A larger value indicates a more significant improvement in accuracy, and better accuracy and quality of the global optimum. If... η A value ≤0 indicates that the global optimum may be a local optimum or the result of a failed search.

[0053] For example, the effectiveness of the global search can be evaluated using the diversity of solutions, and the formula for the diversity of solutions can be as follows: ; In the formula: For the dimension of the solution, The initial number of data sets. Indicates the first The generation The initial dataset is Numerical values ​​in dimensions Indicates the first Replace all initial datasets in the 1st... Standard deviation in dimensions and They represent The upper and lower bounds of the dimensional variable. A higher Diversity(t) value indicates that the parameters to be optimized are more dispersed during the iteration process, and that it has a better global exploration capability. A Diversity(t) value that is too low indicates that the iteration converges to a local region too early, and the global optimum is likely to be a local optimum rather than a global optimum.

[0054] S105: Substitute the global optimal value into the target hysteresis model to generate the hysteresis loop of the soft magnetic material under the corresponding working conditions.

[0055] As one approach, the global optimum is substituted into the target hysteresis model to generate the hysteresis loop corresponding to the operating condition. Comparing the hysteresis loop with the measured hysteresis loop reveals that: if the hysteresis loop closely matches the measured hysteresis loop, it indicates good fit between the global optimum and the target hysteresis model; if the hysteresis loop deviates significantly from the measured hysteresis loop, the problem can be identified in reverse, such as an unreasonable setting of the parameter range to be optimized, or a mismatch between the preset characteristics of the soft magnetic material and its actual characteristics, thus allowing for adjustments to the optimization strategy.

[0056] like Figure 2 As shown, to make the global optimum more accurate, after obtaining the individual optimum and the global optimum in each iteration, the following steps are also included: S201: Perform cluster analysis on the optimal values ​​of all individuals to obtain each cluster category and its corresponding cluster center; As one implementation method, the parameter value of each parameter to be optimized in all individual optimal values ​​is verified to ensure that the parameter value of each parameter to be optimized in all individual optimal values ​​is within the value range of the corresponding parameter to be optimized. The parameter value of each parameter to be optimized in the individual optimal values ​​is processed to map each parameter value to the [0,1] interval. This processing formula can be (parameter value to be optimized - minimum value of the parameter to be optimized in all individual optimal values) / (maximum value of the parameter to be optimized in all individual optimal values ​​- minimum value of the parameter to be optimized in all individual optimal values). This setting eliminates the dimensional differences between different parameters to be optimized. Based on the dimension of the parameter to be optimized in the individual optimal values, the number of clusters is set, typically 1 to 2 times the dimension. All individual optimal values ​​are classified according to similarity. The K-means clustering algorithm can be used, and the similarity can be obtained by iterative clustering using Euclidean distance to obtain the cluster categories and the cluster centers for each cluster category. Cluster analysis is performed on the optimal values ​​of all individuals. By dividing the parameters to be optimized into groups with different characteristics through clustering, it is ensured that subsequent optimization can still cover the key areas of the range of values ​​of the parameters to be optimized, and avoid the algorithm from converging to a local optimum too early.

[0057] S202: Weighted fusion of a cluster center and any cluster center that is different from it to obtain the candidate data value corresponding to the cluster center; As one implementation method, for the target cluster center, a center of a different category is randomly selected from the remaining cluster centers for weighted fusion. The weights should reflect the principle of prioritizing the target cluster center. Therefore, the weighting formula can be as follows: ; In the formula: μ c Candidate data values; , There are two cluster centers; These are the weighting coefficients.

[0058] After weighted fusion, the obtained candidate data values ​​are corrected according to the projection constraint mechanism to ensure that the parameters to be optimized conform to the characteristics of soft magnetic materials.

[0059] Furthermore, for the same target cluster center, it can be sequentially and weightedly merged with multiple cluster centers of different categories, which enriches the diversity of the search for parameters to be optimized compared with single-category weighted fusion.

[0060] S203: Subtract the optimal values ​​of any two different individuals to obtain the optimal difference, scale each optimal difference to obtain the scaled difference, and superimpose the candidate data value with at least one scaled difference to obtain the variant data value corresponding to the cluster center. As one implementation method, from all individual optimal values, two optimal values ​​from different cluster categories are selected. The difference between the two optimal values ​​is calculated separately for each dimension of the parameter to be optimized. The difference is multiplied by a scaling factor to obtain a directional variance. The candidate data values ​​are then superimposed with the directional variance to obtain the variable data values. The variable data values ​​are then corrected according to a projection constraint mechanism to ensure that the parameter to be optimized conforms to the characteristics of soft magnetic materials. The difference between individual optimal values ​​reflects the direction of characteristic differences in the parameter to be optimized. Scaling the difference and superimposing it on the candidate data values ​​is equivalent to fine-tuning along the direction of superior differences, which is more likely to approach the global optimum than random mutation and avoids getting trapped in local optima.

[0061] Furthermore, the scaling factor gradually decreases as the number of iterations increases. A larger scaling factor is used in the early stage of the iteration to enhance the global exploration capability, while a smaller scaling factor is used in the later stage of the iteration to focus on local fine optimization.

[0062] For example, in the early stages of iteration F ∈[0.1, 0.3], later stage of iteration F ∈[0.05, 0.1]. The formula for calculating the variant data values ​​is shown below: ; In the formula: v represents the variability data value; Candidate data values; , These are the optimal values ​​for individuals in two different cluster categories.

[0063] S204: Perform dimensional cross-validation between the parameters to be optimized in the individual optimal value and the parameters to be optimized in the corresponding variability data value to obtain the cross-validation data value; As one implementation method, cross-probability constraints are set, including a first constraint and a second constraint. The first constraint is that the random number is less than a preset cross-probability value, and the random number is less than 0. It is generated within the range of 1, and the crossover probability value ranges from 0.4. 0.7; The second constraint is that the dimension of the parameter to be optimized during the dimension crossing is consistent with the random dimension, and the random dimension is selected from the dimension of the parameter to be optimized in the individual optimal values; The algorithm sequentially checks whether each parameter to be optimized in the individual optimal value satisfies the first or second constraint. If it does, the corresponding parameter in the individual optimal value is updated to the parameter corresponding to the mutated data value; otherwise, the parameter remains unchanged. All parameters to be optimized in the individual optimal value are then updated to obtain cross-data values. These cross-data values ​​are then corrected according to the projection constraint mechanism to ensure that the parameters to be optimized conform to the characteristics of soft magnetic materials. This dimensional cross-operation, while preserving the characteristics of high-quality parameters to be optimized, achieves iterative upgrades towards a better direction through directional dimensional exchange.

[0064] S205: Input the cross-data values ​​and individual optimal values ​​into the objective function respectively, obtain the individual optimal value when the output of the objective function is minimized, and determine the global optimal value with the smallest output of the objective function from all individual optimal values.

[0065] As one implementation method, iteration stops when the number of iterations reaches a preset maximum, or when the rate of change of the objective function output value corresponding to all individual optimal values ​​within a consecutive preset number of iterations is less than a set threshold. The last individual optimal value obtained after stopping iteration is compared with the cross-data value and the corresponding objective function output value obtained by inputting them into the objective function. If the objective function output value corresponding to the cross-data value is smaller, the cross-data value is considered the individual optimal value; otherwise, the individual optimal value is retained. The value with the smallest objective function output value among all individual optimal values ​​is selected as the global optimal value.

[0066] With the above settings, taking the individual optimal value as the core operation object, and through the full-link logic of projection constraint to ensure the minimum, clustering to condense high-quality features, mutation to introduce global differences, cross-personalized optimization, and optimal value closed-loop update, the problem of strong coupling and easy boundary crossing of the target hysteresis model parameters is solved, and the global exploration and local convergence capabilities of the optimization algorithm are balanced, ultimately achieving high-precision, high-efficiency, and highly adaptable hysteresis loop simulation.

[0067] In some embodiments, to verify the adaptability and excellent performance of the hysteresis loop simulation method for soft magnetic materials of this application under different saturation levels and different DC bias conditions, an experimental platform was built using a 1K107B nanocrystalline toroidal core as the experimental object, and comparative experiments were carried out. The specific implementation process is as follows: The 1K107B nanocrystalline toroidal core was selected as the test sample. Its detailed parameters are shown in Table 1. This material is widely used in electrical equipment such as motors and transformers, and its hysteresis characteristics are typical.

[0068] Table 1

[0069] The core of the experimental platform consists of a Chroma programmable soft magnetic material AC testing system, a fully digital data acquisition system, an oscilloscope, a 5KW 10Q resistor, a programmable AC power supply, and a 1K107B nanocrystalline toroidal core. Figure 3 As shown. Wherein: Programmable AC power supplies are used to provide adjustable amplitude alternating voltage and DC bias voltage to achieve precise control under different operating conditions. The Chroma testing system combines Ampere's law and Faraday's law of electromagnetic induction to simultaneously measure magnetic field strength H and magnetic flux density B, eliminating measurement errors caused by phase differences. The all-digital data acquisition system stores the measured data of H and B in parallel, providing basic data support for subsequent model verification.

[0070] The Energetic hysteresis model was selected, and the parameters to be optimized and the experimental parameters were determined. The experimental parameters included 100 parameter vectors, 5 clusters, a maximum number of iterations of 200, an inertia weight that decreased linearly from 0.9 to 0.4, a crossover probability of 0.7, and a scaling factor of 0.8. The root mean square error, the percentage improvement in model prediction accuracy, the diversity of solutions, and the relative error of key parameters were used to evaluate the performance of the simulation method.

[0071] The experimental results of the hysteresis loop simulation method for soft magnetic materials in this application under different saturation conditions are as follows: The degree of saturation is achieved by adjusting the ratio of the maximum magnetic flux density Bm to the saturation magnetic flux density Bs. The saturation magnetic flux density Bs is an inherent property of the 1K107B material and remains constant. By adjusting the output voltage amplitude of the programmable AC power supply, the maximum magnetic flux density Bm is changed, thereby obtaining four typical operating conditions with Bm / Bs ratios of 1.000 (saturated state), 0.730 (near-saturated state), 0.453 (half-saturated state), and 0.176 (low-saturated state).

[0072] For each Bm / Bs ratio, the measured values ​​of the magnetic field strength H and magnetic flux density B of a 1K107B magnetic core were measured using an experimental platform, and the corresponding measured hysteresis loops were generated, such as... Figure 4 As shown; Based on the simulation method of this application (PBSO-DE, Particle Swarm Optimization - Differential Evolution), the parameters of the Energetic model are identified according to the measured data, and a hysteresis loop prediction model is constructed. Simultaneously, four optimization algorithms—Genetic Algorithm (GA), Simulated Annealing (SA), Particle Swarm Optimization (PSO), and Brainstorm Optimization (BSO)—were used to construct a comparative model to ensure the objectivity of the experimental comparison. The optimal parameter vectors under the four operating conditions were substituted into the Energetic hysteresis model to generate predicted hysteresis loops, which were then compared and analyzed with the measured loops.

[0073] The comparison results of the predicted hysteresis loops of the five algorithms with the measured loops under different saturation conditions at different Bm / Bs ratios are as follows: Figure 5 As shown, Figure 5 a, Figure 5 b、 Figure 5 c. Figure 5 d represents the comparison results under saturated, near-saturated, semi-saturated, and low-saturation operating conditions, respectively. Combined with... Figures 6-9 The evaluation index data shows that: The simulation method of this application has the highest fit between the predicted hysteresis loop and the measured hysteresis loop under all saturation conditions, and the RMSE value is significantly lower than that of the other four algorithms. Moreover, it does not fluctuate significantly as the Bm / Bs ratio decreases. The improvement percentage of model prediction accuracy reached over 98%, far exceeding the 60%-80% of traditional algorithms, indicating excellent parameter identification accuracy; The diversity of solutions remains at a high level, avoiding the problem that traditional algorithms are prone to getting trapped in local optima under low saturation conditions; The relative error of the parameters to be optimized is stable at around 5%, which is significantly lower than the 10%-30% error of traditional algorithms, proving the stability of the simulation method of this application in extracting the parameters to be optimized under different saturation conditions.

[0074] The experimental results of the hysteresis loop simulation method for soft magnetic materials in this application under different DC bias conditions are as follows: The DC bias condition is achieved by superimposing DC bias voltages of different amplitudes in an alternating electric field. Keeping the amplitude of the alternating voltage constant (corresponding to an alternating magnetic flux density of 1.0T), four typical DC bias conditions are obtained by superimposing DC bias magnetic flux densities of 0.0T, 0.1T, 0.2T, and 0.3T respectively through a programmable AC power supply.

[0075] For each DC bias condition, the measured values ​​of H and B of the 1K107B magnetic core were measured using an experimental platform, and a measured hysteresis loop was generated, such as... Figure 10 As shown; Using the same parameter settings as the experiments under different saturation conditions, hysteresis loop prediction models were constructed for each condition. Output the predicted hysteresis loops of each model, compare them with the measured loops, and calculate various evaluation indicators.

[0076] The comparison results of the hysteresis loops of the five algorithms under different DC bias conditions and the experimentally measured loops under different DC bias voltages are as follows: Figure 11 As shown, Figure 11 a, Figure 11 b、 Figure 11 c. Figure 11 d represents the comparison results for four typical DC bias conditions with alternating voltage amplitudes superimposed at 0.0T, 0.1T, 0.2T, and 0.3T, respectively. Combined with... Figures 11-15 The evaluation index data shows that: As the DC bias flux density increases from 0.0T to 0.3T, the hysteresis loop gradually shifts to the positive direction. However, the hysteresis loop predicted by the simulation method in this application always maintains a high degree of agreement with the measured hysteresis loop, while the prediction deviation of the other four algorithms gradually increases with the increase of the bias voltage. Under the four bias conditions, the RMSE value of the simulation method in this application is the smallest and fluctuates gently. The improvement percentage of model prediction accuracy exceeds 98%, the diversity of solutions is maintained within a reasonable range, and the relative error of the parameters to be optimized does not exceed 5%. The SA and GA algorithms show significant convergence stagnation under high DC bias conditions (0.3T), with relative errors of the parameters to be optimized exceeding 20%. However, the simulation method in this application effectively adapts to changes in bias conditions through the synergistic effect of cluster fusion and local search.

[0077] Comparative experiments under different saturation levels and DC bias conditions verified that the hysteresis loop simulation method for soft magnetic materials proposed in this application significantly outperforms the four optimization algorithms (GA, SA, PSO, and BSO) in terms of root mean square error, model prediction accuracy, solution diversity, and relative error of the parameters to be optimized under all experimental conditions. The experimental results fully demonstrate that this application can accurately meet the hysteresis analysis requirements of soft magnetic materials under multiple operating conditions.

[0078] like Figure 16 As shown, this application also provides a hysteresis loop simulation device, including a sampling module, a processing module, and an execution module; The sampling module is used to determine various parameters to be optimized for the soft magnetic material through the target hysteresis model. The parameters to be optimized meet the preset value range based on the material data of the soft magnetic material. The processing module performs at least two samplings on each parameter to be optimized, with each sampling yielding an initial dataset. The initial dataset from each sampling is input into the target hysteresis model to obtain the corresponding predicted magnetic field strength. Based on the hysteresis properties of the soft magnetic material, the measured magnetic field strength of the soft magnetic material is determined. An objective function is constructed based on the predicted and measured magnetic field strength values. The module iterates over the parameters to be optimized in different dimensions of the initial dataset, extracting different parameters from each initial dataset to form a learning vector. The learning vector is subtracted step-by-step from the parameters to be optimized in the initial dataset to obtain a dimension bias vector. The current iteration speed of the objective function is determined based on the dimension bias vector, and the current iteration speed is superimposed on the initial dataset to obtain the iterated target dataset. The target dataset and the initial dataset are input into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized. The execution module is used to substitute the global optimal value into the target hysteresis model to generate the hysteresis loop of the soft magnetic material under the corresponding working conditions.

[0079] like Figure 17 As shown in the figure, this application embodiment also provides an electronic device, including at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the program is executed by the processing unit, the processing unit performs the above-mentioned hysteresis loop simulation method for soft magnetic materials.

[0080] This application also provides a readable storage medium storing a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the above-described hysteresis loop simulation method for soft magnetic materials.

[0081] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive).

[0082] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0083] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The above descriptions are merely preferred embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A method for simulating the hysteresis loop of a soft magnetic material, characterized in that, The method includes: The various parameters to be optimized for the soft magnetic material are determined by the target hysteresis model. The parameters to be optimized satisfy a preset range of values ​​based on the material data of the soft magnetic material. Each parameter to be optimized is sampled at least twice, and each sampling yields an initial dataset. The initial dataset from each sampling is input into the target hysteresis model to obtain the corresponding predicted magnetic field strength. Based on the hysteresis properties of the soft magnetic material, the measured magnetic field strength of the soft magnetic material is determined. An objective function is constructed based on the predicted magnetic field strength and the measured magnetic field strength. The optimization parameters of different dimensions in the initial dataset are iterated, and different optimization parameters are extracted from different initial datasets to form learning vectors. The learning vectors are subtracted from the optimization parameters in a set of initial datasets step by step to obtain dimensionality bias vectors. The current iteration speed of the objective function is determined based on the dimensionality bias vectors, and the current iteration speed is superimposed on the set of initial datasets to obtain the iterated target dataset. The target dataset and the initial datasets are input into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized. Substituting the global optimum into the target hysteresis model, a hysteresis loop of the soft magnetic material under the corresponding working condition is generated.

2. The method according to claim 1, characterized in that, The current iteration speed of the objective function is determined based on the dimensional deviation vector, and the formula for the current iteration speed is as follows: ； In the formula: Let be the inertia weight for the t-th iteration; For the target dataset i The velocity in the t-th iteration; C r The learning factor is a constant. For the target dataset i The learning vector; For the target dataset i The optimal value for an individual in the t-th iteration.

3. The method according to claim 2, characterized in that, The inertia weight decreases linearly from a preset maximum inertia weight to a preset minimum inertia weight with the number of iterations.

4. The method according to claim 1 or 2, characterized in that, The step of inputting the target dataset and the initial dataset into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized includes: By inputting the target dataset and the initial dataset into the objective function, the initial individual optimal value and the initial global optimal value are obtained when the output of the objective function is minimized. Cluster analysis was performed on all the initial individual optimal values ​​to obtain each cluster category and its corresponding cluster center; A weighted fusion is performed between one of the cluster centers and any other cluster center that is different from it to obtain the candidate data value corresponding to the cluster center; The optimal difference is obtained by subtracting the optimal values ​​of any two different individuals. Each optimal difference is then scaled to obtain a scaled difference. The candidate data value is superimposed with at least one of the scaled differences to obtain the variant data value corresponding to the cluster center. The parameters to be optimized in the initial individual optimal value are cross-dimensionally intersected with the parameters to be optimized in the corresponding mutated data values ​​to obtain cross-data values. The cross-data values ​​and the initial individual optimal values ​​are respectively input into the objective function to obtain the individual optimal value when the output of the objective function is minimized. The global optimal value with the smallest output of the objective function is determined from all the individual optimal values.

5. The method according to claim 4, characterized in that, Before performing cluster analysis on the optimal values ​​of all the initial individuals to obtain each cluster category and its corresponding cluster center, the method further includes: Determine whether the value of each parameter to be optimized in the initial individual optimal value exceeds the corresponding value range. If it does, adjust the value of the parameter to be optimized in the individual optimal value to the boundary value of the value range.

6. The method according to claim 4, characterized in that, The step of performing dimensional cross-validation between the parameter to be optimized in the initial individual optimal value and the parameter to be optimized in the corresponding mutated data value to obtain cross-validation data values ​​includes: A crossover probability constraint is set, comprising a first constraint and a second constraint. The first constraint is that the random number is less than a preset crossover probability value, and the random number is less than or equal to 0. The value of 1 is generated within the range of 1; the second constraint is that the dimension of the parameter to be optimized that is undergoing dimension crossing is consistent with the random dimension, and the random dimension is selected from the dimension of the parameter to be optimized in the initial individual optimal value; Sequentially determine whether each parameter to be optimized in the initial individual optimal value satisfies the first constraint or the second constraint. If it satisfies, update the parameter to be optimized in the initial individual optimal value to the parameter to be optimized corresponding to the mutated data value; otherwise, the parameter to be optimized in the initial individual optimal value remains unchanged. The parameters to be optimized in the initial individual optimal value are updated to obtain the cross data value.

7. The method according to claim 1, characterized in that, The parameters to be optimized include at least one of the following: demagnetization factor, adaptive geometry of magnetic domains or grains, proportional constant related to saturated magnetic field, material anisotropy related constant, and pinning point density related constant.

8. A hysteresis loop simulation device for soft magnetic materials, characterized in that, include: The sampling module is used to determine various parameters to be optimized for the soft magnetic material through the target hysteresis model. The parameters to be optimized satisfy a preset value range based on the material data of the soft magnetic material. The processing module is used to sample each of the parameters to be optimized at least twice, and each sampling yields an initial dataset; The initial dataset from each sampling is input into the target hysteresis model to obtain the corresponding predicted magnetic field strength. Based on the hysteresis properties of the soft magnetic material, the measured magnetic field strength of the soft magnetic material is determined. An objective function is constructed based on the predicted magnetic field strength and the measured magnetic field strength. The optimization parameters of different dimensions in the initial dataset are iterated, and different optimization parameters are extracted from different initial datasets to form learning vectors. The learning vectors are subtracted from the optimization parameters in a set of initial datasets step by step to obtain dimensionality bias vectors. The current iteration speed of the objective function is determined based on the dimensionality bias vectors, and the current iteration speed is superimposed on the set of initial datasets to obtain the iterated target dataset. The target dataset and the initial datasets are input into the objective function to obtain the individual optimal value and the global optimal value when the output of the objective function is minimized. The execution module is used to substitute the global optimal value into the target hysteresis model to generate the hysteresis loop of the soft magnetic material under the corresponding working conditions.

9. An electronic device, characterized in that, It includes at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program that, when executed by the processing unit, causes the processing unit to perform the hysteresis loop simulation method for soft magnetic materials as described in any one of claims 1 to 7.

10. A readable storage medium, characterized in that, It stores a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the hysteresis loop simulation method for soft magnetic materials as described in any one of claims 1 to 7.

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