Hysteresis separation method and device

Abstract

The present invention relates to a hysteresis separation method and device, specifically to the field of magnetic material modeling. The method obtains a quasi-static hysteresis loop of a magnetic material; performs area element separation processing on the quasi-static hysteresis loop to obtain an area element curve; the area element size is the length of the line connecting the two points where the quasi-static hysteresis loop intersects with the magnetic field intensity #imgabs0#; determines an expression for the area element curve based on the Preisach distribution function, performs parameter identification on the expression of the area element curve Sc(H) to obtain an irreversible magnetization component model; determines the irreversible magnetization component, determines the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, fits the reversible magnetization component to determine the reversible magnetization component model; and determines the overall hysteresis model of the magnetic material based on the irreversible magnetization component model and the reversible magnetization component model. This method simplifies the model calculation process, reduces parameter identification complexity, and improves model accuracy.

Description

Technical Field

[0001] The present invention relates to the field of magnetic material modeling, and in particular to a hysteresis separation method and device. Background Art

[0002] The hysteresis loop of a magnetic material is an important characteristic curve of its magnetization behavior in an alternating magnetic field, reflecting the reversible and irreversible movement of magnetic domains under the action of an external magnetic field. In related technologies, the modeling methods of the hysteresis loop mainly include the Preisach model and the experimental separation method. The Preisach model has a good fitting effect on the irreversible magnetization part, but a poor fitting effect on the reversible magnetization part. The experimental separation method requires the measurement of multiple first-order and second-order hysteresis curves, which is a cumbersome process and has high requirements for experimental equipment. In addition, some methods separate the magnetization components through overall parameter identification, but these methods have high computational complexity, are time-consuming, and have limited accuracy. Summary of the Invention

[0003] In order to address the deficiencies of the prior art, the purpose of this application is to provide a hysteresis separation method and device, which can simplify the model calculation process, reduce the complexity of parameter identification, and improve model accuracy.

[0004] In a first aspect, the present application provides a hysteresis separation method, the method comprising:

[0005] Obtain the quasi-static hysteresis loop of the magnetic material. The quasi-static hysteresis loop is a closed curve showing the change of magnetic induction intensity B with magnetic field intensity H when the magnetic material is in a periodic alternating magnetic field.

[0006] The quasi-static hysteresis loop is separated by area element to obtain the area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the relationship between the quasi-static hysteresis loop and the magnetic field intensity. The length of the line connecting the two intersecting points;

[0007] The expression of the area element curve Sc(H) is determined based on the Preisach distribution function, and the parameters of the expression of the area element curve Sc(H) are identified based on the curve data corresponding to the area element curve Sc(H), thereby obtaining the irreversible magnetization component model;

[0008] Determine the irreversible magnetization component based on the irreversible magnetization component model, determine the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determine the reversible magnetization component model by fitting the reversible magnetization component;

[0009] According to the irreversible magnetization component model and the reversible magnetization component model, the overall hysteresis model of the magnetic material is determined. The overall hysteresis model can predict the hysteresis curve under different excitation conditions.

[0010] In one embodiment, the quasi-static hysteresis loop is subjected to area element separation processing to obtain an area element curve Sc(H), including:

[0011] For magnetic field strength The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element;

[0012] Based on magnetic field strength The magnetic field strength between The size of the corresponding area element determines the area element curve Sc(H).

[0013] In one embodiment, the magnetic field strength The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element includes:

[0014] Interpolate the rising edge data and falling edge data of the quasi-static hysteresis loop to obtain the magnetic field intensity The magnetic field strength between The magnetic induction intensity at the falling edge and the rising edge magnetic induction intensity ;

[0015] For each magnetic field strength , according to the magnetic field strength The corresponding falling edge magnetic induction intensity and the rising edge magnetic induction intensity The difference between The size of the corresponding area element.

[0016] In one embodiment, the measurement frequency range of the quasi-static hysteresis loop is 0.1 Hz to 10 Hz;

[0017] In determining the magnetic field strength The magnetic field strength between When the size of the corresponding area element is calculated, the size of the area element is calculated point by point using the magnetic field intensity change step ΔH, and the magnetic field intensity change step ΔH does not exceed 1% of the magnetic field intensity Hs.

[0018] In one embodiment, an expression of the area element curve Sc(H) is determined based on the Preisach distribution function, and parameter identification is performed on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model, including:

[0019] The area element curve Sc(H) is derived under the Preisach model to obtain the initial expression of the area element curve Sc(H). The initial expression of the area element curve Sc(H) is fitted with a set function to obtain the expression of the area element curve Sc(H) with the parameters to be identified.

[0020] Based on the curve data corresponding to the area element curve Sc(H), parameter identification is performed on the expression of the area element curve Sc(H) with the parameters to be identified, and an irreversible magnetization component model is obtained; wherein, the parameter identification is performed by using one of a simulated annealing algorithm and a particle swarm method.

[0021] In one embodiment, the area element curve Sc(H) is derived under the Preisach model to obtain an initial expression of the area element curve Sc(H), including:

[0022] Determining magnetic field strength The intersection with the falling edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the intersection of the falling edge Expressed as: ;

[0023] Determining magnetic field strength The intersection with the rising edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the rising edge intersection Expressed as: ;

[0024] The magnetic induction intensity at the intersection of the falling edge The magnetic induction intensity at the intersection with the rising edge Subtract and get the magnetic field strength The initial expression of the area element curve Sc(H) at is: .

[0025] In one embodiment, the expression of the area element curve Sc(H) is: using a set function to fit the initial expression of the area element curve Sc(H) to obtain the expression of the area element curve Sc(H) with the parameters to be identified, including:

[0026] Based on the Preisach distribution density function and and They are independent of each other, and decoupling results in the following decoupling results: ;

[0027] Based on the decoupling results and the initial expression of the area element curve Sc(H), the expression of the area element curve Sc(H) with the parameters to be identified is obtained.

[0028] In one embodiment, the expression of the area element curve Sc(H) with the parameters to be identified is:

[0029] ;

[0030] in, 、 、 Represent the parameters to be identified.

[0031] In one embodiment, determining the irreversible magnetization component based on the irreversible magnetization component model, determining the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determining the reversible magnetization component model by fitting the reversible magnetization component includes:

[0032] Determine the irreversible magnetization component of each magnetic field intensity point through the irreversible magnetization component model;

[0033] Subtract the irreversible magnetization component from the loop data of the quasi-static hysteresis loop to determine the reversible magnetization component;

[0034] A reversible magnetization component model is constructed, and the reversible magnetization component model is fitted and parameter identified through the reversible magnetization component to determine the reversible magnetization component model.

[0035] In a second aspect, the present application further provides a hysteresis separation device, comprising:

[0036] An acquisition module is used to obtain a quasi-static hysteresis loop of a magnetic material. The quasi-static hysteresis loop is a closed curve showing the change of magnetic induction intensity B with magnetic field intensity H when the magnetic material is in a periodic alternating magnetic field.

[0037] The area element separation module is used to perform area element separation on the quasi-static hysteresis loop to obtain the area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the relationship between the quasi-static hysteresis loop and the magnetic field strength. The length of the line connecting the two intersecting points;

[0038] A parameter identification module is used to determine an expression of the area element curve Sc(H) based on the Preisach distribution function, and to perform parameter identification on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H), thereby obtaining an irreversible magnetization component model; the parameter identification module is further used to determine the irreversible magnetization component based on the irreversible magnetization component model, determine the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determine the reversible magnetization component model by fitting the reversible magnetization component;

[0039] The model generation module is used to determine the overall hysteresis model of the magnetic material based on the irreversible magnetization component model and the reversible magnetization component model. The overall hysteresis model can predict the hysteresis curve under different excitation conditions.

[0040] The above-mentioned hysteresis component method obtains the quasi-static hysteresis loop of the magnetic material and then performs area element separation processing on it to obtain the area element curve Sc(H), which is based on the length of the line connecting the two points where the quasi-static hysteresis loop intersects with the magnetic field intensity H. The expression of the area element curve Sc(H) is determined using the Preisach distribution function, and parameter identification is performed based on the curve data to obtain the irreversible magnetization component model. The irreversible magnetization component is determined using this model, and the reversible magnetization component is determined in combination with the quasi-static hysteresis loop data. The reversible magnetization component model is obtained by fitting the reversible magnetization component. The irreversible and reversible magnetization component models are combined to construct an overall hysteresis model that can predict hysteresis curves under different excitation conditions. This method simplifies the experimental process, reduces the complexity of parameter identification, improves model accuracy, and provides a reliable basis for the prediction and application of magnetic material properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flow chart of a hysteresis separation method in one embodiment;

[0042] Figure 2 A flow chart for obtaining an area element curve in one embodiment;

[0043] Figure 3 For one embodiment, the magnetic field strength is determined The magnetic field strength between Flowchart of the size of the corresponding area element;

[0044] Figure 4 A flowchart of obtaining an irreversible magnetization component model in one embodiment;

[0045] Figure 5 In one embodiment Schematic diagram of the integration area at the two points intersecting the hysteresis loop and the size of the area element;

[0046] Figure 6is a schematic diagram of the relationship between a quasi-static hysteresis loop and an area element curve in one embodiment;

[0047] Figure 7 A flow chart for determining a reversible magnetization component model in one embodiment;

[0048] Figure 8 FIG. 4 is a diagram of a hysteresis separation device in one embodiment. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solutions and advantages of this application more clear, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application. Unless otherwise defined, the technical terms or scientific terms involved in this application should have the general meaning understood by people with ordinary skills in the technical field to which this application belongs.

[0050] In one embodiment, Figure 1 As shown, a hysteresis separation method is provided, which includes the following steps:

[0051] Step 101: Obtain a quasi-static hysteresis loop of a magnetic material. The quasi-static hysteresis loop is a closed curve showing how the magnetic induction intensity B changes with the magnetic field intensity H when the magnetic material is in a periodic alternating magnetic field.

[0052] Quasi-static hysteresis loops are obtained experimentally for magnetic materials. Quasi-static hysteresis loops are measured for magnetic materials under quasi-static conditions. Quasi-static conditions refer to a process in which the state changes slowly and is approximately in equilibrium. Under quasi-static conditions, when a magnetic material is placed in an alternating magnetic field, its magnetic flux density, B, changes with the magnetic field intensity, H, forming a closed curve. This closed curve is known as the quasi-static hysteresis loop.

[0053] It should be noted that under the action of an alternating magnetic field, the magnetic domains will undergo reversible bending and irreversible movement, causing the change in magnetic induction intensity B to lag behind the change in magnetic field intensity H, thereby forming a closed quasi-static hysteresis loop. The shape and area of ​​the quasi-static hysteresis loop can reflect the magnetization characteristics of the magnetic material.

[0054] Step 102: Perform area element separation on the quasi-static hysteresis loop to obtain an area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the relationship between the quasi-static hysteresis loop and the magnetic field strength. The length of the line connecting the two intersecting points;

[0055] To separate the reversible and irreversible magnetization components in a quasi-static hysteresis loop, the concept of an area element is introduced. The area element size is defined as the length of the line connecting the two points where the quasi-static hysteresis loop intersects the magnetic field intensity H. That is, at a point on the quasi-static hysteresis loop, the length of the line connecting the two points with the same magnetic field intensity H is the area element size at that point.

[0056] By extracting the area element size at each point on the quasi-static hysteresis loop, we can generate the area element curve Sc(H). This curve reflects the changes in the area enclosed by the quasi-static hysteresis loop. The area enclosed by the quasi-static hysteresis loop is related to the energy loss during the magnetization process. The reversible magnetization process does not involve energy loss, so the reversible magnetization curve does not enclose an area. However, the irreversible magnetization process does involve energy loss, and the area enclosed by the quasi-static hysteresis loop is entirely due to the irreversible magnetization component.

[0057] Step 103: determining an expression of the area element curve Sc(H) based on the Preisach distribution function, and performing parameter identification on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model;

[0058] The Preisach distribution function describes the distribution of hysteresis operators within a magnetic material. The flipping behavior of these hysteresis operators determines the shape of the quasi-static hysteresis loop. The area element curve Sc(H) is derived by extracting the size of the area element on the quasi-static hysteresis loop. The area element size is defined as the length of the line connecting the two points where the quasi-static hysteresis loop intersects the magnetic field intensity H. The area element curve Sc(H) reflects the changes in the area enclosed by the quasi-static hysteresis loop. The area enclosed by the quasi-static hysteresis loop is related to the energy loss during the magnetization process, which is primarily caused by the irreversible magnetization component.

[0059] By linking the area element curve with the Preisach distribution function, through mathematical deduction, we can obtain the expression of the area element curve Sc(H), which involves the integral of the Preisach distribution function, that is, the expression of the area element curve Sc(H) can be expressed as the result of integrating the distribution probability density of a specific area in the Preisach plane.

[0060] After obtaining the expression for the area element curve Sc(H), parameter identification is performed on this expression. The purpose of parameter identification is to determine the unknown parameters in the Preisach distribution function so that the area element curve Sc(H) calculated based on the unknown parameters is as close as possible to the actual measured curve data. This process usually uses an optimization algorithm, such as the particle swarm optimization (PSO), to adjust the parameters until the optimal parameter combination is found, minimizing the error between the simulated area element curve and the experimental data. The Preisach distribution function obtained through parameter identification can be used to simulate the irreversible magnetization component, and then establish an irreversible magnetization component model. The irreversible magnetization component model can more accurately describe the irreversible behavior of magnetic materials during the magnetization process.

[0061] Step 104: determining the irreversible magnetization component based on the irreversible magnetization component model, determining the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determining the reversible magnetization component model by fitting the reversible magnetization component;

[0062] Determining the irreversible magnetization component based on the irreversible magnetization component model involves using a pre-established irreversible magnetization component model to calculate the irreversible magnetization portion of a magnetic material under different magnetic field intensities. Determining the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component involves subtracting the determined irreversible magnetization component from the experimentally measured quasi-static hysteresis loop data to separate the reversible magnetization component. The quasi-static hysteresis loop contains all information about the magnetization process of a magnetic material, including both reversible and irreversible components. Subtracting the irreversible component leaves the reversible magnetization component, which represents the effect of the reversible motion of magnetic domains on magnetization.

[0063] The reversible magnetization component model can be determined by fitting the reversible magnetization component. This involves fitting the separated reversible magnetization component data using mathematical methods (such as the least squares method). This process aims to find a mathematical expression that accurately describes the variation of the reversible magnetization component and, in turn, establish the reversible magnetization component model. The reversible magnetization component model can be used to predict and analyze the reversible magnetization behavior of magnetic materials under different conditions.

[0064] Step 105: Determine an overall hysteresis model of the magnetic material based on the irreversible magnetization component model and the reversible magnetization component model. The overall hysteresis model can predict hysteresis curves under different excitation conditions.

[0065] The irreversible magnetization component model describes the hysteresis phenomenon caused by the irreversible motion of magnetic domains during the magnetization process of magnetic materials, while the reversible magnetization component model describes the effect of reversible motion of magnetic domains on magnetization. By combining the irreversible and reversible magnetization component models, a comprehensive hysteresis model can be obtained that fully reflects the magnetization behavior of magnetic materials.

[0066] It should be noted that the global hysteresis model not only includes the area enclosed by the quasi-static hysteresis loop (related to energy loss) described by the irreversible magnetization component model, but also includes the reversible changes in magnetization described by the reversible magnetization component model. Therefore, the global hysteresis model can more accurately simulate the hysteresis curve of magnetic materials under different excitation conditions (such as alternating magnetic fields of different frequencies and amplitudes).

[0067] In this embodiment, after obtaining the quasi-static hysteresis loop of the magnetic material, it is subjected to area element separation processing to obtain the area element curve Sc(H), which is based on the length of the line connecting the two points where the quasi-static hysteresis loop intersects with the magnetic field intensity H. The expression of the area element curve Sc(H) is determined using the Preisach distribution function, and parameter identification is performed based on the curve data to obtain an irreversible magnetization component model. The irreversible magnetization component is determined using this model, and the reversible magnetization component is determined in combination with the quasi-static hysteresis loop data. The reversible magnetization component model is obtained by fitting the reversible magnetization component. The irreversible and reversible magnetization component models are combined to construct an overall hysteresis model that can predict hysteresis curves under different excitation conditions. This method simplifies the experimental process, reduces the complexity of parameter identification, improves model accuracy, and provides a reliable basis for the prediction and application of magnetic material properties.

[0068] In one embodiment, Figure 2 As shown, the quasi-static hysteresis loop is subjected to area element separation processing to obtain the area element curve Sc(H), which includes the following steps:

[0069] Step 201: Magnetic field strength The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element;

[0070] In the magnetic field strength Increase to Reduce to In the process, the change of magnetic induction intensity B lags behind the change of H, forming a closed quasi-static hysteresis loop. It should be noted that area element separation is an analytical method used to extract irreversible magnetization information related to energy loss in the quasi-static hysteresis loop. The area element size is defined as the length of the line connecting the two points where the quasi-static hysteresis loop intersects with the magnetic field intensity H. For the magnetic field intensity range Each magnetic field strength within , we can find two corresponding points on the quasi-static hysteresis loop, which have the same magnetic field strength. But the magnetic induction intensity B is different. The length of the line between the two points is the magnetic field intensity. The size of the area element at the location.

[0071] Step 202: Based on the magnetic field strength The magnetic field strength between The size of the corresponding area element determines the area element curve Sc(H).

[0072] By the magnetic field strength Select multiple magnetic field intensities with a certain step size , and calculate each The area element size at can be obtained as a series of discrete area element data points. Connecting these discrete area element data points forms an area element curve Sc(H), which reflects the trend of the area enclosed by the quasi-static hysteresis loop as the magnetic field strength changes.

[0073] In this embodiment, the area element curve Sc(H) can show the trend of the area enclosed by the quasi-static hysteresis loop changing with the magnetic field intensity.

[0074] In one embodiment, Figure 3 As shown, for magnetic field strength The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element includes the following steps:

[0075] Step 301: Interpolate the rising edge data and the falling edge data of the quasi-static hysteresis loop to obtain the magnetic field strength The magnetic field strength between The magnetic induction intensity at the falling edge and the rising edge magnetic induction intensity ;

[0076] The quasi-static hysteresis loop consists of a rising edge and a falling edge, which correspond to the magnetic field intensity H changing from Increase to and from Reduce to On the rising and falling edges, the magnetic induction intensity B changes with the change of H, but due to the hysteresis effect, the change of B lags behind the change of H.

[0077] In order to more accurately describe the shape and characteristics of the quasi-static hysteresis loop, it is necessary to interpolate the data of the rising and falling edges of the quasi-static hysteresis loop. The interpolation method can be linear interpolation, polynomial interpolation or other suitable interpolation algorithms. The purpose of interpolation is to estimate more data points between the known measurement data points, so as to obtain a smoother curve. For each magnetic field strength , through interpolation processing, the magnetic induction intensity of the falling edge can be obtained respectively and the rising edge magnetic induction intensity Together, these data points form a detailed description of the quasi-static hysteresis loop.

[0078] Step 302: For each magnetic field strength , according to the magnetic field strength The corresponding falling edge magnetic induction intensity and the rising edge magnetic induction intensity The difference between The size of the corresponding area element.

[0079] In the magnetic field strength range For each magnetic field strength , through interpolation processing, the magnetic induction intensity corresponding to the rising edge and the falling edge can be obtained respectively and The size of the area element is defined as the magnetic induction intensity at the falling edge and the rising edge magnetic induction intensity At the same magnetic field strength The difference can reflect the irreversible magnetization characteristics of the quasi-static hysteresis loop at this magnetic field strength, that is, the energy loss caused by the irreversible motion of the magnetic domain. at and By measuring the difference between the two, a series of discrete area element points can be obtained, and then the area element curve Sc(H) can be formed.

[0080] In this embodiment, the quasi-static hysteresis loop is interpolated to obtain the magnetic field strength The rising and falling magnetic induction intensity and By calculating each Department and The difference between the two values ​​is used to obtain the area element size, forming the area element curve Sc(H). This method can effectively extract irreversible magnetization information and provide data support for the analysis and prediction of the magnetization behavior of magnetic materials.

[0081] In one embodiment, the measurement frequency range of the quasi-static hysteresis loop is 0.1 Hz to 10 Hz;

[0082] In determining the magnetic field strength The magnetic field strength between When the size of the corresponding area element is calculated, the size of the area element is calculated point by point using the magnetic field intensity change step ΔH, and the magnetic field intensity change step ΔH does not exceed 1% of the magnetic field intensity Hs.

[0083] The measurement frequency range of the quasi-static hysteresis loop is 0.1Hz to 10Hz. The selection of this frequency range ensures that the measurement process is in a quasi-static condition, that is, in the low frequency range, the magnetization process of the magnetic material is mainly dominated by the hysteresis effect.

[0084] In determining the magnetic field strength The magnetic field strength between When calculating the size of the corresponding area element, the size of the area element is calculated point by point using the step size ΔH of the magnetic field intensity change. The step size ΔH of the magnetic field intensity change does not exceed 1% of the magnetic field intensity Hs. This means that within the magnetic field intensity range, the magnetic field intensity is gradually increased or decreased using very small steps, ensuring that the data points are dense enough to accurately capture the details of the quasi-static hysteresis loop.

[0085] In this embodiment, this high-precision data acquisition method provides reliable basic data support for subsequent area element separation and model building.

[0086] In one embodiment, Figure 4 As shown, the expression of the area element curve Sc(H) is determined based on the Preisach distribution function, and based on the curve data corresponding to the area element curve Sc(H), the expression of the area element curve Sc(H) is parameter identified to obtain the irreversible magnetization component model, including the following steps:

[0087] Step 401: Derivation of the area element curve Sc(H) under the Preisach model to obtain an initial expression of the area element curve Sc(H), fitting the initial expression of the area element curve Sc(H) using a set function to obtain an expression of the area element curve Sc(H) with the parameters to be identified;

[0088] An initial expression for the area element curve Sc(H) is derived under the Preisach model. This expression, based on the Preisach distribution function, describes the distribution of the hysteresis operator within a magnetic material. The area element curve Sc(H) reflects how the area enclosed by the quasi-static hysteresis loop changes with the magnetic field intensity H. Its initial expression is obtained by integrating the distribution probability density over a specific region in the Preisach plane.

[0089] To simplify calculations and improve the model's applicability, a predefined function (such as a Gaussian or Lorentzian function) is used to fit the initial expression of the surface element curve Sc(H), introducing parameters to be identified. These parameters can be optimized using experimental data to ensure that the fitted surface element curve Sc(H) accurately reflects the magnetization characteristics of the magnetic material, resulting in an expression for the surface element curve Sc(H) with the parameters to be identified.

[0090] Step 402: Based on the curve data corresponding to the area element curve Sc(H), parameter identification is performed on the expression of the area element curve Sc(H) with the parameters to be identified to obtain an irreversible magnetization component model; wherein the parameter identification is performed using one of a simulated annealing algorithm and a particle swarm optimization method.

[0091] Common optimization algorithms include simulated annealing and particle swarm optimization. Both methods can effectively search the parameter space to find the optimal solution. Simulated annealing is a stochastic optimization algorithm based on the physical annealing process, simulating the solid annealing process to find the global optimal solution. Particle swarm optimization is a swarm intelligence optimization algorithm that simulates the foraging behavior of bird flocks and uses the experience of both individuals and the group to find the optimal solution.

[0092] During the parameter identification process, an algorithm (such as the particle swarm optimization method) is selected to adjust the parameters to be identified in the expression of the surface element curve Sc(H). Through iterative optimization, the error between the fitted curve and the experimental data is minimized, resulting in an optimal set of parameters. With the optimal parameters determined, the surface element curve Sc(H) accurately reflects the irreversible magnetization characteristics of the magnetic material, thereby establishing an irreversible magnetization component model.

[0093] In one embodiment, Figure 5 As shown in the figure, the initial expression of the area element curve Sc(H) is derived under the Preisach model, including:

[0094] Determining magnetic field strength The intersection with the falling edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the intersection of the falling edge Expressed as: ;

[0095] Determining magnetic field strength The intersection with the rising edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the rising edge intersection Expressed as: ;

[0096] The magnetic induction intensity at the intersection of the falling edge The magnetic induction intensity at the intersection with the rising edge Subtract and get the magnetic field strength The initial expression of the area element curve Sc(H) at is: .

[0097] It should be noted that in the Preisach model, α and β They represent the upper switching value and lower switching value of the hysteresis operator respectively. Exceed α When , the output state of the hysteresis operator jumps from −1 to +1, indicating that the magnetization direction is consistent with the direction of the external magnetic field; and when Lower than β When , the output state jumps from +1 to −1, indicating that the magnetization direction is opposite to the direction of the external magnetic field.

[0098] Specifically, when the magnetic field strength H= At , determine the intersection point of the falling edge of the quasi-static hysteresis loop. In the Preisach plane, when β> When , the output of the hysteresis operator , indicating that the magnetization direction is opposite to the direction of the external magnetic field; and the rest , indicating that the magnetization direction is consistent with the direction of the external magnetic field. The magnetic induction intensity at the intersection of the falling edge It consists of the contributions from two integration regions, DEF and ADEC, and is expressed as: ;

[0099] where the integration region DEF corresponds to β> The integral region ADEC corresponds to β≤ part.

[0100] Furthermore, the rising edge intersection of the quasi-static hysteresis loop is determined. In the Preisach plane, when α < When , the output of the hysteresis operator , indicating that the magnetization direction is consistent with the direction of the external magnetic field; and the rest , indicating that the magnetization direction is opposite to the direction of the external magnetic field. The magnetic induction intensity at the intersection of the rising edge It consists of the contributions of two integral regions ABD and BDFC and is expressed as:

[0101] ;

[0102] Among them, the integration area ABD corresponds to α< The integral region BDFC corresponds to α≥ part.

[0103] The magnetic induction strength of the falling edge intersection The magnetic induction intensity at the intersection with the rising edge Subtracting, we get the magnetic field strength H= The initial expression of the area element curve Sc(H) at . The area element curve Sc(H) reflects the change of the area enclosed by the quasi-static hysteresis loop, and its initial expression is:

[0104] .

[0105] The integration area BDEC is the magnetic field intensity in the Preisach plane. The specific area of ​​interest, i.e. the area element size is Figure 5 The shaded area is twice the result of integrating the probability density of the Preisach distribution.

[0106] In one embodiment, Figure 5 As shown, Figure 5 The distribution of the hysteresis operator in the Preisach plane is shown, which is used to describe the magnetization behavior of magnetic materials. The figure contains the α-axis and the β-axis, which represent the upper switching value and the lower switching value of the hysteresis operator respectively. Points A, B, C, D, E, and F represent different states of the hysteresis operator. The DEF and BDEC regions are related to specific magnetic field strengths and are used to calculate the magnetic induction intensity and area element curves. The solid line represents the distribution boundary and the dotted line represents the reference line, which is used to determine the position of the relevant areas and points under specific magnetic field strengths. The figure is marked as a specific magnetic field strength value, and and As the saturation value of the magnetic field strength, the boundaries of the Preisach plane are defined.

[0107] In one embodiment, Figure 6 As shown, Figure 6 The relationship between the quasi-static hysteresis loop of a magnetic material and the area element curve Sc(H) is shown. The horizontal axis H(au) represents the magnetic field strength in arbitrary units (au). The horizontal axis ranges from -1.2 to 1.2, indicating the magnetic field strength in The vertical axis B(T) represents the magnetic induction intensity, and its unit is Tesla (T). The vertical axis ranges from -1.2 to 1.2, which represents the range of change of magnetic induction intensity. B ( H ) represents the quasi-static hysteresis loop, which describes the magnetic induction intensity of magnetic materials in a periodic alternating magnetic field. B With the magnetic field strength H The curve shows a typical hysteresis loop shape, including the rising edge and falling edge .dotted line Sc ( H ) represents the area element curve, which reflects the change of the area enclosed by the hysteresis loop with the magnetic field intensity. H 's changing trend.

[0108] H = Indicates the magnetic field strength H A specific value of , under this magnetic field strength, calculate the size of the area element under this magnetic field strength. Indicates the magnetic field strength H = The magnetic induction intensity at the intersection of the falling edge of the quasi-static hysteresis loop. Indicates the magnetic field strength H = The magnetic induction intensity at the intersection of the rising edge of the quasi-static hysteresis loop. Sc ( ) indicates the magnetic field strength H = The area element size at the falling edge is defined as the magnetic induction intensity and the rising edge magnetic induction intensity The size of the area element reflects the irreversible magnetization characteristics of the hysteresis loop at this magnetic field strength.

[0109] In one embodiment, the expression of the area element curve Sc(H) is: the initial expression of the area element curve Sc(H) is fitted by a set function to obtain the expression of the area element curve Sc(H) with the parameters to be identified, including:

[0110] Based on the Preisach distribution density function and and They are independent of each other, and decoupling results in the following decoupling results: ;

[0111] Based on the decoupling results and the initial expression of the area element curve Sc(H), the expression of the area element curve Sc(H) with the parameters to be identified is obtained.

[0112] The initial expression is based on the Preisach distribution density function, which is obtained by integrating the distribution density function of a specific area in the Preisach plane. To simplify the calculation and improve the applicability of the model, it is usually assumed that the Preisach distribution density function is independent of α and β, that is, the decoupling assumption:

[0113] ;

[0114] The decoupling hypothesis can decompose the two-dimensional distribution density function into the product of two one-dimensional functions, thereby simplifying subsequent integral calculations.

[0115] Based on the decoupling results and the initial expression for the area element curve Sc(H), an expression for the area element curve Sc(H) with the parameters to be identified is obtained. A function (such as a Gaussian function or a Lorentzian function) is used to fit the initial expression for the area element curve Sc(H), introducing the parameters to be identified. The parameters to be identified are optimized using experimental data to ensure that the fitted curve is as close as possible to the actual measured data.

[0116] Specifically, the Preisach distribution function can be fitted using a widely used setting function, which is:

[0117] .

[0118] Furthermore, based on the decoupling results and the initial expression of the area element curve Sc(H), the expression of the area element curve Sc(H) is obtained by fitting the distribution Preisach distribution function using the set function:

[0119]

[0120] .

[0121] Furthermore, the fitted The expression Integrate to obtain the area element curve with the parameters to be identified , The expression is:

[0122] .

[0123] in, 、 、 are parameters related to material properties and can be obtained through parameter identification; Use n different sets of material property related parameters 、 、 To fit the same Sc(H) function; Represents the current magnetic field strength and is the independent variable of the formula.

[0124] In one embodiment, Figure 7 As shown, the irreversible magnetization component is determined based on the irreversible magnetization component model, the reversible magnetization component is determined based on the quasi-static hysteresis loop and the irreversible magnetization component, and the reversible magnetization component model is determined by fitting the reversible magnetization component, including the following steps:

[0125] Step 701: determining the irreversible magnetization component of each magnetic field intensity point using an irreversible magnetization component model;

[0126] The irreversible magnetization component model describes the distribution law of hysteresis operators inside magnetic materials through the distribution density function. The irreversible magnetization component can be obtained by integrating the distribution density function of a specific area in the Preisach plane. Calculate each point by point The irreversible magnetization component at can be used to obtain the irreversible magnetization component curve. This curve reflects the irreversible magnetization characteristics of magnetic materials under different magnetic field intensities.

[0127] Step 702: Subtract the irreversible magnetization component from the loop data in the quasi-static hysteresis loop to determine the reversible magnetization component;

[0128] The quasi-static hysteresis loop contains all the information about the magnetization process of a magnetic material, including the combined effects of the reversible and irreversible magnetization components. Subtracting the irreversible magnetization component from the quasi-static hysteresis loop data yields the reversible magnetization component, which represents the effect of the reversible motion of magnetic domains on magnetization.

[0129] Step 703: constructing a reversible magnetization component model, performing fitting and parameter identification on the reversible magnetization component model through the reversible magnetization component, and determining the reversible magnetization component model.

[0130] The reversible magnetization component model is used to describe the reversible motion of magnetic domains during magnetization. The reversible magnetization component data can be obtained by subtracting the irreversible magnetization component from the quasi-static hysteresis loop.

[0131] To build a reversible magnetization component model, a mathematical function (such as a polynomial, exponential, or trigonometric function) is typically used to fit the reversible magnetization component data. The fitting process minimizes the error between the fitted curve and the actual measured data by adjusting the parameters in the function. Common optimization algorithms include the least squares method and gradient descent.

[0132] Parameter identification is the process of determining the unknown parameters in a model through optimization algorithms. By adjusting these parameters, the model can more accurately describe the variation of the reversible magnetization component. The resulting reversible magnetization component model can be used to predict and analyze the reversible magnetization behavior of magnetic materials under different conditions.

[0133] Based on the same concept, Figure 8 As shown, the present application also provides a hysteresis separation device, which includes:

[0134] An acquisition module 801 is used to acquire a quasi-static hysteresis loop of a magnetic material. The quasi-static hysteresis loop is a closed curve showing the change of magnetic induction intensity B with magnetic field intensity H when the magnetic material is in a periodic alternating magnetic field.

[0135] The area element separation module 802 is used to perform area element separation processing on the quasi-static hysteresis loop to obtain the area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the relationship between the quasi-static hysteresis loop and the magnetic field strength. The length of the line connecting the two intersecting points;

[0136] a parameter identification module 803 for determining an expression for the area element curve Sc(H) based on the Preisach distribution function, and performing parameter identification on the expression for the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H), thereby obtaining an irreversible magnetization component model; the parameter identification module is further configured to determine the irreversible magnetization component based on the irreversible magnetization component model, determine the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determine the reversible magnetization component model by fitting the reversible magnetization component;

[0137] The model generation module 804 is used to determine the overall hysteresis model of the magnetic material according to the irreversible magnetization component model and the reversible magnetization component model. The overall hysteresis model can predict the hysteresis curve under different excitation conditions.

[0138] In one embodiment, the area element separation module 802 performs area element separation processing on the quasi-static hysteresis loop to obtain an area element curve Sc(H), which is specifically used to: The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element; based on the magnetic field strength The magnetic field strength between The size of the corresponding area element determines the area element curve Sc(H).

[0139] In one embodiment, the area element separation module 802 is based on the magnetic field strength. The quasi-static hysteresis loops between the two are separated by area elements to determine the magnetic field strength. The magnetic field strength between The size of the corresponding area element is specifically used to interpolate the rising edge data and falling edge data of the quasi-static hysteresis loop to obtain the magnetic field strength The magnetic field strength between The magnetic induction intensity at the falling edge and the rising edge magnetic induction intensity ; For each magnetic field strength , according to the magnetic field strength The corresponding falling edge magnetic induction intensity and the rising edge magnetic induction intensity The difference between The size of the corresponding area element.

[0140] In one embodiment, the area element separation module 802 is specifically used to measure the quasi-static hysteresis loop in a frequency range of 0.1 Hz to 10 Hz; The magnetic field strength between When the size of the corresponding area element is calculated, the size of the area element is calculated point by point using the magnetic field intensity change step ΔH, and the magnetic field intensity change step ΔH does not exceed 1% of the magnetic field intensity Hs.

[0141] In one embodiment, the parameter identification module 803 determines an expression of the area element curve Sc(H) based on the Preisach distribution function, and performs parameter identification on the expression of the area element curve Sc(H) based on the curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model. Specifically, the module 803 is used to: derive the area element curve Sc(H) under the Preisach model to obtain an initial expression of the area element curve Sc(H), fit the initial expression of the area element curve Sc(H) using a set function to obtain an expression of the area element curve Sc(H) with the parameters to be identified; perform parameter identification on the expression of the area element curve Sc(H) with the parameters to be identified based on the curve data corresponding to the area element curve Sc(H) to obtain the irreversible magnetization component model; wherein the parameter identification is performed using one of a simulated annealing algorithm and a particle swarm optimization method.

[0142] In one embodiment, the parameter identification module 803 derives the area element curve Sc(H) under the Preisach model to obtain an initial expression of the area element curve Sc(H), specifically for:

[0143] Determining magnetic field strength The intersection with the falling edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the intersection of the falling edge Expressed as: ;

[0144] Determining magnetic field strength The intersection with the rising edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the rising edge intersection Expressed as: ;

[0145] The magnetic induction intensity at the intersection of the falling edge The magnetic induction intensity at the intersection with the rising edge Subtract and get the magnetic field strength The initial expression of the area element curve Sc(H) at is: .

[0146] In one embodiment, the expression of the area element curve Sc(H) in the parameter identification module 803 is: the initial expression of the area element curve Sc(H) is fitted by the set function to obtain the expression of the area element curve Sc(H) with the parameters to be identified, which is specifically used for: based on the Preisach distribution density function and and They are independent of each other, and decoupling results in the following decoupling results: Based on the decoupling results and the initial expression of the area element curve Sc(H), the expression of the area element curve Sc(H) with the parameters to be identified is obtained.

[0147] In one embodiment, the expression of the area element curve Sc(H) with the parameters to be identified in the parameter identification module 803 is:

[0148] ;

[0149] in, 、 、 Represent the parameters to be identified.

[0150] In one embodiment, the parameter identification module 803 determines the irreversible magnetization component based on the irreversible magnetization component model, determines the reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determines the reversible magnetization component model by fitting the reversible magnetization component. Specifically, the module 803 is configured to: determine the irreversible magnetization component at each magnetic field intensity point using the irreversible magnetization component model; subtract the irreversible magnetization component from the loop data in the quasi-static hysteresis loop to determine the reversible magnetization component; construct a reversible magnetization component model, and perform fitting and parameter identification on the reversible magnetization component model using the reversible magnetization component to determine the reversible magnetization component model.

[0151] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0152] The above embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A hysteresis separation method, characterized in that: The method comprises: Obtaining a quasi-static hysteresis loop of the magnetic material, wherein the quasi-static hysteresis loop is a closed curve showing the change of magnetic induction intensity B with magnetic field intensity H of the magnetic material in a periodic alternating magnetic field; The quasi-static hysteresis loop is subjected to area element separation processing to obtain an area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the relationship between the quasi-static hysteresis loop and the magnetic field strength. The length of the line connecting the two intersecting points; Determining an expression of the area element curve Sc(H) based on a Preisach distribution function, and performing parameter identification on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model; determining an irreversible magnetization component based on the irreversible magnetization component model, determining a reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determining a reversible magnetization component model by fitting the reversible magnetization component; determining an overall hysteresis model of the magnetic material according to the irreversible magnetization component model and the reversible magnetization component model, wherein the overall hysteresis model can predict hysteresis curves under different excitation conditions; The quasi-static hysteresis loop is subjected to area element separation processing to obtain an area element curve Sc(H), including: for the magnetic field intensity The quasi-static hysteresis loops are separated by area element to determine the magnetic field strength The magnetic field strength between The size of the corresponding area element; based on the magnetic field strength The magnetic field strength between The size of the corresponding area element determines the area element curve Sc(H).

2. The hysteresis separation method according to claim 1, characterized in that For the magnetic field strength The quasi-static hysteresis loops are separated by area element to determine the magnetic field strength The magnetic field strength between The size of the corresponding area element includes: Interpolate the rising edge data and the falling edge data of the quasi-static hysteresis loop to obtain the magnetic field strength The magnetic field strength between The magnetic induction intensity at the falling edge and the rising edge magnetic induction intensity ; For each magnetic field strength , according to the magnetic field strength The corresponding falling edge magnetic induction intensity and the rising edge magnetic induction intensity The difference between the two determines the magnetic field strength. The size of the corresponding area element.

3. The hysteresis separation method according to claim 2, characterized in that The measurement frequency range of the quasi-static hysteresis loop is 0.1 Hz to 10 Hz; In determining the magnetic field strength The magnetic field strength between When the size of the corresponding area element is calculated, the size of the area element is calculated point by point using the magnetic field intensity change step ΔH, and the magnetic field intensity change step ΔH does not exceed 1% of the magnetic field intensity Hs.

4. The hysteresis separation method according to claim 1, characterized in that An expression of the area element curve Sc(H) is determined based on the Preisach distribution function, and parameter identification is performed on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model, including: Deducing the area element curve Sc(H) under the Preisach model to obtain an initial expression of the area element curve Sc(H), fitting the initial expression of the area element curve Sc(H) with a set function to obtain an expression of the area element curve Sc(H) with the parameters to be identified; Based on the curve data corresponding to the area element curve Sc(H), parameter identification is performed on the expression of the area element curve Sc(H) with the parameters to be identified to obtain an irreversible magnetization component model; wherein the parameter identification is performed by one of a simulated annealing algorithm and a particle swarm method.

5. The hysteresis separation method according to claim 4, characterized in that: The initial expression of the area element curve Sc(H) is derived under the Preisach model, including: Determining magnetic field strength The intersection of the falling edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the intersection of the falling edge Expressed as: ; where α and β represent the upper switching value and lower switching value of the hysteresis operator inside the magnetic material, respectively. represents the output state of the hysteresis operator, Indicates β> The integral area of Indicates β≤ The integration area of ​​; represents the distribution density function of the hysteresis operator inside the magnetic material on the Preisach plane; Determining magnetic field strength The intersection of the rising edge of the quasi-static hysteresis loop; Part , the rest , the magnetic induction intensity at the rising edge intersection Expressed as: ;in, Indicates α< The integral area of Indicates α≥ The integration area of ​​; The magnetic induction intensity at the intersection of the falling edge The magnetic induction intensity at the intersection with the rising edge Subtract and get the magnetic field strength The initial expression of the area element curve Sc(H) at , the initial expression of the area element curve Sc(H) is: ;in, Indicates the magnetic field strength The associated integration region.

6. The hysteresis separation method according to claim 5, characterized in that: The expression of the area element curve Sc(H) is: the initial expression of the area element curve Sc(H) is fitted by a set function to obtain the expression of the area element curve Sc(H) with the parameters to be identified, including: Based on the Preisach distribution density function and and There is an independent relationship between them, and decoupling results in the following decoupling results: ; Based on the decoupling result and the initial expression of the area element curve Sc(H), an expression of the area element curve Sc(H) with the parameters to be identified is obtained.

7. The hysteresis separation method according to claim 5, characterized in that: The expression of the area element curve Sc(H) with the parameters to be identified is: ； in, 、 、 Represent the parameters to be identified.

8. The hysteresis separation method according to claim 1, characterized in that: Determining an irreversible magnetization component based on the irreversible magnetization component model, determining a reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determining the reversible magnetization component model by fitting the reversible magnetization component, comprising: Determining the irreversible magnetization component at each magnetic field intensity point using the irreversible magnetization component model; subtracting the irreversible magnetization component from loop data in the quasi-static hysteresis loop to determine the reversible magnetization component; A reversible magnetization component model is constructed, and fitting and parameter identification are performed on the reversible magnetization component model through the reversible magnetization component to determine the reversible magnetization component model.

9. A hysteresis separation device, characterized in that: The device performs the hysteresis separation method according to any one of claims 1 to 8, and the device comprises: An acquisition module is used to acquire a quasi-static hysteresis loop of a magnetic material, where the quasi-static hysteresis loop is a closed curve showing the change of magnetic induction intensity B with magnetic field intensity H of the magnetic material in a periodic alternating magnetic field; An area element separation module is used to perform area element separation processing on the quasi-static hysteresis loop to obtain an area element curve Sc(H); the area element curve Sc(H) is obtained based on the size of the area element, which is the ratio of the area element size to the quasi-static hysteresis loop and the magnetic field strength. The length of the line connecting the two intersecting points; a parameter identification module, configured to determine an expression of the area element curve Sc(H) based on a Preisach distribution function, and perform parameter identification on the expression of the area element curve Sc(H) based on curve data corresponding to the area element curve Sc(H) to obtain an irreversible magnetization component model; the parameter identification module is further configured to determine an irreversible magnetization component based on the irreversible magnetization component model, determine a reversible magnetization component based on the quasi-static hysteresis loop and the irreversible magnetization component, and determine the reversible magnetization component model by fitting the reversible magnetization component; The model generation module is used to determine the overall hysteresis model of the magnetic material according to the irreversible magnetization component model and the reversible magnetization component model, wherein the overall hysteresis model can predict the hysteresis curve under different excitation conditions.

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