Two-dimensional vector hysteresis modeling method considering temperature-stress coupling effects

Abstract

The application relates to a two-dimensional vector magnetic hysteresis modeling method considering temperature-stress coupling effects, comprising the following steps: collecting two-dimensional magnetic characteristic data under different temperature and stress conditions, and establishing temperature and stress related magnetic parameters; constructing a temperature-stress related HVHM operator, and constructing an HVHM operator space to generate a magnetization state vector; establishing an SAE network and training the same to obtain an HVHM-SAE two-dimensional vector magnetic hysteresis model; predicting two-dimensional magnetic flux density components of a soft magnetic material under given temperature-stress conditions and an applied magnetic field trajectory, and forming corresponding two-dimensional vector magnetic hysteresis trajectories. The application realizes unified characterization of temperature, stress and two-dimensional magnetization behavior, can realize high-precision prediction of two-dimensional vector magnetic hysteresis characteristics of a soft magnetic material under complex working conditions such as temperature change, stress change and two-dimensional rotating magnetization, and provides a more reliable theoretical model and calculation tool for electromagnetic field analysis of electrical equipment, core loss evaluation, magnetic material performance research and optimized design.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic material magnetic property modeling and analysis technology, and in particular to a two-dimensional vector hysteresis modeling method that considers the effects of temperature-stress coupling. Background Technology

[0002] Soft magnetic materials are core functional materials in power transformers, motors, reactors, and other electromagnetic energy conversion equipment. Their magnetic properties directly affect the energy conversion efficiency, operating losses, and electromagnetic characteristics of the equipment. In engineering applications, the core is typically formed by stacking electrical steel sheets, amorphous alloys, nanocrystalline materials, or soft magnetic composite materials. During long-term operation, the core material is not only subjected to alternating magnetic fields but also affected by factors such as ambient temperature changes, mechanical loads, and assembly stresses. Changes in temperature and stress alter the internal magnetic domain structure and domain wall motion, thereby causing changes in parameters such as permeability, coercivity, remanent magnetic induction, and iron loss. Therefore, establishing a hysteresis model that accurately reflects magnetization behavior under temperature and stress is of great significance for improving the accuracy of electromagnetic field calculations and performance prediction capabilities of electrical equipment.

[0003] Meanwhile, in many practical electromagnetic devices, the magnetization state of soft magnetic materials is not a simple one-dimensional alternating magnetization. For example, in the joint areas of transformer cores, the teeth of motor stators and rotors, and corner regions, the direction and amplitude of the magnetic field often change simultaneously, and the magnetization vector inside the material exhibits rotational or complex trajectory motion characteristics. In this case, there is a significant two-dimensional or even multi-dimensional vector coupling relationship between the magnetic induction intensity and the magnetic field intensity, which traditional scalar hysteresis theory cannot accurately describe. Therefore, how to model the hysteresis characteristics under complex vector magnetization conditions has become an important research direction in the field of electromagnetic field analysis.

[0004] Currently, modeling methods for hysteresis phenomena in soft magnetic materials mainly include hysteresis models based on physical mechanisms, data-driven neural network models, and hybrid modeling methods that combine both. Physical models establish the magnetization laws of materials by describing processes such as magnetic domain motion, magnetization reversal, or hysteresis unit response, possessing a certain degree of physical interpretability. Data-driven models utilize machine learning methods such as neural networks to fit the complex nonlinear relationship between magnetic field input and magnetization response, offering advantages in handling high-dimensional data and complex mappings. In recent years, to balance physical constraints and learning capabilities, researchers have further explored combining traditional hysteresis operators with neural networks, improving model performance by integrating prior physical knowledge with data learning mechanisms.

[0005] However, existing technologies still face many challenges in two-dimensional vector magnetization scenarios under the combined effects of temperature and stress. First, most existing models are built under fixed environmental conditions or single operating conditions, and their model parameters usually correspond to specific temperature or stress states. When operating conditions change, parameter re-identification is often required, making it difficult to reflect the essential influence of temperature and stress on the magnetization process at the model structure level. Second, many traditional hysteresis models are mainly constructed for scalar alternating magnetization processes, and have limited ability to describe the magnetic field-magnetic induction intensity relationship under rotational magnetization and vector magnetization conditions. Even if some vector models can consider changes in magnetization direction, they still lack an effective mechanism to express the coupling effect of external factors such as temperature and stress.

[0006] Furthermore, while purely data-driven models possess strong nonlinear fitting capabilities, they typically lack explicit physical constraints, requiring a large number of training samples to simultaneously learn hysteresis memory features, path dependence effects, anisotropy characteristics, and the influence of temperature and stress. When the training data coverage is insufficient, the model is prone to declining generalization ability. Existing hybrid modeling methods, although incorporating some hysteresis operator structures, have not yet formed a unified modeling framework that deeply integrates temperature-related parameters, stress-related parameters, and the two-dimensional vector hysteresis representation mechanism. On the other hand, most existing neural network training processes use the prediction error of discrete sampling points as the optimization objective, lacking specific constraints on key information such as the overall shape characteristics of the hysteresis loop, the local trajectory evolution law, and the loop's enclosing area. Therefore, even if the model achieves high accuracy in point value prediction, problems such as hysteresis trajectory distortion, loop closure deviation, and loss estimation errors may still occur, thus affecting the accurate representation of rotational magnetization characteristics and core loss features.

[0007] In summary, existing hysteresis modeling techniques for soft magnetic materials struggle to simultaneously address the combined effects of temperature-stress variations, two-dimensional vector magnetization characteristics, and complex nonlinear mapping relationships. This results in room for improvement in model accuracy and applicability when performing electromagnetic field analysis, core loss prediction, and optimization design of electrical equipment under varying temperature and stress conditions. Therefore, there is an urgent need to propose a hysteresis modeling method that comprehensively considers temperature, stress, and two-dimensional vector magnetization characteristics to enhance the descriptive ability and prediction accuracy of the magnetization behavior of soft magnetic materials under complex operating conditions. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a two-dimensional vector hysteresis modeling method that considers the influence of temperature-stress coupling.

[0009] This invention is achieved through the following technical solution: A two-dimensional vector hysteresis modeling method considering the effects of temperature-stress coupling includes the following steps: S1. Collect two-dimensional magnetic property data under different temperature and stress conditions, and establish temperature and stress-related magnetic parameters; S2. Construct a temperature-stress related HVHM operator based on temperature and stress-related magnetic parameters, and construct a temperature-stress related HVHM operator space to generate a magnetization state vector; S3. The SAE network is trained based on the magnetization state vector and the corresponding two-dimensional magnetic flux density target data to obtain a temperature-stress related HVHM-SAE two-dimensional vector hysteresis model. S4. Based on the temperature-stress related HVHM-SAE two-dimensional vector hysteresis model, predict the two-dimensional magnetic flux density components of soft magnetic materials under given temperature-stress conditions and applied magnetic field trajectories, and form the corresponding two-dimensional vector hysteresis trajectories.

[0010] According to the above technical solution, preferably, in step S1, two-dimensional magnetic property data under different temperature and stress conditions are collected, including the corresponding magnetic field strength component H. x H y Magnetic flux density component B x B y Temperature T, stress magnitude σ, and stress direction θ σ .

[0011] According to the above technical solution, preferably, in step S1, the temperature-related magnetic parameters include the temperature-related spontaneous magnetization M(T), the temperature-related magnetocrystalline anisotropy constant K(T), and the temperature-related saturation magnetostriction coefficient λ. s (T); Stress-related magnetic parameters include the stress-induced magnetoelastic anisotropy coefficient K. σ Equivalent magnetocrystalline anisotropy constant K eff and the equivalent easy magnetization axis direction ψ eff .

[0012] According to the above technical solution, preferably, step S2 includes: Temperature and stress-related magnetic parameters are incorporated into the total free energy expression, and the temperature-stress related critical surface is determined based on energy extremum conditions and stability conditions. An operator space composed of multiple temperature-stress related HVHM operators is constructed to characterize the magnetization response under different magnetization states and different energy levels; The two-dimensional external magnetic field trajectory is input into the temperature-stress related HVHM operator space to obtain the two-dimensional output of each temperature-stress related HVHM operator, and they are spliced ​​together to form a temperature-stress related magnetization state vector. After generating the magnetization state vector, the magnetization state vector and the corresponding two-dimensional magnetic flux density target data are normalized.

[0013] According to the above technical solution, preferably, in step S2, the temperature-stress related critical surface is determined, and when the applied magnetic field passes through the critical surface, the magnetization direction of the operator is updated based on the principle of minimum energy.

[0014] According to the above technical solution, preferably, in step S3, during the end-to-end global fine-tuning stage of the SAE network, a two-dimensional hysteresis trajectory constraint mechanism based on point values, differences, and closed areas is used to optimize the network parameters.

[0015] According to the above technical solution, preferably, step S4 includes: Based on the temperature to be predicted, the stress to be predicted, and the corresponding external magnetic field trajectory, a temperature-stress related magnetization state vector is generated and normalized. The normalized magnetization state vector is input into the temperature-stress related HVHM-SAE two-dimensional vector hysteresis model, and the two-dimensional magnetic flux density of the soft magnetic material to be predicted is output. Based on the output two-dimensional magnetic flux density data, the two-dimensional vector hysteresis trajectory of the soft magnetic material under the corresponding temperature-stress and magnetization conditions is obtained.

[0016] The beneficial effects of this invention are: This invention establishes temperature-dependent spontaneous magnetization, temperature-dependent magnetocrystalline anisotropy constant, and stress-dependent equivalent anisotropy, and incorporates these parameters into the total free energy expression of the HVHM vector hysteresis operator. This allows the energy distribution, critical surface characteristics, and magnetization direction evolution of the HVHM operator to be dynamically adjusted with temperature and stress changes, thus directly integrating the influence of temperature-stress coupling factors on the magnetization behavior of soft magnetic materials into the hysteresis modeling process. Compared to existing models that mainly rely on parameter re-identification or empirical correction to adapt to changes in operating conditions, this invention can reflect the effects of temperature and stress on the two-dimensional vector hysteresis characteristics from the perspective of magnetization mechanism, improving the physical consistency and prediction accuracy of the model under complex operating conditions.

[0017] This invention further constructs an operator space composed of multiple temperature-stress related HVHM operators, and uses this operator space to map the trajectory of the applied two-dimensional magnetic field, converting the original magnetic field input into a magnetization state vector containing magnetization history features, path dependence features, temperature features, stress features, and vector magnetization state features. Compared with directly using magnetic field strength as network input or using traditional scalar hysteresis operators to extract features, this invention can more fully characterize the intrinsic correlation between the change in magnetic field direction and the evolution of magnetization state during two-dimensional rotational magnetization, improving the expressive power of complex vector magnetization behavior.

[0018] This invention employs a gray-box modeling framework combining a temperature-stress related HVHM operator space and an SAE network. The HVHM operator space extracts magnetization memory and state features with clear physical meaning, while the SAE network establishes the nonlinear mapping between the magnetization state vector and the two-dimensional magnetic flux density. By organically integrating the physical mechanism model with the deep learning model, the network does not need to simultaneously learn hysteresis memory effects, path dependencies, and the influence of temperature and stress from the original data. This reduces the difficulty of model training and the requirement for training samples, while maintaining strong nonlinear fitting capabilities and improving the model's physical interpretability, generalization ability, and engineering applicability.

[0019] Furthermore, this invention introduces a two-dimensional hysteresis trajectory constraint mechanism during SAE network training, consisting of point value error, first-order difference error, and closed area error. This allows the model optimization process to not only focus on the point-to-point error between the predicted and actual magnetic flux density values, but also simultaneously constrain the local variation trend and overall hysteresis trajectory area characteristics. Compared to existing methods that only use point value error as the training objective, this invention effectively reduces the shape distortion and area deviation of the two-dimensional hysteresis trajectory, improves the geometric consistency between the predicted and actual trajectories, and thus more accurately characterizes the rotational magnetization characteristics and hysteresis loss characteristics related to iron loss.

[0020] Therefore, this invention can achieve high-precision prediction of the two-dimensional vector hysteresis characteristics of soft magnetic materials under complex working conditions such as temperature changes, stress changes, and two-dimensional rotational magnetization, providing a more reliable theoretical model and calculation tool for electromagnetic field analysis of electrical equipment, core loss assessment, magnetic material performance research, and optimization design. Attached Figure Description

[0021] Figure 1 This is a flowchart of the two-dimensional vector hysteresis modeling method provided by the present invention.

[0022] Figure 2 This is a schematic diagram of the structure of the two-dimensional vector hysteresis model provided by the present invention.

[0023] Figure 3 This is a schematic diagram comparing the B-trajectory of the model predictions and experimental measurements under conditions of 125℃-5MPa. Detailed Implementation

[0024] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0025] Example 1: This invention provides a two-dimensional vector hysteresis modeling method considering the effects of temperature-stress coupling, comprising the following steps: Step S1. Collect two-dimensional magnetic property data under different temperature and stress conditions, and establish temperature and stress-related magnetic parameters.

[0026] Two-dimensional rotational magnetization excitation was applied to a soft magnetic material under different temperatures and stresses, and the corresponding magnetic field intensity components H were collected. x H y Magnetic flux density component B x B y Temperature T, stress magnitude σ, and stress direction θ σ .

[0027] Step S2. Construct a temperature-stress related HVHM operator based on temperature and stress-related magnetic parameters, and construct a temperature-stress related HVHM operator space to generate a magnetization state vector.

[0028] First, by establishing temperature-dependent and stress-dependent magnetic parameters and incorporating them into the energy expression system of the HVHM vector hysteresis operator, the model can reflect the influence of temperature and stress changes on the magnetization process of soft magnetic materials from the perspective of magnetization mechanism. This overcomes the limitation of traditional models that are only applicable to fixed operating conditions or single environmental conditions, improving the model's adaptability and prediction accuracy under multiple temperature and stress conditions. Then, a temperature-stress dependent HVHM operator space is constructed. The magnetization state is characterized by multiple discrete energy levels of vector hysteresis operators, enabling the simultaneous recording of magnetization history, vector magnetization state information, and environmental condition information, thus achieving an effective description of the two-dimensional rotational magnetization process. Compared to traditional scalar hysteresis models, this invention can more accurately characterize the two-dimensional vector relationship between magnetic field strength and magnetic flux density, improving the reliability of magnetic property prediction under complex magnetization conditions.

[0029] Specifically, based on the current operating temperature T of the soft magnetic material, temperature-dependent magnetic parameters are established for the subsequent construction of the temperature-dependent HVHM operator. These temperature-dependent magnetic parameters include the temperature-dependent spontaneous magnetization M(T), the temperature-dependent magnetocrystalline anisotropy constant K(T), and the temperature-dependent saturation magnetostriction coefficient λ. s (T).

[0030] The reference temperature T0 is selected as room temperature (25℃), and an expression for the spontaneous magnetization intensity as a function of temperature is established based on the Weiss theory of ferromagnetic materials:

[0031] Where M(T) is the spontaneous magnetization at temperature T. Let T be the saturation spontaneous magnetization at the reference temperature T0. CWhere is the Curie temperature of the material, and n is a constant related to the material properties. T is the measured operating temperature, and T0 is the selected reference temperature; T C It can be obtained by Curie temperature testing; n can be identified through multi-temperature magnetic property experimental data.

[0032] Simultaneously, an expression for the magnetocrystalline anisotropy constant as a function of temperature is established:

[0033] Where K(T) is the magnetocrystalline anisotropy constant at temperature T, K(T0) is the magnetocrystalline anisotropy constant at reference temperature T0, and α K The proportionality coefficient is related to the material properties and can be identified through experimental data on magnetic properties.

[0034] Through the above processing, M(T) and K(T) corresponding to the current temperature are obtained. Furthermore, the temperature-dependent saturation magnetostriction coefficient λ is... s (T), which can be identified through multi-temperature magnetostriction experimental data; when the temperature variation range is small, it can also be approximated as a constant. For different temperature samples, the corresponding temperature-dependent magnetic parameters are calculated in the above manner. The outputs of this step are M(T) and K(T), which serve as the basic parameters for subsequently constructing the temperature-dependent HVHM operator and the temperature-dependent HVHM operator space.

[0035] Based on the established temperature-dependent magnetic parameters, stress-dependent magnetic parameters are further established according to the current working stress state of the soft magnetic material, which are used for the subsequent construction of the stress-dependent HVHM operator. The stress-dependent magnetic parameters include the stress-induced magnetoelastic anisotropy coefficient K. σ Equivalent magnetocrystalline anisotropy constant K eff and the equivalent easy magnetization axis direction ψ eff .

[0036] The stress state can be uniaxial stress or planar multiaxial stress. When a soft magnetic material is subjected to uniaxial mechanical stress, the stress state can be expressed by the following parameters: σ, θ σ Where σ represents the magnitude of stress, with tensile stress taking a positive value and compressive stress taking a negative value; θ σ Let be the angle between the stress direction and the reference direction. When a soft magnetic material is subjected to planar multiaxial stress, the stress state can be expressed as:

[0037] Where, σ xx σ yy and τ xy These are the plane stress tensor components.

[0038] Stress enters the total free energy of magnetic particles through the magnetoelastic energy term. For uniaxial stress, the magnetoelastic energy can be expressed as:

[0039] Where, λ s (T) is the saturation magnetostriction coefficient at temperature T, and θ is the magnetization direction angle.

[0040] For multiaxial stress, the magnetoelastic properties can be expressed as:

[0041] By equating the direction-dependent part of the magnetoelastic energy term to stress-induced anisotropy, we can obtain the stress-induced magnetoelastic anisotropy coefficient:

[0042] Among them, K σ (T,σ) represents the equivalent anisotropic strength caused by mechanical stress. This parameter characterizes the effect of stress on the stability of the magnetization direction. When λ s When (T)σ>0, the stress direction tends to become the equivalent easy magnetization direction; when λ s When (T)σ<0, the direction perpendicular to the stress direction tends to become the equivalent easy magnetization direction.

[0043] The original temperature-dependent magnetocrystalline anisotropy and stress-induced magnetoelastic anisotropy are combined to obtain the total anisotropy:

[0044] Where K(T) is the temperature-dependent magnetocrystalline anisotropy constant, and ψ0 is the original easy magnetization axis direction of the material. The above expression can be further equivalent to:

[0045] Where C is a constant independent of the magnetization direction and does not affect the solution for the magnetization direction; K eff (T,σ) is the equivalent magnetocrystalline anisotropy constant under the combined effects of temperature and stress, ψ eff It represents the equivalent easy magnetization axis direction under the combined effects of temperature and stress.

[0046] The equivalent magnetocrystalline anisotropy constant can be expressed as:

[0047] The equivalent easy magnetization axis direction can be expressed as:

[0048] Where atan2(⋅,⋅) is used to determine the quadrant where the equivalent easy magnetization axis lies. Through the above processing, K corresponding to the current temperature and current stress state is obtained. σ (T,σ), K eff (T,σ) and ψ eff .

[0049] The temperature-dependent spontaneous magnetization M(T), temperature-dependent magnetocrystalline anisotropy constant K(T), and stress-induced magnetoelastic anisotropy coefficient K were obtained. σ (T,σ), equivalent magnetocrystalline anisotropy constant K eff (T,σ) and the equivalent easy magnetization axis direction ψ eff Then, the above parameters are introduced into the energy expression of the HVHM operator to construct the temperature-stress related HVHM operator.

[0050] For a magnetic particle, its total free energy under temperature-stress coupling can be expressed as:

[0051] Where E(T,σ) is the total free energy of the magnetic particle under the combined effects of temperature T and stress σ; V is the volume of the magnetic particle; K eff (T,σ) is the equivalent magnetocrystalline anisotropy constant, which comprehensively reflects the coupled influence of temperature and stress on the anisotropic strength; ψ eff The equivalent easy magnetization axis direction reflects the deflection of the original easy axis direction by stress-induced anisotropy; θ M θ is the angle between the magnetization vector M and the reference direction; μ0 is the free permeability; M(T) is the temperature-dependent spontaneous magnetization; Ha is the applied magnetic field strength; θ H The angle between the applied magnetic field and the reference direction.

[0052] To facilitate the solution of the stable magnetization state, we introduce a method with the equivalent easy magnetization axis direction ψ. eff A rotating coordinate system with reference direction.

[0053]

[0054] The total free energy in the equivalent easy magnetization axis coordinate system can then be expressed as:

[0055] Based on the extremum and stability conditions of the total free energy E(T,σ), the stable magnetization state of the HVHM operator under temperature-stress coupling is determined, and the conditions are as follows:

[0056] The first derivative condition is used to determine the equilibrium position of the magnetization direction, and the second derivative condition is used to determine whether the equilibrium position is a stable state.

[0057] Furthermore, based on the above extreme value conditions and stability conditions, the critical surface equation of the temperature-stress related HVHM operator in the equivalent easy magnetization axis coordinate system is obtained:

[0058] Where e is the fixed energy value on the equipotential line, the magnitude of which determines the stable state of each point on the equipotential line, and k is the temperature-stress coefficient, the expression of which is:

[0059] The critical surface is used to determine whether the magnetization state of the operator has been updated: when the applied magnetic field is inside the critical surface, the operator maintains the magnetization direction of the previous moment; when the applied magnetic field passes through the critical surface, the operator updates the magnetization direction according to the principle of minimum energy.

[0060] In this implementation, after the applied magnetic field crosses the critical surface, the Newton iteration method is used to find the minimum point of the temperature-stress related total free energy E(T,σ), and the magnetization direction corresponding to this minimum point is used as the update direction of the HVHM operator. This method is used to determine the new steady state after a sudden change in the magnetization direction.

[0061] Through the above steps, the HVHM operator under the combined effects of temperature T and stress σ is obtained. The energy distribution, critical surface shape, and magnetization direction update results of this operator are all related to temperature and stress, and can be used as the basic building blocks of the subsequent temperature-stress related HVHM operator space.

[0062] After obtaining the temperature-stress related HVHM operator, an operator space consisting of multiple temperature-stress related HVHM operators is constructed. This operator space is used to characterize the state of the applied two-dimensional magnetic field trajectory and provides a basis for the subsequent generation of magnetization state vectors.

[0063] Specifically, let the trajectory of the applied two-dimensional magnetic field be: H(t) = [H x (t),H y (t)] T Under the combined effects of temperature T and stress σ, N discrete energy values ​​are selected: {e i} i=1 N And based on each discrete energy value, a corresponding temperature-stress related HVHM operator is constructed: {P i (H(t);e i ,T,σ)} i=1 N Among them, P i (H(t);e i (T,σ) represents the i-th temperature-stress related HVHM operator, e i This represents the discrete energy value corresponding to the operator, where T represents the current temperature and σ represents the current stress state.

[0064] The applied two-dimensional magnetic field trajectory H(t) is input into the aforementioned N temperature-stress related HVHM operators to obtain the two-dimensional output of each operator. Then, the outputs of each operator are concatenated sequentially to form a temperature-stress related magnetization state vector:

[0065] Here, ψ(t,T,σ) represents the magnetization state vector at time t under temperature T, stress state (σ,θσ). Since each HVHM operator outputs a two-dimensional magnetization state quantity, the dimension of the magnetization state vector is 2N when the number of operators is N.

[0066] In the operator space, different HVHM operators correspond to different discrete energy levels, used to characterize the magnetization behavior of soft magnetic materials under different steady states, different critical surface scales, and different magnetization response ranges. For different temperature-stress conditions, the operator index set and the discrete energy value set {e} are preserved. i To ensure consistency in the characteristic dimensions of the operator space output under different temperature-stress conditions, the output varies with temperature T and stress state (σ, θ). Simultaneously, since each operator contains temperature-stress related parameters, the operator output varies with temperature T and stress state (σ, θ). σ ) has changed.

[0067] In a specific implementation, the operator space consists of multiple temperature-stress related HVHM operators, with discrete energy values ​​distributed across multiple intervals. Specifically, most energy values ​​can be positioned within the small e-value interval to improve the resolution of the strongly nonlinear near-saturation region; a relatively large number of energy values ​​can be positioned within the middle e-value interval to characterize the intermediate magnetization region; and a few energy values ​​can be positioned within the large e-value interval to characterize the deeply stable magnetization state. The specific number and range of e-values ​​can be adjusted according to the material type, temperature range, applied stress, magnetic flux density level, and modeling accuracy requirements.

[0068] Through the above steps, the external two-dimensional magnetic field trajectory is converted into a magnetization state vector containing temperature information, stress information, magnetization history information, and vector magnetization state information. This vector serves as the input feature for subsequent SAE network training and prediction.

[0069] After generating the temperature-stress-dependent magnetization state vector, the magnetization state vector and the corresponding two-dimensional magnetic flux density target data are normalized. The normalization process includes the magnetization state vector: ψ(t,T,σ) And the corresponding two-dimensional magnetic flux density vector: B(t) = [B x (t),B y (t)] T A fixed-range linear normalization method is used to map the magnetization state vectors and magnetic flux density data in the training and test samples to a unified numerical range. Usually, the mapping is further mapped to the interval [-1,1] or [0,1] according to the needs of network training.

[0070] To ensure data scale consistency across different temperature-stress and magnetic flux density levels, the training and test sets use the same normalization range. The normalized magnetization state vector is used as the input to the SAE network, and the normalized two-dimensional magnetic flux density vector is used as the output target of the SAE network. After the model prediction is completed, the SAE network output is inversely normalized using the same normalization parameters to obtain B in the form of the actual physical quantity. x (t) and B y (t).

[0071] The above normalization process can unify the data scale under different temperature conditions, stress conditions, and magnetic flux density levels, thereby improving the stability of SAE network training and the consistency of prediction results.

[0072] Step S3. Train the SAE network based on the magnetization state vector and the corresponding two-dimensional magnetic flux density target data to obtain a temperature-stress related HVHM-SAE two-dimensional vector hysteresis model.

[0073] After normalizing the magnetization state vector and the two-dimensional magnetic flux density data, an SAE network is established and trained using normalized training samples to obtain the nonlinear mapping relationship between the magnetization state vector and the two-dimensional magnetic flux density. This application employs a hybrid modeling architecture combining the HVHM operator and the SAE network. The HVHM operator is responsible for extracting physically meaningful magnetization state features, while the SAE network is responsible for establishing the nonlinear mapping relationship between the magnetization state and the magnetic flux density, thus organically integrating physical mechanism modeling and data-driven modeling. This method not only preserves the physical interpretability of the hysteresis model but also reduces the difficulty for neural networks to directly learn the hysteresis memory effect, path dependence characteristics, and the influence of environmental factors, reducing the training data requirements and improving the model's generalization ability and stability.

[0074] Specifically, the normalized temperature-stress-dependent magnetization state vector is used as the input to the SAE network: ψ norm (t,T,σ) The corresponding normalized two-dimensional magnetic flux density vector is used as the output target of the SAE network: B norm (t)=[B x,norm (t),B y,norm (t)] T The SAE network is used to establish the following mapping relationship: B norm (t)=F SAE (ψ norm (t,T,σ)) Among them, F SAE (⋅) represents the nonlinear mapping function learned by the SAE network.

[0075] In one implementation, the SAE network is formed by stacking multiple autoencoders. Each autoencoder includes an encoder and a decoder for layer-by-layer feature extraction and compressed representation of the input features. Since the magnetization state vector generated by the temperature-stress-dependent HVHM operator space has a high dimension and there is a certain correlation between the features in each dimension, the main magnetization state features can be extracted through the SAE network, and a nonlinear relationship between them and the two-dimensional magnetic flux density output can be established.

[0076] SAE network training can be divided into two stages: The first stage is layer-by-layer unsupervised pre-training. Each autoencoder in the SAE network is trained layer by layer, enabling each layer to learn a compressed representation of the input features of the previous layer and obtain better initial network parameters. This stage improves the quality of network parameter initialization and reduces the risk of getting trapped in poor local optima during subsequent global training. The second stage is end-to-end global fine-tuning. After layer-by-layer pre-training, the autoencoder layers are stacked to form a complete SAE network, and the entire network is trained end-to-end with supervised input using the magnetization state vector and output two-dimensional magnetic flux density. This stage further optimizes the SAE network parameters, improving the model's output performance. x (t) and B y (t) matches the experimental measurement.

[0077] In one specific implementation, when the temperature-stress correlated HVHM operator space outputs a 320-dimensional magnetization state vector, the SAE network can employ a 320-100-50-20 layer-by-layer decreasing structure for feature compression and nonlinear mapping. This network structure is only a specific implementation; in practical applications, the number of network layers, the number of hidden layer nodes, and the activation function can be adjusted according to the number of operators, material type, temperature range, stress application, number of samples, and prediction accuracy requirements.

[0078] During training, stochastic gradient descent with momentum can be used to optimize network parameters. In one specific implementation, the number of iterations, batch size, learning rate, momentum coefficient, and activation function can be set during the AE pre-training stage; the number of iterations, early stopping conditions, and model selection criteria can be further set during the global fine-tuning stage. In this embodiment, a combination of the Sigmoid activation function, AE layer-by-layer pre-training, and global fine-tuning is used, and the model with the lowest validation loss is selected as the final model through multiple repeated training iterations.

[0079] After training, the trajectory of the applied two-dimensional magnetic field at the temperature and stress T-σ to be predicted is input into the temperature-stress related HVHM operator space to generate the corresponding magnetization state vector. This magnetization state vector is then normalized and input into the trained SAE network to obtain the normalized two-dimensional magnetic flux density prediction value. Subsequently, inverse normalization is performed based on the normalization parameters to obtain the two-dimensional magnetic flux density prediction result in the form of the actual physical quantity.

[0080] Through the above steps, the predicted results of two-dimensional magnetic flux density under given temperature-stress and two-dimensional applied magnetic field trajectory conditions can be obtained, and the temperature-stress related two-dimensional vector hysteresis trajectory can be further formed.

[0081] In addition, during the end-to-end global fine-tuning stage of the SAE network, in order to accurately capture the geometric characteristics of the two-dimensional hysteresis trajectory, a two-dimensional hysteresis trajectory constraint mechanism based on point values, differences, and closed areas is adopted to optimize the network parameters.

[0082] Suppose the predicted two-dimensional magnetic flux density output by the SAE network is:

[0083] The target value of the two-dimensional magnetic flux density obtained from the experiment is: B(t) = [B x (t),B y (t)] T The total training loss is:

[0084] Among them, L point L is the point error loss, used to constrain the deviation between predicted and experimental point values; diff The first-order difference loss is used to constrain the changing trend of the predicted trajectory and the experimental trajectory between adjacent sampling points; L area A closed area constraint for the two-dimensional magnetic flux density trajectory is used to improve the geometric consistency of the predicted trajectory; w p w d w aThese are the weighting coefficients for the corresponding loss terms.

[0085]

[0086]

[0087]

[0088]

[0089] Where N represents the total number of time steps in the trajectory segment; n is the sample index; and D is the output dimension. This represents the magnetic flux density vector predicted in the nth step; is the corresponding true value; sn is the scalar sample weight in the nth step; and represent the first-order difference between the predicted trajectory and the target trajectory at step n; Let be the edge weight of the nth difference term; and Predicted trajectory and target B, respectively. x –B y The area of ​​the region enclosed by the trajectory; and , where n represents the x and y components of the target magnetic flux density at step n.

[0090] Sample weights s n Higher values ​​are assigned to peaks and valleys, high curvature inflection points, and abrupt change inflection points, allowing the network to focus on the key features of hysteresis loops. To reduce sensitivity to random initialization, multiple training iterations are performed using different random seeds, and the model with the lowest total validation loss is retained.

[0091] During training, L is used as the optimization objective in the global fine-tuning phase of the SAE network, and the SAE network parameters are updated through backpropagation. Higher sample weights can be set for peak points, valley points, high curvature inflection points, regions of abrupt changes in magnetization direction, or error-sensitive regions to enhance the model's ability to learn key regions of the two-dimensional hysteresis trajectory. p w d w a It can be adjusted according to material type, temperature range, stress conditions, magnetic flux density level, number of training samples, and prediction accuracy requirements.

[0092] After the above training, a method is obtained that can predict two-dimensional magnetic flux density components based on the temperature-stress related magnetization state vector. The SAE network model.

[0093] Step S4. Based on the temperature-stress related HVHM-SAE two-dimensional vector hysteresis model, predict the two-dimensional magnetic flux density components of the soft magnetic material under given temperature-stress conditions and applied magnetic field trajectory, and form the corresponding two-dimensional vector hysteresis trajectory.

[0094] After training the SAE network, a temperature-stress related HVHM-SAE two-dimensional vector hysteresis model is obtained. For the temperature and stress to be predicted, T-σ, and the corresponding two-dimensional applied magnetic field trajectory: H(t) = [H x (t),H y (t)] T First, the temperature-stress related magnetization state vector ψ(t,T,σ) is generated according to the aforementioned steps and then normalized. Next, the normalized magnetization state vector is input into the trained SAE network to obtain the normalized two-dimensional magnetic flux density prediction result. Finally, through inverse normalization, the actual physical quantity form of the two-dimensional magnetic flux density output is obtained.

[0095] in, These are the predicted magnetic flux density components in the x and y directions, respectively.

[0096] Based on the output This allows for the further acquisition of two-dimensional vector hysteresis trajectories of soft magnetic materials under corresponding temperature-stress and magnetization conditions. These trajectories can be used to characterize the magnetization response of materials under temperature-stress variations and two-dimensional rotational magnetization conditions, including the shape of the hysteresis trajectory, the trend of local magnetization changes, the characteristics of magnetic flux density distribution, and the area of ​​the closed trajectory.

[0097] Through the above-mentioned output and application methods, this invention can accurately predict the two-dimensional magnetic flux density response and corresponding vector hysteresis trajectory of soft magnetic materials under given temperature, stress and applied two-dimensional magnetic field trajectory conditions. It provides a more accurate basic model for the study of magnetic properties of soft magnetic materials, electromagnetic field simulation of electrical equipment, core loss calculation and structural optimization design, which helps to improve the design accuracy, operating efficiency and performance evaluation level of related equipment.

[0098] Example 2: Based on the two-dimensional vector hysteresis modeling method disclosed in the above examples, this example uses a B25AV1300 non-oriented electrical steel sheet as the test object. The sample is cross-shaped, with an overall size of 80mm × 80mm and a limb width of 10mm. A two-dimensional magnetic measurement system is used for rotational magnetization testing. The test temperature range is 25-200℃, and the applied stress range is 0-20MPa. The excitation frequency is 50Hz, and 200 points are sampled per cycle. The magnetic field strength component (H) is measured. x Hy ) and magnetic flux density component (B x B y (), used as training and validation data for the model.

[0099] With a reference temperature of 25℃, 160 temperature-stress related HVHM operators were constructed, and the energy value e was discrete. i The operators are distributed across three regions: 80 in [-0.5, -8.0] (near-saturation, strongly nonlinear region), 50 in [-8.0, -20.0] (intermediate region), and 30 in [-20.0, -50.0] (deeply stable region). Each operator outputs a two-dimensional magnetization vector, which is concatenated to obtain a 320-dimensional magnetization state vector ψ(t,T,σ). The number of operators and energy levels remain consistent under different temperature-stress conditions.

[0100] The SAE network takes a 320-dimensional magnetization state vector as input and outputs a two-dimensional magnetic flux density (B0). x B y The network structure is 320-100-50-20, with decreasing hidden layers and a Sigmoid activation function. Training consists of two phases: layer-by-layer pre-training: 500 iterations, batch size 50, learning rate 1.0, momentum 0.5, using weight binding; global fine-tuning: 1000 iterations, batch size 50, learning rate 0.2, momentum 0.5, early stopping patience 30, minimum improvement 10. -6 .

[0101] Using a composite loss function:

[0102] Among them, w p =1, w d =0.3, w a =0.3. L point L is the point mean square error. diff For the first-order difference error, L area For B x -B y Area of ​​closure error. The training was repeated 5 times, and the parameters with the lowest validation loss were selected as the model prediction parameters.

[0103] The experimental data were fitted using the constructed temperature-stress dependent HVHM-SAE model, and the results are as follows: Figure 3 As shown, the root mean square error is 0.0223T, verifying the accuracy. Specifically, Figure 3The diagram shows a comparison of the B-trajectories of the model's predicted values ​​and experimental measurements under conditions of 125℃-5MPa. The predicted trajectories and experimental values ​​are basically consistent in shape. The error, calculated using the root mean square (RMS) method, is 0.0223T. The error is within acceptable limits under non-room temperature and non-zero stress conditions, demonstrating the model's ability to generalize across conditions and verifying its accuracy.

[0104] In summary, this invention introduces temperature-dependent and stress-dependent magnetic parameters into the HVHM vector hysteresis operator, constructing a temperature-stress-dependent HVHM operator space. This achieves unified modeling of temperature, stress, and two-dimensional vector magnetization behavior, enabling the characterization of the influence of temperature-stress coupling factors on the hysteresis properties of soft magnetic materials from the perspective of magnetization mechanism. By converting the two-dimensional magnetic field trajectory into a magnetization state vector containing magnetization history, path dependence, temperature information, stress information, and vector magnetization state information, and establishing a nonlinear mapping relationship between the magnetization state and the two-dimensional magnetic flux density using an SAE network, the prediction accuracy and generalization ability under complex operating conditions are improved while maintaining physical interpretability. Furthermore, by introducing a two-dimensional hysteresis trajectory constraint mechanism, simultaneously constraining the point value error, local variation trend, and closed area characteristics of the predicted trajectory, the geometric consistency of the two-dimensional hysteresis trajectory and the characterization accuracy of hysteresis loss-related characteristics are improved. This provides more accurate and reliable technical support for the magnetic property analysis of soft magnetic materials, electromagnetic field calculation of electrical equipment, and core loss assessment.

[0105] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A two-dimensional vector hysteresis modeling method considering the effects of temperature-stress coupling, characterized in that, Includes the following steps: S1. Collect two-dimensional magnetic property data under different temperature and stress conditions, and establish temperature and stress-related magnetic parameters; S2. Construct a temperature-stress related HVHM operator based on temperature and stress-related magnetic parameters, and construct a temperature-stress related HVHM operator space to generate a magnetization state vector; S3. The SAE network is trained based on the magnetization state vector and the corresponding two-dimensional magnetic flux density target data to obtain a temperature-stress related HVHM-SAE two-dimensional vector hysteresis model. S4. Based on the temperature-stress related HVHM-SAE two-dimensional vector hysteresis model, predict the two-dimensional magnetic flux density components of soft magnetic materials under given temperature-stress conditions and applied magnetic field trajectories, and form the corresponding two-dimensional vector hysteresis trajectories.

2. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 1, characterized in that, In step S1, two-dimensional magnetic property data under different temperatures and stress conditions are collected, including corresponding magnetic field strength components H x 、 y , magnetic flux density components B x 、 B y , temperatures T, stress magnitudes σ, and stress directions θ σ .

3. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 2, characterized in that, In step S1, the temperature-dependent magnetic parameters include the temperature-dependent spontaneous magnetization M(T), the temperature-dependent magnetocrystalline anisotropy constant K(T), and the temperature-dependent saturation magnetostriction coefficient λ. s (T).

4. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 2, characterized in that, In step S1, the stress-related magnetic parameters include the stress-induced magnetoelastic anisotropy coefficient K. σ Equivalent magnetocrystalline anisotropy constant K eff and the equivalent easy magnetization axis direction ψ eff .

5. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 1, characterized in that, Step S2 includes: Temperature and stress-related magnetic parameters are incorporated into the total free energy expression, and the temperature-stress related critical surface is determined based on energy extremum conditions and stability conditions. An operator space composed of multiple temperature-stress related HVHM operators is constructed to characterize the magnetization response under different magnetization states and different energy levels; The two-dimensional external magnetic field trajectory is input into the temperature-stress related HVHM operator space to obtain the two-dimensional output of each temperature-stress related HVHM operator, and they are spliced ​​together to form a temperature-stress related magnetization state vector.

6. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 5, characterized in that, In step S2, the temperature-stress related critical surface is determined. When the applied magnetic field passes through the critical surface, the magnetization direction of the operator is updated based on the principle of minimum energy.

7. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 5, characterized in that, Step S2 also includes: After generating the magnetization state vector, the magnetization state vector and the corresponding two-dimensional magnetic flux density target data are normalized.

8. The two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to claim 7, characterized in that, In step S3, during the end-to-end global fine-tuning stage of the SAE network, a two-dimensional hysteresis trajectory constraint mechanism based on point values, differences, and closed areas is used to optimize the network parameters.

9. A two-dimensional vector hysteresis modeling method considering the effect of temperature-stress coupling according to any one of claims 1-8, characterized in that, Step S4 includes: Based on the temperature to be predicted, the stress to be predicted, and the corresponding external magnetic field trajectory, a temperature-stress related magnetization state vector is generated and normalized. The normalized magnetization state vector is input into the temperature-stress related HVHM-SAE two-dimensional vector hysteresis model, and the two-dimensional magnetic flux density of the soft magnetic material to be predicted is output. Based on the output two-dimensional magnetic flux density data, the two-dimensional vector hysteresis trajectory of the soft magnetic material under the corresponding temperature-stress and magnetization conditions is obtained.

Images