J-a hysteresis model parameter identification method and system based on physical information neural network

Abstract

This invention discloses a method and system for parameter identification of the J-A hysteresis model based on a physical information neural network, belonging to the field of data processing technology. Addressing the difficulty in balancing computational efficiency and physical plausibility in existing ferromagnetic material parameter identification techniques, this invention constructs a physical information neural network, embedding the J-A hysteresis model differential equation as a physical constraint into the loss function, and constructing a multi-objective joint optimization function with data fitting loss and parameter boundary constraints. During backpropagation, the network parameters and the J-A parameters to be identified are updated synchronously. This achieves a deep integration of data-driven and physical mechanisms, accelerating the solution process and significantly improving computational efficiency through neural networks, while ensuring the physical interpretability of the parameters through physical equation constraints, effectively avoiding non-physical interpretations. This provides reliable technical support for high-precision hysteresis modeling of electromagnetic devices.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, specifically to a method and system for parameter identification of the JA hysteresis model based on a physical information neural network. Background Technology

[0002] In engineering applications such as power transformers, motors, and electromagnetic devices, accurately characterizing the hysteresis properties of ferromagnetic materials is the core foundation for equipment performance analysis and optimization design. The Jiles-Atherton hysteresis model (JA hysteresis model) has become the mainstream hysteresis modeling scheme due to its clear physical meaning of parameters and wide applicability. The accuracy and efficiency of its parameter identification directly determine the modeling effect. Existing mainstream intelligent optimization identification methods such as genetic algorithms, particle swarm optimization, and simulated annealing all transform parameter identification into a pure numerical optimization problem, which has inherent technical barriers: First, identification relies on a large number of iterations and forward calculations of hysteresis curves, resulting in low computational efficiency and difficulty in meeting the real-time requirements of engineering. Second, it is highly sensitive to initial parameter values ​​and algorithm hyperparameters, leading to poor stability of identification results. Third, it only uses curve fitting error as the optimization objective, without incorporating the physical constraints of the JA model, which easily produces unacceptable results where the mathematical fit is satisfactory but the physical meaning is invalid, and the model prediction is prone to failure under multiple operating conditions. The core concept of the aforementioned existing technology is to achieve parameter optimization by minimizing the hysteresis loop fitting error through intelligent optimization algorithms. Its inherent defect is that it does not embed the physical constraints of the JA model differential equation into the entire optimization process, and cannot simultaneously take into account identification efficiency, result stability and physical rationality, which seriously restricts the application of hysteresis modeling in scenarios such as real-time monitoring and fault diagnosis. Summary of the Invention

[0003] The purpose of this invention is to address the problem that existing ferromagnetic material parameter identification techniques struggle to balance computational efficiency and physical plausibility. It proposes a method and system for identifying parameters of the JA hysteresis model based on a physical information neural network. By constructing a joint loss function using measured hysteresis loop data, the JA model differential equation, and the prior range of parameters as parallel supervisory information, and synchronously updating the network parameters and the JA parameters to be identified during backpropagation, this method significantly shortens the parameter identification time while ensuring that the identification results strictly satisfy the physical laws of magnetization in ferromagnetic materials, thereby significantly improving modeling accuracy and reliability in engineering applications.

[0004] In a first aspect, one technical solution provided in this embodiment of the invention is: a method for identifying parameters of a JA hysteresis model based on a physical information neural network, comprising:

[0005] The measured data of the hysteresis loop of the ferromagnetic material to be identified are obtained. The measured data of the hysteresis loop includes the magnetic field strength and its corresponding magnetization state. The magnetic field strength is used as the input, the magnetization state is used as the output, and the differential equation of the JA hysteresis model is embedded as a physical constraint loss term into the loss function to construct a physical information neural network.

[0006] The measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model are used as parallel supervision information to construct an objective function that includes network parameters and the parameters to be identified of the JA hysteresis model.

[0007] The physical information neural network is iteratively trained to minimize the objective function, and the network parameters of the physical information neural network and the parameters to be identified of the JA hysteresis model are updated synchronously during the backpropagation process of each iteration.

[0008] The target optimization value of the parameter to be identified is extracted from the physical information neural network that meets the convergence condition and used as the parameter identification result of the ferromagnetic material to be identified.

[0009] As an optional approach, the steps of constructing a physical information neural network by using magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function include:

[0010] Construct a neural network that includes an input layer, multiple fully connected hidden layers, and an output layer;

[0011] The normalized magnetic field strength is used as the input of the neural network, and the normalized magnetization state is used as the output of the neural network; the parameters to be identified in the JA hysteresis model are used as the trainable variables of the neural network.

[0012] The first derivative of the magnetization state at the output end with respect to the magnetic field strength at the input end is calculated by automatic differentiation, and the theoretical derivative of the magnetization state at the output end with respect to the magnetic field strength at the input end is calculated based on the parameters to be identified in the current iteration.

[0013] The physical constraint loss term is constructed using the residual between the first derivative and the theoretical derivative, and then embedded into the overall loss function of the neural network to construct the physical information neural network.

[0014] As an optional approach, the step of using the measured hysteresis loop data, the differential equation of the JA hysteresis model, and the prior physical range of the JA hysteresis model parameters as parallel supervision information is as follows:

[0015] Based on the deviation between the predicted magnetization state output by the physical information neural network and the normalized measured magnetization state, a data fitting loss term is constructed as the first supervision information.

[0016] The physical constraint loss term embedded in the loss function of the physical information neural network is used as the second supervision information;

[0017] Based on the degree of deviation between the current value of the parameter to be identified and the prior physical range, a parameter boundary constraint loss term is constructed as the third supervision information;

[0018] The first, second, and third supervisory information are weighted and combined to obtain the objective function with network parameters and parameters to be identified as optimization variables.

[0019] As an optional approach, the step of constructing the parameter boundary constraint loss term based on the deviation between the current value of the parameter to be identified and the prior physical range is as follows:

[0020] For each parameter to be identified, a physical value range is preset, and the range includes a lower limit value and an upper limit value;

[0021] Determine whether the current value of each parameter to be identified falls within the corresponding physical value range;

[0022] For parameters whose current value is lower than the lower limit, the lower boundary penalty is calculated based on the difference between the lower limit and the current value; for parameters whose current value is higher than the upper limit, the upper boundary penalty is calculated based on the difference between the current value and the upper limit; for parameters whose current value is within the range, the boundary penalty is zero.

[0023] The lower and upper boundary penalties of each parameter are assigned corresponding weight coefficients and then summed to generate the parameter boundary constraint loss term; wherein the weight coefficients are positively correlated with the lower or upper boundary penalties.

[0024] As an alternative approach, the step of iteratively training the physical information neural network to minimize the objective function is as follows:

[0025] Configure the adaptive moment estimation optimizer and set the initial learning rate and learning rate decay strategy;

[0026] In each iteration, the normalized magnetic field strength is input into the physical information neural network, the magnetization state is predicted by forward propagation, and the total loss value of the current iteration is calculated according to the objective function.

[0027] The gradients of the total loss value with respect to the network parameters and the parameters to be identified are calculated using the backpropagation algorithm, respectively.

[0028] Based on the gradient of the parameter to be identified, the network parameters and the parameter to be identified are updated synchronously using the adaptive moment estimation optimizer;

[0029] The current learning rate is adjusted according to the learning rate decay strategy, and the weight coefficients of each loss term in the objective function are dynamically adjusted.

[0030] Repeat the above iterative process until the preset convergence condition is met.

[0031] As an optional approach, the steps for adjusting the current learning rate according to the learning rate decay strategy and dynamically adjusting the weight coefficients of each loss term in the objective function are as follows:

[0032] Based on the preset decay period and decay factor, the initial learning rate is decayed in a stepwise manner according to the current iteration number to obtain the updated current learning rate;

[0033] Obtain the gradient norm of each loss term with respect to the network parameters in the current iteration;

[0034] Based on the gradient norm ratio of each loss term, the weight coefficients of each loss term in the objective function are recalculated using the gradient normalization method.

[0035] The updated current learning rate and recalculated weight coefficients are applied to the parameter update process in subsequent iterations.

[0036] As an optional solution, the convergence condition includes at least one of the following: the objective function value is lower than a first preset threshold, the physical constraint loss term value is lower than a second preset threshold, the change in the objective function value within a consecutive preset number of iterations is lower than a third preset threshold, and the number of iterations reaches a preset maximum number of iterations.

[0037] Secondly, an embodiment of the present invention also provides a technical solution: a JA hysteresis model parameter identification system based on a physical information neural network, applicable to the JA hysteresis model parameter identification method based on a physical information neural network as described in the first aspect, comprising:

[0038] The data acquisition module is used to acquire measured data of the hysteresis loop of the ferromagnetic material to be identified.

[0039] The network construction module constructs a physical information neural network by taking magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function.

[0040] The objective function construction module constructs an objective function containing network parameters and the parameters to be identified of the JA hysteresis model by using the measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model as parallel supervision information.

[0041] The training optimization module iteratively trains the physical information neural network by minimizing the objective function, and synchronously updates the network parameters of the physical information neural network and the parameters to be identified of the JA hysteresis model during the backpropagation process of each iteration.

[0042] The parameter extraction module is used to extract the target optimization value of the parameter to be identified from the physical information neural network that meets the convergence condition, as the parameter identification result of the ferromagnetic material to be identified.

[0043] Thirdly, one technical solution provided in the embodiments of the present invention is: an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of the first aspects.

[0044] Fourthly, one technical solution provided in the embodiments of the present invention is: a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the method as described in any of the first aspects.

[0045] The present invention has at least the following substantial beneficial effects:

[0046] (1) This application embeds the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function of the physical information neural network. It uses automatic differentiation technology to calculate the derivative of the magnetization state with respect to the magnetic field strength in real time, and uses the residual between the derivative and the theoretical derivative of the model to construct physical constraint supervision information. This ensures that the neural network must satisfy the differential physical laws in the hysteresis evolution process while fitting the measured data. In this way, the dual guidance of "data-driven fitting" and "physical law-driven constraint" is realized in the parameter optimization process, ensuring that the identification results not only approximate the measured curve numerically, but also strictly conform to the magnetization physical nature of ferromagnetic materials in terms of mechanism. This significantly improves the generalization ability and prediction reliability of the model under multiple working conditions.

[0047] (2) This application sets the parameters to be identified in the JA hysteresis model as trainable variables of the neural network, constructs an end-to-end mapping structure with magnetic field strength as input and magnetization state as output, and constructs a joint objective function in parallel using measured data loss, physical constraint loss and parameter boundary constraint loss in each iteration training. The network weights and model parameters are updated synchronously during backpropagation through an adaptive moment estimation optimizer, which realizes the deep integration and collaborative optimization of parameter identification and neural network training. This significantly reduces the iterative overhead of repeatedly forward calculating the hysteresis curve in traditional methods, and significantly improves the convergence speed and computational efficiency of parameter identification. It provides a feasible technical path for engineering scenarios with high timeliness requirements such as real-time monitoring and online diagnosis.

[0048] (3) This application introduces a boundary constraint loss term based on the prior physical range of the parameters into the objective function, quantifies the deviation between the current value of each parameter to be identified and the preset physical interval into a differentiable penalty function, and dynamically adjusts the weight coefficient of each loss term in combination with the gradient normalization method. This allows the parameter update process to make full use of the guidance of data and physical information, and effectively suppress the drift of parameters to non-physical regions. In this way, a soft constraint barrier of the feasible region of parameters is built in the optimization process, which significantly reduces the dependence on the initial value of the parameters, improves the robustness of the identification process and the stability of the results, and ensures that physically consistent and numerically stable parameter optimization values ​​can be obtained under different initial conditions and noise environments.

[0049] The above description of the invention is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0050] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0051] Figure 1 This is a flowchart of the JA hysteresis model parameter identification method based on physical information neural network according to an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram of the physical information neural network architecture according to an embodiment of the present invention.

[0053] Figure 3 This is a graph showing the convergence process of parameter identification in an embodiment of the present invention.

[0054] Figure 4 This is a curve comparing the convergence speeds of PINN and PSO in an embodiment of the present invention.

[0055] Figure 5 This is a block diagram of the JA hysteresis model parameter identification system based on physical information neural network according to an embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only one preferred embodiment of this invention and are only used to explain this invention. They do not limit the scope of protection of this invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0057] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the operations (or steps) as sequential processes, many of the operations (or steps) can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but it may also have additional steps not included in the figures; the process may correspond to a method, function, procedure, subroutine, subroutine, etc.

[0058] Example 1: As Figure 1 As shown, one technical solution provided in this embodiment of the invention is: a method for identifying parameters of a JA hysteresis model based on a physical information neural network, comprising:

[0059] S1. Obtain the measured data of the hysteresis loop of the ferromagnetic material to be identified. The measured data of the hysteresis loop includes the magnetic field strength and its corresponding magnetization state. Using the magnetic field strength as input and the magnetization state as output, the differential equation of the JA hysteresis model is embedded as a physical constraint loss term into the loss function to construct a physical information neural network.

[0060] It should be noted that in the step of obtaining the measured hysteresis loop data of the ferromagnetic material to be identified, the measured hysteresis loop data is a physical observation set that maps the magnetic field strength H (unit: A / m) of the ferromagnetic material under alternating excitation conditions to the corresponding magnetization state (magnetization intensity M or magnetic induction intensity B). For example, the HB data of 30Q120 oriented silicon steel sheet under a 50Hz alternating magnetic field collected by a magnetic material tester is a set of {(H1,B1),(H2,B2),…,(H n B n This step collects measured data of hysteresis characteristics under real working conditions, providing a unique and accurate monitoring benchmark for parameter identification that fits the actual engineering situation, thus avoiding the problem of deviation between pure simulation data and actual physical characteristics.

[0061] Understandably, in order to overcome the problems of low computational efficiency and frequent non-physical interpretation caused by the traditional JA hysteresis model parameter identification relying solely on data fitting and lacking constraints from the physical laws of magnetization, this application first obtains measured data of hysteresis loops of ferromagnetic materials to provide engineering physical observation basis, and then constructs a physical information neural network with magnetic field strength as input and magnetization state as output, embedding the physical constraint loss term of the differential equation of the JA hysteresis model, so as to realize the integrated fusion of measured data supervision and constraints from the physical laws of magnetization of ferromagnetic materials.

[0062] As an optional embodiment, after acquiring the measured hysteresis loop data of the ferromagnetic material to be identified, a preprocessing step is also included for the acquired hysteresis loop measured data. Specifically, this includes: denoising the acquired data pairs: using a Savitzky-Golay filter, setting the window length to 5-11 sampling points, and the polynomial order to 2-3. The filtered data pairs are represented as { }

[0063] Furthermore, the denoised data is normalized:

[0064] Wherein, the magnetic field strength is normalized: Magnetic induction intensity normalization: ;

[0065] in, H i ' is the th after Savitzky-Golay filtering i Each magnetic field strength sample value (A / m); max(|H'|) is the maximum absolute value of the filtered magnetic field strength, i.e., the normalized reference value; similarly, B i ' is the filtered number i Each magnetic flux density value (T); () is the normalization benchmark.

[0066] This makes the normalized data range [-1,1] or [0,1].

[0067] Furthermore, the training set and validation set are divided randomly according to an 8:2 or 7:3 ratio. The training set is used for parameter identification, and the validation set is used to evaluate generalization performance.

[0068] As an optional embodiment, the steps of constructing a physical information neural network by taking magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function are shown in S11~S14.

[0069] S11. Construct a neural network that includes an input layer, multiple fully connected hidden layers, and an output layer.

[0070] It should be noted that the input layer receives the normalized magnetic field strength H. norm The input dimension is l; hidden layers: containing L fully connected layers (L=4,5,6), the calculation formula for the l-th layer is: h l =σ(W l ·h l-1 +b l ); where: W l b is the weight matrix of the l-th layer; l Here is the bias vector for the l-th layer; σ(·) is the activation function, using the Tanh function; h0=H norm For input, h L This is the output of the last hidden layer; Output layer: Output magnetization M or magnetic flux density B, calculated using the formula: M pred =W out ·h L +b out Or B pred =μ0(H+M pred )=μ0H+μ0W out ·h L +μ0b out Where μ0 = 4π × 10 -7 H / m is the vacuum permeability; therefore, the parameters that can participate in the training of the PINN model include: neural network parameters: i NN ={W1,b1,W2,b2,...,W L ,b L W out ,b out};JA physical parameters: i JA ={ M s ,a,a,k,c};in, M s , The saturation magnetization is a These are the parameters for interdomain interaction. α The interdomain coupling coefficient is... k The pinning effect strength parameter, c Reversible magnetization coefficient ； All trainable parameters: i ={ i NN , i JA}

[0071] It is understandable that, such as Figure 2As shown, this embodiment specifically constructs a fully connected network architecture consisting of a 1D input layer, an L-layer (L=4,5,6) N (N=64, 128, or 256) fully connected hidden layer (using the Tanh activation function), and a 1D output layer. By constructing a deep network structure adapted to the nonlinear mapping characteristics of hysteresis, it achieves efficient fitting of the complex nonlinear relationship of the hysteresis loop.

[0072] S12. The normalized magnetic field strength is used as the input of the neural network, and the normalized magnetization state is used as the output of the neural network; the parameters to be identified in the JA hysteresis model are used as the trainable variables of the neural network.

[0073] It should be noted that the normalized magnetic field strength and magnetic induction intensity are normalized to the [-1,1] interval, and the parameters to be identified in the JA hysteresis model are... M s ,a,a,k,c As a trainable variable of the network, the convergence of network training is accelerated by unifying the data scale, while the identification of physical parameters is transformed into a network training task, providing support for the synchronous updating of network parameters and physical parameters.

[0074] S13. Calculate the first derivative of the magnetization state of the output terminal with respect to the magnetic field strength of the input terminal through automatic differentiation, and at the same time calculate the theoretical derivative of the magnetization state of the output terminal with respect to the magnetic field strength of the input terminal as determined by the differential equation of the JA hysteresis model based on the currently iterated parameters to be identified.

[0075] It should be noted that the magnetization at the output terminal is calculated through automatic differentiation. M pred The predicted value of the first derivative of the magnetic field strength H at the input terminal, i.e., dM / dH: Secondly, the network's current predicted values... JA parameters to be identified i JA ={ Ms. , a , α , k , c Substituting the values ​​into the following calculation steps, we obtain the theoretical value of dM / dH. Specifically:

[0076] The first step is to calculate the effective magnetic field H. e H e =H+ α M; H is the applied magnetic field strength; M is the total magnetization;

[0077] The second step is to calculate the rate of change of irreversible magnetization with respect to the applied magnetic field. ; It is the irreversible magnetization intensity; It is a hysteresis-free magnetization intensity; This is the magnetic field direction coefficient; Pinning effect intensity parameters;

[0078] The third step is to substitute the equation into the JA total differential equation to obtain the theoretical derivative. Specifically, it is expressed as:

[0079] ;

[0080] in, ; It is a hysteresis-free magnetization intensity; The saturation magnetization; The function is a hyperbolic cotangent function. In this embodiment, the predicted value of the rate of change of magnetization is accurately obtained by means of automatic differentiation, and the theoretical value is obtained by combining the physical model, so as to provide an accurate calculation basis for quantifying the physical constraint residual.

[0081] S14. Construct a physical constraint loss term using the residual between the first derivative and the theoretical derivative, and embed the physical constraint loss term into the overall loss function of the neural network to construct the physical information neural network.

[0082] Understandably, the physical constraint loss term is constructed using the residual between the first derivative and the theoretical derivative and embedded into the overall loss function of the neural network. The formula for the physical constraint loss term is: , The number of training set samples; this physical constraint loss term, by penalizing the residuals of the differential equation, ensures that the magnetization law learned by the network conforms to physical laws. When L physics When the value approaches 0, it means that the rate of magnetization change output by the neural network at each sampling point matches the theoretical value of the JA differential equation, thus ensuring the identification parameters. i JA This embodiment satisfies the physical laws of magnetization of ferromagnetic materials. It transforms the physical laws of the differential equations of the JA hysteresis model into trainable loss constraints, forcing the network output to strictly conform to the physical mechanism of magnetization of ferromagnetic materials, thus eliminating the generation of non-physical solutions from the training mechanism.

[0083] S2. Using the measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model as parallel supervision information, construct an objective function that includes network parameters and the parameters to be identified of the JA hysteresis model.

[0084] Understandably, to address the technical shortcomings of traditional JA hysteresis model parameter identification, which relies solely on single data fitting supervision and lacks physical mechanism constraints and parameter boundary limitations, resulting in insufficient fitting accuracy and susceptibility to non-physical interpretations, this embodiment uses measured hysteresis loop data, JA hysteresis model differential equations, and the prior physical range of JA hysteresis model parameters as triple parallel supervision information. Data fitting loss terms, physical constraint loss terms, and parameter boundary constraint loss terms are sequentially constructed and weighted and fused into a unified objective function. This achieves multi-dimensional collaborative constraints of data observation supervision, magnetization physical mechanism supervision, and parameter physical range supervision, providing balanced and accurate training guidance for the synchronous optimization of neural network parameters and the parameters to be identified in the JA hysteresis model.

[0085] As an optional embodiment, the step of using the measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model as parallel supervision information is shown in S21~S24.

[0086] S21. Based on the deviation between the predicted magnetization state output by the physical information neural network and the normalized measured magnetization state, a data fitting loss term is constructed as the first supervision information.

[0087] Understandably, the data fitting loss term is used to measure the fitting error between the network's predicted curve and the measured curve, and is expressed in the form of mean squared error (MSE), specifically: Wherein: N train B is the number of samples in the training set; pred (H i ;θ) represents the network in a magnetic field of strength H i The predicted magnetic flux density depends on all trainable parameters. i B meas (H i ) represents the actual measured or simulated value of the magnetic flux density; ||·|| 2 The L2 norm squared is represented; the contextualized physical meaning of the data fitting loss term is the numerical fitting deviation between the network-predicted magnetic induction intensity and the measured magnetic induction intensity of ferromagnetic materials (such as 30Q120 oriented silicon steel sheets). This embodiment realizes the constraint of network output based on measured physical observation data, ensuring the basic numerical fitting accuracy of parameter identification.

[0088] S22. The physical constraint loss term embedded in the loss function of the physical information neural network is used as the second supervision information.

[0089] It is understandable that the physical constraint loss term of the differential equation of the JA hysteresis model embedded in the loss function of the physical information neural network has a contextualized physical meaning that the rate of change of magnetization intensity of the network output strictly fits the physical law of magnetization differential of ferromagnetic materials. This technique enables the standardization of the network training process from the perspective of magnetization mechanism, and avoids the network output from deviating from the inherent physical characteristics of the JA model.

[0090] S23. Based on the degree of deviation between the current value of the parameter to be identified and the prior physical range, construct a parameter boundary constraint loss term as the third supervision information.

[0091] Understandably, to ensure that the identified JA parameters are within a physically reasonable range, a soft constraint penalty term is introduced: L boundary = w Ms ·ReLU(- M s ) + w a ·ReLU(- a )+ w α ·[ReLU(- α )+ReLU( α -1)]+ w k ·ReLU(- k )+ w c ·[ReLU(- c )+ReLU( c -1)]; where ReLU( x )=max(0, x () represents the modified linear unit function; w Ms , w a , w α , w k , w c The penalty weight coefficients for each parameter typically range from 10 to 100. In this embodiment, based on the deviation of the current values ​​of the parameters Ms, a, α, k, and c to be identified (JA) from the prior physical range, a parameter boundary constraint loss term is constructed as the third supervisory information. Its contextualized physical meaning is to apply soft penalties to parameters that exceed the limits, such as negative saturation magnetization or reversible magnetization exceeding 1. Through this technique, the parameters to be identified are limited to a physically reasonable range, thus preventing the generation of non-physical interpretations from the source.

[0092] S24. Perform a weighted combination of the first supervision information, the second supervision information, and the third supervision information to obtain an objective function with network parameters and parameters to be identified as optimization variables.

[0093] It can be understood that the objective function can be expressed as: L total = λ1·L data + λ2·L physics + λ3·L boundary ; where λ1, λ2, and λ3 are weight coefficients and an adaptive adjustment strategy is adopted. In this embodiment, a weighted combination of the first supervision information, the second supervision information, and the third supervision information is performed to obtain an objective function with network parameters and parameters to be identified in the J-A hysteresis model as optimization variables. Through this technical means, the triple supervision information is integrated into a unified optimization objective, providing a stable and balanced optimization guidance for subsequent synchronous update of network parameters and physical parameters.

[0094] As an optional embodiment, the step of constructing a parameter boundary constraint loss term according to the deviation degree between the current value of the parameter to be identified and the prior physical range is as shown in S231~S236.

[0095] S231. Preset a physical value range for each parameter to be identified, and the range includes a lower limit value and an upper limit value.

[0096] It can be understood that by presetting a physical value range for each parameter to be identified, that is, setting physical compliance ranges including upper and lower limits for the core parameters to be identified in the J-A hysteresis model, namely the saturation magnetization Ms, the magnetic domain interaction parameter a, the magnetic domain coupling coefficient α, the pinning effect parameter k, and the reversible magnetization coefficient c. For example, Ms>0, a>0, 0<α<1, k>0, 0<c<1. By clarifying the physical rationality judgment criteria for each parameter, a standardized basis is provided for subsequent boundary penalty calculation.

[0097] S232. Respectively judge whether the current value of each parameter to be identified falls within the corresponding physical value range.

[0098] It can be understood that in this embodiment, it is respectively judged whether the current value of each parameter to be identified falls within the corresponding physical value range, that is, the matching state between the real-time values of Ms, a, α, k, and c during training iteration and the preset range is monitored in real time. Through this technical means, parameter out-of-bounds situations are accurately identified, and the targeted triggering of boundary constraints is achieved.

[0099] S233. For a parameter whose current value is lower than the lower limit value, calculate a lower boundary penalty amount based on the difference between the lower limit value and the current value.

[0100] Understandably, for parameters whose current value is lower than the lower limit, the lower boundary penalty is calculated based on the difference between the lower limit and the current value. For example, when Ms < 0, the lower boundary penalty is 0 - Ms. This technique accurately quantifies the degree of parameter lower boundary violation, providing a calculable penalty basis for parameter lower limit violations.

[0101] S234. For parameters whose current value is higher than the upper limit value, calculate the upper boundary penalty based on the difference between the current value and the upper limit value.

[0102] Understandably, for parameters whose current value is higher than the upper limit, the upper boundary penalty is calculated based on the difference between the current value and the upper limit. For example, when c>1, the upper boundary penalty is c-1. This technique accurately quantifies the degree of parameter upper boundary violation, providing a calculable penalty basis for parameter upper limit violations.

[0103] S235. For parameters whose current value is within the specified interval, the boundary penalty is zero.

[0104] It is understandable that for parameters whose current value is within the physical range, the boundary penalty is set to zero. For example, the penalty is 0 when 0 < α < 1. This technique ensures that physically compliant parameters are not subject to additional penalties and maintains the normal training gradient of the parameters.

[0105] S236. After assigning corresponding weight coefficients to the lower boundary penalty and upper boundary penalty of each parameter, the weight coefficients are summed to generate the parameter boundary constraint loss term; wherein, the weight coefficients are positively correlated with the lower boundary penalty or the upper boundary penalty.

[0106] Understandably, the parameter boundary constraint loss term L is generated by summing the weights of the lower and upper boundary penalties of each parameter, which are then assigned weights positively correlated with the penalty amounts. boundary = w Ms ·ReLU(- M s ) + w a ·ReLU(- a )+ w α ·[ReLU(- α )+ReLU( α -1)]+ w k ·ReLU(- k )+ w c ·[ReLU(- c )+ReLU( c-1)]; This technique integrates discrete boundary penalty quantities into continuously differentiable loss terms, adapting to the optimization mechanism of backpropagation in neural networks.

[0107] S3. Iteratively train the physical information neural network to minimize the objective function, and synchronously update the network parameters of the physical information neural network and the identification parameters of the JA hysteresis model during the backpropagation process of each iteration.

[0108] Understandably, to address the technical problems of poor fit between network parameters and physical parameters, slow convergence speed, and susceptibility to local optima caused by step-by-step optimization in traditional JA hysteresis model parameter identification, this embodiment takes minimizing the multi-objective total loss function of fused data fitting, physical constraints, and parameter boundaries as the core optimization guideline. Iterative training is carried out on the physical information neural network, and in the backpropagation process of each iteration, the network parameters such as weights and biases of the neural network are updated synchronously with the physical parameters to be identified, such as the saturation magnetization and magnetic domain interaction parameters of the JA hysteresis model. This achieves synergistic iterative optimization of the network's nonlinear fitting ability and the rationality of the JA model's physical parameters, providing a core training mechanism to support the final output of accurate and physically compliant parameter identification results.

[0109] As an optional embodiment, the step of iteratively training the physical information neural network to minimize the objective function is shown in S31-S36.

[0110] S31. Configure the adaptive moment estimation optimizer and set the initial learning rate and learning rate decay strategy.

[0111] Understandably, this involves configuring an adaptive moment estimation optimizer and setting the initial learning rate and learning rate decay strategy; specifically, using the Adam optimizer and configuring the initial learning rate value. or =1×10 -3 Exponential decay rate β 1 = 0.9, β 2 = 0.999, numerical stability term e =1×10 -8 Combined with a step-by-step learning rate decay strategy or epoch = or initial ×γ floor(epoch / step_size) Where γ=0.9, step_size=1000, or initial =1×10 -3(Initial learning rate). In this embodiment, the nonlinear optimization characteristics of hysteresis parameter identification (such as for 30Q120 oriented silicon steel sheet) are configured with an adaptive optimization mechanism. This technology provides a stable and adaptive optimization basis for parameter updates, adapting to the nonlinear gradient optimization requirements of hysteresis modeling.

[0112] S32. In each iteration, the normalized magnetic field strength is input into the physical information neural network, the magnetization state is predicted by forward propagation, and the total loss value of the current iteration is calculated according to the objective function.

[0113] Understandably, in each iteration, the normalized magnetic field strength is input into the physical information neural network, and the magnetization state is predicted through forward propagation, based on the objective function L. total =λ1·L data +λ2·L physics +λ3·L boundary The total loss value of the current iteration is calculated. In this embodiment, the normalized magnetic field strength is substituted into the network output to predict the magnetic induction intensity, and the weighted calculation of the triple loss of data fitting, physical constraints, and parameter boundaries is completed. This technique accurately quantifies the overall training bias of the current iteration parameter combination, providing a complete numerical basis for subsequent gradient calculation.

[0114] S33. Calculate the gradient of the total loss value with respect to the network parameters and the parameters to be identified using the backpropagation algorithm.

[0115] It is understandable that the total loss value is calculated against the network parameters using the backpropagation algorithm. i NN and parameters to be identified i JA gradient , This embodiment uses the chain rule to solve the optimization direction and adjustment range of the neural network weight bias and the five JA parameters. This technique accurately obtains the update direction of the two types of parameters, providing quantitative gradient support for synchronous optimization.

[0116] S34. Based on the gradient of the parameter to be identified, the network parameters and the parameter to be identified are updated synchronously using the adaptive moment estimation optimizer.

[0117] It is understood that, based on the gradient of the parameters to be identified, the network parameters and the parameters to be identified are updated synchronously using an adaptive moment estimation optimizer. In this embodiment, the weights W and bias b of the neural network and the Ms, a, α, k, and c parameters of the JA model are adjusted synchronously, rather than the traditional step-by-step independent optimization. This technique achieves the coordinated adaptation of network fitting characteristics and physical parameters, avoiding deviation from the global optimal solution by optimizing a single parameter.

[0118] S35. Adjust the current learning rate according to the learning rate decay strategy, and dynamically adjust the weight coefficients of each loss term in the objective function.

[0119] It is understood that the current learning rate is adjusted according to the learning rate decay strategy, and the weight coefficients of each loss term in the objective function are dynamically adjusted. Specifically, the learning rate is decayed stepwise according to the number of iterations, and the gradient normalization method is used to update λ1, λ2, and λ3. In this embodiment, the learning rate is reduced as the training process progresses and the gradient contribution of the three losses is balanced. This technique avoids training oscillations in the later stages and ensures the balanced role of data supervision, physical supervision, and boundary supervision.

[0120] S36. Repeat the above iterative process until the preset convergence condition is met.

[0121] Understandably, in order to continuously iterate and optimize until the parameter identification results meet the dual requirements of accuracy and physical rationality, the above iterative process is repeated until the preset convergence condition is met, ensuring that the training terminates at the optimal and physically compliant parameter state.

[0122] As an optional embodiment, the steps of adjusting the current learning rate according to the learning rate decay strategy and dynamically adjusting the weight coefficients of each loss term in the objective function are shown in S351~S354.

[0123] S351. Based on the preset decay period and decay factor, the initial learning rate is decayed in a stepwise manner according to the current iteration number to obtain the updated current learning rate.

[0124] Understandably, based on a preset decay period and decay factor, the initial learning rate is decayed in a stepwise manner according to the current iteration number to obtain the updated current learning rate. Specifically, a stepwise decay formula is used. or epoch = or initial ×γ floor(epoch / step_size) Where γ=0.9, step_size=1000, or initial =1×10 -3 (Initial learning rate); This refers to the training process for identifying parameters of ferromagnetic materials (such as 30Q120 oriented silicon steel sheets). The parameter update step size is gradually reduced with each iteration. This technique avoids parameter oscillations and loss fluctuations caused by excessively large learning rates in the later stages of training.

[0125] S352. Obtain the gradient norm of each loss term with respect to the network parameters in the current iteration.

[0126] Understandably, obtaining the gradient norm of each loss term with respect to the network parameters in the current iteration involves calculating the data fitting loss term L.data Physical constraint loss term L physics Parameter boundary constraint loss term L boundary The gradient norm of the total trainable parameters θ , , This embodiment quantifies the actual contribution of the three losses to parameter updates in the current iteration, and uses this technique to accurately measure the training influence of each supervision item, providing an objective quantitative basis for weight balance adjustment.

[0127] S353. Based on the gradient norm ratio of each loss term, recalculate the weight coefficient of each loss term in the objective function according to the gradient normalization method.

[0128] Understandably, based on the gradient norm ratio of each loss term, the weight coefficients of each loss term in the objective function are recalculated using the gradient normalization method. (i=1,2,3), this embodiment eliminates the constraint imbalance caused by the difference in loss values ​​by balancing the gradient contribution magnitude of the three losses. This technique ensures that the constraints of data fitting, physical mechanism and parameter boundary supervision on training are balanced.

[0129] S354. Apply the updated current learning rate and the recalculated weight coefficients to the parameter update process in subsequent iterations.

[0130] Understandably, by applying the updated current learning rate and the recalculated weight coefficients to the parameter update process in subsequent iterations, this embodiment will substitute the adaptively adjusted learning rate and loss weights into the next round of forward and backward propagation. This technique continuously ensures the optimization stability and directional accuracy of subsequent iterations, and promotes the training to converge quickly and smoothly to the optimal solution.

[0131] S4. Extract the target optimization value of the parameter to be identified from the physical information neural network that meets the convergence condition, and use it as the parameter identification result of the ferromagnetic material to be identified.

[0132] As an optional embodiment, the convergence condition includes at least one of the following: the objective function value is lower than a first preset threshold, the physical constraint loss term value is lower than a second preset threshold, the change in the objective function value within a consecutive preset number of iterations is lower than a third preset threshold, and the number of iterations reaches a preset maximum number of iterations.

[0133] It is understandable that the training termination state is determined based on preset multiple convergence conditions, including the objective function value L. total <1×10 -6 (First preset threshold), physical constraint loss term value L physics <1×10 -5(Second preset threshold) The change in the objective function value over 100 consecutive iterations is less than 1×102 -8 (Third preset threshold) When the number of iterations reaches the preset maximum number of iterations of 10,000, the parameter identification task of ferromagnetic materials (such as 30Q120 oriented silicon steel sheets) in this embodiment comprehensively judges whether the training meets the standard from four dimensions: numerical fitting accuracy, physical constraint compliance, training stability, and upper limit of computing resources. This technical means realizes the accurate determination of the training termination node, taking into account identification accuracy, physical rationality, and computational efficiency; the target optimization value of the parameter to be identified is extracted from the physical information neural network that meets the convergence condition, which is used to extract the core physical parameters of the JA hysteresis model after network co-training optimization. , , , , This technique obtains the optimal physical parameters that have undergone triple verification through data supervision, physical constraints, and boundary limitations. The extracted target optimization values ​​are then used as the parameter identification results for the ferromagnetic material to be identified. The contextual physical meaning is that the converged compliant parameters are used as the standard JA model parameters for modeling the hysteresis characteristics of the corresponding ferromagnetic material. This technique provides accurate and reliable parameter support for hysteresis simulation, performance optimization, and fault diagnosis of electromagnetic equipment such as power transformers and motors.

[0134] As a specific example of Embodiment 1, the JA model parameter identification of 30Q120 oriented silicon steel sheets is carried out, and the specific implementation scheme is as follows:

[0135] Step 1: Data Acquisition and Preprocessing;

[0136] Data Acquisition: In this embodiment, the JA model forward calculation method is used to generate hysteresis loop data of 30Q120 oriented silicon steel sheets. First, a set of JA model parameters that conform to the material properties of 30Q120 are given as true values. Then, the theoretical hysteresis curve is generated by numerically solving the JA equation. Finally, measurement noise is superimposed to simulate the actual test data.

[0137] It should be noted that this embodiment uses synthetic data for principle verification in order to quantitatively assess the identification error using known real parameters. In practical engineering applications, measured BH data obtained from Epstein squares, single-piece testers, or comprehensive magnetic material testing platforms should be used.

[0138] Given JA model parameters (true values): Saturation magnetization: M s =1.418×10 6 A / m; Domain wall interaction parameters: a =525.0 A / m; Domain wall coupling parameters: α=0.00458; Domain wall pinning parameters: k =261.5 A / m; Reversible magnetization: c =0.422. Based on the given five JA parameters, the Runge-Kutta method is used to numerically solve the JA differential equations to calculate the magnetization M and magnetic flux density B under the action of the excitation magnetic field H. The hysteresis nonlinearity is considered in the solution process. Five complete excitation cycles are set, with 200 data points sampled in each cycle. The steady-state data of the fifth cycle is extracted to eliminate the influence of the initial transient state.

[0139] To simulate random errors in actual measurements, Gaussian white noise with a mean of 0 and a standard deviation of σ = 0.012T is superimposed on the theoretically calculated magnetic flux density B value to obtain the measured data B. meas =B theory +N(0,0.012 2 ).

[0140] Noise Reduction: The original measurement data contains high-frequency noise due to sensor noise and electromagnetic interference. A Savitzky-Go filter is used for smoothing, with the following parameters: window length: 7 (i.e., 3 points before and after); polynomial order: 3 (cubic polynomial fitting); boundary processing: the mirror expansion method is used to process boundary points. After filtering, the noise standard deviation decreases from 0.012T in the original data to 0.003T, improving the signal-to-noise ratio by approximately 75%. Data Normalization: To accelerate neural network training convergence, the data is normalized: H... norm =H / 1000 (normalizes the magnetic field strength to the [-1,1] interval); B norm =B / 1.5 (normalize the magnetic field strength to the [-1,1] interval).

[0141] Dataset split: The 500 samples are split in an 8:2 ratio: training set: 400 samples (index 1-400); validation set: 100 samples (index 401-500).

[0142] Division method: Divide in sequence to maintain the continuity of the magnetization process.

[0143] Step 2: Network structure design and initialization;

[0144] Network architecture: A 4-layer fully connected neural network is constructed, with the following structure: Input layer: 1 neuron (receiving H... norm Hidden layer 1: 128 neurons, activation function Tanh; Hidden layer 2: 128 neurons, activation function Tanh; Hidden layer 3: 128 neurons, activation function Tanh; Hidden layer 4: 128 neurons, activation function Tanh; Output layer: 1 neuron (output M) norm Or Bnorm ).

[0145] Total network parameters: Layer 1: (1+1)×128=256 parameters (weights + biases); Layers 2-4: (128+1)×128×3=49,536 parameters; Output layer: (128+1)×1=129 parameters; Total neural network parameters: 49,921

[0146] JA parameters: 5 ( M s , a , α , k , c Total number of trainable parameters: 49,926.

[0147] Parameter initialization: Neural network parameters: Initialized using a Xavier uniform distribution, for example, the weights W1 of layer 1 are initialized from... Medium sampling, JA parameters: Based on literature data and experience of 30Q120 silicon steel sheets, initial values ​​are set as follows: M s 0 =1.05×10 6 A / m; a 0 =505A / m; α 0 =0.005; k 0 =255A / m; c 0 =0.45.

[0148] Step 3: Training execution;

[0149] Hyperparameter settings: Optimizer: Adam; Initial learning rate: or 0 = 1 × 10 -3 Learning rate decay: Decrease to 0.9 times the original rate every 1000 epochs; Batch size: Full batch (N train =400); Maximum number of epochs: 10,000; Initial values ​​of loss weights: λ1=1.0, λ2=1.0, λ3=0.1; Weight update frequency: λ1, λ2, λ3 are updated once every 100 epochs.

[0150] Training process monitoring: Initial loss value: L total 0 =1.234 (L) data =0.856,L physics =0.312,L boundary=0.066); Key epoch record: Epoch500: Ltotal=0.0342 (L data =0.0198,L physics =0.0131,L boundary =0.0013); Epoch 1000: Learning rate decays to 9×10 -4 L total =0.00812; Epoch2000: Learning rate decays to 8.1×10 -4 L total =0.00156; Epoch3000: L total =3.24×10 -4 ; Epoch4000: L total =8.15×10 -5 ;Epoch5000:L total =2.31×10 -5 ;Epoch5823:L total =9.7×10 -7 <1×10 -6 The training terminates when convergence condition 1 is met; total time: 32 minutes.

[0151] Loss values ​​at convergence: L data =3.2×10 -7 (Data fitting error); L physics =8.1×10 -6 (Physical equation residuals); L boundary =0 (all parameters satisfy the boundary conditions); L total =9.7×10 -7 .

[0152] Step 4: Parameter identification results;

[0153] After training convergence, the final five JA parameters are obtained: =1.430×10 6 A / m; =518.6A / m; =0.00462; =264.3A / m; =0.418.

[0154] Parameter physical rationality check: M s >0 (1.430×10 6 (A / m is within a reasonable range) a >0 (518.6 A / m falls within the literature range of 400-700 A / m); 0< α<1 (0.00462 is within the literature range of 0.001-0.01); k >0 (264.3 A / m is within the literature range of 200-400 A / m); 0< c <1 (0.418 is within the literature range of 0.3-0.6); all parameters meet the physical constraints and are within the typical parameter range of 30Q120 silicon steel sheets, indicating that the identification results are reasonable and reliable.

[0155] Step 5: Accuracy Assessment

[0156] Training set accuracy: Coefficient of determination: R 2 =0.9952; Mean Absolute Error: MAE=0.0142T (relative error 0.95%)

[0157] Root mean square error: RMSE = 0.0188T; Maximum error: max|ΔB| = 0.0385T (occurring at H = -842A / m).

[0158] Accuracy of key feature points: Remanence Br: Measured value 1.512T, predicted value 1.499T, error 0.86%; Coercivity Hc: Measured value 68.3A / m, predicted value 67.2A / m, error 1.61%; Saturation magnetization Bs: Measured value 1.498T, predicted value 1.485T, error 0.87%.

[0159] Comparison and verification with existing technologies. The PINN method and PSO method of this invention were compared on a unified hardware platform with the following configuration: Intel(R) Core(TM) Ultra7155H (1.40GHz) processor, 32.0G RAM, and a 64-bit operating system. Figure 3 This is the parameter identification and convergence process of the method in this patent. Figure 4 This is a comparison of the convergence speed of the two methods. Table 1 shows the performance comparison results of the two methods on 30Q120 oriented silicon steel (1.5T, 50Hz).

[0160] Table 1. Performance Comparison Table

[0161]

[0162] Example 2, another technical solution provided in this embodiment of the invention is: a JA hysteresis model parameter identification system based on a physical information neural network, applicable to the JA hysteresis model parameter identification method based on a physical information neural network as described in Example 1, such as... Figure 5 As shown, it includes:

[0163] The data acquisition module is used to acquire measured data of the hysteresis loop of the ferromagnetic material to be identified.

[0164] The network construction module constructs a physical information neural network by taking magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function.

[0165] The objective function construction module constructs an objective function containing network parameters and the parameters to be identified of the JA hysteresis model by using the measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model as parallel supervision information.

[0166] The training optimization module iteratively trains the physical information neural network by minimizing the objective function, and synchronously updates the network parameters of the physical information neural network and the parameters to be identified of the JA hysteresis model during the backpropagation process of each iteration.

[0167] The parameter extraction module is used to extract the target optimization value of the parameter to be identified from the physical information neural network that meets the convergence condition, as the parameter identification result of the ferromagnetic material to be identified.

[0168] Understandably, to implement the JA hysteresis model parameter identification method based on physical information neural networks of this invention into a modular and collaborative execution system, and to solve the technical problems of low computational efficiency, lack of physical mechanism constraints, poor stability of identification results, and susceptibility to non-physical interpretations in traditional hysteresis parameter identification systems, the data acquisition module collects measured data of the magnetic field strength and corresponding magnetization state hysteresis loop of the ferromagnetic material to be identified under alternating excitation conditions, providing a real and practical physical observation data foundation for the entire identification system; the network construction module takes magnetic field strength as input and magnetization state as output, embeds the differential equation of the JA hysteresis model as a physical constraint loss term into the network loss function, constructs a physical information neural network that combines data fitting ability and physical law constraints, and provides core architectural support for parameter collaborative training; Objective The function construction module uses measured hysteresis loop data, JA hysteresis model differential equations, and the prior physical range of JA parameters as triple parallel supervision information to construct a unified objective function that integrates network parameters and JA parameters to be identified, providing a balanced constraint guide for system optimization. The training and optimization module iteratively trains the physical information neural network with minimizing the objective function as the core guide. During the backpropagation process of each iteration, the network parameters and the JA hysteresis model parameters to be identified are updated synchronously. With the help of adaptive optimization strategies and dynamic hyperparameter adjustment mechanisms, the training process achieves fast and stable convergence. After the system training meets the preset multiple convergence conditions, the parameter extraction module extracts the target optimization values ​​of the parameters to be identified from the physical information neural network and uses them as the final parameter identification results of the ferromagnetic material to be identified, outputting JA hysteresis model parameters with qualified accuracy and physical compliance.

[0169] Example 3, one embodiment provided in this invention is: an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of Examples 1.

[0170] Example 4: One technical solution provided in this embodiment of the invention is a computer-readable storage medium storing a computer program thereon, wherein the program, when executed by a processor, implements the method described in any one of Examples 1.

[0171] Through the above description of the embodiments, those skilled in the art will understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the specific device can be divided into different functional modules to complete all or part of the functions described above.

[0172] In the embodiments provided in this application, it should be understood that the disclosed structures and methods can be implemented in other ways. For example, the structural embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another structure, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between structures or units, and may be electrical, mechanical, or other forms.

[0173] The units described as separate components may or may not be physically separate. A component shown as a unit can be one or more physical units; that is, it can be located in one place or distributed in multiple different locations. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0174] Furthermore, in the embodiments of this application, the functional units can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0175] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0176] The specific embodiments described above are preferred embodiments of the JA hysteresis model parameter identification method and system based on physical information neural network of the present invention, and are not intended to limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to the specific embodiments described above. All equivalent changes made in accordance with the shape and structure of the present invention are within the protection scope of the present invention.

Claims

1. A method for parameter identification of JA hysteresis model based on physical information neural network, characterized in that, include: Acquire measured data of the hysteresis loop of the ferromagnetic material to be identified, wherein the measured data of the hysteresis loop includes the magnetic field strength and its corresponding magnetization state. A physical information neural network is constructed by using magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function. The measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model are used as parallel supervision information to construct an objective function that includes network parameters and the parameters to be identified of the JA hysteresis model. The physical information neural network is iteratively trained to minimize the objective function, and the network parameters of the physical information neural network and the parameters to be identified of the JA hysteresis model are updated synchronously during the backpropagation process of each iteration. The target optimization value of the parameter to be identified is extracted from the physical information neural network that meets the convergence condition and used as the parameter identification result of the ferromagnetic material to be identified.

2. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 1, characterized in that, The steps for constructing a physical information neural network, which uses magnetic field strength as input, magnetization state as output, and embeds the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function, include: Construct a neural network that includes an input layer, multiple fully connected hidden layers, and an output layer; The normalized magnetic field strength is used as the input of the neural network, and the normalized magnetization state is used as the output of the neural network; the parameters to be identified in the JA hysteresis model are used as the trainable variables of the neural network. The first derivative of the magnetization state at the output end with respect to the magnetic field strength at the input end is calculated by automatic differentiation, and the theoretical derivative of the magnetization state at the output end with respect to the magnetic field strength at the input end is calculated based on the parameters to be identified in the current iteration. The physical constraint loss term is constructed using the residual between the first derivative and the theoretical derivative, and then embedded into the overall loss function of the neural network to construct the physical information neural network.

3. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 1, characterized in that, The steps for using the measured hysteresis loop data, the differential equation of the JA hysteresis model, and the prior physical range of the JA hysteresis model parameters as parallel supervision information are as follows: Based on the deviation between the predicted magnetization state output by the physical information neural network and the normalized measured magnetization state, a data fitting loss term is constructed as the first supervision information. The physical constraint loss term embedded in the loss function of the physical information neural network is used as the second supervision information; Based on the degree of deviation between the current value of the parameter to be identified and the prior physical range, a parameter boundary constraint loss term is constructed as the third supervision information; The first, second, and third supervisory information are weighted and combined to obtain the objective function with network parameters and parameters to be identified as optimization variables.

4. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 3, characterized in that, The step of constructing the parameter boundary constraint loss term based on the deviation between the current value of the parameter to be identified and the prior physical range is as follows: For each parameter to be identified, a physical value range is preset, and the range includes a lower limit value and an upper limit value; Determine whether the current value of each parameter to be identified falls within the corresponding physical value range; For parameters whose current value is lower than the lower limit, the lower boundary penalty is calculated based on the difference between the lower limit and the current value; for parameters whose current value is higher than the upper limit, the upper boundary penalty is calculated based on the difference between the current value and the upper limit; for parameters whose current value is within the range, the boundary penalty is zero. The lower and upper boundary penalties of each parameter are assigned corresponding weight coefficients and then summed to generate the parameter boundary constraint loss term; wherein the weight coefficients are positively correlated with the lower or upper boundary penalties.

5. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 1, characterized in that, The steps for iteratively training the physical information neural network to minimize the objective function are as follows: Configure the adaptive moment estimation optimizer and set the initial learning rate and learning rate decay strategy; In each iteration, the normalized magnetic field strength is input into the physical information neural network, the magnetization state is predicted by forward propagation, and the total loss value of the current iteration is calculated according to the objective function. The gradients of the total loss value with respect to the network parameters and the parameters to be identified are calculated using the backpropagation algorithm, respectively. Based on the gradient of the parameter to be identified, the network parameters and the parameter to be identified are updated synchronously using the adaptive moment estimation optimizer; The current learning rate is adjusted according to the learning rate decay strategy, and the weight coefficients of each loss term in the objective function are dynamically adjusted. Repeat the above iterative process until the preset convergence condition is met.

6. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 5, characterized in that, The steps for adjusting the current learning rate according to the learning rate decay strategy and dynamically adjusting the weight coefficients of each loss term in the objective function are as follows: Based on the preset decay period and decay factor, the initial learning rate is decayed in a stepwise manner according to the current iteration number to obtain the updated current learning rate; Obtain the gradient norm of each loss term with respect to the network parameters in the current iteration; Based on the gradient norm ratio of each loss term, the weight coefficients of each loss term in the objective function are recalculated using the gradient normalization method. The updated current learning rate and recalculated weight coefficients are applied to the parameter update process in subsequent iterations.

7. The method for parameter identification of the JA hysteresis model based on a physical information neural network according to claim 1, characterized in that, The convergence conditions include at least one of the following: the objective function value is lower than a first preset threshold, the physical constraint loss term value is lower than a second preset threshold, the change in the objective function value within a consecutive preset number of iterations is lower than a third preset threshold, and the number of iterations reaches a preset maximum number of iterations.

8. A JA hysteresis model parameter identification system based on a physical information neural network, applicable to the JA hysteresis model parameter identification method based on a physical information neural network as described in any one of claims 1 to 7, characterized in that, include: The data acquisition module is used to acquire measured data of the hysteresis loop of the ferromagnetic material to be identified. The network construction module constructs a physical information neural network by taking magnetic field strength as input, magnetization state as output, and embedding the differential equation of the JA hysteresis model as a physical constraint loss term into the loss function. The objective function construction module constructs an objective function containing network parameters and the parameters to be identified of the JA hysteresis model by using the measured data of the hysteresis loop, the differential equation of the JA hysteresis model, and the prior physical range of the parameters of the JA hysteresis model as parallel supervision information. The training optimization module iteratively trains the physical information neural network by minimizing the objective function, and synchronously updates the network parameters of the physical information neural network and the parameters to be identified of the JA hysteresis model during the backpropagation process of each iteration. The parameter extraction module is used to extract the target optimization value of the parameter to be identified from the physical information neural network that meets the convergence condition, as the parameter identification result of the ferromagnetic material to be identified.

9. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 7.

Images