A non-causal magnetic field strength calculation method and system based on an analytical model and a neural network

Abstract

This invention discloses a method and system for calculating non-causal magnetic field strength based on an analytical model and a neural network. The method first obtains a fixed parameter set by fitting the equivalent permeability polynomial parameters of the analytical model based on training samples. Then, it calculates the analytical baseline sequence Ha(t) based on the input magnetic flux density sequence B(t) and the fixed parameters. B(t) and Ha(t) are then constructed as feature sequences containing the original sequence, first-order difference, second-order difference, first-order cumulative sum, and inflection point indicators, respectively. These are concatenated with temperature features copied to the sequence length and input into a trained non-causal sequence neural network model, outputting a residual sequence ΔH(t). The final predicted magnetic field strength value is H(t) = Ha(t) + ΔH(t). This invention performs learning in the residual domain, reducing the difficulty of network modeling, and utilizes a bidirectional long short-term memory network to achieve non-causal inference in offline scenarios with known complete sequences, significantly improving prediction accuracy and generalization ability.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic field numerical calculation and magnetic material measurement technology. Specifically, it relates to a method, system and storage medium for calculating magnetic field strength based on analytical models and non-causal neural networks, which is particularly suitable for complex transient waveforms containing high-frequency ripples and multi-level loops. Background Technology

[0002] In high-frequency power converters such as PFC rectifiers, motor drivers, and wireless charging systems, magnetic components often operate under complex excitation conditions including high-frequency ripple, multi-level hysteresis loops, and aperiodic transients. Accurately retrieving the magnetic field strength H(t) from the measured magnetic flux density B(t) is a crucial prerequisite for core loss modeling and performance optimization. Existing methods for calculating magnetic field strength are mainly divided into two categories: analytical models and purely data-driven neural networks. Common analytical models include the equivalent permeability model, the Jiles-Atherton model, and the Preisach model. These models have clear physical meanings and can characterize the main loop trend of the hysteresis loop. However, these methods face serious accuracy bottlenecks in high-frequency transient and dense small loop scenarios: on the one hand, analytical models heavily rely on idealized waveform assumptions, making it difficult to reflect the dynamic magnetization behavior caused by high-frequency eddy currents and local hysteresis in real time; on the other hand, analytical models are essentially finite-dimensional approximations of infinite-dimensional hysteresis phenomena, and when the excitation contains a large number of local extrema and rapid rates of change, they cannot capture the "historical dependence" characteristic of multiple H values ​​corresponding to the same B value. Therefore, relying solely on analytical models is insufficient to meet the high-precision calculation requirements of modern power electronic devices under wide-bandwidth and high-ripple conditions.

[0003] To overcome the limitations of analytical models, in recent years, academia has widely explored pure data "black box" driven methods based on recurrent neural networks (RNNs) and their variant, long short-term memory networks (LSTMs), to directly learn the nonlinear mapping from B(t) to H(t) end-to-end. However, such pure neural network methods have two inherent drawbacks: First, they lack physical interpretability. Although pure black box models can fit training data, their internal states do not have clear physical meaning, and engineers cannot intervene based on physical priors. Second, the causal reasoning paradigm is mismatched with offline computing scenarios. Existing LSTM models generally adopt a unidirectional (causal) temporal recursive structure, where the H value at each time step depends only on the current and historical B values, failing to utilize "future information" from the complete sequence to perform global optimal correction at the current point. In the typical application scenario of "measuring the complete B sequence first and then calculating H offline," this actively discards key information such as phase alignment, inflection point prediction, and loop closure constraints contained in future time steps. Although some studies have attempted to introduce bidirectional LSTM, they have mostly focused on other fields such as geomagnetic forecasting, and there is still no successful solution to deeply integrate it with the "analytical baseline + residual prediction" paradigm to solve the problem of high-frequency transient small loop magnetic field intensity inversion. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for calculating noncausal magnetic field strength based on analytical models and neural networks, aiming to solve the technical problems of insufficient accuracy of existing analytical models, lack of physical interpretability of pure data-driven models, and inability to utilize future information.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for calculating noncausal magnetic field strength based on analytical models and neural networks includes the following steps:

[0007] (1) Obtain the training sample set, which includes magnetic flux density training sequences. , The true value of the corresponding magnetic field strength training sequence With experimental temperature ,in is the discrete sampling time of each point in the sequence, and N is the total length of the sequence;

[0008] (2) Fit analytical model parameters based on the training sample set to obtain an analytical model with definite parameters, and use the analytical model to calculate The corresponding analytical value of the magnetic field strength training sequence ;

[0009] (3) By , and Constructing the input feature sequence ,

[0010] (4) Calculate the training residuals As a supervisory signal, for the input feature sequence The mean and standard deviation are calculated according to the feature dimension, and normalization is performed. These are used as training inputs for the neural network to train the model. The model can extract temporal features based on the complete input sequence and simultaneously utilize historical and future time information of the sequence to achieve parallel inference of the entire sequence.

[0011] (5) Obtain the magnetic flux density sequence to be predicted and experimental test temperature And the analytical values ​​of the corresponding magnetic field strength sequence are calculated using the analytical model obtained in step (2). ;

[0012] (6) , and Constructing the input feature sequence ;

[0013] (7) The input feature sequence Input the non-causal sequence neural network model trained in step (4), and output the residual prediction value sequence. and according to Obtain the predicted magnetic field strength sequence .

[0014] Furthermore, in steps (2) and (5), the analytical model adopts the form of equivalent permeability:

[0015]

[0016] Among them, equivalent permeability Adopted Description of polynomial fitting methods for independent variables and The nonlinear relationship between them is fitted by the following formula:

[0017]

[0018] And satisfy ;

[0019] In the formula, These are the parameters to be fitted.

[0020] Furthermore, the parameters to be fitted Based on the information known in step (1) and The results were obtained through fitting, with the objective being to minimize:

[0021]

[0022] And during the fitting process Apply positive constraints to satisfy .

[0023] Furthermore, the parameters to be fitted Each sample was fitted and fixed using the same material and temperature, without distinguishing between frequencies.

[0024] Furthermore, in step (3), the input feature sequence includes at least:

[0025] The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence;

[0026] The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence;

[0027] Depend on Constructed temperature feature sequence;

[0028] In step (6), , and Construct the input feature sequence using the same method as in step (3). ,in Corresponding to , Corresponding to , Corresponding to .

[0029] Furthermore, in steps (3) and (6), the first-order difference sequence is defined as:

[0030]

[0031]

[0032] A second-order difference sequence is defined as:

[0033]

[0034] .

[0035] Furthermore, in steps (3) and (6), the first-order cumulative sum sequence is defined as:

[0036]

[0037]

[0038] in The value of time , Expressed in prefix and sum form:

[0039]

[0040] .

[0041] Furthermore, in steps (3) and (6), the inflection point indication sequence is a binary sequence:

[0042]

[0043]

[0044] for At time , when the following conditions are met Select 1 if the value is 1, otherwise select 0.

[0045]

[0046] When the following conditions are met Select 1 if the value is 1, otherwise select 0.

[0047]

[0048] And there are , .

[0049] Furthermore, in steps (3) and (6), the temperature feature sequence It involves replicating the temperature scalar T into a sequence of the same length as the magnetic flux density sequence:

[0050] Furthermore, in steps (4) and (7), the model is a non-causal sequence neural network model.

[0051] Furthermore, the non-causal sequence neural network model is a bidirectional long short-term memory network, and the network structure includes: an input layer whose dimension is consistent with the number of feature channels of the input feature sequence X(t); at least one bidirectional LSTM layer, used to extract forward and backward temporal features based on the complete input sequence and output a feature sequence; and at least one fully connected layer, used to map the features output by the bidirectional LSTM layer to a residual prediction value sequence ΔH(t), and the output dimension of the fully connected layer is 1.

[0052] Furthermore, the number of unidirectional hidden units in the bidirectional LSTM layer is 64; the at least one fully connected layer includes a first fully connected layer and a second fully connected layer, the first fully connected layer has an output dimension of 32 and an activation function of ReLU, the second fully connected layer has an output dimension of 1 and is a linear activation layer; the bidirectional LSTM layer is a single layer, or multiple layers stacked with Dropout layers with a dropout probability of 0.2 between layers.

[0053] The present invention also provides a magnetic field strength calculation system for the method, comprising:

[0054] The analytical baseline calculation module stores pre-fitted equivalent permeability polynomial parameters, which are used to calculate the input magnetic flux density sequence. Calculate the analytical sequence of magnetic field strength ,in for polynomial functions;

[0055] Feature construction module, used to extract from , and temperature Constructing the input feature sequence ;

[0056] The residual prediction module loads a trained model, which is a temporal neural network structure capable of non-causal inference and stores the input feature normalization parameters determined during the training phase; the residual prediction module will input the feature sequence... A single forward computation is performed, and the residual prediction sequence at all time points is output in parallel. ;

[0057] Magnetic field strength synthesis module, used to synthesize and By adding the results point by point, the final predicted magnetic field strength sequence is output. .

[0058] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method for calculating noncausal magnetic field strength based on analytical models and neural networks.

[0059] Beneficial effects: Compared with the prior art, the present invention achieves the following beneficial effects:

[0060] (1) It has clear and complete physical interpretability. The present invention adopts a hybrid architecture of "physical analytical baseline + neural network residual correction". With the equivalent permeability analytical model with clear electromagnetic field physical meaning as the core, the main loop trend baseline of magnetic field strength is obtained through polynomial fitting. The core of the prediction result has clear physical connotation, which solves the industry pain point that pure black box neural network lacks physical meaning and cannot perform engineering intervention based on physical prior.

[0061] (2) Employing a non-causal reasoning paradigm, this invention can fully utilize global information of the sequence. Targeting the typical engineering scenario in the field of magnetic material measurement where "the entire magnetic flux density sequence is first collected, and then the magnetic field strength is retrieved offline," this invention adopts a non-causal reasoning architecture based on a bidirectional long short-term memory network, breaking the limitation of traditional unidirectional time-series models that can only utilize current and historical information for causal reasoning. Based on the complete input sequence, the model can simultaneously extract forward and backward global time-series features, fully utilizing key information such as the magnetic flux density reversal inflection point, hysteresis loop closure constraints, and phase alignment relationships at future moments, significantly improving the prediction accuracy of magnetic field strength under complex excitations containing high-frequency ripple and multi-level hysteresis loops.

[0062] (3) At the same prediction accuracy, the modeling difficulty is much lower than that of a fully black-box neural network. Compared with a fully black-box neural network that learns from the end, this invention pre-extracts the main loop nonlinearity between magnetic flux density and magnetic field strength by analyzing the baseline. The neural network only needs to learn small dynamic deviations in the residual domain, which greatly reduces the fitting dimension and modeling difficulty of the model. Under the premise of achieving the same prediction accuracy, this method requires less training samples, has a simpler network structure, and a faster training convergence speed. At the same time, it greatly reduces the risk of model overfitting, has better generalization performance under working conditions, and significantly lowers the threshold for realizing a high-precision magnetic field strength prediction model. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is an overall flowchart of the magnetic field strength calculation method based on analytical model and non-causal neural network in Embodiment 1 of the present invention;

[0065] Figure 2 This is a schematic diagram of the bidirectional long short-term memory network (BiLSTM) structure in Embodiment 1 of the present invention;

[0066] Figure 3 This is a comparison chart of the predicted magnetic field strength under low-frequency (50kHz) excitation in Embodiment 2 of the present invention;

[0067] Figure 4 This is a comparison chart of the predicted magnetic field strength under high-frequency (800kHz) excitation in Embodiment 2 of the present invention. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments; the embodiments and descriptions in the specification are merely illustrative of the principles of the invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0070] Example 1

[0071] This embodiment implements the noncausal magnetic field strength calculation method based on analytical models and neural networks described in this invention on the MATLAB platform. The operating environment is MATLAB R2023b and above, which supports CPU / GPU parallel computing and fully implements the four core functional modules including feature construction, model training, sequence reasoning, and result evaluation.

[0072] This embodiment focuses on ferrite magnetic materials commonly used in power electronics, and provides a magnetic flux density training sequence. as well as The true value of the corresponding magnetic field strength training sequence For sequences with a length of N=1000 points, the selectable excitation frequencies cover 50kHz, 80kHz, 125kHz, 200kHz, 300kHz, 500kHz, and 800kHz, and the temperature... The selectable values ​​cover 25℃, 50℃, and 70℃. The specific implementation steps are as follows:

[0073] (1) Obtain the training sample set, which includes magnetic flux density training sequences. , The true value of the corresponding magnetic field strength training sequence With experimental temperature ;

[0074] in is the discrete sampling time of each point in the sequence, and N is the total length of the sequence.

[0075] (2) Fit analytical model parameters based on the training sample set to obtain an analytical model with definite parameters;

[0076] Calculate using this analytical model The corresponding analytical value of the magnetic field strength training sequence .

[0077] (3) By , and Constructing the input feature sequence ;

[0078] The input feature sequence includes:

[0079] The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence;

[0080] The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence;

[0081] Depend on Constructed temperature characteristic sequence.

[0082] (4) Calculate the training residuals As a supervisory signal, for the input feature sequence The mean and standard deviation are calculated based on the feature dimensions, and normalization is performed. These are then used as training inputs for a non-causal sequence neural network model. This non-causal sequence neural network model can extract temporal features based on the complete input sequence, utilizing both historical and future time information, thus achieving parallel inference across the entire sequence.

[0083] (5) Obtain the magnetic flux density sequence to be predicted and experimental test temperature And the analytical values ​​of the corresponding magnetic field strength sequence are calculated using the analytical model obtained in step (2). .

[0084] (6) , and Construct the input feature sequence using the same method as in step (3). ;

[0085] in Corresponding to , Corresponding to , Corresponding to .

[0086] (7) The input feature sequence Input the non-causal sequence neural network model trained in step (4), and output the residual prediction value sequence. ;

[0087] according to Obtain the predicted magnetic field strength sequence .

[0088] In one specific implementation of this embodiment, the analytical model adopts the form of equivalent permeability:

[0089]

[0090] The equivalent permeability Adopted Description of polynomial fitting methods for independent variables and The nonlinear relationship between them is fitted by the following formula:

[0091]

[0092] In the formula, These are the parameters to be fitted.

[0093] The fit satisfies It is carried out under the following conditions.

[0094] In one specific embodiment of this example, the parameter to be fitted Based on the information known in step (1) and The result is obtained through fitting, with the fitting objective being to minimize...

[0095]

[0096] And during the fitting process Apply positive constraints to satisfy .

[0097] Parameters to be fitted Each sample was fitted and fixed using the same material and temperature, without distinguishing between frequencies.

[0098] A set of results obtained in this embodiment The results of the fitting parameter calculation are shown in Table 1 below.

[0099] Table 1

[0100] <![CDATA[a1]]> <![CDATA[a2]]> <![CDATA[a3]]> <![CDATA[a4]]> 224.865 277.778 <![CDATA[2.54×10 3 ]]> <![CDATA[3.25×10 4 ]]>

[0101] During both the training and inference phases, the magnetic flux density sequence is input through this fixed-parameter analytical model. The corresponding analytical baseline sequence of magnetic field strength was calculated. .

[0102] In one specific implementation of this embodiment, the first-order difference sequence in steps (3) and (6) is defined as:

[0103]

[0104]

[0105] A second-order difference sequence is defined as:

[0106]

[0107]

[0108] The first-order cumulative sequence in steps (3) and (6) is defined as follows:

[0109]

[0110]

[0111] in The value of time , Expressed in prefix and sum form:

[0112]

[0113]

[0114] The inflection point indicator sequences in steps (3) and (6) are binary sequences:

[0115]

[0116]

[0117] for At time , when the following conditions are met Select 1 if the value is 1, otherwise select 0.

[0118]

[0119] When the following conditions are met Select 1 if the value is 1, otherwise select 0.

[0120]

[0121] And there are , .

[0122] The temperature feature sequences described in steps (3) and (6) It involves replicating the temperature scalar T into a sequence of the same length as the magnetic flux density sequence:

[0123]

[0124] Finally, the above features are constructed into a feature matrix:

[0125]

[0126] We obtain an input feature sequence with 11 dimensions and a sequence length of 1000 for each dimension. .

[0127] In one specific implementation of this embodiment, all training samples are traversed, and a corresponding feature sequence is generated for each sample. Then, normalization is performed on the feature sequences of all training samples. The normalization statistic is calculated along the feature dimension: the feature sequences of all training samples are concatenated along the time dimension, and the mean of each feature channel is calculated. with standard deviation For channels with a standard deviation of 0, set To avoid division by zero errors, the normalization formula is:

[0128]

[0129] The normalized feature sequence is used as the input to the non-causal sequence neural network model.

[0130] In one specific embodiment of this example, the non-causal sequence neural network model described in steps (4) and (7) is a bidirectional long short-term memory network, and the network structure is as follows: Figure 2 As shown, it includes:

[0131] 1) Input layer, dimensions and input feature sequence The number of feature channels is consistent;

[0132] 2) Bidirectional LSTM layer, used to simultaneously extract forward and backward temporal features based on the complete input sequence, and output feature sequence;

[0133] 3) The first fully connected layer is used to perform nonlinear transformation on the output features of the bidirectional LSTM layer;

[0134] 4) The second fully connected layer has an output dimension of 1, corresponding to the residual prediction sequence. The predicted value at each time step.

[0135] The bidirectional LSTM layer uses past and future information of the complete sequence to extract non-causal features, enabling the model to output the residual prediction values ​​of all time steps in parallel during the inference phase.

[0136] In this embodiment, the number of unidirectional hidden layer units is 64, and the fully connected layer sequentially includes an intermediate fully connected layer with an output dimension of 32 and an output fully connected layer with an output dimension of 1.

[0137] Example 2

[0138] In this embodiment, a magnetic field strength calculation system is constructed using MATLAB, including:

[0139] The analytical baseline calculation module stores pre-fitted equivalent permeability polynomial parameters, which are used to calculate the input magnetic flux density sequence. Calculate the analytical sequence of magnetic field strength ,in for A polynomial function, with parameters fixed according to material and temperature;

[0140] Feature construction module, used to construct features from the method of step (3) in embodiment 1. , and temperature Constructing the input feature sequence The features at least include and The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, inflection point indicator sequence, and temperature feature sequence;

[0141] The residual prediction module loads a trained non-causal sequential neural network model. This model employs the bidirectional long short-term memory network structure described in Example 1, or other temporal neural network structures capable of non-causal inference, and stores the input feature normalization parameters determined during the training phase. This module will input the feature sequence... A single forward computation is performed, and the residual prediction sequence at all time points is output in parallel. ;

[0142] Magnetic field strength synthesis module, used to synthesize and By adding the results point by point, the final predicted magnetic field strength sequence is output. :

[0143]

[0144] In this embodiment, the specific training configuration is as follows:

[0145] Optimizer: Adam adaptive moment estimator optimizer;

[0146] Maximum number of training rounds: 40;

[0147] Minimum batch size: 32;

[0148] Initial learning rate: 5e-3;

[0149] Learning rate scheduling strategy: segmented exponential decay, decaying once every 2 training rounds, with a decay factor of 0.75;

[0150] Sample shuffling strategy: Shuffle the samples again in each round of training;

[0151] Gradient threshold: 1.

[0152] After training, the trained network and normalized statistics are... and The feature channel count is packaged into a model structure and saved as a .mat format model file to complete the training and solidification of the model.

[0153] In this embodiment, the root mean square error is used. With loss error The errors in the prediction results of the two indicators are calculated as follows:

[0154]

[0155] in, Represents the root mean square. pass right Discrete form calculation of integrals:

[0156]

[0157] This embodiment uses a test set that was not used in training for batch verification. The test set covers the full frequency range of 50kHz to 800kHz and the full temperature range of 25℃ to 70℃. The verification results are as follows:

[0158] Analytical model The percentage is 19.9%, according to the modified method of this invention. The accuracy rate dropped to 4.27%, representing an improvement of more than an order of magnitude.

[0159] The average relative error of the analytical model is 48.9%, while the average relative error of the method of this invention is reduced to 10.2%, which meets the engineering accuracy requirements for loss modeling of power electronic magnetic components.

[0160] 95% of the test sequences It is 6.54%, the largest. No more than 35.1%.

[0161] Taking two extreme cases, 50kHz and 25℃ and 800kHz and 70℃, as examples, the analytical model results and corrected results for the 50kHz and 25℃ cases are as follows: Figure 3 As shown, the analytical model results and corrected results for the 800kHz, 70℃ conditions are as follows. Figure 4 As shown.

[0162] Example 3

[0163] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the noncausal magnetic field strength calculation method based on analytical models and neural networks described above.

[0164] The storage media include, but are not limited to: read-only memory (ROM), random access memory (RAM), magnetic disk, optical disk, flash memory, solid-state drive (SSD), USB flash drive, etc. The computer program can be written in any programming language, including but not limited to MATLAB, Python, C++, Java, etc.

[0165] In one specific implementation, the storage medium is a USB flash drive, which contains an executable file. When the USB flash drive is inserted into a computer's USB port and loaded and executed by the processor, the following functions can be achieved:

[0166] (1) Read the pre-stored analytical model parameters and the weights of the trained neural network model;

[0167] (2) Read the magnetic flux density sequence to be predicted and temperature ;

[0168] (3) Perform steps (1)-(7) of the non-causal magnetic field strength calculation method based on analytical model and neural network in sequence, and output the magnetic field strength prediction sequence. .

[0169] In another specific implementation, the storage medium is the hard drive of a cloud server. The user uploads the data to be predicted via the network, and the server automatically executes the above method and returns the calculation results to the user.

[0170] 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 non-causal magnetic field strength calculation method based on an analytical model and a neural network, characterized in that: Includes the following steps: (1) Obtain a training sample set, containing a magnetic flux density training sequence , The true value of the corresponding magnetic field intensity training sequence And the experimental temperature , Where Is the discrete sampling time of each point in the sequence, and N is the total length of the sequence; (2) Fit analytical model parameters based on the training sample set to obtain an analytical model with definite parameters, and use the analytical model to calculate The corresponding analytical value of the magnetic field strength training sequence ; (3) By , and Constructing the input feature sequence , (4) Calculate the training residuals As a supervisory signal, for the input feature sequence The mean and standard deviation are calculated according to the feature dimension, and normalization is performed. These are used as training inputs for the neural network to train the model. The model can extract temporal features based on the complete input sequence and simultaneously utilize historical and future time information of the sequence to achieve parallel inference of the entire sequence. (5) Obtain the magnetic flux density sequence to be predicted and experimental test temperature And the analytical values ​​of the corresponding magnetic field strength sequence are calculated using the analytical model obtained in step (2). ; (6) , and Constructing the input feature sequence ; (7) The input feature sequence Input the non-causal sequence neural network model trained in step (4), and output the residual prediction value sequence. and according to Obtain the predicted magnetic field strength sequence .

2. The method according to claim 1, characterized in that: In steps (2) and (5), the analytical model adopts the form of equivalent permeability: Among them, equivalent permeability Adopted Description of polynomial fitting methods for independent variables and The nonlinear relationship between them is fitted by the following formula: And satisfy ; In the formula, These are the parameters to be fitted; The parameters to be fitted Based on the information known in step (1) and The results were obtained through fitting, with the objective being to minimize: And during the fitting process Apply positive constraints to satisfy ; The parameters to be fitted Each sample was fitted and fixed using the same material and temperature, without distinguishing between frequencies.

3. The method according to claim 1, characterized in that: In step (3), the input feature sequence includes at least: The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence; The original sequence, first-order difference sequence, second-order difference sequence, first-order cumulative sum sequence, and inflection point indicator sequence; Depend on Constructed temperature feature sequence; In step (6), , and Construct the input feature sequence using the same method as in step (3). ,in Corresponding to , Corresponding to , Corresponding to .

4. The method according to claim 3, characterized in that: In steps (3) and (6), the first-order difference sequence is defined as: A second-order difference sequence is defined as: 。 5. The method according to claim 3, characterized in that: In steps (3) and (6), the first-order cumulative sum sequence is defined as: in The value of time , Expressed in prefix and sum form: 。 6. The method according to claim 3, characterized in that: In steps (3) and (6), the inflection point indication sequence is a binary sequence: for At time , when the following conditions are met Select 1 if the value is 1, otherwise select 0. When the following conditions are met Select 1 if the value is 1, otherwise select 0. And there are , .

7. The method according to claim 1, characterized in that: In steps (3) and (6), the temperature feature sequence It involves replicating the temperature scalar T into a sequence of the same length as the magnetic flux density sequence:

8. The method according to claim 1, characterized in that: In steps (4) and (7), the model is a non-causal sequence neural network model, which is a bidirectional long short-term memory network. The network structure includes: an input layer whose dimension is consistent with the number of feature channels of the input feature sequence X(t); at least one bidirectional LSTM layer, used to extract forward and backward temporal features based on the complete input sequence and output the feature sequence; at least one fully connected layer, used to map the features output by the bidirectional LSTM layer to the residual prediction value sequence ΔH(t), and the output dimension of the fully connected layer is 1. The number of unidirectional hidden units in the bidirectional LSTM layer is 64; the at least one fully connected layer includes a first fully connected layer and a second fully connected layer, the first fully connected layer has an output dimension of 32 and an activation function of ReLU, the second fully connected layer has an output dimension of 1 and is a linear activation layer; the bidirectional LSTM layer is a single layer, or multiple layers stacked with Dropout layers with a dropout probability of 0.2 between layers.

9. A magnetic field strength calculation system for implementing the method according to any one of claims 1 to 8, characterized in that: include: The analytical baseline calculation module stores pre-fitted equivalent permeability polynomial parameters, which are used to calculate the input magnetic flux density sequence. Calculate the analytical sequence of magnetic field strength ,in for polynomial functions; Feature construction module, used to extract from , and temperature Constructing the input feature sequence ; The residual prediction module loads a trained model, which is a temporal neural network structure capable of non-causal inference and stores the input feature normalization parameters determined during the training phase; the residual prediction module will input the feature sequence... A single forward computation is performed, and the residual prediction sequence at all time points is output in parallel. ; Magnetic field strength synthesis module, used to synthesize and By adding the results point by point, the final predicted magnetic field strength sequence is output. .

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 according to any one of claims 1 to 8.

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