Equivalent circuit parameter prediction method, device, equipment and storage medium

Abstract

The application discloses an equivalent circuit parameter prediction method and device, equipment and a storage medium, and relates to the technical field of electrochemical analysis. The method comprises the following steps: based on an equivalent circuit parameter prediction model, processing unlabeled real impedance spectrum data to obtain predicted parameters and reconstructed impedance spectrum data determined based on the predicted parameters; based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, training the equivalent circuit parameter prediction model to obtain a target equivalent circuit parameter prediction model; and based on the target equivalent circuit parameter prediction model, predicting to-be-predicted impedance spectrum data to obtain target parameters of an equivalent circuit model corresponding to the to-be-predicted impedance spectrum data. In the foregoing manner, the dependence on real parameter labels is eliminated without any parameter labels, self-supervised training is achieved, the real spectrum of a reproduced objective measurement is taken as a target, and the prediction accuracy and reliability of the model are improved.

Description

Technical Field

[0001] This application relates to the field of electrochemical analysis technology, and in particular to methods, apparatus, devices and storage media for predicting equivalent circuit parameters. Background Technology

[0002] Electrochemical impedance spectroscopy (EIS) is a powerful, non-destructive electrochemical characterization technique widely used in fields such as batteries (e.g., state of health (SOH) and state of charge (SOC) assessment of lithium-ion batteries), corrosion science, fuel cells, supercapacitors, medical materials, and materials characterization. For example, in the field of biomedical materials, EIS is often used to assess the degradation rate and corrosion mechanism of bioactive metals such as biodegradable medical zinc alloys to guide performance optimization and biocompatibility studies. EIS obtains information about the internal dynamics and physicochemical processes of an electrochemical system by applying one (or a series of) small-amplitude sinusoidal alternating potential (or current) perturbations and measuring its impedance response at different frequencies. To extract valuable physicochemical information from complex EIS data, the most common method is to fit it to an equivalent circuit model (ECM).

[0003] Because traditional fitting methods rely too heavily on human experience and are inefficient, machine learning is often used to establish a direct mapping between EIS data and EC parameters. Impedance spectrum data (such as the real and imaginary parts of N frequency points) is used as input to the neural network, and the component values ​​of the equivalent circuit (such as R1, C1, R2) are used as outputs (labels). The network is trained by minimizing a loss function such as the mean square error (MSE) between the predicted and true parameter values. However, this direct regression method based on "spectrum-to-parameter" lacks physical constraints and relies on biased "true labels," leading to unreliable prediction results.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main objective of this application is to provide an equivalent circuit parameter prediction method, apparatus, device, and storage medium, aiming to solve the technical problem that traditional machine learning schemes in the prior art rely on biased real labels and the prediction results are unreliable.

[0006] To achieve the above objectives, this application provides an equivalent circuit parameter prediction method, the method comprising:

[0007] Based on the equivalent circuit parameter prediction model, the unlabeled real impedance spectrum data is processed to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters.

[0008] Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, the equivalent circuit parameter prediction model is trained to obtain the target equivalent circuit parameter prediction model.

[0009] Based on the target equivalent circuit parameter prediction model, the impedance spectrum data to be predicted is predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0010] In one embodiment, the equivalent circuit parameter prediction model includes a parameter prediction module and an impedance spectrum reconstruction module, wherein the impedance spectrum reconstruction module has a built-in complex impedance analytical formula for the equivalent circuit model.

[0011] The parameter prediction module is used to predict the unlabeled real impedance spectrum training data to obtain prediction parameters, and then input the prediction parameters into the impedance spectrum reconstruction module.

[0012] The impedance spectrum reconstruction module is used to calculate the complex impedance data of each angular frequency in the preset frequency list under the prediction parameters based on the complex impedance analytical formula, and to separate the real part and imaginary part of the complex impedance data to obtain the reconstructed impedance spectrum data.

[0013] In one embodiment, the step of training the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain the target equivalent circuit parameter prediction model includes:

[0014] Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, the predicted total loss is determined;

[0015] When the predicted total loss does not meet the preset convergence condition, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated based on the predicted total loss. Then, the process of processing the unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model is returned to obtain the predicted parameters and the reconstructed impedance spectrum data determined based on the predicted parameters, until the predicted total loss meets the preset convergence condition.

[0016] When the predicted total loss meets the preset convergence condition, the training of the equivalent circuit parameter prediction model is determined to be complete, and the equivalent circuit parameter prediction model is used as the target equivalent circuit parameter prediction model.

[0017] In one embodiment, the step of determining the predicted total loss based on the reconstructed impedance spectrum data and the unlabeled true impedance spectrum data includes:

[0018] Obtain the first correspondence between reconstructed impedance spectrum data, actual impedance spectrum data, and error indices;

[0019] Based on the reconstructed impedance spectrum data, the unlabeled real impedance spectrum data, and the first correspondence, an error index is calculated;

[0020] Obtain a second correspondence between the error metric and the total predicted loss;

[0021] Based on the error index and the second correspondence, the total predicted loss is determined.

[0022] In one embodiment, the step of updating the weights of the parameter prediction module in the equivalent circuit parameter prediction model based on the total predicted loss includes:

[0023] Based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters, a target gradient between the total predicted loss and the weights of the parameter prediction module is determined.

[0024] Based on the target gradient, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated.

[0025] In one embodiment, the step of determining the target gradient between the total predicted loss and the weights of the parameter prediction module based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters includes:

[0026] Calculate the first gradient between the predicted total loss and the reconstructed impedance spectrum data;

[0027] Calculate the second gradient between the reconstructed impedance spectrum data and the predicted parameters;

[0028] Calculate the third gradient between the predicted parameters and the weights of the parameter prediction module;

[0029] Obtain the third correspondence between the first gradient, second gradient, third gradient and target gradient;

[0030] The target gradient is determined based on the first gradient, the second gradient, the third gradient, and the third correspondence.

[0031] In one embodiment, before the step of processing unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters, the method further includes:

[0032] Obtain the raw impedance spectrum data;

[0033] Based on a preset range, the original impedance spectrum data is normalized to obtain unlabeled real impedance spectrum data.

[0034] Furthermore, to achieve the above objectives, this application also proposes an equivalent circuit parameter prediction device, which includes:

[0035] The training module is used to process unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters.

[0036] The training module is also used to train the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain the target equivalent circuit parameter prediction model.

[0037] The prediction module is used to predict the impedance spectrum data to be predicted based on the target equivalent circuit parameter prediction model, and obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0038] In addition, to achieve the above objectives, this application also proposes an equivalent circuit parameter prediction device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the equivalent circuit parameter prediction method as described above.

[0039] In addition, to achieve the above objectives, the present invention also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the equivalent circuit parameter prediction method described above.

[0040] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the equivalent circuit parameter prediction method described above.

[0041] This application provides an equivalent circuit parameter prediction method. Based on an equivalent circuit parameter prediction model, unlabeled real impedance spectrum data is processed to obtain predicted parameters and reconstructed impedance spectrum data determined based on the predicted parameters. The equivalent circuit parameter prediction model is trained based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain a target equivalent circuit parameter prediction model. Based on the target equivalent circuit parameter prediction model, the impedance spectrum data to be predicted is predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted. This application compares the reconstructed spectrum with the input spectrum. The training signal comes entirely from the input data itself, without any parameter labels, thus eliminating the dependence on real parameter labels and achieving self-supervised training, improving the reliability of the prediction results. Furthermore, it aims to reproduce the true spectrum measured objectively, rather than imitating a potentially inaccurate fitted value, thereby improving the accuracy of the prediction results. This solves the technical problem of unreliable prediction results in traditional machine learning schemes that rely on biased real labels. Attached Figure Description

[0042] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0043] To more clearly illustrate the technical solutions in the embodiments of this application 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.

[0044] Figure 1 This is a flowchart illustrating an embodiment of the equivalent circuit parameter prediction method of this application.

[0045] Figure 2 A schematic diagram of the prediction model structure for the equivalent circuit parameter prediction method provided in Embodiment 1 of this application;

[0046] Figure 3 This is a flowchart illustrating Embodiment 2 of the equivalent circuit parameter prediction method of this application;

[0047] Figure 4 This is a schematic diagram of the parameter prediction module structure of the equivalent circuit parameter prediction method provided in Embodiment 2 of this application;

[0048] Figure 5 A schematic diagram of the traditional model prediction results for the equivalent circuit parameter prediction method provided in Embodiment 2 of this application;

[0049] Figure 6 This is a schematic diagram of the prediction results of the equivalent circuit parameter prediction method provided in Embodiment 2 of this application;

[0050] Figure 7 This is a schematic diagram of the module structure of the equivalent circuit parameter prediction device according to an embodiment of this application;

[0051] Figure 8 This is a schematic diagram of the device structure of the hardware operating environment involved in the equivalent circuit parameter prediction method in the embodiments of this application.

[0052] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0053] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0054] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0055] The main solution of this application embodiment is as follows: Based on the equivalent circuit parameter prediction model, the unlabeled real impedance spectrum data is processed to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters; Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, the equivalent circuit parameter prediction model is trained to obtain the target equivalent circuit parameter prediction model; Based on the target equivalent circuit parameter prediction model, the impedance spectrum data to be predicted is predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0056] Currently, the analysis of EIS data into equivalent circuit parameters mainly relies on traditional fitting schemes and machine learning schemes improved upon these traditional schemes. Traditional fitting schemes primarily use complex nonlinear least squares (CNLS) for fitting, a method heavily reliant on manual operation, which has the following drawbacks:

[0057] Initial value sensitivity. Fitting algorithms (such as the Levenberg-Marquardt method) are very sensitive to the setting of initial parameter values. Inappropriate initial values ​​can easily cause the fitting process to get stuck in a local optimum, resulting in incorrect parameter results.

[0058] Inefficient. This process requires manual intervention and repeated debugging, which is time-consuming and labor-intensive, and cannot meet the needs of high-throughput experimental data processing or real-time online monitoring (such as battery management systems, BMS).

[0059] Traditional machine learning approaches typically use impedance spectrum data (such as the real and imaginary parts of N frequency points) as input and the component values ​​of the equivalent circuit (such as R1, C1, R2) as output (labels). The network is trained by minimizing a loss function such as the mean squared error (MSE) between the predicted and true parameter values. However, this direct "spectrum-to-parameter" regression method has some fundamental flaws:

[0060] It relies on high-quality "real labels". This approach requires a large, labeled training set, meaning that each impedance spectrum must correspond to a set of known, accurate "real" equivalent circuit parameter values.

[0061] The paradox of obtaining "true labels". These "true" parameter labels are usually obtained through a flawed conventional CNLS fitting scheme, which means that the "ceiling" of neural network training is limited by the accuracy of the traditional fitting scheme, and the network is just "imitating" a slow and potentially inaccurate fitting process.

[0062] Lack of physical constraints. During training, the network only attempts to mathematically minimize the L2 loss of the parameters. It does not understand the physical meaning of these parameters combined. This may cause the network to predict a set of parameters that are close to the "label values" in numerical terms. However, when these parameters are substituted into the physical formula of the equivalent circuit for back-calculation, the resulting impedance spectrum deviates greatly from the true input spectrum. In other words, the network lacks "cognition" of the electrochemical mechanism (i.e., the equivalent circuit topology).

[0063] Limitations of synthetic data. To circumvent label acquisition, "synthetic data" (i.e., parameters are set first, and then spectra are generated by formula) can be used for training. However, this results in poor generalization ability of the model to noise, instrument artifacts and non-ideal responses (such as CPE) in real experiments.

[0064] It is evident that traditional methods either rely too heavily on human experience and are inefficient (traditional fitting), or, in the application of machine learning, lack physical constraints and rely on biased "true labels," resulting in unreliable predictions.

[0065] This application provides a solution that compares the reconstructed spectrum with the input spectrum. The training signal comes entirely from the input data itself, without any parameter labels. This eliminates the dependence on real parameter labels, enables self-supervised training, and improves the reliability of prediction results. At the same time, it aims to reproduce the real spectrum of objective measurements, rather than imitating a potentially inaccurate fitted value, thereby improving the accuracy of prediction results. This solves the technical problem of unreliable prediction results in traditional machine learning schemes that rely on biased real labels.

[0066] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device or equivalent circuit parameter prediction device capable of performing the above functions. This embodiment does not specifically limit it in this regard. The following uses an equivalent circuit parameter prediction device as an example to describe this embodiment and the following embodiments.

[0067] This application provides an equivalent circuit parameter prediction method, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the equivalent circuit parameter prediction method of this application.

[0068] In this embodiment, the equivalent circuit parameter prediction method includes steps S10~S30:

[0069] Step S10: Based on the equivalent circuit parameter prediction model, the unlabeled real impedance spectrum data is processed to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters.

[0070] It should be noted that, in order to extract valuable physicochemical information from complex EIS data, neural networks can be used to fit it into an equivalent circuit model (ECM). The equivalent circuit model is typically composed of components such as resistors (R), capacitors (C), inductors (L), constant phase angle elements (CPE), and Warburg impedance (W), used to simulate actual processes in electrochemical systems, such as solution resistance, charge transfer resistance, double-layer capacitance, and diffusion processes. By fitting the experimentally measured impedance spectral data to the selected equivalent circuit, the parameter values ​​of each component can be obtained. These parameter values ​​(such as charge transfer resistance) have clear physical meanings and are key to quantitative analysis and understanding of the system's internal state.

[0071] Furthermore, it should be noted that traditional fitting methods rely too heavily on human experience and are inefficient. Therefore, this embodiment utilizes a neural network to establish a direct mapping relationship between EIS data and EC parameters. Also, since traditional machine learning methods rely on biased true labels, resulting in unreliable predictions, this embodiment improves upon traditional prediction models.

[0072] It is understood that the equivalent circuit parameter prediction model is the model designed in this embodiment for predicting the component parameters of the equivalent circuit (model). In this embodiment, reference is made to... Figure 2 The equivalent circuit parameter prediction model includes a parameter prediction module and an impedance spectrum reconstruction module. The impedance spectrum reconstruction module has a built-in complex impedance analytical formula for the equivalent circuit model.

[0073] In practical implementation, the parameter prediction module generates predicted parameters based on unlabeled real impedance spectrum training data and inputs these predicted parameters into the impedance spectrum reconstruction module. The impedance spectrum reconstruction module then generates reconstructed impedance spectrum data based on the predicted parameters, a preset frequency list, and the complex impedance analytical formula. Specifically, the impedance spectrum reconstruction module calculates the complex impedance data for each angular frequency in the preset frequency list under the predicted parameters using the complex impedance analytical formula, separates the real and imaginary parts of the complex impedance data, and obtains the reconstructed impedance spectrum data.

[0074] It should be noted that the actual impedance spectrum data refers to the actual impedance spectrum data obtained and used for model training. In this embodiment, the data input to the equivalent circuit parameter prediction model are all unlabeled data. The predicted parameters are the component parameters predicted using the equivalent circuit parameter prediction model, and are usually in vector form. The reconstructed impedance spectrum data is the impedance spectrum data obtained by inversion based on the predicted parameters and a preset frequency list, according to the complex impedance analytical formula.

[0075] Additionally, it should be noted that the preset frequency list is a fixed list of frequencies set in advance, containing multiple angular frequencies, i.e. The preset frequency list is neither a training variable for the neural network nor the output of the parameter prediction module. Instead, it is a constant tensor from external input. Its contents are determined during data preprocessing based on the sampling frequencies of the original experimental data and are passed as configuration parameters to the impedance spectrum reconstruction module during model initialization. It serves as a crucial anchor point for the impedance spectrum reconstruction module to perform correct calculations, thereby ensuring the reconstruction of the impedance spectrum data. It can be compared with real impedance spectrum data Calculations are performed at exactly the same frequency points, ensuring that the subsequent loss function can perform accurate point-to-point error comparisons.

[0076] Understandably, the first part of the model is a trainable parameter prediction module (from the input layer to the penultimate layer), which is a standard neural network, such as an MLP or CNN, responsible for receiving the preprocessed true impedance spectrum vector. As input, it outputs a K-dimensional vector of predicted parameters. Where K is the number of equivalent circuit parameters to be predicted. The second part of the model is the impedance spectrum reconstruction module (i.e., the last layer), which is a non-trainable, prior-knowledge-based fixed computational layer. This module has built-in precise physical and mathematical formulas for the equivalent circuit, such as the complex impedance analytical formula. ,in, It is angular frequency and component parameter vector The function. The impedance spectrum reconstruction module receives the prediction parameter vector from the first part. Given a fixed frequency list (i.e., a preset frequency list), the corresponding reconstructed impedance spectrum data is calculated strictly according to the built-in physical formulas. , Data structures and inputs Totally consistent.

[0077] Furthermore, in one feasible implementation, before step S10, the following steps may be included: acquiring raw impedance spectrum data; and normalizing the raw impedance spectrum data based on a preset range to obtain unlabeled real impedance spectrum data.

[0078] It should be noted that the raw impedance spectrum data, i.e. the initially obtained impedance spectrum data without preprocessing, is a collection of complex impedances measured within a predetermined frequency range. After preprocessing, it can be used as input to the neural network. The preset range is the pre-defined normalization range, for example: [0,1]. In this embodiment, the preprocessing includes at least linear normalization processing.

[0079] Understandably, preprocessing is required before inputting the data into the model. In practice, the original impedance spectrum data is linearly normalized to map it to the range [0,1], resulting in unlabeled true impedance spectrum data. Subsequently, the preprocessed unlabeled true impedance spectrum data is input into the model.

[0080] Step S20: Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, train the equivalent circuit parameter prediction model to obtain the target equivalent circuit parameter prediction model.

[0081] It should be noted that the target equivalent circuit parameter prediction model is the model that can be applied after the equivalent circuit parameter prediction model has been trained.

[0082] In one feasible implementation, step S20 may include steps S201 to S203:

[0083] Step S201: Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, determine the predicted total loss;

[0084] It should be noted that in this embodiment, it is not necessary to set real labels for the equivalent circuit parameters when training the model. During the training process, an unlabeled true impedance spectrum is used. After forward propagation, the predicted parameter vectors are generated sequentially through the parameter prediction module. Then, the reconstructed impedance spectrum is generated through the impedance spectrum reconstruction module. .

[0085] It is understandable that the total prediction loss is the loss function obtained during model training. In this embodiment, the key loss function is not the one that compares the prediction parameters. Instead of comparing with the true labels, it compares the reconstructed spectrum. Compared with the original input spectrum The differences between them.

[0086] In one feasible implementation, step S201 may include: obtaining a first correspondence between reconstructed impedance spectrum data, real impedance spectrum data and error index; calculating an error index based on the reconstructed impedance spectrum data, the unlabeled real impedance spectrum data and the first correspondence; obtaining a second correspondence between the error index and the predicted total loss; and determining the predicted total loss based on the error index and the second correspondence.

[0087] It should be noted that the error index is used to characterize the reconstructed impedance spectrum. Compared with the true impedance spectrum of the original input The differences between them, such as mean square error, mean absolute error, and complex domain weighted loss, are not specifically limited in this embodiment.

[0088] Additionally, it should be noted that the first correspondence between the reconstructed impedance spectrum data, the true impedance spectrum data, and the error index is the calculation formula for the error index. For example, when the error index is the mean square error, the first correspondence is the reconstructed impedance spectrum. Compared with the true impedance spectrum of the original input The formula for calculating the mean square error between them is, i.e. .

[0089] Understandably, the error metric and the total prediction loss... The second correspondence between them is the calculation formula for the predicted total loss. For example, the predicted total loss = error index 1 + error index 2, that is... Total predicted loss = error index, i.e. This embodiment does not impose specific limitations on this.

[0090] It should be understood that the corresponding error index is calculated based on the difference between the reconstructed impedance spectrum data and the true impedance spectrum data, and then the final total predicted loss is calculated based on the error index.

[0091] Step S202: When the total predicted loss does not meet the preset convergence condition, based on the total predicted loss, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated, and the process of processing the unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model is returned to obtain the predicted parameters and the reconstructed impedance spectrum data determined based on the predicted parameters, until the total predicted loss meets the preset convergence condition.

[0092] In one feasible implementation, the step of updating the weights of the parameter prediction module in the equivalent circuit parameter prediction model based on the total predicted loss includes: determining a target gradient between the total predicted loss and the weights of the parameter prediction module based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters; and updating the weights of the parameter prediction module in the equivalent circuit parameter prediction model based on the target gradient.

[0093] Understandably, this is necessary to update the weights of the parameter prediction module. It is necessary to calculate the total loss prediction. Weights The gradient, i.e. the target gradient, is used by the optimizer to reconstruct the impedance spectrum based on this "spectrum-spectrum" difference. Compared with the true impedance spectrum of the original input The difference between them is used to calculate the final target gradient.

[0094] In one feasible implementation, the step of determining the target gradient between the total predicted loss and the weights of the parameter prediction module based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters includes: calculating a first gradient between the total predicted loss and the reconstructed impedance spectrum data; calculating a second gradient between the reconstructed impedance spectrum data and the prediction parameters; calculating a third gradient between the prediction parameters and the weights of the parameter prediction module; obtaining a third correspondence between the first gradient, the second gradient, the third gradient, and the target gradient; and determining the target gradient based on the first gradient, the second gradient, the third gradient, and the third correspondence.

[0095] Understandably, the calculation of the target gradient follows backpropagation and the chain rule. According to the chain rule, this target gradient can be decomposed into three main parts: the first gradient, the second gradient, and the third gradient. The third correspondence between the first gradient, the second gradient, the third gradient, and the target gradient is the formula for calculating the target gradient, as shown below:

[0096]

[0097] In the formula, For the first gradient, For the second gradient, The third gradient, The target gradient.

[0098] It should be noted that the first gradient is the gradient between the predicted total loss and the reconstructed impedance spectrum data, i.e., the gradient of the predicted total loss with respect to the reconstructed impedance spectrum data, which is directly derived from the selected loss function; the second gradient is the gradient between the reconstructed impedance spectrum data and the predicted parameters, i.e., the gradient of the reconstructed impedance spectrum data with respect to the predicted parameters, representing how the physical formula of the equivalent circuit changes with the predicted parameters. The derivative tensor changes with the change in parameters. Essentially, it characterizes in which direction each parameter should be slightly modified to reduce loss in the neural network. The third gradient, the gradient between the predicted parameters and the weights of the parameter prediction module, can be propagated backward to each layer of the parameter prediction module, eventually reaching the weights. .

[0099] Understandably, the entire training process utilizes physical formulas as strong constraints, forcing the parameter prediction module to learn how to output the "correct" parameters that can reproduce the true spectrum.

[0100] Step S203: When the predicted total loss meets the preset convergence condition, it is determined that the training of the equivalent circuit parameter prediction model is complete, and the equivalent circuit parameter prediction model is used as the target equivalent circuit parameter prediction model.

[0101] It should be noted that the preset convergence condition is the condition that the model needs to meet to converge. For example, the total predicted loss should decrease by less than 10% over 10 consecutive training epochs. -6 It can be flexibly adjusted according to actual needs, and no specific restrictions are imposed on it.

[0102] Understandably, when the total prediction loss during training meets the preset convergence criteria, the model can be considered converged. This means the equivalent circuit parameter prediction model has been trained and can be used as the final target model for inference and prediction. Conversely, when the total prediction loss during training does not meet the preset convergence criteria, the model is considered unconverged. This means the weights of the parameter prediction module in the model need further updating; the target gradient is calculated based on the total prediction loss, and the weights are updated accordingly.

[0103] Step S30: Based on the target equivalent circuit parameter prediction model, predict the impedance spectrum data to be predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0104] It should be noted that the impedance spectrum data to be predicted is the impedance spectrum data for which the equivalent circuit element parameters need to be determined. The target parameters are the equivalent circuit element parameters of the final predicted impedance spectrum data, which are usually in vector form.

[0105] Understandably, after model training is complete, a target equivalent circuit parameter prediction model is obtained, which can be used for inference and prediction. At this point, a new true impedance spectrum is obtained. The input is fed into the trained model, and a forward propagation is performed. Only the output vector of the parameter prediction module is extracted. This vector is The final predicted values ​​of the corresponding equivalent circuit parameters. During the inference phase, the output and loss function of the impedance spectrum reconstruction module are no longer used.

[0106] This embodiment provides an equivalent circuit parameter prediction method. Based on an equivalent circuit parameter prediction model, unlabeled real impedance spectrum data is processed to obtain predicted parameters and reconstructed impedance spectrum data determined based on the predicted parameters. The equivalent circuit parameter prediction model is trained based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain a target equivalent circuit parameter prediction model. Based on the target equivalent circuit parameter prediction model, the impedance spectrum data to be predicted is predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted. This embodiment compares the reconstructed spectrum with the input spectrum. The training signal comes entirely from the input data itself, without any parameter labels, thus eliminating the dependence on real parameter labels and achieving self-supervised training, improving the reliability of the prediction results. Furthermore, it aims to reproduce the real spectrum measured objectively, rather than imitating a potentially inaccurate fitted value, thereby improving the accuracy of the prediction results. In addition, it effectively utilizes the physical constraints of the equivalent circuit, significantly reducing data preparation costs and improving model generalization ability and prediction accuracy.

[0107] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in Embodiment 1 above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 3 Step S10 may include steps S101 to S102:

[0108] Step S101: Based on the parameter prediction module, predict the unlabeled real impedance spectrum training data to obtain the predicted parameters;

[0109] It should be noted that the reference Figure 4 The parameter prediction module can include convolutional layers, pooling layers, and multiple fully connected layers (dense). The activation function can be ReLU (Linear Rectification function), and the convolutional layers are used to handle local correlations in the impedance spectrum data. The parameter prediction module is responsible for receiving the preprocessed true impedance spectrum vector. As input, it outputs a K-dimensional vector of prediction parameters. .

[0110] Understandably, if a Randle circuit is chosen... As an equivalent circuit model, it encompasses series resistance, charge transfer processes, electric double-layer effects, and Warburg diffusion processes, exhibiting typical electrochemical representativeness. Therefore, the parameter vector that the neural network needs to predict includes... , , , , There are a total of five key component values, among which, For the resistance of the solution, For charge transfer resistor, For the amplitude parameters of a constant phase angle element (CPE), The phase index of the CPE, This is the Warburg coefficient.

[0111] Step S102: Based on the impedance spectrum reconstruction module, the predicted parameters, the complex impedance analytical formula, and the preset frequency list are inverted to obtain the reconstructed impedance spectrum data.

[0112] In one feasible implementation, step S102 may include: calculating the complex impedance data of each angular frequency in the preset frequency list under the prediction parameters based on the impedance spectrum reconstruction module; and separating the real part and imaginary part of the complex impedance data based on the impedance spectrum reconstruction module to obtain the reconstructed impedance spectrum data.

[0113] It's important to note that the primary condition for the analytical formula of complex impedance is differentiability. This is because model training relies on the gradient successfully passing through this layer, propagating back from the loss function to the parameter prediction module to update the network weights. This means that all mathematical operations in the formula must be continuous and differentiable. The impedance formulas for common equivalent circuit elements (R, L, C, CPE, Warburg) are all continuous and differentiable, allowing the gradient to pass through this layer smoothly. The output of this formula must be a complex impedance that matches the dimension of the input impedance spectrum and is separated into its real part before loss calculation. and the virtual part This is to enable point-to-point mean square error (MSE) calculation with the real and imaginary parts of the original input impedance spectrum.

[0114] Understandably, assuming the Randle circuit is chosen as the equivalent circuit model, the impedance spectrum reconstruction module will receive the predicted parameters output by the parameter prediction module during each forward propagation. and a preset list of fixed frequencies For each angular frequency in the list This module will strictly follow the built-in Randle circuit complex impedance analytical formula for calculation, as shown below:

[0115]

[0116] in, It is a series impedance. It is the parallel impedance of the charge transfer resistor and the CPE. It is the Warburg impedance.

[0117] It should be understood that, due to Since it is a complex number, the impedance spectrum reconstruction module needs to use complex algebra to separate it into its real part. and the virtual part The real and imaginary parts of all frequency points in the list are separated to obtain the reconstructed impedance spectrum vector. .

[0118] Understandably, conventional neural network (NN) schemes can be considered "black boxes," potentially predicting a set of parameters that are mathematically close to the label but physically meaningless. This embodiment, by embedding the physical formula of the equivalent circuit in the last layer as a strong constraint, ensures that any set of parameters predicted by the network is "self-consistent" with the physical model; that is, their combination can indeed (from the network's perspective) optimally reproduce the original spectrum. Similar to conventional NN schemes, the training process in this embodiment may be time-consuming, but once training is complete, its inference process is in milliseconds, eliminating the need for time-consuming and laborious line-by-line debugging. This makes it highly suitable for scenarios such as real-time status monitoring in battery management systems (BMS) or high-throughput material screening.

[0119] Assuming that the traditional neural network model used in conventional machine learning schemes is the same as the parameter prediction module used in this embodiment, both include convolutional layers, pooling layers, and multiple fully connected layers. The traditional neural network model adopts the conventional "spectral-value" supervised learning paradigm, and its last fully connected layer has an output dimension of 5, directly corresponding to the predicted parameters. During model training, it is necessary to obtain a large number of true parameter labels beforehand, which are fitted using the traditional complex nonlinear least squares method. Its loss function Focus on minimizing prediction parameters With parameter real label The Euclidean distance or mean squared error (MSE) between the parameters. The effectiveness of this training model is limited by the true labels of the parameters used. The accuracy and robustness.

[0120] Using the equivalent circuit parameter prediction model in this embodiment, the parameter prediction module still outputs a dimension of 5, generating a predicted parameter vector. This layer uses ReLU or Softplus activation functions to ensure that the output physical parameters are positive. The impedance spectrum reconstruction module (physical information layer) is a non-trainable, hard-coded formula for calculating the complex impedance of the Randle circuit. The computing module, which receives With a fixed list of frequencies, the impedance spectrum is inverted and reconstructed. , Dimensions and input Same. Self-supervised loss function: The model minimizes... Training is then performed. This "spectrum-to-spectrum" comparison mechanism allows the gradient signal to pass through the physical formula layer, forcing the neural network to learn a set of parameters that must be physically optimal to reconstruct the original input spectrum.

[0121] By training a traditional neural network model and an equivalent circuit parameter prediction model, and evaluating their prediction performance on the same test set, significant differences were found between the two. (Reference) Figure 5 , Figure 5 The horizontal axis represents the real part of the impedance (Zre), and the vertical axis represents the imaginary part of the negative impedance (-Zimg). The unit for both axes is ohms (Ω). Figure 5 It is evident that traditional neural network models exhibit significant generalization limitations on the test set, particularly regarding equivalent circuit element values, especially charge transfer resistance. When the data is in the high-value range, a visible deviation and inconsistency appears between the predicted and actual spectra. This demonstrates that while traditional models perform reasonably well within the parameter space of the training set, their learned parameter mapping relationships lack physical constraints. Once the data enters the sparse or high-value region, the predicted parameter combinations produce significant errors when substituted into the physical formulas, exhibiting extremely low physical self-consistency. In contrast, the equivalent circuit parameter prediction model in this embodiment demonstrates superior robustness and accuracy. (Reference) Figure 6 , Figure 6 The horizontal axis represents the real part of the impedance (Zre), and the vertical axis represents the imaginary part of the negative impedance (-Zimg). The unit for both axes is ohms (Ω). Figure 6It is evident that within the same high-value region and the entire parameter range, the predicted spectrum perfectly fits the actual spectrum. This result strongly demonstrates the role of the impedance spectrum reconstruction module: by using the physical consistency of "spectrum-spectrum" as the sole optimization objective, the network is forced to learn the inherent and precise physical relationship between the parameters and the spectrum. This means that the parameters predicted in this embodiment are not only mathematically reasonable but also physically highly self-consistent, thereby overcoming the fundamental defects of traditional models in prediction accuracy and generalization ability, and solving the problem of model error increasing with component values. It can utilize massive amounts of unlabeled data for efficient training and outperforms traditional supervised learning-based neural network methods in both prediction accuracy and physical rationality.

[0122] This embodiment provides an equivalent circuit parameter prediction method. Based on the parameter prediction module, it predicts parameters from unlabeled real impedance spectrum training data. Based on the impedance spectrum reconstruction module, it inverts the predicted parameters to obtain reconstructed impedance spectrum data. This embodiment compares the reconstructed spectrum with the input spectrum. The training signal comes entirely from the input data itself, without any parameter labels, thus eliminating the dependence on real parameter labels and achieving self-supervised training, improving the reliability of the prediction results. Furthermore, it aims to reproduce the real spectrum measured objectively, rather than imitating a potentially inaccurate fitted value, thereby improving the accuracy of the prediction results. In addition, it effectively utilizes the physical constraints of the equivalent circuit, significantly reducing data preparation costs and improving model generalization ability and prediction accuracy.

[0123] It should be noted that the above examples are only for understanding this application and do not constitute a limitation on the equivalent circuit parameter prediction method of this application. Any simple transformations based on this technical concept are all within the protection scope of this application.

[0124] This application also provides an equivalent circuit parameter prediction device, please refer to... Figure 7 The equivalent circuit parameter prediction device includes:

[0125] Training module 10 is used to process unlabeled real impedance spectrum data based on an equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters.

[0126] The training module 10 is also used to train the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain the target equivalent circuit parameter prediction model.

[0127] Prediction module 20 is used to predict the impedance spectrum data to be predicted based on the target equivalent circuit parameter prediction model, and obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0128] In one feasible implementation, the equivalent circuit parameter prediction model includes a parameter prediction module and an impedance spectrum reconstruction module, wherein the impedance spectrum reconstruction module has a built-in complex impedance analytical formula for the equivalent circuit model.

[0129] The parameter prediction module is used to predict the unlabeled real impedance spectrum training data to obtain prediction parameters, and then input the prediction parameters into the impedance spectrum reconstruction module.

[0130] The impedance spectrum reconstruction module is used to calculate the complex impedance data of each angular frequency in the preset frequency list under the prediction parameters based on the complex impedance analytical formula, and to separate the real part and imaginary part of the complex impedance data to obtain the reconstructed impedance spectrum data.

[0131] In one feasible implementation, the prediction module 20 is further configured to determine the total predicted loss based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data;

[0132] When the predicted total loss does not meet the preset convergence condition, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated based on the predicted total loss. Then, the process of processing the unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model is returned to obtain the predicted parameters and the reconstructed impedance spectrum data determined based on the predicted parameters, until the predicted total loss meets the preset convergence condition.

[0133] When the predicted total loss meets the preset convergence condition, the training of the equivalent circuit parameter prediction model is determined to be complete, and the equivalent circuit parameter prediction model is used as the target equivalent circuit parameter prediction model.

[0134] In one feasible implementation, the prediction module 20 is further configured to obtain a first correspondence between the reconstructed impedance spectrum data, the actual impedance spectrum data and the error index;

[0135] Based on the reconstructed impedance spectrum data, the unlabeled real impedance spectrum data, and the first correspondence, an error index is calculated;

[0136] Obtain a second correspondence between the error metric and the total predicted loss;

[0137] Based on the error index and the second correspondence, the total predicted loss is determined.

[0138] In one feasible implementation, the prediction module 20 is further configured to determine a target gradient between the total prediction loss and the weights of the parameter prediction module based on the total prediction loss, the reconstructed impedance spectrum data, and the prediction parameters.

[0139] Based on the target gradient, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated.

[0140] In one feasible implementation, the prediction module 20 is further configured to calculate a first gradient between the total predicted loss and the reconstructed impedance spectrum data;

[0141] Calculate the second gradient between the reconstructed impedance spectrum data and the predicted parameters;

[0142] Calculate the third gradient between the predicted parameters and the weights of the parameter prediction module;

[0143] Obtain the third correspondence between the first gradient, second gradient, third gradient and target gradient;

[0144] The target gradient is determined based on the first gradient, the second gradient, the third gradient, and the third correspondence.

[0145] In one feasible implementation, the training module 10 is also used to acquire raw impedance spectrum data;

[0146] Based on a preset range, the original impedance spectrum data is normalized to obtain unlabeled real impedance spectrum data.

[0147] The equivalent circuit parameter prediction device provided in this application, employing the equivalent circuit parameter prediction method in the above embodiments, can solve the technical problem that traditional machine learning schemes rely on biased real labels, resulting in unreliable prediction results. Compared with the prior art, the beneficial effects of the equivalent circuit parameter prediction device provided in this application are the same as those of the equivalent circuit parameter prediction method provided in the above embodiments, and other technical features in the equivalent circuit parameter prediction device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0148] This application provides an equivalent circuit parameter prediction device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the equivalent circuit parameter prediction method in the first embodiment described above.

[0149] The following is for reference. Figure 8The diagram illustrates a structural schematic suitable for implementing the equivalent circuit parameter prediction device of the embodiments of this application. The equivalent circuit parameter prediction device in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 8 The equivalent circuit parameter prediction device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0150] like Figure 8 As shown, the equivalent circuit parameter prediction device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in ROM (Read Only Memory) 1002 or a program loaded from storage device 1003 into RAM (Random Access Memory) 1004. RAM 1004 also stores various programs and data required for the operation of the equivalent circuit parameter prediction device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via bus 1005. Input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touch screens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the equivalent circuit parameter prediction device to communicate wirelessly or wiredly with other devices to exchange data. Although the figures show equivalent circuit parameter prediction devices with various systems, it should be understood that implementation or possession of all the systems shown is not required. More or fewer systems may be implemented alternatively.

[0151] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0152] The equivalent circuit parameter prediction device provided in this application, employing the equivalent circuit parameter prediction method in the above embodiments, can solve the technical problem that traditional machine learning schemes rely on biased real labels, resulting in unreliable prediction results. Compared with the prior art, the beneficial effects of the equivalent circuit parameter prediction device provided in this application are the same as those of the equivalent circuit parameter prediction method provided in the above embodiments, and other technical features in this equivalent circuit parameter prediction device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0153] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0154] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0155] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the equivalent circuit parameter prediction method in the above embodiments.

[0156] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0157] The aforementioned computer-readable storage medium may be included in the equivalent circuit parameter prediction device; or it may exist independently and not assembled into the equivalent circuit parameter prediction device.

[0158] The aforementioned computer-readable storage medium carries one or more programs. When these programs are executed by the equivalent circuit parameter prediction device, the equivalent circuit parameter prediction device: processes unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters; trains the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain a target equivalent circuit parameter prediction model; and predicts the impedance spectrum data to be predicted based on the target equivalent circuit parameter prediction model to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

[0159] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0160] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0161] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0162] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described equivalent circuit parameter prediction method. This solves the technical problem that traditional machine learning schemes rely on biased real labels, resulting in unreliable prediction results. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the equivalent circuit parameter prediction method provided in the above embodiments, and will not be repeated here.

[0163] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the equivalent circuit parameter prediction method described above.

[0164] The computer program product provided in this application can solve the technical problem that traditional machine learning schemes rely on biased true labels, resulting in unreliable prediction results. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the equivalent circuit parameter prediction method provided in the above embodiments, and will not be repeated here.

[0165] The above are only some embodiments of this application and do not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A method for predicting equivalent circuit parameters, characterized in that, The method includes: Based on the equivalent circuit parameter prediction model, unlabeled real impedance spectrum data is processed to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters. The equivalent circuit parameter prediction model includes a parameter prediction module and an impedance spectrum reconstruction module. The impedance spectrum reconstruction module has a built-in complex impedance analytical formula of the equivalent circuit model. The parameter prediction module is used to predict the unlabeled real impedance spectrum training data to obtain prediction parameters. The prediction parameters are input into the impedance spectrum reconstruction module. The impedance spectrum reconstruction module is used to calculate the complex impedance data of each angular frequency in the preset frequency list under the prediction parameters based on the complex impedance analytical formula. The real part and imaginary part of the complex impedance data are separated to obtain the reconstructed impedance spectrum data. Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, the equivalent circuit parameter prediction model is trained to obtain the target equivalent circuit parameter prediction model. The total prediction loss is determined by comparing the difference between the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, and the model is trained based on the total prediction loss. Based on the target equivalent circuit parameter prediction model, the impedance spectrum data to be predicted is predicted to obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

2. The method as described in claim 1, characterized in that, The step of training the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain the target equivalent circuit parameter prediction model includes: Based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, the predicted total loss is determined; When the predicted total loss does not meet the preset convergence condition, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated based on the predicted total loss. Then, the process of processing the unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model is returned to obtain the predicted parameters and the reconstructed impedance spectrum data determined based on the predicted parameters, until the predicted total loss meets the preset convergence condition. When the predicted total loss meets the preset convergence condition, the training of the equivalent circuit parameter prediction model is determined to be complete, and the equivalent circuit parameter prediction model is used as the target equivalent circuit parameter prediction model.

3. The method as described in claim 2, characterized in that, The step of determining the predicted total loss based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data includes: Obtain the first correspondence between reconstructed impedance spectrum data, actual impedance spectrum data, and error indices; Based on the reconstructed impedance spectrum data, the unlabeled real impedance spectrum data, and the first correspondence, an error index is calculated; Obtain a second correspondence between the error metric and the total predicted loss; Based on the error index and the second correspondence, the total predicted loss is determined.

4. The method as described in claim 2, characterized in that, The step of updating the weights of the parameter prediction module in the equivalent circuit parameter prediction model based on the total predicted loss includes: Based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters, a target gradient between the total predicted loss and the weights of the parameter prediction module is determined. Based on the target gradient, the weights of the parameter prediction module in the equivalent circuit parameter prediction model are updated.

5. The method as described in claim 4, characterized in that, The step of determining the target gradient between the total predicted loss and the weights of the parameter prediction module based on the total predicted loss, the reconstructed impedance spectrum data, and the prediction parameters includes: Calculate the first gradient between the predicted total loss and the reconstructed impedance spectrum data; Calculate the second gradient between the reconstructed impedance spectrum data and the predicted parameters; Calculate the third gradient between the predicted parameters and the weights of the parameter prediction module; Obtain the third correspondence between the first gradient, second gradient, third gradient and target gradient; The target gradient is determined based on the first gradient, the second gradient, the third gradient, and the third correspondence.

6. The method according to any one of claims 1 to 5, characterized in that, Before the step of processing unlabeled real impedance spectrum data based on the equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters, the method further includes: Obtain the raw impedance spectrum data; Based on a preset range, the original impedance spectrum data is normalized to obtain unlabeled real impedance spectrum data.

7. An equivalent circuit parameter prediction device, characterized in that, The device includes: A training module is used to process unlabeled real impedance spectrum data based on an equivalent circuit parameter prediction model to obtain prediction parameters and reconstructed impedance spectrum data determined based on the prediction parameters. The equivalent circuit parameter prediction model includes a parameter prediction module and an impedance spectrum reconstruction module. The impedance spectrum reconstruction module has a built-in complex impedance analytical formula of the equivalent circuit model. The parameter prediction module is used to predict the unlabeled real impedance spectrum training data to obtain prediction parameters, and input the prediction parameters into the impedance spectrum reconstruction module. The impedance spectrum reconstruction module is used to calculate the complex impedance data of each angular frequency in a preset frequency list under the prediction parameters based on the complex impedance analytical formula, and separate the real part and imaginary part of the complex impedance data to obtain the reconstructed impedance spectrum data. The training module is also used to train the equivalent circuit parameter prediction model based on the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data to obtain the target equivalent circuit parameter prediction model. The total prediction loss is determined by comparing the difference between the reconstructed impedance spectrum data and the unlabeled real impedance spectrum data, and the model is trained based on the total prediction loss. The prediction module is used to predict the impedance spectrum data to be predicted based on the target equivalent circuit parameter prediction model, and obtain the target parameters of the equivalent circuit model corresponding to the impedance spectrum data to be predicted.

8. An equivalent circuit parameter prediction device, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the equivalent circuit parameter prediction method as described in any one of claims 1 to 6.

9. A storage medium, characterized in that, The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the steps of the equivalent circuit parameter prediction method as described in any one of claims 1 to 6.

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