Method for predicting battery capacity in early charging phase based on physical information neural network model

Abstract

The present application relates to the technical field of battery capacity prediction, and discloses a method for predicting battery capacity in early charging stage based on a physical information neural network model, comprising: performing charging and discharging cycle tests on a plurality of lithium ion batteries by using an intermittent current interruption (ICI) method; obtaining voltage signal data within a specified time period after charging to an early fixed capacity and extracting features; setting the capacity as a target value, and constructing a data set of the features and the target value; dividing a plurality of battery data sets to obtain a training set and a test set; training the model based on the training set, calculating evaluation indexes of the trained model; testing the early charging feature data of other batteries, evaluating the predicted capacity and the real capacity based on the evaluation indexes, and determining the accuracy of the model. The present application only needs the early charging detailed test data of a single battery, can quickly predict the capacity of other batteries in the early charging process, and significantly reduces the test cost and time.

Description

Technical Field

[0001] This invention relates to the field of battery capacity prediction technology, and in particular to a method for predicting battery capacity in the early stages of charging based on a physical information neural network model. Background Technology

[0002] In recent years, with the rapid development of lithium-ion batteries, the accurate prediction of the remaining useful life (RUL) and the assessment of the full life cycle (FLC) of lithium-ion batteries have received widespread attention. With the widespread application of lithium batteries in electric vehicles, wearable devices, energy storage systems, and other fields, their performance reliability and long-term safety have become critical issues. Accurately predicting the state of health (SOH) and full life cycle (FLC) of batteries is essential for improving the intelligence level of battery management systems, extending battery life, and ensuring the safe operation of equipment. Traditional battery health assessment methods mainly rely on long-term charge-discharge cycle tests. Some batteries also require constant-current intermittent titration (GITT) to calculate the ion diffusion coefficient of lithium-ion batteries. However, due to the long relaxation time, their commercialization is not high. Electrochemical impedance spectroscopy (EIS) is generally performed during the battery production stage. However, if EIS testing is performed after the lithium-ion battery is packaged, the battery needs to be disassembled, which is not only time-consuming and costly, but also makes it difficult to monitor the battery's health status in real time in practical applications. As numerous enterprises and research institutions continue to deepen their research on lithium-ion batteries, a large number of aging datasets covering different battery types, environmental conditions, and cycling conditions have been gradually constructed and improved. These data record detailed information on the battery's electrochemical behavior, capacity decay trajectory, cycle life performance, and thermal management characteristics during cycling. The accumulation of such high-quality datasets provides solid support for estimating the state of health (SOH) and remaining service life (FLC) of lithium-ion batteries using data-driven methods. Based on this rich data, researchers can develop more accurate machine learning models and algorithms, further improving the predictive ability of lithium-ion battery performance degradation patterns and ultimately achieving reliable assessment of their lifespan.

[0003] Currently, research is focused on exploring battery health assessment methods based on intermittent current interruption (ICI), particularly in combining real-time charge / discharge capacity with voltage response characteristics after current interruption. However, this research is still primarily experimentally validated, and the reliability and technological maturity of practical applications need further improvement. In contrast, domestic attention to this technological approach is relatively limited, especially research on fusing real-time capacity data with ICI characteristics for lithium battery capacity prediction, which is still in its early stages. Therefore, a method capable of efficiently and accurately predicting the capacity of multiple batteries based on limited battery data would not only help fill the research gap in this area but also potentially provide a more precise and efficient solution for battery health management. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting battery capacity in the early stages of charging based on a physical information neural network model, which solves the problems of high cost, long cycle and large error that traditional capacity prediction methods usually rely on long-term testing of a large number of battery samples.

[0005] This invention provides a method for predicting battery capacity in the early stages of charging based on a physical information neural network model, comprising: Multiple lithium-ion batteries were subjected to charge-discharge cycle tests using an intermittent current interruption method. The voltage signal data is acquired during a specified time period after the initial fixed capacity is reached during the charge-discharge cycle test, and features are extracted based on the voltage signal data. The features include diffusion coefficient features, resistance features, diffusion parameter features, area features, curvature features, mean features, standard deviation features, kurtosis features, skewness features, slope features, and entropy features. Set the capacity to the target value and construct a dataset of features and the target value; The dataset is divided into two parts: the dataset corresponding to one lithium-ion battery is divided into the training set, and the dataset corresponding to the remaining lithium-ion batteries is divided into the test set. Select a physical information neural network model, train the physical information neural network model based on the training set, and calculate the evaluation index of the trained physical information neural network model. Keeping the trained physical information neural network model unchanged, we tested the early charging characteristic data of other batteries and evaluated the predicted capacity and the actual capacity based on the evaluation index to determine the accuracy of the trained physical information neural network model.

[0006] Preferably, the intermittent current interruption method specifically involves: constant current charging / discharging for 150 seconds, followed by a 10-second interruption, until fully charged; then constant current charging / discharging for another 150 seconds, followed by a 10-second interruption, until fully discharged; finally, resting for 1 hour. During charge-discharge cycle testing, the test voltage was 2.7V-4.35V, and one voltage signal was recorded every 0.1s.

[0007] Preferably, the fixed capacity is 948.5mAh; The interrupt current range is denoted as the ICI range, and each ICI range includes 101 voltage signals; The recovery current range is denoted as the CC range, and each CC range includes 1501 voltage signals.

[0008] Preferably, the diffusion coefficient characteristic D is calculated as follows: ; in, , This is the voltage value before the current interruption. This is the voltage value before the next current interruption. , The slope of the straight line fitted between the 101 voltage signals in the ICI interval and time 1 / 2; The resistance characteristic R 1s The formula for calculation is: ; in, , This is the voltage value before the current interruption. The voltage value is 1 second after the current is interrupted, I = 3250mA, and the constant current value is 3250mA. The formula for calculating the diffusion parameter characteristic k is: ; Where I = 3250mA, is the constant current value. The slope of the straight line fitted between the 101 voltage signals in the ICI interval and time 1 / 2; The area feature includes S ICI S CC The formula for calculating the area feature is: ; Among them, S ICI S represents the area characteristic of the ICI interval. CC The area characteristics of the CC interval, E ICI The ICI voltage curve is located in the ICI range, E CC Here is the CC voltage curve for the CC interval, dt = 0.1s, which is the time interval; The curvature feature includes The formula for calculating the curvature feature is: ; Where k represents the curvature feature, which is the curvature of the first three discrete points of each of the ICI and CC voltage curves after calculating their curvature. ICI1 k represents the curvature of the first discrete point of the ICI voltage curve. ICI2 k represents the curvature of the second discrete point of the ICI voltage curve. ICI3 k represents the curvature of the third discrete point of the ICI voltage curve. CC1 k represents the curvature of the first discrete point of the CC voltage curve. CC2k represents the curvature of the second discrete point of the CC voltage curve. CC3 This represents the curvature of the third discrete point on the CC voltage curve. This represents the first derivative of the voltage curve. Represents the second derivative of the voltage curve; The mean feature includes The formula for calculating the mean characteristic is: ; The standard deviation characteristics include The formula for calculating the standard deviation characteristic is: ; The kurtosis characteristics include: Ku ICI Ku CC The formula for calculating the kurtosis feature is: ; The skewness feature includes Sk ICI Sk CC The formula for calculating the skewness characteristic is: ; The slope feature includes a ICI a CC The formula for calculating the slope feature is: ; The entropy features include HICI and H. CC The entropy feature is calculated as follows: ; Where μ represents the mean feature, σ represents the standard deviation feature, Ku represents the kurtosis feature, Sk represents the skewness feature, a represents the slope feature, and H represents the entropy feature. All calculations are performed using discrete data points in the ICI and CC intervals.

[0009] Preferably, the capacity is calculated using the ampere-hour integration method, and the formula for the ampere-hour integration method is: ; Where Q is the battery capacity, t0 and t are the start and end times, and I(t) is the instantaneous current.

[0010] Preferably, the physical information neural network model consists of a main network and a dynamic network. The main network takes 24 features (x, t) as input and outputs a capacity target value (u) through a multilayer perceptron network structure. The input features of the dynamic network are (x, t) and (u). , The output value is the capacity decay rate, expressed as ; The calculation formula for the physical information neural network model is as follows: ; in, Main network For time series t The dynamic equations for battery degradation are constructed for the kinetic network.

[0011] Preferably, the physical information neural network model adopts three loss function solution methods, namely data loss function, partial differential equation loss function and physical monotonic consistency loss function; The formula for solving the data loss function is as follows: ; The formula for solving the loss function of a partial differential equation is: ; The formula for solving the physical monotonic consistency loss function is: ; Total loss function: , where α and β are trade-off parameters.

[0012] Preferably, the evaluation metrics include: accuracy R 2 Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE).

[0013] Compared with existing technologies, the advantages of this invention lie in its intermittent current interruption (ICI) method and physical information neural network (PINN). It extracts multiple feature datasets from voltage data generated by intermittent current interruptions. These datasets use readily available voltage values ​​for multiple calculations as features. The capacity is obtained using the ampere integral method as the target value. A PINN model with excellent predictive performance is trained using one battery, and then used to predict the early capacity of other batteries during the charging process. Keeping the trained model unchanged, the resulting predictive model can accurately predict the capacity of other batteries. This method requires only data from a single battery to predict the capacity of multiple batteries, resulting in less and more precise training data and superior prediction performance. Attached Figure Description

[0014] 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, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating the method for predicting battery capacity in the early stages of charging based on a physical information neural network model, as described in this invention. Figure 2 This is a capacity cycling diagram of lithium-ion batteries in the training set of this invention. Figure 3 This is a training effect diagram of the training set in an embodiment of the present invention; Figure 4 These are the predicted performance graphs of four lithium-ion batteries in the embodiments of the present invention; Figure 5 This is a diagram showing the lithium-ion battery ICI charge / discharge protocol and feature extraction in an embodiment of the present invention. Figure 6 This is a framework diagram of the physical information neural network model in an embodiment of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0017] like Figure 1 As shown, this invention provides a method for predicting battery capacity in the early stages of charging based on a physical information neural network model. It can accurately predict the capacity of multiple lithium-ion batteries during the charging process using data from a single lithium-ion battery. Traditional lithium-ion battery capacity prediction methods often require extensive data collection and analysis for each battery, which is not only time-consuming and labor-intensive but also costly. The method of this invention, however, uses an intermittent current interruption method to perform charge-discharge cycle testing, acquiring key voltage signal data and extracting various features, greatly improving the effectiveness and relevance of the data.

[0018] Specifically, it includes: Step S1: Perform charge-discharge cycle tests on multiple lithium-ion batteries using an intermittent current interruption method.

[0019] The intermittent current interruption method specifically involves: charging / discharging at a constant current (3250mA, 1C rate) for 150s, followed by a 10s interruption, until fully charged; then charging / discharging at a constant current for 150s, followed by a 10s interruption, until fully discharged; finally, resting for 1 hour; during the charge-discharge cycle test, the test voltage is 2.7V-4.35V, and one voltage signal is recorded every 0.1s. Figure 5This is an example of the lithium-ion battery ICI charge / discharge protocol and feature extraction diagram in this invention, such as... Figure 5 As shown, a 1-hour rest period is performed after each complete charge-discharge protocol to allow the lithium ions inside the battery to remain in balance.

[0020] In this embodiment, the lithium-ion battery used is an 18650 lithium-ion battery.

[0021] Step S2: Obtain voltage signal data within a specified time period after charging to an early fixed capacity during the charge-discharge cycle test, and extract features based on the voltage signal data. The features include diffusion coefficient features, resistance features, diffusion parameter features, area features, curvature features, mean features, standard deviation features, kurtosis features, skewness features, slope features, and entropy features.

[0022] The fixed capacity is 948.5mAh, meaning the extracted data corresponds to the data from the seventh ICI test, at which point the corresponding charging capacity is 948.5mAh.

[0023] The interrupt current range is denoted as the ICI range, and each ICI range includes 101 voltage signals; the recovery current range is denoted as the CC range, and each CC range includes 1501 voltage signals.

[0024] The formula for calculating the diffusion coefficient characteristic D is: ; in, , This is the voltage value before the current interruption. This is the voltage value before the next current interruption. , The slope of the straight line fitted to the 101 voltage signals in the ICI interval with time 1 / 2 ( and (160-second interval, 10-second interruption and 150-second resumption). The resistance characteristic R 1s The formula for calculation is: ; in, , This is the voltage value before the current interruption. The voltage value is 1 second after the current is interrupted, I = 3250mA, and the constant current value is 3250mA. The formula for calculating the diffusion parameter characteristic k is: ; Where I = 3250mA, is the constant current value. The slope of the straight line fitted between the 101 voltage signals in the ICI interval and time 1 / 2; The area feature includes S ICI S CC The formula for calculating the area feature is: ; Among them, S ICI S represents the area characteristic of the ICI interval. CC The area characteristics of the CC interval, , E ICI The ICI voltage curve is located in the ICI range, E CC Here is the CC voltage curve for the CC interval, dt = 0.1s, which is the time interval; The curvature feature includes The formula for calculating the curvature feature is: ; Where k represents the curvature feature, which is the curvature of the first three discrete points of each of the ICI and CC voltage curves after calculating their curvature. ICI1 k represents the curvature of the first discrete point of the ICI voltage curve. ICI2 k represents the curvature of the second discrete point of the ICI voltage curve. ICI3 k represents the curvature of the third discrete point of the ICI voltage curve. CC1 k represents the curvature of the first discrete point of the CC voltage curve. CC2 k represents the curvature of the second discrete point of the CC voltage curve. CC3 The curvature of the third discrete point of the CC voltage curve is represented by y. i Represents the voltage curve. This represents the first derivative of the voltage curve. Represents the second derivative of the voltage curve; The mean feature includes The formula for calculating the mean characteristic is: ; These represent the mean characteristics of the ICI voltage curve and the mean characteristics of the CC voltage curve, respectively.

[0025] The standard deviation characteristics include The formula for calculating the standard deviation characteristic is: ; These represent the standard deviation characteristics of the ICI voltage curve and the CC voltage curve, respectively.

[0026] The kurtosis characteristics include: Ku ICIKu CC The formula for calculating the kurtosis feature is: ; Ku ICI Ku CC These represent the kurtosis characteristics of the ICI voltage curve and the CC voltage curve, respectively.

[0027] The skewness feature includes Sk ICI Sk CC The formula for calculating the skewness characteristic is: ; Sk ICI Sk CC These represent the skewness characteristics of the ICI voltage curve and the CC voltage curve, respectively.

[0028] The slope feature includes a ICI a CC The formula for calculating the slope feature is: ; a ICI a CC These represent the slope characteristics of the ICI voltage curve and the CC voltage curve, respectively.

[0029] The entropy feature includes H ICI H CC The entropy feature is calculated as follows: ; H ICI H CC These represent the entropy characteristics of the ICI voltage curve and the CC voltage curve, respectively.

[0030] Where μ represents the mean feature, σ represents the standard deviation feature, Ku represents the kurtosis feature, Sk represents the skewness feature, a represents the slope feature, and H represents the entropy feature. All calculations are performed using discrete data points in the ICI and CC intervals.

[0031] Understandably, clarifying the specific operational procedures, test voltage range, and data recording frequency of the intermittent current interruption method makes charge-discharge cycle testing more standardized and accurate. The fixed capacity setting and the clarification of the number of voltage signals in the ICI and CC intervals provide clear standards for subsequent data processing and feature extraction. The provision of various feature calculation formulas ensures the accuracy and consistency of feature extraction, enabling the model to be trained and predicted based on accurate feature data. This precise data acquisition and feature extraction method further improves the accuracy and reliability of early capacity prediction for the charging process of multiple other lithium-ion batteries using physical information neural network models with data from a single lithium-ion battery.

[0032] Step S3: Set the capacity to the target value and construct a dataset of features and target values.

[0033] The capacity is calculated using the ampere-hour integration method, and the formula for the ampere-hour integration method is: ; Where Q is the battery capacity, t0 and t are the start and end times, and I(t) is the instantaneous current. Figure 2 Capacity cycling plot of lithium-ion batteries used in the training set.

[0034] Understandably, using the ampere-hour integration method to calculate battery capacity allows for a precise determination of the battery's actual capacity based on the changes in current over time during charging and discharging. This calculation method fully considers the dynamic changes in current over different time periods, and compared to some traditional fixed-parameter estimation methods, it more accurately reflects the battery's true capacity state. In practical applications of lithium-ion batteries, the battery current fluctuates continuously with changes in load. The ampere-hour integration method can track these current changes in real time and convert them into a capacity value through integration, providing more accurate data support for battery management and use. For electric vehicles, accurate battery capacity information helps drivers more accurately grasp the vehicle's range and rationally plan driving routes and charging times.

[0035] Step S4: Divide the dataset into a training set and a test set, with the dataset corresponding to one of the lithium-ion batteries as the training set and the dataset corresponding to the remaining lithium-ion batteries as the test set.

[0036] Step S5: Select a physical information neural network model, train the physical information neural network model based on the training set, and calculate the evaluation index of the trained physical information neural network model.

[0037] Figure 6 This is a framework diagram of the physical information neural network model in an embodiment of the present invention, such as... Figure 6As shown, the physical information neural network model consists of a main network and a dynamic network. The main network takes 24 features (x, t) as input and outputs a capacity target value (u) through a multilayer perceptron network structure. The 24 features include the 23 existing features (x) obtained in step 2 and one time series feature (t). The multilayer perceptron network structure includes one input layer, two hidden layers and one output layer. The input features of the dynamic network are (x, t) and (u). The output value is the capacity decay rate, expressed as The input features have a total of 49 dimensions. The calculation formula for the physical information neural network model is as follows: ; in, Main network For time series t The dynamic equations for battery degradation are constructed for the kinetic network.

[0038] The physical information neural network model employs three loss function solution methods: data loss function, partial differential equation loss function, and physical monotonic consistency loss function. The formula for solving the data loss function is as follows: ; The formula for solving the loss function of a partial differential equation is: ; The formula for solving the physical monotonic consistency loss function is: ; Total loss function: , where α and β are trade-off parameters. Represents the data loss function. This represents the loss function of a partial differential equation. This represents the physical monotonic consistency loss function. This represents the total loss function.

[0039] Evaluation metrics include: accuracy (R) 2 Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE).

[0040] Accuracy R 2 The formula for calculation is: ; The formula for calculating the mean absolute error (MAE) is: ; The formula for calculating the mean squared error (MSE) is: ; The formula for calculating the root mean square error (RMSE) is: ; The formula for calculating the Mean Absolute Percentage Error (MAPE) is: ; Among them, Y i It is the actual capacity value, y i This is the capacity prediction value from the ML model. It is the average of all true capacity values. When R 2 The closer the value is to 1, the closer the MSE is to 0, indicating better model accuracy, i.e., better predictive performance.

[0041] Understandably, employing a physical information neural network model and specific loss function solution methods, combined with multiple evaluation metrics, provides a more scientific, accurate, and comprehensive solution for lithium-ion battery capacity prediction. The physical information neural network model combines the main network and the dynamic network, fully mining the physical information and dynamic change patterns in battery data, thus predicting battery capacity more accurately. Through solving three loss functions, the model can be optimized in multiple aspects, including data fitting, partial differential equation constraints, and physical monotonicity consistency, ensuring that the prediction results both conform to actual data and follow the physical laws of battery degradation.

[0042] The introduction of multiple evaluation metrics provides a multi-faceted perspective for assessing model performance. Accuracy RA 2 These metrics can intuitively reflect the degree of fit between model predictions and actual values. Mean absolute error (MAE), mean squared error (MSE), and root mean square error (RMSE) can measure the magnitude of the deviation between predicted and actual values, while mean absolute percentage error (MAPE) can evaluate model performance from the perspective of relative error. These evaluation metrics complement each other, enabling a comprehensive and objective assessment of the model's strengths and weaknesses, and helping researchers to promptly identify and improve any problems with the model.

[0043] Step S6: Keep the trained physical information neural network model unchanged, use the early charging feature data of other batteries for testing, and evaluate the predicted capacity and the actual capacity based on the evaluation index to determine the accuracy of the trained physical information neural network model.

[0044] Figure 3 This is a training effect diagram of the training set of the present invention, and Table 1 is a fitting table of the training set.

[0045] Table 1 ; The feasibility of the model was evaluated by training and testing on characteristic data of the early charging process of multiple lithium-ion batteries. Figure 4 The predicted performance of four lithium-ion batteries is shown in Figure 2, and Table 2 presents the performance data. These results demonstrate the feasibility of the method, enabling accurate prediction of the full lifespan capacity during the early stages of battery charging. The method also reveals that by extracting features from the early charging process of a single battery, the physical laws governing capacity decay based on PINN are derived. Applying this model to other batteries allows for accurate prediction of the total battery capacity during a given charge, leveraging the early charging process characteristics of those batteries. This enables early capacity prediction, making rapid capacity prediction technology economically feasible.

[0046] Table 2 ; Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program goods. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program goods embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0047] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program goods according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0048] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0049] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting battery capacity in the early stages of charging based on a physical information neural network model, characterized in that, include: Multiple lithium-ion batteries were subjected to charge-discharge cycle tests using an intermittent current interruption method. The voltage signal data is acquired during a specified time period after the initial fixed capacity is reached during the charge-discharge cycle test, and features are extracted based on the voltage signal data. The features include diffusion coefficient features, resistance features, diffusion parameter features, area features, curvature features, mean features, standard deviation features, kurtosis features, skewness features, slope features, and entropy features. Set the capacity to the target value and construct a dataset of features and the target value; The dataset is divided into two parts: the dataset corresponding to one lithium-ion battery is divided into the training set, and the dataset corresponding to the remaining lithium-ion batteries is divided into the test set. Select a physical information neural network model, train the physical information neural network model based on the training set, and calculate the evaluation index of the trained physical information neural network model. Keeping the trained physical information neural network model unchanged, we tested it using early charging characteristic data from other batteries, and evaluated the predicted capacity and the actual capacity based on evaluation metrics to determine the accuracy of the trained physical information neural network model.

2. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 1, characterized in that, The intermittent current interruption method is as follows: charge / discharge at a constant current for 150 seconds, then interrupt for 10 seconds until fully charged; then charge / discharge at a constant current for 150 seconds, then interrupt for 10 seconds until fully discharged; finally, let stand for 1 hour. During charge-discharge cycle testing, the test voltage was 2.7V-4.35V, and one voltage signal was recorded every 0.1s.

3. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 2, characterized in that, The fixed capacity is 948.5mAh; The interrupt current range is denoted as the ICI range, and each ICI range includes 101 voltage signals; The recovery current range is denoted as the CC range, and each CC range includes 1501 voltage signals.

4. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 3, characterized in that, The formula for calculating the diffusion coefficient characteristic D is: ； in, , This is the voltage value before the current interruption. This is the voltage value before the next current interruption. , The slope of the straight line fitted between the 101 voltage signals in the ICI interval and time 1 / 2; The resistance characteristic R 1s The formula for calculation is: ； in, , This is the voltage value before the current interruption. The voltage value is 1 second after the current is interrupted, I = 3250mA, and the constant current value is 3250mA. The formula for calculating the diffusion parameter characteristic k is: ； Where I = 3250mA, is the constant current value. The slope of the straight line fitted between the 101 voltage signals in the ICI interval and time 1 / 2; The area feature includes S ICI S CC The formula for calculating the area feature is: ； Among them, S ICI S represents the area characteristic of the ICI interval. CC The area characteristics of the CC interval, , E ICI The ICI voltage curve is located in the ICI range, E CC Here is the CC voltage curve for the CC interval, dt = 0.1s, which is the time interval; The curvature feature includes The formula for calculating the curvature feature is: ； Where k represents the curvature feature, which is the curvature of the first three discrete points of each of the ICI and CC voltage curves after calculating their curvature. ICI1 k represents the curvature of the first discrete point of the ICI voltage curve. ICI2 k represents the curvature of the second discrete point of the ICI voltage curve. ICI3 k represents the curvature of the third discrete point of the ICI voltage curve. CC1 k represents the curvature of the first discrete point of the CC voltage curve. CC2 k represents the curvature of the second discrete point of the CC voltage curve. CC3 This represents the curvature of the third discrete point on the CC voltage curve. This represents the first derivative of the voltage curve. Represents the second derivative of the voltage curve; The mean feature includes The formula for calculating the mean characteristic is: ； The standard deviation characteristics include The formula for calculating the standard deviation characteristic is: ； The kurtosis characteristics include: Ku ICI Ku CC The formula for calculating the kurtosis feature is: ； The skewness feature includes Sk ICI Sk CC The formula for calculating the skewness characteristic is: ； The slope feature includes a ICI a CC The formula for calculating the slope feature is: ； The entropy feature includes H ICI H CC The entropy feature is calculated as follows: ； Where μ represents the mean feature, σ represents the standard deviation feature, Ku represents the kurtosis feature, Sk represents the skewness feature, a represents the slope feature, and H represents the entropy feature. All calculations are performed using discrete data points in the ICI and CC intervals.

5. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 1, characterized in that, The capacity is calculated using the ampere-hour integration method, and the formula for the ampere-hour integration method is: ； Where Q is the battery capacity, t0 and t are the start and end times, and I(t) is the instantaneous current.

6. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 1, characterized in that, The physical information neural network model consists of a main network and a dynamic network. The main network takes 24 features (x, t) as input and outputs a capacity target value (u) through a multilayer perceptron network structure. The input features of the dynamic network are (x, t) and (u). , The output value is the capacity decay rate, expressed as ; The calculation formula for the physical information neural network model is as follows: ； in, Main network The partial derivative with respect to the time series t, The dynamic equations for battery degradation are constructed for the kinetic network.

7. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 6, characterized in that, The physical information neural network model employs three loss function solution methods: data loss function, partial differential equation loss function, and physical monotonic consistency loss function. The formula for solving the data loss function is as follows: ； The formula for solving the loss function of a partial differential equation is: ； The formula for solving the physical monotonic consistency loss function is: ； Total loss function: , where α and β are trade-off parameters.

8. The method for predicting battery capacity in the early stages of charging based on a physical information neural network model according to claim 1, characterized in that, Evaluation metrics include: accuracy R 2 Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE).

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