CN114295999A - Lithium ion battery SOH prediction method and system based on indirect health index - Google Patents
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Abstract
The invention discloses a lithium ion battery SOH prediction method based on indirect health indexes. The technical scheme adopted by the invention is as follows: extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes; automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model; taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model; and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction. According to the method, the prediction of the SOH of the lithium ion battery is realized by adopting a multi-core Gaussian process regression model which considers the indirect health indexes of partial voltage and current data in the charging process and combines the parameter adjustment of a particle swarm optimization algorithm.
Description
Technical Field
The invention relates to the technical field of lithium ion battery health state assessment, in particular to a lithium ion battery SOH prediction method and system based on indirect health indexes.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The lithium ion battery plays a vital role in the storage and use processes of clean energy by virtue of light weight, good stability, no memory effect, high energy density and the like. However, with the increase of the number of charging and discharging times, the lithium ion battery may age due to various physical and chemical mechanisms, which may affect the normal operation of the electrical equipment, and even may cause catastrophic accidents. In order to ensure safe, stable and efficient operation of the battery, accurate diagnosis of the health state of the lithium ion battery is required.
The existing lithium ion battery State Of Health (SOH) prediction methods can be roughly divided into two categories: model-based methods and data-driven based methods. The model-based method is mainly used for constructing a degradation mathematical model of the lithium ion battery based on an equivalent circuit model and an electrochemical mechanism model. However, the accuracy of prediction in this method is closely related to the complexity of the model, and a model with high accuracy is difficult to construct due to the high non-linearity of the battery system. The data-driven-based method does not relate to a specific reaction mechanism and can be realized in a battery management system, and the primary task is to extract the characteristic values of model training. The extraction of the characteristics can obtain meaningful information from the original data on the premise of not influencing the model performance, and the training process is simplified. The extraction of the health indexes with reasonableness and high correlation is beneficial to improving the accuracy of the battery degradation modeling. The machine learning model has larger prediction result by the setting of the hyper-parameters. For this reason, data-driven methods often need to be used in combination with other optimization algorithms to determine the hyper-parameters of the model, reduce errors caused by manual intervention, and improve long-term prediction performance.
Although the existing research is relatively comprehensive, the problem that the storage time characteristics of the electrical energy storage and the hydrogen energy storage are not considered comprehensively still exists.
Disclosure of Invention
In order to solve the problems, the invention provides a lithium ion battery SOH prediction method and system based on indirect health indexes, which adopts a multi-core Gaussian Process Regression (GPR) model which considers the indirect health indexes of partial voltage and current data in the charging Process and combines with the parameter adjustment of a particle swarm optimization algorithm so as to realize the prediction of the lithium ion battery SOH.
The invention adopts a technical scheme that: a lithium ion battery SOH prediction method based on indirect health indexes comprises the following steps:
extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes;
automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model;
taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model;
and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction.
And optimizing the key parameters by adopting a Particle Swarm Optimization (PSO) to solve the problem of parameter selection.
Further, the Gaussian process regression model is modified into a multi-core Gaussian process regression model by utilizing the Gaussian kernel function and the sine square kernel function. The invention uses Gaussian kernel function to describe the capacity degradation, uses sine square kernel function to reduce the influence of regeneration phenomenon, and uses the combination of the two to accurately predict the capacity degradation curve of the lithium ion battery.
Further, after the indirect health index is extracted, quantitative analysis is carried out on the correlation between the extracted indirect health index and the capacity by adopting a pearson correlation coefficient, and the effectiveness of the indirect health index is verified.
Furthermore, after quantitative analysis, Kalman filtering is adopted to carry out filtering optimization on the extracted indirect health index so as to improve the correlation between the indirect health index and the capacity. The filtered characteristic is closer to the original capacity curve, and the correlation coefficient is obviously improved.
Further, the extraction content of the indirect health index is as follows:
a voltage curve in the constant-current charging process and a current curve in the constant-voltage charging process form a group of curve families in the whole life cycle process of the lithium ion battery, and a discrete coefficient is introduced as a characteristic to express the difference of each cycle curve; the dispersion coefficient is a normalized measure of the dispersion degree of the probability distribution, and is used for comparing the dispersion degrees of different sample data, and is defined as:
wherein, cvarIs a dispersion coefficient, σ is a standard deviation of the samples, μ is an average value of the samples, N is the number of samples, xiFor the samples, μ is defined as:
wherein X represents voltage or current data during charging, X0And XeThe starting and ending voltage or current values for a selected interval of a cycle, Time is the elapsed Time for that interval.
The other technical scheme adopted by the invention is as follows: a lithium ion battery SOH prediction system based on indirect health indicators, comprising:
an indirect health index extraction unit: extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes;
PSO-MK-GPR model building unit: automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model;
a model training unit: taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model;
SOH prediction unit: and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction.
Compared with the prior art, the invention has the beneficial effects that:
for the optimization of the hyper-parameters, the traditional mode is to solve by adopting a minimized negative log-likelihood function, solve the partial derivative by solving the partial derivative of the negative log-likelihood function and realize the maximization of the partial derivative by adopting a conjugate gradient method, however, the method has too strong dependence on the initial value and is easy to fall into the local optimization. The optimal hyper-parameter of the GPR model is automatically searched in the sample training process by adopting the PSO, a particle swarm optimization-based multi-core Gaussian process regression model (PSO-MK-GPR) is established, and the defects of the conjugate gradient algorithm are overcome.
The prediction value obtained by the method not only can accurately predict the capacity degradation, but also can accurately capture the capacity regeneration phenomenon. The GPR model can not only give the predicted value of the SOH, but also calculate the confidence interval of the predicted value of the SOH.
The invention has higher prediction precision and reliability. The different prediction starting points are tested, although the prediction starting points have obvious difference, the difference of SOH prediction performance is small, the influence of the prediction starting points on the method is small, and the PSO-MK-GPR model has strong generalization capability.
The feasibility and effectiveness of the prediction of the invention are verified by using National Aeronautics and astronautics and Space Administration (NASA) battery experimental data. Experimental results show that the prediction of the invention has higher precision and practical value.
Drawings
Fig. 1 is a graph illustrating normalized filter health index and capacity of a cell according to an embodiment of the present invention (fig. 1a is a graph illustrating normalized filter health index and capacity of a B0005 cell, fig. 1B is a graph illustrating normalized filter health index and capacity of a B0006 cell, fig. 1c is a graph illustrating normalized filter health index and capacity of a B0007 cell, and fig. 1d is a graph illustrating normalized filter health index and capacity of a B0018 cell);
FIG. 2 is a flow chart of an algorithm of the PSO-MK-GPR model of the invention;
FIG. 3 is a flow chart of a method for optimizing operation provided by the present invention;
fig. 4 is a structural diagram of an optimized operation system provided by the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example 1
The SOH prediction methods of the existing lithium ion batteries can be roughly divided into two categories: model-based methods and data-driven based methods. The model-based method is mainly used for constructing a degradation mathematical model of the lithium ion battery based on an equivalent circuit model and an electrochemical mechanism model. However, the accuracy of prediction in this method is closely related to the complexity of the model, and a model with high accuracy is difficult to construct due to the high non-linearity of the battery system. The data-driven-based method does not relate to a specific reaction mechanism and can be realized in a battery management system, and the primary task is to extract the characteristic values of model training. The extraction of the characteristics can obtain meaningful information from the original data on the premise of not influencing the model performance, and the training process is simplified. The extraction of the health indexes with reasonableness and high correlation is beneficial to improving the accuracy of the battery degradation modeling. The machine learning model has larger prediction result by the setting of the hyper-parameters. For this reason, data-driven methods often need to be used in combination with other optimization algorithms to determine the hyper-parameters of the model, reduce errors caused by manual intervention, and improve long-term prediction performance.
The invention provides a prediction method for realizing lithium ion battery SOH by considering indirect health indexes of partial voltage and current data in a charging process and combining a multi-core GPR model with particle swarm optimization algorithm parameter adjustment, as shown in FIG. 3, firstly, extracting indirect health indexes (HI for short) from a charging voltage curve and a charging current curve of a battery, carrying out quantitative analysis on the correlation between the extracted HI and capacity by adopting pearson correlation coefficients, and carrying out filter optimization on the extracted HI by adopting Kalman filtering, thereby further improving the correlation between the HI and the capacity. Then, the aging process of the lithium ion battery is modeled by using a GPR model based on the combined kernel function so as to realize SOH prediction. The PSO algorithm is adopted to optimize the key parameters, so that the problem of parameter selection is solved. Finally, the feasibility and effectiveness of the method are verified by NASA battery experimental data. Experimental results show that the method has high precision and practical value.
Key problem explanation:
1. battery aging data
The cell aging data used in the present invention is from the NASA emms excellent prediction center (PCoE) lithium ion cell dataset. Each battery runs three working modes of charging, discharging and impedance at room temperature. The charging is firstly carried out in a constant current mode of 1.5A, and constant voltage charging is adopted until the voltage rises to 4.2V until the charging current is reduced to 20 mA. The discharge was performed at a constant current of 2A until the voltage of the B0005, B0006, B0007, B0018 cells dropped to 2.7V, 2.5V, 2.2V and 2.5V, respectively. The normalized filter health index and capacity of the B0005, B0006, B0007, B0018 cells are shown schematically in fig. 1.
2. Extraction of indirect health indicators
The voltage curve in the constant current charging process and the current curve in the constant voltage charging process form a group of curve families in the whole life cycle process of the lithium ion battery, and discrete coefficients are introduced as characteristics to represent the difference of each cycle curve. The coefficient of dispersion (coeffient of variation) is a normalized measure of the degree of dispersion of the probability distribution, which is used to compare the degrees of dispersion of different sample data. It is defined as:
wherein c isvarIs a dispersion coefficient, σ is a standard deviation of the samples, μ is an average value of the samples, N is a number of the samples, and μ is defined as:
wherein X represents voltage or current data during charging, X0And XeIs a certainThe start and end voltage or current values of the selected interval are cycled, and Time is the elapsed Time of the interval. The mean value is defined in such a way to avoid the influence caused by different sampling frequencies of each period.
3. Evaluation and selection of indirect health indicators
For the data-driven mathematical model, the selection of the features with higher correlation is beneficial to improving the prediction accuracy. However, the trend of the variation varies from HI to HI, and it is difficult to directly judge the correlation of HI with capacity. To quantify the degree of correlation of the features with the volume, Pearson correlation coefficients were introduced. The calculation formula is as follows:
wherein A, B represents the population of feature and volume samples, respectively. The larger the absolute value of the calculated correlation coefficient, the higher the correlation between the two variables. When the absolute value of the correlation coefficient is equal to 1, the absolute value represents the complete correlation between the two variables; the correlation coefficient is equal to 0, indicating no linear correlation.
And calculating the correlation coefficient of the discrete coefficient characteristics and the capacity in different intervals according to the formula 3. Finally, the optimal voltage interval with the highest correlation is selected to be [3.8V, 4.2V ], and the optimal current interval is [0.3A,1.0A ]. The correlation coefficient of the health characteristics with the capacity in this interval is shown in table 1.
TABLE 1 correlation coefficient of health characteristics with capacity
| B0005 | B0006 | B0007 | B0018 | |
| Cvar_CC_V | 0.9974 | 0.9954 | 0.9890 | 0.9880 |
| Cvar_CV_C | 0.9788 | 0.9371 | 0.9682 | 0.9062 |
4. Optimization of indirect health indicators
Compared with the original capacity curve, the HI extracted by the method has certain noise pollution, which inevitably influences the final prediction precision of the capacity model. Therefore, the invention selects Kalman filtering KF to filter the extracted HI data.
Kalman filtering is an optimized recursive algorithm for digital processing. The method takes the minimum mean square error as the optimal prediction principle, and realizes the update of the predicted value of the state variable by using the current observation value and the predicted value at the previous moment based on the state space model of the signal and the noise. The state equation and the measurement equation are as follows:
in the formula, xkAs state quantity, herein extracted health feature data; k is a radical ofkIs the Kalman gain; z is a radical ofkRepresents a pair xkThe noise pollution measurement of (2).
5. Selection of the method
(1) Gauss process regression
The Gaussian process regression is an algorithm which is based on the Bayesian theory, can output a prediction mean value, a variance and a confidence interval and provides probability prediction. The GPR model is determined by its mean function and covariance function:
where f (x) is the output target and x is the input vector of dimension n. The probability distribution of the output function f (x) is:
f(x)～GP(m(x),k(x,x′)) (6)
considering the application of real scenes, the observed value output can be represented by an implicit function:
wherein y is an output observed value considering the influence of noise, ε is a mean value of 0 and a variance of
White gaussian noise. The available prior distribution is:
the joint prior distribution of predicted and measured values is:
where K (X, X) is an n-dimensional symmetric positive definite covariance matrix.
Is a noise covariance matrix. I isnIs an n-dimensional unit matrix. X is a training set, X*For the test set, Y is the measured value data set, Y*Is a predictive value data set. k is a radical ofijFor describing variable xiAnd xjThe higher the similarity, the larger the value thereof.
Observed value y*The posterior distribution of (A) is:
wherein the content of the first and second substances,
as a mean matrix:
cov(y*) As a covariance matrix:
the 95% confidence interval for the predicted results is:
after the mean value and the variance are determined, the hyper-parameters are optimized in the training process, and then the GPR model can be obtained. The GPR model is generally a zero-mean function and can be obtained by preprocessing data. The covariance function may be selected in various ways, but the capacity curve of the lithium ion battery as the prediction target cannot satisfy the prediction requirement only by using the GPR model of the single covariance function due to the capacity regeneration phenomenon.
Not only paying attention to the degradation trend of the battery, but also not neglectingA capacity regeneration phenomenon of the battery. For this purpose, the invention uses Gaussian kernel function to describe capacity degradation, uses sine square kernel function to reduce the influence of regeneration phenomenon, and uses the combination of the two to accurately predict the capacity degradation curve of the lithium ion battery. The super parameter combination at this time is
For the optimization of the hyperparameter, the traditional method is to solve by adopting a minimized negative log-likelihood function. The partial derivatives are solved by solving the negative log-likelihood function, and the solution is carried out by maximizing the partial derivatives by adopting a conjugate gradient method, however, the method has too strong dependence on the initial value and is easy to fall into local optimum. The optimal hyper-parameter of the GPR model is automatically searched in the sample training process by adopting the PSO, and the PSO-MK-GPR model is established so as to overcome the defect of the conjugate gradient algorithm.
(2) Particle swarm algorithm
The Particle Swarm Optimization (PSO) is an optimization algorithm based on the behavior of the population and the individual designed by simulating the foraging behavior of birds and fish, and achieves the purpose of optimal population through the cooperation between individuals. Each particle in the population has only two attributes, position and velocity, which correspond to a candidate solution. The flight process of the particle is the searching process of the particle, the position of the particle is judged to be good or bad through the fitness value, the best position which the particle individual experiences is called individual optimum position pbest, and the best position which the population group experiences is called global optimum position gbest. The position and velocity update formula of the particle i is:
wherein the content of the first and second substances,
for flight of the kth iteration of particle iA line velocity vector;
a position vector for the kth iteration of particle i; c. C1,c2The acceleration constant is used for adjusting the maximum learning step length; r is1,r2Is two value ranges of [0,1 ]]Random function between them to increase randomness; and omega is an inertia weight and is a non-negative value so as to adjust the search range of the solution space. PSO together contains c1,c2And omega three hyperparameters. The method is set to be 0.8,0.5 and 0.5, the optimal hyper-parameter of the GPR model is automatically searched in the sample training process by adopting the PSO, the PSO-MK-GPR model is established, and an algorithm flow chart is shown in FIG. 2.
In order to verify the performance of the method, the invention takes the root mean square error RMSE and the average absolute error MAE as evaluation indexes, and the calculation formula is as follows:
example 2
The embodiment provides a lithium ion battery SOH prediction system based on an indirect health index, which is composed of an indirect health index extraction unit, a PSO-MK-GPR model establishment unit, a model training unit and an SOH prediction unit, as shown in FIG. 4.
An indirect health index extraction unit: extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes;
PSO-MK-GPR model building unit: automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model;
a model training unit: taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model;
SOH prediction unit: and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction.
Specifically, the Gaussian process regression model is modified into a multi-core Gaussian process regression model by utilizing a Gaussian kernel function and a sine square kernel function.
Specifically, after the indirect health index is extracted, quantitative analysis is performed on the correlation between the extracted indirect health index and the capacity by using a pearson correlation coefficient, and the effectiveness of the indirect health index is verified.
After quantitative analysis is carried out, Kalman filtering is adopted to carry out filtering optimization on the extracted indirect health index, and the correlation between the indirect health index and the capacity is improved.
In the indirect health index extraction unit, the extraction content of the indirect health index is as follows:
a voltage curve in the constant-current charging process and a current curve in the constant-voltage charging process form a group of curve families in the whole life cycle process of the lithium ion battery, and a discrete coefficient is introduced as a characteristic to express the difference of each cycle curve; the dispersion coefficient is a normalized measure of the dispersion degree of the probability distribution, and is used for comparing the dispersion degrees of different sample data, and is defined as:
wherein, cvarIs a dispersion coefficient, σ is a standard deviation of the samples, μ is an average value of the samples, N is the number of samples, xiFor the samples, μ is defined as:
wherein X represents voltage or current data during charging, X0And XeSelected for a certain cycleThe starting and ending voltage or current values of the interval, Time is the Time elapsed for the interval.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (10)
1. A lithium ion battery SOH prediction method based on indirect health indexes is characterized in that,
extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes;
automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model;
taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model;
and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction.
2. The lithium ion battery SOH prediction method based on the indirect health index of claim 1, wherein a Gaussian process regression model is modified into a multi-core Gaussian process regression model by using a Gaussian kernel function and a sine square kernel function.
3. The lithium ion battery SOH prediction method based on the indirect health index as claimed in claim 1, wherein after the indirect health index is extracted, a pearson correlation coefficient is used to perform quantitative analysis on the correlation between the extracted indirect health index and capacity, and the validity of the indirect health index is verified.
4. The lithium ion battery SOH prediction method based on the indirect health index as claimed in claim 3, wherein after the quantitative analysis, Kalman filtering is adopted to perform filtering optimization on the extracted indirect health index, so as to improve the correlation between the indirect health index and the capacity.
5. The lithium ion battery SOH prediction method based on the indirect health indicator as claimed in claim 1, wherein the indirect health indicator is extracted as follows:
a voltage curve in the constant-current charging process and a current curve in the constant-voltage charging process form a group of curve families in the whole life cycle process of the lithium ion battery, and a discrete coefficient is introduced as a characteristic to express the difference of each cycle curve; the dispersion coefficient is a normalized measure of the dispersion degree of the probability distribution, and is used for comparing the dispersion degrees of different sample data, and is defined as:
wherein, cvarIs a dispersion coefficient, σ is a standard deviation of the samples, μ is an average value of the samples, N is the number of samples, xiFor the samples, μ is defined as:
wherein X represents voltage or current data during charging, X0And XeThe starting and ending voltage or current values for a selected interval of a cycle, Time is the elapsed Time for that interval.
6. A lithium ion battery SOH prediction system based on indirect health indicators, comprising:
an indirect health index extraction unit: extracting discrete coefficients of voltage and current curves in partial charging process of the lithium ion battery as indirect health indexes;
PSO-MK-GPR model building unit: automatically searching the optimal hyper-parameter of the multi-core Gaussian process regression model in the sample training process by adopting a particle swarm algorithm, and establishing the multi-core Gaussian process regression model based on particle swarm optimization, namely a PSO-MK-GPR model;
a model training unit: taking the indirect health index as input and the capacity as output, and sending the indirect health index and the capacity into a PSO-MK-GPR model for training to obtain a lithium ion battery aging model;
SOH prediction unit: and (4) transmitting the online extracted characteristic data into a trained PSO-MK-GPR model to realize SOH prediction.
7. The system of claim 6, wherein the Gaussian process regression model is modified to a multi-core Gaussian process regression model using a Gaussian kernel function and a sine square kernel function.
8. The lithium ion battery SOH prediction system based on the indirect health indicator of claim 6, wherein after the indirect health indicator is extracted, a pearson correlation coefficient is used to perform quantitative analysis on the correlation between the extracted indirect health indicator and capacity, and the validity of the indirect health indicator is verified.
9. The lithium ion battery SOH prediction system based on indirect health indicators of claim 8, wherein after quantitative analysis, Kalman filtering is used to optimize the extracted indirect health indicators, so as to improve the correlation between the indirect health indicators and the capacity.
10. The system of claim 6, wherein the indirect health indicator extraction unit extracts the indirect health indicator as follows:
a voltage curve in the constant-current charging process and a current curve in the constant-voltage charging process form a group of curve families in the whole life cycle process of the lithium ion battery, and a discrete coefficient is introduced as a characteristic to express the difference of each cycle curve; the dispersion coefficient is a normalized measure of the dispersion degree of the probability distribution, and is used for comparing the dispersion degrees of different sample data, and is defined as:
wherein, cvarIs a dispersion coefficient, σ is a standard deviation of the samples, μ is an average value of the samples, N is the number of samples, xiFor the samples, μ is defined as:
wherein X represents voltage or current data during charging, X0And XeThe starting and ending voltage or current values for a selected interval of a cycle, Time is the elapsed Time for that interval.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115201686A (en) * | 2022-07-12 | 2022-10-18 | 中国科学技术大学 | Lithium ion battery health state assessment method under incomplete charging and discharging data |
| CN115201686B (en) * | 2022-07-12 | 2023-08-29 | 中国科学技术大学 | Lithium ion battery health state assessment method under incomplete charge and discharge data |
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