CN109917292A - A kind of lithium ion battery life-span prediction method based on DAUPF - Google Patents
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Abstract
A kind of lithium ion battery life-span prediction method based on DAUPF of the present invention, sampling section first, the double adaptive factor is added on the basis of UKF algorithm, to the state value and covariance obtained after Sigma point set one-step prediction as guidance, a UT transformation is carried out again, is obtained new Sigma point set, is brought observational equation into, new observed quantity is obtained, to obtain recycling sample average and covariance for the first time；An adaptive factor is updated after improving UKF algorithm and being partially completed one cycle, then is improved UKF algorithm circulation next time.Enter PF process after the completion of sampling, obtains after once exporting predicted value, update another adaptive factor, complete a DAUPF process；Finally predict test data.Present invention improves UPF algorithm sampling section, the addition of the double adaptive factor enables algorithm have more strong robustness, and two step UT transformation makes adaptive factor more preferably incorporate algorithm, and algorithm prediction effect is more acurrate.
Description
Technical Field
The invention relates to a lithium ion battery service life prediction method based on DAUPF (double-adaptive sampling electrodeless Kalman particle filter algorithm), belonging to the technical field of lithium battery health management.
Background
Lithium ion batteries have been successfully used in many consumer electronics products (e.g., mobile phones, notebook computers, and electric vehicles), and have been gradually expanded to the fields of military communication, navigation, aviation, aerospace, and the like. The safety of lithium ion batteries is receiving more and more attention. The battery life is defined as the number of cycles or age of charge and discharge. The chemicals in the battery gradually degrade as the operating time of the battery increases, and battery failure can have serious consequences. The U.S. California fire department states that a Tesla Model S vehicle auto-ignites in a parking lot and re-ignites in a trailer yard several hours later, without collision and other handling of the vehicle during the two auto-ignitions. It is very important to accurately predict the service life of the lithium ion battery. State of health estimation (SOH) and remaining life prediction are key to battery health management, which can ensure safe use of lithium ion batteries.
Currently, there are two types of prediction methods for lithium batteries. One is a nonparametric model method, and the other is a parametric model method.
Examples of the nonparametric method include a neural network method and a machine learning method. Wu et al estimate the Remaining Useful Life (RUL) of a lithium ion battery using a Feed Forward Neural Network (FFNN) and Monte Carlo (IS) method. Zhang et al used a neural network based on long-short term memory (LSTM) to predict the remaining useful life of the battery. Examples of the machine learning method include support vector classification (SVM), Support Vector Regression (SVR), and Relevance Vector Machine (RVM) method. Tobar et al apply a method of improved nuclear adaptive filtering to the prediction of electric bicycle battery voltage.
Parametric models are most commonly used in various filtering algorithms. The Particle Filter (PF) method is an approximate Bayesian filter algorithm based on Monte Carlo simulation. The core idea is to use discrete random sampling points to approximate the probability density function of the system random variable. The seedling and the like predict the residual service life of the battery by a particle filtering method, and the obtained particle filtering can well predict the residual service life of the lithium ion battery. Saha et al establish a battery system framework to predict the remaining useful life of the battery at different discharge rates via PF. The particle filtering method is applicable to any non-linear non-gaussian environment, but depends on the selected reference distribution and state a posteriori estimation.
Extended Kalman (EKF) and Unscented Kalman (UKF) are modified Kalman Filter (KF) algorithms. The EKF has the advantages of weak nonlinearity and good prediction effect in a less-noise environment. The dong et al extracted an Adaptive Extended Kalman (AEKF) algorithm based on the recursive least square method, and found that the AEKF suppressed noise well. Ramadan et al analyze and compare various EKF algorithms to obtain a parameter model that is required to predict the state of charge (SOC) of a battery, and the quality of the EKF algorithms is closely related to the accuracy of the model. The UKF has the advantages of no loss on the model and relatively high calculation precision. Zheng proposes an integrated UKF method to predict the RUL of the battery, and estimates the parameters of the battery by using future residual errors, so that the short-term capacity of the battery can be accurately predicted, but the prediction precision cannot be further improved because the UKF cannot adjust the model parameters.
The particle filtering and the Kalman filtering have advantages and disadvantages respectively, and the advantages of the two algorithms can make up for the mutual deficiency, so that the extended Kalman particle filtering method and the unscented Kalman particle filtering method are provided. Seedling et al successfully predicted the RUL of the cell by using the infinite kalman particle filter (UPF) algorithm. But the algorithm is too dependent on the number of particles, the size of the data set, and the quality of the historical data. Zhang et al can maintain particle diversity and predict the remaining life of a lithium ion battery using a UPF algorithm based on Markov-Monte Carlo. Chen et al used a second order gaussian model and UPF to predict battery life.
The UPF algorithm is used for guiding particle sampling by the UKF algorithm in a sampling stage. And performing PF algorithm step after sampling, calculating weight, and performing normalization treatment. And judging whether resampling is carried out or not, and copying and eliminating the particle set. And calculating the mean value of the particle set to obtain an estimated output value. And analyzing the data after the iteration is finished. The structure is shown in fig. 1.
Due to introduction of UKF algorithm to guide sampling, the UPF algorithm is easily influenced by constraint of Gaussian noise and reference distribution; in addition, after the conventional ut (unknown transform) transform is transformed, the state value is updated, a certain error exists between the sigma distribution of the updated state value and the sigma distribution before updating, and if the sigma distribution used before updating is used to calculate parameters such as the observation prediction value, a certain influence is also exerted on the prediction result.
Disclosure of Invention
The invention aims to provide a lithium ion battery service life prediction method based on DAUPF (digital up-conversion), aiming at solving the problem that a UPF algorithm is easily influenced by noise and reference distribution, and firstly, an adaptive factor is added into the DAUPF algorithm. Considering that the traditional UPF algorithm is the combination of UKF and PF algorithm, adaptive factors are added in the sampling stage and the prediction stage respectively, and the adaptive factors can adjust parameter distribution, thereby making up the defects of the two algorithms. Secondly, the probability density is given by using a UKF algorithm in a sampling stage, the UKF can carry out UT conversion during sampling, and sigma distribution given by the UT conversion is inaccurate due to the fact that a new self-adaptive factor needs to be added after the UT conversion in the first step. In addition, the state value is updated after the conventional UT conversion, a certain error exists between the sigma distribution of the updated state value and the sigma distribution before updating, and if parameters such as an observation predicted value and the like are calculated by using the sigma distribution proposed before updating, a certain influence is generated on a prediction result. Based on the two reasons, the DAUPF algorithm carries out UT conversion once again after the state value is updated to obtain a new sigma point set, and then the parameters such as the observation predicted value and the like are calculated. The validity of the DAUPF algorithm is verified by using lithium battery experimental data of an advanced life cycle engineering center of Maryland university, and is compared with extended Kalman filtering, unscented Kalman filtering, particle filtering, extended Kalman particle filtering and unscented Kalman particle filtering.
The invention discloses a lithium ion battery service life prediction method based on DAUPF, which adopts the following technical scheme for solving the problems: firstly, a sampling part adds double self-adaptive factors on the basis of a UKF algorithm, then guides a Sigma point set to predict in one step to obtain a state value and covariance, and then carries out UT conversion once to obtain a new Sigma point set which is brought into an observation equation to obtain a new observed quantity, thereby obtaining a first-cycle sample mean value and covariance; and after the UKF algorithm improvement part completes one cycle, updating one adaptive factor in the double adaptive factors, and then performing the next UKF algorithm improvement cycle. Entering a PF process after sampling is finished, updating another adaptive factor after a primary output predicted value is obtained, and finishing a DAUPF process; finally, test data is predicted.
The invention relates to a lithium ion battery service life prediction method based on DAUPF, which specifically comprises the following steps:
step1, initializing parameters;
step2, entering into an improved UKF to guide particle distribution;
step3. calculating Sigma point set for the first time through UT transformation to obtain
Step4, adding a double adaptive factor to obtain
Step5. calculating mean and covariance from the Sigma point set obtained at step3
Step6, using the mean value and covariance obtained from step5, and performing UT transformation again to obtain a new Sigma point set
Step7. obtaining the observation prediction value by predicting the new Sigma point set obtained by step6Obtaining new observation value by observation predicted value and state predicted value through non-trace transformation calculationMean and covariance
Step8, calculating Kalman gain, variance and state updating;
step9. update the first adaptive factorA value;
and step10, judging whether sampling is finished or not. If the weight normalization is finished, performing the next weight normalization processing, otherwise entering step 2;
step11, calculating the weight by using the mean value and the variance obtained by the step1-9 sampling part through normalization processing to obtain a normalized weight;
step12, resampling particles; updating data, updating state, updating variance and taking the mean value as final estimation.
Obtaining a predicted value, and updating the value of the adaptive factor β;
step14. judge whether the iteration is finished. If so, evaluating the algorithm, otherwise, entering step 2;
step15. evaluation algorithm.
Wherein, the parameters initialized by Step1 include: initialized state valueWherein,in order to observe the initial state values of the equation,to initialize the covariance matrix.
Step2 is a starting sampling phase, the whole sampling phase circulates for N times, and the sampling phase is as follows: step2-Step 9.
Wherein Step3 specifically comprises the following steps: calculating a Sigma Point set of 2n +1 sample pointsWherein, the point setFrom point Xk-1Andthe composition of the components, wherein,as a scaling function.
Wherein Step4 specifically comprises the following steps:two adaptive factors are added, and the initial values of the two adaptive factors are 1. The first adaptive factor isWherein Z isk-1Is the observed value of the previous sampling point,the observed prediction value obtained at Step7 in the previous cycle. The second adaptive factor isWherein Z isk-1For true value of the system, Zupfk-1And (4) obtaining a predicted value after the Step13 DAUPF algorithm finishes the previous cycle.
Wherein Step5 is a one-Step prediction of sampling points, and the average value isByAnd calculating to obtain the result, wherein,the Sigma point set obtained in Step3 is substituted into the nonlinear transformation function. Covariance WhereinWherein λ α2(n+κ)-n；α＝1；ρ＝0；κ＝2。
Wherein Step6 is the second UT transformation, generates a new Sigma point set,
wherein, the point setBy pointAndcomposition of, whereinThe mean value obtained in Step5.
Wherein Step7 observes the predicted valueNew Sigma Point set from Step6And substituting the state equation function to obtain the target. New observed valuePrediction of values from observationsAnd obtaining the weight. New mean valueAnd weighting the new observation value and the observation predicted value. New covarianceNew Sigma Point set from Step6Mean values obtained in Stap5And weighting the new observation value and the observation predicted value.
Wherein Step8 calculates Kalman gain Kk，Is the new mean value in Step7With new covarianceProduct of inverse matrices. Updated system covarianceBy Kalman gain KkWith the new mean valueAnd (4) calculating. Updated stateFrom the new Sigma point set in step6Kalman gain KkObserved value Z of current sampling pointkAnd new observed valueThe difference of (a) is calculated.
Wherein, Step9 updates the first adaptive factor, and the specific steps are the same as Step4.
Wherein, the Step13 obtains a predicted value, the predicted value ZupfkAnd substituting the normalized weight value into the state equation function to obtain the normalized weight value, and updating a second self-adaptive factor.
Step14 is a judging Step for judging whether the algorithm is completed.
The invention relates to a lithium ion battery service life prediction method based on DAUPF, which has the advantages and effects that: the sampling part of the UPF algorithm is improved, the algorithm has stronger robustness due to the addition of the double adaptive factors, and the adaptive factors can be better integrated into the algorithm due to the two-step UT conversion, so that the algorithm prediction effect is more accurate.
Drawings
Fig. 1 shows a flow chart of the UPF algorithm.
FIG. 2 is a flow chart of the method of the present invention.
Fig. 3 is a graph showing the capacity change of the data A3, a5, A8 and a12 of lithium ion batteries of group 4 university of maryland.
Fig. 4a is a graph comparing the true value of a3 battery data with the results of four algorithms.
Fig. 4b shows the absolute error of the true a3 battery data versus the four algorithms.
Fig. 5a to 5d are graphs showing the error probability density of the true value of the a3 battery data and the four algorithms.
Fig. 6a shows an AME diagram of 101 cycles of a3 battery data.
Fig. 6b shows the RMSE graph for 101 cycles of a3 battery data.
Fig. 6c shows the AME of A8 battery data for 101 cycles.
Fig. 6d shows the RMSE graph for 101 cycles of A8 battery data.
FIG. 7a shows the AME values for each algorithm for different battery data.
FIG. 7b shows the RMSE values for each algorithm for different battery data.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
As shown in fig. 2, the method for predicting the service life of a lithium ion battery based on DAUPF of the present invention specifically includes the following steps:
step one, initializing parameters, comprising: initialized state valueWherein,in order to observe the initial state values of the equation,to initialize the covariance matrix.
And step two, entering an improved UKF to guide the particle distribution. The method comprises the following steps of starting a sampling stage, circulating the whole sampling stage for N times, and carrying out the whole sampling stage: from step two to step nine.
Step three, calculating a Sigma point set for the first time through UT conversion to obtainThe method specifically comprises the following steps: calculating a Sigma Point set of 2n +1 sample pointsWherein, the point setFrom point Xk-1Andthe composition of the components, wherein,as a scaling function.
Step four, adding a double self-adaptive factor to obtainThe method specifically comprises the following steps: two adaptive factors are added, and the initial values of the two adaptive factors are 1. The first adaptive factor isWherein Z isk-1Is the observed value of the previous sampling point,the observation prediction value obtained in the step seven of the previous cycle. The second adaptive factor isWherein Z isk-1For true value of the system, Zupfk-1And a predicted value obtained after the thirteen DAUPF algorithm completes the cycle of the previous period is obtained.
Step five, calculating the mean value and the covarianceStep five is samplingOne step prediction of points, mean ofByAnd calculating to obtain the result, wherein,substituting the Sigma point set obtained in the third step into a nonlinear transformation function to obtain the Sigma point set; covarianceWherein Wherein λ α2(n+κ)-n；α＝1；ρ＝0；κ＝2；
And sixthly, performing UT conversion again to obtain a new Sigma point set. By a second UT transformation, a new Sigma point set is generatedWherein, the point setBy pointAnd composition of, whereinAnd 5, obtaining the average value in the step five.
Seventhly, predicting to obtain an observation predicted value; calculating by using the observation predicted value and the state predicted value through unscented transformation to obtain a new observation value, a new mean value and a new covariance; the method comprises the following specific steps:
observation of predicted values
New observed value
The new mean value is weighted by the new observed value and the observed predicted value, i.e.
New covariance from the New Sigma Point set obtained in step sixMean value obtained in step fiveThe new observed value is weighted with the predicted observed value, i.e.
Step eight: and calculating Kalman gain, variance and state update.
Kalman gain
Updated system covariance by kalman gain kkWith the new mean valueIs calculated to obtain
The updated state is represented by the new Sigma point set in step sixKalman gain kkObserved value and new observed value of current sampling pointIs calculated as a difference of (i) i
Nine, updating the first adaptive factorThe value is obtained.Wherein Z isk-1Is the observed value of the previous sampling point,the observation prediction value obtained in the step seven of the previous cycle.
And step ten, judging whether sampling is finished or not. If the weight normalization is finished, performing the next weight normalization processing, otherwise, returning to the step two;
step eleven, calculating the weight by using the mean value and the variance obtained by the sampling part completed in the step one to the step nine, and obtaining a normalized weight by normalization processing;
and step twelve, resampling particles. Updating data, updating state, updating variance and taking the mean value as final estimation;
step thirteen, obtaining a predicted value, updating the value of the adaptive factor β, and obtaining the predicted valueSubstituting the normalized weight value into the state equation function to obtain the second adaptive factorWherein Z iskFor true value of the system, ZupfkAnd a predicted value is obtained after the thirteen DAUPF algorithm completes a cycle.
And step fourteen, judging whether iteration is finished. If the algorithm is finished, evaluating the algorithm, otherwise, returning to the step two; wherein, the second step to the third step are a periodic cycle of the DAUPF algorithm, and the DAUPF algorithm is set by requirements for several times.
And fifteen, evaluating an algorithm.
The specific embodiment is as follows:
the experiment uses matlab to simulate, based on the experimental data of lithium batteries of the advanced life cycle engineering center of the university of maryland, No.03,05,08 and 12 are selected as experimental data, the experimental data of 4 groups of lithium ion batteries is shown in figure 3, and the experiment uses the same type of batteries with different capacity degradation rates and the same brand of batteries, and is carried out under the same working condition. The charge and discharge test method of the lithium battery comprises the following steps: the ArbinBT2000 battery test system is used for carrying out charge and discharge tests at room temperature, and when the charge or discharge voltage reaches the cut-off voltage specified by a manufacturer, a charge or discharge process is completed. The rated capacity of the battery is 0.9Ah, and the discharge current is 0.4 Ah.
The lower initial values a, b, c, d are the values obtained after fitting No.03,05,08, 12. The process noise and process noise variance are set to 0.0001 and 0.001, respectively. The experimental observation model uses a capacity attenuation model Zk＝a*exp(b*k)+cexp(d*k)。
1. Setting the initial value a to-0.0000083499; 0.055237; c is 0.90097; substitution of d-0.00088543To obtain Is provided with Z0＝0.9208。
2. The sampling phase is cycled for N times
3.
4.
5. A second UT transformation is performed and,
6.
7.
R＝0.0001
8.
9. updating the adaptation factor ①
10. Completing the sampling for 1 time, and repeating the steps 2-10 for the subsequent sampling. The above is data of only one cycle.
11. And sampling the mean value and the variance obtained by the part, and carrying out normalization processing to calculate the weight so as to obtain a normalized weight.
12.
Updating the adaptation factor ②
13. The above values are prediction data Zupf obtained by performing a DAUPF cycle, and the program needs to be continuously operated to predict more data.
The validity of the DAUPF algorithm is verified by using lithium battery experimental data of the advanced life cycle engineering center of the university of Maryland, and compared with extended Kalman filtering, unscented Kalman filtering, particle filtering, extended Kalman particle filtering and unscented Kalman particle filtering.
In order to illustrate the accuracy of the prediction effect of the DAUPF, the experiment is respectively compared with UKF, PF and UPF, and the initial parameters and error values of the four algorithms are consistent with the initial parameter values and error values of the DAUPF.
Fig. 4 and 5 correspond to battery data a3, fig. 4a and 4b show the prediction results and absolute errors, respectively, and fig. 5a to 5d are error probability density diagrams.
In the figure, the black curve represents the output true value; circles represent the predicted outcome of the PF; the square grid is a prediction result of the UKF algorithm; the diamond is a UPF algorithm result; the cross sign is the DAUPF prediction result; the horizontal line is the battery capacity failure threshold. As can be seen from fig. 4a, the prediction effect is significantly improved with the continuous improvement of the filtering method, wherein the line represented by the DAUPF algorithm is closer to the line represented by the true value. From the absolute error fig. 4b it can be seen that the absolute error of the DAUPF is minimal, the PF is least effective, and the predicted effect is worse the further up to the point of failure. It can be seen from fig. 5a to 5d that the DAUPF algorithm of the present invention is most stable and has the strongest robustness.
The experiment was completed for 101 cycles, and the resulting MAE and RMSE after each cycle were recorded and plotted as line graphs as shown in FIGS. 6 a-6 d. The closer the RMSE and MAE values are to 0, the more accurate the prediction method is. It can be seen from the figure that, for different data sets A3 and A8, different data volumes, different process noise and observation noise, the MAE value and RMSE value of the predicted value of the DAUPF algorithm are the smallest compared with other algorithms, and are twice smaller than the UPF error with the best prediction effect, and the stability of the algorithm is also stronger than that of other algorithms (from the horizontal axis, it can be seen that the DAUPF algorithm can reduce the influence of observation noise and process noise of various sizes). Therefore, the DAUPF algorithm of the present invention predicts better performance than several other algorithms.
As can be seen from fig. 7a and 7b, the PF algorithm is not ideal for predicting the a3 data set, i.e. the particle filter has a poor prediction effect on the data set with fewer data points. The UKF algorithm has a good prediction effect on data with large data fluctuation. The UPF algorithm has good prediction effect on different data sets, but the data sets with few data points have certain influence on the prediction accuracy of the UPF algorithm. The prediction effect of the DAUPF algorithm under different data sets is better than that of other algorithms, the error is minimum, the DAUPF algorithm is most stable, and the robustness is stronger.
Claims (9)
1. A lithium ion battery service life prediction method based on DAUPF is characterized in that: the method specifically comprises the following steps:
step1, initializing parameters;
step2, entering into an improved UKF to guide particle distribution;
step3. calculating Sigma point set for the first time through UT transformation to obtain
Step4. adding a double adaptive factorTo obtain
Step5. calculating mean and covariance from the Sigma point set obtained at step3
Step6, using the mean value and covariance obtained from step5, and performing UT transformation again to obtain a new Sigma point set
Step7. obtaining the observation prediction value by predicting the new Sigma point set obtained by step6Obtaining new observation value by observation predicted value and state predicted value through non-trace transformation calculationMean and covariance
Step8, calculating Kalman gain, variance and state updating;
step9. update the first adaptive factorA value;
step10, judging whether sampling is finished or not; if the weight normalization is finished, performing the next weight normalization processing, otherwise entering step 2;
step11, calculating the weight by using the mean value and the variance obtained by the step1-9 sampling part through normalization processing to obtain a normalized weight;
step12, resampling particles; updating data, state updating, variance updating, mean as final estimate
Obtaining a predicted value, and updating the value of the adaptive factor β;
step14, judging whether iteration is finished or not; if so, evaluating the algorithm, otherwise, entering step 2;
step15. evaluation algorithm.
2. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: the parameters initialized by Step1 include: initialized state valueWherein,in order to observe the initial state values of the equation,to initialize the covariance matrix.
3. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: the Step3 is specifically as follows: calculating a Sigma Point set of 2n +1 sample pointsWherein, the point setFrom point Xk-1Andthe composition of the components, wherein,as a scaling function.
4. A method according to claim 1The lithium ion battery service life prediction method of DAUPF is characterized in that: the Step4 is specifically as follows:adding two adaptive factors, wherein the initial values of the two adaptive factors are 1; the first adaptive factor isWherein Z isk-1Is the observed value of the previous sampling point,the observation predicted value obtained for Step7 in the previous cycle; the second adaptive factor isWherein Z isk-1For true value of the system, Zupfk-1And (4) obtaining a predicted value after the Step13 DAUPF algorithm finishes the previous cycle.
5. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: step5 is a one-Step prediction of sampling points, and the average value isByAnd calculating to obtain the result, wherein,substituting the Sigma point set obtained in Step3 into a nonlinear transformation function to obtain a product; covariance WhereinWherein λ α2(n+κ)-n；α＝1；ρ＝0；κ＝2。
6. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: step6 is the second UT transform, generating a new Sigma point set,wherein, the point setBy pointAndcomposition of, whereinThe mean value obtained in Step5.
7. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: the Step7 observed prediction valueNew Sigma Point set from Step6Substituting the state equation function to obtain; new observed valuePrediction of values from observationsObtaining the weight; new mean valueWeighting the new observation value and the observation predicted value to obtain the new observation value; new covarianceNew Sigma Point set from Step6Mean values obtained in Stap5And weighting the new observation value and the observation predicted value.
8. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: the Step8 calculates Kalman gain KkNew mean value in Step7With new covarianceThe product of the inverse matrices; updated system covarianceBy Kalman gain KkWith the new mean valueCalculating to obtain; updated stateFrom the new Sigma point set in step6Kalman gain KkObserved value Z of current sampling pointkAnd new observed valueThe difference of (a) is calculated.
9. The method of claim 1, wherein the method for predicting the lifetime of a lithium ion battery based on DAUPF comprises: the Step13 obtains a predicted value, namely ZupfkAnd substituting the normalized weight value into the state equation function to obtain the normalized weight value, and updating a second self-adaptive factor.
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| CN110492866A (en) * | 2019-07-22 | 2019-11-22 | 航天东方红卫星有限公司 | A kind of kalman filter method of pair of moving target |
| CN111680848A (en) * | 2020-07-27 | 2020-09-18 | 中南大学 | Battery life prediction method based on prediction model fusion and storage medium |
| CN112285568A (en) * | 2020-10-21 | 2021-01-29 | 合肥工业大学 | Estimation method of residual discharge time based on energy state of power lithium battery |
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| CN112285568B (en) * | 2020-10-21 | 2023-11-14 | 合肥工业大学 | Method for estimating residual discharge time based on energy state of power lithium battery |
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