CN109917292A - A DAUPF-based Li-ion Battery Life Prediction Method - Google Patents

Abstract

The invention is a DAUPF-based lithium-ion battery life prediction method. First, in the sampling part, double adaptive factors are added on the basis of the UKF algorithm, and the state value and covariance obtained after one-step prediction of the Sigma point set are used as a guide, and then a UT is performed again. Transform, get a new Sigma point set, bring it into the observation equation, get a new observation, and get the sample mean and covariance of the first cycle; update an adaptive factor after completing a cycle in the improved UKF algorithm, and then proceed to the next One cycle of improving the UKF algorithm. After the sampling is completed, it enters the PF process, and after obtaining an output predicted value, another adaptive factor is updated to complete a DAUPF process; finally, the test data is predicted. The invention improves the sampling part of the UPF algorithm, the addition of dual adaptive factors makes the algorithm more robust, the two-step UT transformation makes the adaptive factors better integrate into the algorithm, and the prediction effect of the algorithm is more accurate.

Description

A DAUPF-based Li-ion Battery Life Prediction Method

technical field

The invention relates to a lithium ion battery life prediction method based on DAUPF (Dual Adaptive Sampling Stepless Kalman Particle Filter Algorithm), and belongs to the technical field of lithium battery health management.

Background technique

Lithium-ion batteries have been successfully used in many consumer electronic products (such as mobile phones, notebook computers and electric vehicles), and gradually expanded to military communications, navigation, aviation, aerospace and other fields. The safety of lithium-ion batteries has been paid more and more attention by more and more people. The battery life is defined by the number of charge-discharge cycles or years of use. The chemical substances in the battery will gradually age as the battery operating time increases, and battery failure can cause serious consequences. Cal Fire said a Tesla Model S spontaneously ignited in a parking lot and reignited in a trailer a few hours later. Therefore, it is very important to accurately predict the service life of lithium-ion batteries. State-of-health (SOH) estimation and remaining life prediction are the keys to battery health management, which can ensure the safe use of lithium-ion batteries.

At present, there are two types of prediction methods for lithium batteries. One is the non-parametric model method, and the other is the parametric model method.

Nonparametric methods include neural network methods and machine learning methods. Wu et al. used a feedforward neural network (FFNN) with a Monte Carlo (IS) method to estimate the remaining useful life (RUL) of lithium-ion batteries. Zhang et al. used a long short-term memory-based neural network (LSTM) to predict the remaining battery life. Machine learning methods include support vector classification (SVM), support vector regression (SVR), correlation vector machine (RVM) and so on. Tobar et al. applied the improved kernel adaptive filtering method to the prediction of electric bicycle battery voltage.

The most common parametric model method is various filtering algorithms. Among them, the particle filter (PF) method is an approximate Bayesian filtering algorithm based on Monte Carlo simulation. The core idea is to use some discrete random sampling points to approximate the probability density function of the random variables of the system. Miao et al. used particle filtering to predict the remaining service life of batteries, and concluded that particle filtering can well predict the remaining service life of lithium-ion batteries. B.Saha et al. established a battery system framework to predict the remaining service life of batteries at different discharge rates by PF. The particle filter method is suitable for any nonlinear non-Gaussian environment, but depends on the chosen reference distribution and state posterior estimates.

Extended Kalman (EKF) and Unscented Kalman (UKF) are improved Kalman Filter (KF) algorithms. The advantage of EKF is that it has weak nonlinearity and has a better prediction effect in a less noisy environment. Dong et al. proposed the Adaptive Extended Kalman (AEKF) algorithm based on the recursive least squares method, and concluded that AEKF can suppress noise well. H.S. Ramadan et al. analyzed and compared various EKF algorithms, and concluded that predicting the battery state of charge (SOC) requires an accurate parameter model, and the quality of the EKF algorithm is closely related to the accuracy of the model. The advantage of UKF is that there is no loss on the model and the calculation accuracy is relatively high. Zheng proposed an integrated UKF method to predict the battery RUL, using the future residuals to estimate the battery parameters, which can accurately predict the short-term capacity of the battery, but since the UKF cannot adjust the model parameters, the prediction accuracy cannot be further improved.

Particle filter and Kalman filter have their own advantages and disadvantages, and the advantages of the two algorithms can make up for each other's shortcomings, so there are extended Kalman particle filter and unscented Kalman particle filter. Miao et al. successfully predicted the RUL of the battery by using the infinite Kalman particle filter (UPF) algorithm. However, the algorithm relies too much on the number of particles, the size of the dataset, and the quality of historical data. Zhang et al. used a UPF algorithm based on Markov Linked Monte Carlo to predict the remaining life of lithium-ion batteries while maintaining particle diversity. Chen et al. used a second-order Gaussian model and UPF to predict battery life.

The UPF algorithm uses the UKF algorithm to guide particle sampling in the sampling stage. After the sampling is completed, the PF algorithm steps are performed, the weights are calculated, and normalization is performed. Determine whether to perform resampling, copy and eliminate the particle collection. Calculate the particle set mean to get the estimated output value. Analyze the data after the iteration. Its structure is shown in Figure 1.

Due to the introduction of the UKF algorithm to guide the sampling, the UPF algorithm is susceptible to the constraints of Gaussian noise and the influence of the reference distribution; in addition, the traditional UT (Unscented Transform) will update the state value after transformation, and the sigma distribution of the updated state value is different from the unscented transform. There is a certain error between the sigma distributions before the update. If the sigma distribution used before the update is used to calculate the observed predicted value and other parameters, it will also have a certain impact on the prediction results.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a DAUPF-based lithium-ion battery life prediction method for the above-mentioned problems. First, in order to solve the problem that the UPF algorithm is easily affected by noise and reference distribution, we add an adaptive method to the DAUPF algorithm. factor. Considering that the traditional UPF algorithm is a combination of the UKF and PF algorithms, an adaptive factor is added in the sampling stage and the prediction stage respectively. The adaptive factor can adjust the parameter distribution to make up for the shortcomings of the two algorithms. Secondly, the UKF algorithm needs to be used to give the probability density in the sampling stage. UKF will perform UT transformation during sampling. Since a new adaptive factor needs to be added after the first UT transformation, the sigma distribution given by the UT transformation will be inaccurate. In addition, after the traditional UT transformation, the state value will be updated. There is a certain error between the sigma distribution of the updated state value and the sigma distribution before the update. If the sigma distribution proposed before the update is used to calculate the observation prediction The parameters such as the value will have a certain impact on the prediction results. Based on the above two reasons, the DAUPF algorithm of the present invention performs a UT transformation after the state value is updated to obtain a new sigma point set, and then calculates parameters such as the observed predicted value. This paper uses the lithium battery experimental data of the University of Maryland Advanced Life Cycle Engineering Center to verify the effectiveness of the DAUPF algorithm, and conducts experiments with extended Kalman filter, unscented Kalman filter, particle filter, extended Kalman particle filter, and unscented Kalman particle filter. Compared.

The present invention is a DAUPF-based lithium-ion battery life prediction method. In order to solve the above problem, the technical solution adopted is: firstly, in the sampling part, double adaptive factors are added on the basis of the UKF algorithm, and then the Sigma point set is guided to predict the state in one step. value and covariance, perform another UT transformation to obtain a new Sigma point set, bring it into the observation equation, and obtain a new observation value, thereby obtaining the sample mean and covariance of the first cycle; complete a cycle in the improved UKF algorithm part Then update one of the adaptive factors in the dual adaptive factors, and then perform the next cycle of improving the UKF algorithm. After the sampling is completed, it enters the PF process, and after obtaining an output predicted value, another adaptive factor is updated to complete a DAUPF process; finally, the test data is predicted.

A DAUPF-based lithium-ion battery life prediction method of the present invention specifically includes the following steps:

Step1. Initialize parameters;

Step2. Enter the improved UKF to guide particle distribution;

Step3. Calculate the Sigma point set for the first time through UT transformation, and get

Step4. Add dual adaptive factors to get

Step5. Calculate the mean and covariance through the Sigma point set obtained in step3

Step6. Use the mean and covariance obtained in step5, and perform UT transformation again to obtain a new Sigma point set

Step7. Obtain the observed predicted value by predicting the new Sigma point set obtained in step6 Use the observed predicted value and the state predicted value to calculate the new observed value through unscented transformation mean and covariance

Step8. Calculate Kalman gain, variance and state update;

Step9. Update the first adaptive factor value;

Step10. Determine whether sampling is completed. If completed, proceed to the next step of weight normalization, otherwise go to step2;

Step11. Use the mean and variance obtained from the sampling part of step1-9, normalize the calculation weight, and obtain the normalized weight;

Step12. Particle resampling; update data, state update, variance update, and mean as the final estimate.

Step13. Get the predicted value and update the adaptive factor β value;

Step14. Determine whether the iteration is completed. If completed, evaluate the algorithm, otherwise go to step2;

Step15. Evaluation algorithm.

Wherein, the parameters initialized in Step1 include: initialization state value in, is the initial state value of the observation equation, to initialize the covariance matrix.

Wherein, the Step2 is a start sampling stage, the whole sampling stage is cycled N times, and the sampling stages are: Step2-Step9.

The Step 3 is specifically: calculating the Sigma point set of 2n+1 sampling points Among them, the point set By point X _k-1 and consists of, is the scaling function.

Wherein, the Step4 is specifically: Two adaptive factors are added, and the initial value of the two adaptive factors is 1. The first adaptive factor is Among them, Z _k-1 is the observation value of the previous sampling point, It is the observed predicted value obtained in Step7 in the previous cycle. The second adaptive factor is Among them, Z _k-1 is the real value of the system, and Zupf _k-1 is the predicted value obtained after the DAUPF algorithm in Step 13 completes the previous cycle.

Among them, the Step5 is the one-step prediction of the sampling point, and the mean is Depend on Calculated, where, It is obtained by substituting the Sigma point set obtained in Step 3 into the nonlinear transformation function. Covariance in where λ=α ² (n+κ)-n; α=1; ρ=0; κ=2.

Among them, the Step6 is the second UT transformation to generate a new Sigma point set,

Among them, the point set by point and composed of, where, points is the mean value obtained in Step 5.

Among them, the Step7 observes the predicted value The new Sigma point set obtained in Step6 Substitute into the state equation function to get. new observations Predicted values from observations weighted. new mean It is obtained by weighting the new observations and the observed predictions. new covariance The new Sigma point set obtained in Step6 Mean obtained in Stap5 The new observations are weighted with the observed predictions.

Wherein, the Step8 calculates the Kalman gain K _k , is the new mean in Step7 with the new covariance Product of inverse matrices. updated system covariance Gain _K with the new mean by Kalman Calculated. updated status From the new Sigma point set in step6 The Kalman gain K _k , the observation value Z _k of the current sampling point and the new observation value difference is calculated.

The Step 9 updates the first adaptive factor, and the specific steps are the same as the Step 4.

The step 13 obtains the predicted value, and the predicted value Zupf _k is obtained by substituting the normalized weight into the state equation function, and the second adaptive factor is updated.

The Step 14 is a judging step, judging whether the algorithm is completed.

A DAUPF-based lithium-ion battery life prediction method of the present invention has the advantages and effects that the sampling part of the UPF algorithm is improved, the addition of dual adaptive factors makes the algorithm more robust, and the two-step UT transformation makes the automatic The adaptation factor can be better integrated into the algorithm, so that the prediction effect of the algorithm is more accurate.

Description of drawings

Figure 1 shows the flow chart of the UPF algorithm.

Figure 2 shows a flow chart of the method of the present invention.

Figure 3 shows the capacity change curve diagram of four groups of lithium-ion battery data A3, A5, A8, and A12 of the University of Maryland.

Figure 4a shows the comparison between the real value of the A3 battery data and the results of the four algorithms.

Figure 4b shows the absolute error plot of the real value of the A3 battery data and the four algorithms.

Figures 5a to 5d show the true value of the A3 battery data and the error probability density diagrams of the four algorithms.

Figure 6a shows the AME plot for 101 cycles of A3 battery data.

Figure 6b shows the RMSE plot of the A3 battery data for 101 cycles.

Figure 6c shows the AME plot for 101 cycles of A8 battery data.

Figure 6d shows the RMSE plot for 101 cycles of the A8 battery data.

Figure 7a shows the AME values of each algorithm under different battery data.

Figure 7b shows the RMSE values of each algorithm under different battery data.

Detailed ways

The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

As shown in Figure 2, a DAUPF-based lithium-ion battery life prediction method of the present invention, the specific process is as follows:

Step 1. Initialize parameters, including: initialization state value in, is the initial state value of the observation equation, to initialize the covariance matrix.

Step 2: Enter the improved UKF to guide particle distribution. This step is the beginning of the sampling phase, the entire sampling phase is cycled N times, and the entire sampling phase is: from step 2 to step 9.

Step 3. Calculate the Sigma point set for the first time through UT transformation, and get Specifically: Calculate the Sigma point set of 2n+1 sampling points Among them, the point set By point X _k-1 and consists of, is the scaling function.

Step 4. Add dual adaptive factors to get Specifically, two adaptive factors are added, and the initial value of the two adaptive factors is 1. The first adaptive factor is Among them, Z _k-1 is the observation value of the previous sampling point, Predicted values for the observations from step seven in the previous cycle. The second adaptive factor is Among them, Z _k-1 is the real value of the system, and Zupf _k-1 is the predicted value obtained after the DAUPF algorithm in step 13 completes the previous cycle.

Step 5. Calculate the mean and covariance Step 5 is a one-step prediction of the sampling point, and the mean is Depend on Calculated, where, Substitute the Sigma point set obtained in step 3 into the nonlinear transformation function to obtain; covariance in where λ=α ² (n+κ)-n; α=1; ρ=0; κ=2;

Step 6: Perform UT transformation again to obtain a new Sigma point set. Through the second UT transformation, a new Sigma point set is generated Among them, the point set by point and composed of, where, points is the mean value obtained in step 5.

Step 7: Predict to obtain the observed predicted value; use the observed predicted value and the state predicted value to calculate the new observed value, mean and covariance through unscented transformation; the details are as follows:

observed predicted value

new observations

The new mean is obtained by weighting the new observations and the observed predicted values, namely

The new covariance is the new set of Sigma points obtained in step six The mean value obtained in step 5 The new observed value is weighted with the observed predicted value, that is

Step 8: Calculate the Kalman gain, variance and state update.

Kalman Gain

The updated system covariance is given by the Kalman gain _k with the new mean calculated, that is

The updated state is determined by the new set of Sigma points in step six Kalman gain k _k , observations at the current sampling point and new observations The difference of , is calculated, that is

Step 9. Update the first adaptive factor value. Among them, Z _k-1 is the observation value of the previous sampling point, Predicted values for the observations from step seven in the previous cycle.

Step 10. Determine whether the sampling is completed. If completed, proceed to the next step of weight normalization, otherwise return to step 2;

Step 11: Use the mean value and variance obtained from the sampling part completed in Step 1 to Step 9, normalize the calculation weight, and obtain the normalized weight value;

Step 12, particle resampling. Update data, state update, variance update, mean as final estimate;

Step 13: Obtain the predicted value and update the adaptive factor β value. Predictive value In order to get the normalized weights into the state equation function, update the second adaptive factor Among them, Z _k is the real value of the system, and Zupf _k is the predicted value obtained after the DAUPF algorithm completes one cycle in step 13.

Step 14: Determine whether the iteration is completed. If completed, evaluate the algorithm, otherwise return to step 2; where steps 2 to 13 are one cycle of the DAUPF algorithm, and the number of cycles of the DAUPF algorithm is set by requirements.

Step 15: Evaluate the algorithm.

Specific examples:

This experiment uses matlab for simulation. Based on the lithium battery experimental data of the Advanced Life Cycle Engineering Center of the University of Maryland, No.03, 05, 08 and 12 are selected as the experimental data. The experimental data of 4 groups of lithium-ion batteries are shown in Figure 3. The experiments were carried out under the same working conditions using the same type of batteries of the same brand with different capacity degradation rates. The charging and discharging test method of lithium battery is as follows: use the ArbinBT2000 battery test system to conduct the charging and discharging test at room temperature, and complete a charging or discharging process when the charging or discharging voltage reaches the cut-off voltage specified by the manufacturer. The rated capacity of the battery is 0.9Ah, and the discharge current is 0.4Ah.

The initial values a, b, c, and d below are the values obtained after fitting No. 03, 05, 08, and 12. Process noise and process noise variance were set to 0.0001 and 0.001, respectively. This experimental observation model uses the capacity decay model Z _k =a*exp(b*k)+cexp(d*k).

1. Substitute the initial value a=-0.0000083499; b=0.055237; c=0.90097; d=-0.00088543 get Let Z ₀ =0.9208.

2. The sampling phase is cycled N times

3.

4.

5. Perform the second UT transformation,

6.

7.

R=0.0001

8.

9. Update the adaptive factor①

10. Complete 1 sampling, and repeat steps 2-10 for subsequent sampling. The above data is only for one cycle.

11. The mean and variance obtained in the sampling part are normalized to calculate the weight, and the normalized weight is obtained.

12.

Update adaptive factor ②

13. The above values are the predicted data Zupf obtained by performing one DAUPF cycle. If you want to predict more data, you need to continue to run the program.

The validity of the DAUPF algorithm is verified by using the lithium battery experimental data of the Advanced Life Cycle Engineering Center of the University of Maryland. comparing.

In order to illustrate the accuracy of the prediction effect of DAUPF, this experiment was compared with UKF, PF and UPF respectively. The initial parameters and error values of the four algorithms were consistent with the initial parameter values and error values of DAUPF of the present invention.

Figures 4 and 5 correspond to the battery data A3. Figures 4a and 4b show the prediction results and absolute errors, respectively. Figures 5a to 5d are error probability density diagrams.

In the figure, the black curve represents the actual output value; the circle represents the prediction result of PF; the square is the prediction result of the UKF algorithm; the diamond is the result of the UPF algorithm; the cross symbol is the prediction result of DAUPF; the horizontal line is the battery capacity failure threshold. As can be seen from Figure 4a, with the continuous improvement of the filtering method, the prediction effect has been significantly improved, in which the line represented by the DAUPF algorithm is closer to the line represented by the true value. From the absolute error in Figure 4b, it can be seen that the absolute error of DAUPF is the smallest, the PF effect is the worst, and the prediction effect is worse as it reaches the failure point. It can be seen from Fig. 5a to Fig. 5d that the DAUPF algorithm of the present invention is the most stable and has the strongest robustness.

This experiment carried out 101 cycles completely. The MAE and RMSE obtained after each cycle were recorded and drawn as a line graph as shown in Figures 6a-6d. The closer the RMSE value and MAE value are to 0, the more accurate the prediction method is. It can be seen from the figure that under different data sets A3, A8, different data amounts, 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 the relative prediction effect is better than that of other algorithms. The best UPF error is twice as small, and the stability of the algorithm is also stronger than other algorithms (from the horizontal axis, it can be seen that the DAUPF algorithm can reduce the influence of observation noise of various sizes and process noise). Therefore, the DAUPF algorithm of the present invention has better prediction performance compared with other algorithms.

It can be seen from Figures 7a and 7b that the prediction effect of the PF algorithm for the A3 data set is not very satisfactory, that is, the particle filter has a poor prediction effect on the data set with few data points. The UKF algorithm has a better prediction effect for data with large data fluctuations. The UPF algorithm has a good prediction effect on different data sets, but it can also be seen from the data that the data set with fewer data points has a certain impact on the prediction accuracy of the UPF algorithm. The prediction effect of the DAUPF algorithm of the present invention is better than other algorithms under different data sets, with the smallest error, the most stable and stronger robustness.

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 X_k-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 is_k-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 is_k-1For true value of the system, Zupf_k-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 K_kNew mean value in Step7With new covarianceThe product of the inverse matrices; updated system covarianceBy Kalman gain K_kWith the new mean valueCalculating to obtain; updated stateFrom the new Sigma point set in step6Kalman gain K_kObserved value Z of current sampling point_kAnd 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 Zupf_kAnd substituting the normalized weight value into the state equation function to obtain the normalized weight value, and updating a second self-adaptive factor.