CN110888077A

CN110888077A - Accelerated lithium ion battery life evaluation method based on ARIMA time sequence

Info

Publication number: CN110888077A
Application number: CN201911060360.XA
Authority: CN
Inventors: 王勋; 顾正建; 卢存; 黄惠; 严媛
Original assignee: WUXI PRODUCT QUALITY SUPERVISION AND INSPECTION INSTITUTE
Current assignee: WUXI PRODUCT QUALITY SUPERVISION AND INSPECTION INSTITUTE
Priority date: 2019-10-30
Filing date: 2019-10-30
Publication date: 2020-03-17

Abstract

The invention discloses an ARIMA time sequence-based lithium ion battery service life accelerated evaluation method, which is compared with an empirical model and a support vector machine algorithm to find that the ARIMA algorithm has an absolute acceleration evaluation error of approximately 1.2 percent of root mean square acceleration evaluation error value of approximately 1.4 percent, a linear model absolute acceleration evaluation error of approximately 1.4 percent of root mean square acceleration evaluation error value of approximately 1.7 percent and a Verhulst absolute acceleration evaluation error of approximately 7.5 percent of root mean square acceleration evaluation error value of approximately 7.6 percent under two groups of experimental data; the calculation efficiency is high, the accelerated evaluation trend which is the same as that of the empirical model is obtained under the same sample, but the accelerated evaluation precision is obviously improved, and the whole calculation time is short. Within the 95% confidence interval, the actual value can well fall within the acceleration evaluation range, and for detection or power station operation staff, whether the battery needs to be replaced or not can be predicted in advance.

Description

Accelerated lithium ion battery life evaluation method based on ARIMA time sequence

Technical Field

The invention relates to an accelerated evaluation method for service life of a lithium ion battery based on an ARIMA time sequence.

Background

The lithium ion battery is the first choice in the field of energy storage due to the advantages of large energy density, high output power, long cycle life, wide working temperature range, low self-discharge rate and the like. However, the failure of the lithium battery as an energy storage device often leads to a decrease in the reliability of the entire system, causing economic losses and possibly disabling the entire grid system. Accurate estimation of the remaining battery life (RUL) can not only improve the reliability of a battery management system, replace the battery which is about to fail, ensure the safe and efficient operation of the battery pack, but also ensure the safety of equipment which takes a lithium ion battery as a main energy storage and energy supply element in the operation process to a great extent, avoid the occurrence of accidents and reduce the operation cost. Braatz et al developed a new big data-driven model, and could accurately accelerate the evaluation of the battery life by logistic regression method by only using early cycle data to build a variance model without analyzing the battery degradation mechanism. When the service cycle number of the battery is less than 300 circles, the RUL accelerated assessment algorithm based on the data-driven support vector machine, the related vector machine, the neural network and the particle filter lithium ion battery has strong applicability. ARIMA shows great advantage for accelerated data evaluation when the cycle life is longer.

The basic idea for accelerated assessment using the ARIMA model is: after the non-stationary time sequence is converted into the stationary time sequence, the hysteresis value of the dependent variable and the present value and the hysteresis value of the random error term are regressed, and the optimal accelerated assessment in the sense of reaching the minimum variance is approximately described by a corresponding mathematical model

ARIMA (differential autoregressive-moving average model) modeling of ARIMA time series models generally requires the stationarity of the time series, i.e., the fit obtained by the time series of samples continues "inertially" following the existing morphology over a period of time in the future, and the mean and variance of the series do not change significantly.

First order Difference of ▽ y_t＝y_t-y_t-1

Second order Difference ▽ 2y_t＝y_t-2y_t-1-y_t-2

And an autoregressive model (AR) which describes the relationship between the current value and the historical value and uses the historical time data of the variable to evaluate the variable. The formula for the autoregressive process of order P is defined as:

wherein y is_tIs the current value, μ is a constant term, p is the order, γ_iIs the autocorrelation coefficient, ε_tIs an error.

When the autoregressive model is used, self data must be used for accelerated evaluation, the time sequence must have autocorrelation, if the autocorrelation coefficient is too small, the autocorrelation cannot be adopted, and the autoregressive model is only suitable for accelerated evaluation of the phenomenon related to the self earlier stage

Moving average Model (MA), which focuses on the accumulation of error terms in the regression model, the formula for the q-th order autoregressive process is defined as:

the moving average method can effectively eliminate random fluctuation in accelerated evaluation

Autoregressive moving average model (ARMA), a combination of autoregressive and moving average, the formula defined as:

disclosure of Invention

The invention aims to overcome the defects that the service life of a lithium ion battery is long in evaluation time and the accuracy of an accelerated evaluation method needs to be further improved in the prior art, and provides an ARIMA time sequence-based method for accelerated evaluation of the service life of the lithium ion battery.

In order to solve the technical problems, the invention provides the following technical scheme:

a lithium ion battery life accelerated evaluation method based on an ARIMA time sequence comprises the following steps:

s1: selecting reasonable acceleration evaluation data, and selecting cycle life capacity data in a certain interval to establish a time series model;

s2: carrying out preliminary stability judgment on the time sequence by testing unit root test;

s3: carrying out stabilization treatment on the non-stationary sequence; generally, the first order difference can eliminate the linear trend, and the second order difference can eliminate the quadratic curve trend;

s4: performing ARMA (p, q) model selection on the differentiated stationary sequence, observing the truncation number and the tailing number of the ACF image and the PACF image to perform model selection, and determining the order of the model by an AIC order determination method;

TABLE 1 determination of ARIMA (p, d, q) orders

Tail cutting: within a confidence interval (95% of the points meet the rule)

S5: judging the significance of the model, and verifying the rationality of the selection of the hysteresis order;

s6: and (5) applying the model to carry out accelerated evaluation on the service life of the ion battery.

Further, the identification and establishment of the ARIMA model in S4 includes the following steps:

(1) determining p and q values of ARIMA model

Determining the order p, d in the ARIMA (p, d, q) model through analyzing the autocorrelation function and the partial autocorrelation function of the new sequence DY;

(2) selecting the optimal model

For different values of q, establishing an ARIMA model from a low order to a high order respectively, performing parameter estimation, calculating all AIC values, and selecting a model which enables the AIC value to be minimum, namely an optimal model;

(3) determining model parameters

And estimating the significance of the parameter check value of the model to determine whether the established model is a feasible model.

Further, in S4, the ARIMA (p, d, q) order is determined as follows:

the attenuation of ACF graph of AR (p) model tends to zero, and the p-order truncation of PACF graph;

the ACF graph of the MA (q) model is truncated after q-order, and the attenuation of the PACF graph tends to zero;

the attenuation of the ACF image after q order of ARMA (p, q) model tends to zero, and the attenuation of the PACF image after p order tends to zero;

tail cutting: falling within the confidence interval.

Further, the accuracy of the algorithm can be judged by using the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE);

in the formula: m is the length of the acceleration evaluation data, yi is the capacity value of the i-th acceleration evaluation, and is the real capacity value of the i-th time.

The invention has the following beneficial effects:

firstly, the ARIMA time series model provided by the invention is used for calculating the remaining service life and the confidence interval thereof, and the more the accelerated evaluation samples are, the higher the accelerated evaluation precision is. Compared with experiments performed by an empirical model and a support vector machine algorithm, analysis results show that the support vector machine has an overfitting phenomenon, the absolute acceleration evaluation error of the ARIMA algorithm under two groups of experimental data is approximately 1.2%, the absolute acceleration evaluation error of the linear model is approximately 1.4%, the absolute acceleration evaluation error of the Verhulst is approximately 7.5%, and the accuracy of the ARIMA time sequence model in actual cycle life budget is verified.

The method is high in operation efficiency, and when 800 samples are used as training data, compared with other accelerated evaluation methods, the accelerated evaluation trend the same as that of an empirical model is obtained under the same samples, but the accelerated evaluation precision is obviously improved, and the whole calculation time is short. Within the 95% confidence interval, the actual value can well fall within the acceleration evaluation range, and whether the battery needs to be replaced or not can be predicted in advance for detection or power station operation workers.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

fig. 1 is a battery capacity degradation curve of samples # 1 and # 2;

FIG. 2 is a line graph of the new sequence DY for sample # 1;

FIG. 3 is a 600cycleARIMA accelerated assessment curve (1 #);

FIG. 4 is a 600cycleARIMA accelerated assessment curve (2 #);

FIG. 5 is a 700cycleARIMA accelerated assessment curve (1 #);

FIG. 6 is a 700cycleARIMA accelerated assessment curve (2 #);

FIG. 7 is a 800cycleARIMA accelerated assessment curve (1 #);

FIG. 8 is a 800cycleARIMA accelerated assessment curve (2 #);

FIG. 9 is a linear fit model;

FIG. 10 is a Verhust fitting model;

FIG. 11 is an SVM acceleration evaluation curve;

FIG. 12 is a technical roadmap for the present invention.

Detailed Description

The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.

Examples

Lithium battery aging test

In order to effectively verify the RUL accelerated assessment method of the lithium ion battery provided by the invention, the RUL accelerated assessment is carried out by taking the capacity data of the battery as the sample data of the experiment, so that the accelerated assessment capability of the method provided by the invention is assessed.

The experimental method comprises the following steps: the experimental object is selected to be a soft package battery, the rated capacity of the soft package battery is 50Ah, the soft package battery is divided into 2 samples, a cyclic charge-discharge experiment is carried out in an environment box at 45 ℃, and the current, the voltage and the temperature of a positive tab of the battery are recorded in real time.

And (3) charging process: the charging is carried out at a constant current of 50A until the voltage of the battery is 3.6V, the charging is changed into constant voltage charging, and the charging is finished when the current is less than 2.5A.

And (3) discharging: the battery was discharged at a constant current of 100A, and the discharge was stopped when the battery voltage dropped to 2V.

And (4) standing for 1h after the charging and discharging are finished, carrying out cyclic test according to the charging and discharging mode, and meanwhile, calculating the real-time charging and discharging capacity of the battery in each charging and discharging period by using an ampere-hour integration method.

And selecting different capacity attenuation intervals to perform time series life accelerated evaluation, and obtaining a degradation curve for the battery capacity accelerated evaluation through a simulation experiment. When the battery is continuously charged and discharged and the capacity reaches the end of the service life, namely the battery capacity is attenuated to reach about 80% of the initial capacity, the experiment is ended.

Curve of capacity degradation

The degradation curves for the two models of cells were completed based on the true values of the capacities, as shown in fig. 1. The initial discharge capacity of the two sample cells was 52Ah, and the APT of the cells was 41.6Ah with 80% of the initial discharge capacity as a cut-off point. It can be seen that the aging degree of different batteries is different when the batteries are charged and discharged in the same charging and discharging manner, the life cut-off point of the 1# battery is 1015 cycles, the life cut-off point of the 2# battery is 1316 cycles, and the capacity of the lithium ion battery is accelerated to decay with the increase of the charging and discharging times, so that the performance of the lithium ion battery is degraded in various reasons, such as the speed of temperature rise is accelerated, the internal resistance is increased, and the like.

Time series stationarity test

1) And carrying out stabilization test on the original sequence

The selection of parameters of the ARIMA model is elaborated by adopting a # 1 battery. Firstly, adopting ADF unit root inspection method to make stability inspection of original sequence. If the ADF test statistic is less than the test threshold of less than 1%, the original hypothesis can be rejected and the data considered stationary. The test results are shown in table 2. ADF statistic for pro-sequence Y was a test threshold of-3.25 greater than 1% (-3.44). The original hypothesis was accepted at 1% confidence interval and the original sequence was considered non-stationary without ADF test.

TABLE 2 results of stability test of original sequence

2) Making a first order difference to the original sequence

Because the original sequence is non-stationary, it is necessary to perform a first order difference on the original sequence and define the generated new sequence as DY. A line graph of DY is made, as shown in FIG. 2.

3) Smoothing test of first order difference sequence

Observing fig. 2, it is found that DY fluctuates up and down around the mean, and it is preliminarily judged that the DY sequence is stable. The new sequence DY was checked for stationarity using EVIEWS software, and the results are shown in Table 3.

TABLE 3 DY stationarity test results

4) Determining the difference order

The ADF statistic for the new sequence DY is-3.52 < -3.44, and passes the ADF test at a confidence interval of 1%. Meanwhile, the observation of FIG. 2 shows that the new sequence fluctuates around the mean value without obvious trend, indicating that the new sequence DY is stable. Therefore, the order d of the ARIMA (p, d, q) model is determined to be 1.

Identification and establishment of ARIMA model

1) Determining p and q values of ARIMA model

The order p, d in the ARIMA (p, d, q) model is determined by analyzing the autocorrelation function of the new sequence DY and the partial autocorrelation function.

The autocorrelation function and partial autocorrelation function of DY are shown in the following table.

TABLE 4 DY autocorrelation function and partial autocorrelation function

According to the tailing of the sample PACF graph (the performance is not obvious), and the sample ACF graph 5 order truncation, the MA (5) model can be preliminarily judged. If the hysteresis order of the ACF graph is difficult to be seen from the graph, the hysteresis order can be properly relaxed to 6 steps. Namely, the MA (6) model is preliminarily determined.

2) Selecting optimal model

And (3) establishing an ARIMA model from a low order to a high order for different values of q, and performing parameter estimation. All AIC values are calculated and the model that minimizes the AIC values is selected. Namely the optimal model. The AIC values for each model are shown in Table 5

TABLE 5 AIC values for the models

	AIC	SC	HQ
				MA(1)	-7.003	-6.9811	-6.9946
MA(2)	-7.0907	-7.0613	-7.0793
				MA(3)	-7.1835	-7.1468	-7.1692
MA(4)	-7.2765	-7.2325	-7.2594
				MA(5)	-7.2874	-7.2360	-7.2674
MA(6)	-7.3071	-7.2484	-7.2842

Observing the table 5, it can be found that for different values of q, the AIC value of the ARIMA (0,1,6) model is the smallest in the established ARIMA model. The model was initially determined to be ARIMA (0,1, 6).

3) Determining model parameters

The parameters of the model are estimated and the results are shown in table 6.

Table 6: parameter estimation of a model

As can be seen from table 6, the significance of the parameter check values of the estimation model is less than 0.1. Therefore, at a 10% confidence level, the ARIMA (0,1,6) model is a viable model. The results obtained were:

RUL accelerated assessment

The acceleration evaluation start time of the 1# and 2# batteries was set to 600. First, the experiment was performed on the 1# battery, and the results shown in fig. six were obtained. The black dashed line represents the failure threshold of the battery, the black line represents the experimental measurement data of the battery, and the green line represents the accelerated evaluation value of the battery obtained by the time-series algorithm of ARIMA. The blue and red bars represent the upper and lower accelerated assessment limits of the capacity by the ARIMA algorithm, respectively. To further verify the validity of the algorithm, ARIMA time series simulations were performed on # 2 cells, and the results of the model obtained as ARIMA (0,1,4) are shown in fig. seven.

The results of the inventive process used are shown in Table 7.

TABLE 7ARIMA acceleration evaluation values and their upper and lower acceleration evaluation limits

It can be seen from this that:

the ARIMA parameter setting in the invention has direct influence on the accelerated evaluation result of the capacity, and the parameter selection of models under different sample selections may be different. Accelerated evaluation is carried out on the 1# and 2# batteries, the first 600, 700 and 800 groups of data are respectively selected as training data, and the accelerated evaluation error is shown in a table 8.

TABLE 8 sample Battery acceleration evaluation error

As can be seen from the accelerated evaluation error tables of two batteries in table 8, the ARIMA model can better accelerate the evaluation of the battery cycle life. And training the data to accelerate the assessment, the accuracy of the accelerated assessment being substantially higher. And the method has higher operation efficiency. And in a 95% confidence interval, the actual value can well fall in an accelerated evaluation range, and for detection or power station operation workers, whether the battery needs to be replaced or not can be predicted in advance.

Comparative experimental analysis of ARIMA algorithm and other accelerated evaluation methods

To further illustrate the effectiveness of the ARIMA time series algorithm, the algorithm is now compared to the empirical accelerated assessment method and the support vector machine algorithm accelerated assessment error.

TABLE 9 mathematical expression form of empirical model of service life of common power battery

TABLE 10 empirical accelerated estimate fitting model

From FIGS. 9-10, it can be seen that the results of the fitting of the empirical model, R for the linear and Verhulst models²Both can reach 0.99, which indicates that the empirical model can be well matched with the scatter point when the first 700 training data are selected for fitting. From the effect of late-stage acceleration evaluation, the linear model acceleration evaluation life cut-off point is 1224, the Verhulst model acceleration evaluation life cut-off point is 1378, and the linear model acceleration evaluation life cut-off point has a larger error from the real life cut-off point.

The SVM support vector machine is used as one of machine learning algorithms, and the universality of the model is ensured on the premise of less samples by adopting a structure risk minimization principle. When solving the linear fitting and classification problems, the sample nonlinearity is high, and the support vector machine has obvious advantages when solving the problems. Fig. 11 shows the results of regression acceleration evaluation of the first 700 turns of data for battery # 1 using the SVM algorithm. It can be seen from fig. 11 that the fitting of the early samples can achieve a good effect, but the samples show an over-fit phenomenon when used for accelerated evaluation, so that the accelerated evaluation value greatly deviates from the actual value.

In order to accurately analyze and compare the above algorithms, the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) are introduced to evaluate the accuracy of the algorithm. Failure points are not considered in the following discussion because the correlation vector machine algorithm does not reach.

TABLE 11 RUL accelerated assessment error

From table 11, it can be obtained that the errors of the ARIMA algorithm are all smaller than the algorithm model error of the empirical sequence, i.e. the accelerated evaluation accuracy of the ARIMA algorithm is higher than that of the empirical algorithm and the machine learning algorithm.

By discussing the differences and advantages of the accelerated evaluation method based on data driving, an empirical sequence model, a machine learning algorithm and an ARIMA time sequence model are further researched, the accelerated evaluation of the three methods is carried out by taking actual battery aging data as a training sample, and the results are compared to find that:

(1) the SVM can achieve a better effect on the classification of training data, but the SVM is not suitable for the RUL accelerated evaluation of the battery because the SVM generates obvious overfitting problem on the accelerated evaluation of the data. The empirical model method reflects the attenuation trend of the battery in the aspect of accelerating the evaluation curve, and the fitting degree in the training set sample is high. However, in the later data accelerated evaluation, the deviation value becomes large slowly. The ARIMA time series model obtains the same accelerated evaluation trend as the empirical model under the same sample, but the accelerated evaluation precision is obviously improved, and the whole calculation time is shorter.

(2) The absolute acceleration evaluation error of the ARIMA algorithm under two groups of experimental data is approximately 1.2%, the absolute acceleration evaluation error of the linear model is approximately 1.4%, and the absolute acceleration evaluation error of the Verhulst is approximately 7.5%, so that the accuracy of the cycle life budget of the ARIMA time series model under the condition of large data volume is verified, and the life cut-off confidence interval of the battery is considered.

(3) The method has the unique characteristic that the accuracy of the ARIMA time sequence algorithm on the accelerated evaluation of the battery life with a longer life interval is verified, the uncertainty and the random factors of the content attenuation of the battery in a normal cycle interval can be effectively reflected, and the method is in accordance with the actual situation.

Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that various changes, modifications and substitutions can be made without departing from the spirit and scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims

1. A lithium ion battery life accelerated evaluation method based on an ARIMA time sequence is characterized by comprising the following steps:

s1: selecting reasonable acceleration evaluation data, and selecting cycle life capacity data of a certain interval to establish a time series model;

s2: the checking unit carries out preliminary stability judgment on the time sequence according to the checking;

s3: carrying out stabilization treatment on the non-stationary sequence;

s4: performing ARIMA (p, q) model selection on the differentiated stationary sequence, observing the truncation number and the tailing number of the ACF image and the PACF image to perform model selection, and determining the order of the model by an AIC order determination method;

2. The ARIMA time series-based lithium ion battery life accelerated assessment method of claim 1, wherein a first order difference is used to eliminate linear trends in S3.

3. The ARIMA time series-based lithium ion battery life acceleration evaluation method according to claim 2, wherein the quadratic curve trend is eliminated by using a second order difference in S3.

4. The ARIMA time series-based lithium ion battery life accelerated assessment method of claim 1, wherein the identification and establishment of the ARIMA model in S4 comprises the steps of:

(1) determining p and q values of ARIMA model

(2) selecting the optimal model

(3) determining model parameters

5. The method for accelerated assessment of lifetime of li-ion batteries based on ARIMA time series according to claim 1 or 4, wherein in S4 the ARIMA (p, d, q) order is determined as follows:

tail cutting: falling within the confidence interval.

6. The method for accelerated assessment of lifetime of li-ion batteries based on ARIMA time series according to claim 1, wherein the accuracy of the algorithm can be evaluated using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE);