CN103399279A - Method for predicting cycle life of fused lithium ion battery based on EKF (Extended Kalman Filter) method and AR (AutoRegressive) model - Google Patents

Abstract

The invention discloses a method for predicting the cycle life of a fused lithium ion battery based on an EKF (Extended Kalman Filter) method and an AR (AutoRegressive) model, namely the method for predicting the cycle life of the lithium ion battery. The purpose is to solve the problem that the current methods based on models have a low adaptive capacity to different batteries and different working states. The method comprises the following steps: 1, measuring the capability data of the lithium ion battery to be measured on line, storing the data, and preprocessing the data; 2, based on the EKF method, determining the parameters of the state space model of the lithium ion battery; 3, according to the established state space model of the lithium ion battery, estimating the state of the lithium ion battery to be measured, and utilizing the output of the AR model to update the state of the lithium ion battery to be measured; causing the state space model of the lithium ion battery to obtain the capability data of the battery in each charging and discharging cycle, and comparing the data with the failure threshold of the lithium ion battery to be measured to obtain the residual life of the lithium ion battery. The method is used for predicting the cycle life of the lithium ion battery.

Description

Based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology

Technical field

The present invention relates to a kind of cycle life of lithium ion battery Forecasting Methodology, particularly a kind of based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology.

Background technology

At present for lithium ion battery residual life (Remaining Useful Life, RUL) method of prediction roughly is divided into Physical modeling based (Model-based Prognostics) and based on data driving (Data-Driven) method, the electronics lithium battery to be measured complicated for failure mechanism, that model is difficult to set up, most of research concentrates on the method that based on data drives.In data-driven method, comprise statistics driving method such as particle filter (the Particle Filter of a class based on statistical filtering, PF), Kalman filtering (Kalman Filter, KF) and EKF (Extended Kalman Filter, EKF), by setting up lithium battery state transition equation to be measured, realize prediction and upgrade, take into full account lithium battery interior state transitions characteristic to be measured, but a certain degradation model lacks adaptability to dissimilar battery and different operating state; Another kind of method such as autoregressive moving average (Autoregressive Moving average, the ARMA) model that is based on the clear data driving, have the characteristic of analyzing the feature of data own and not considering the lithium battery to be measured that data belong in mind.At present, the hybrid predicting framework that statistical filtering method and clear data driving method are merged constantly is suggested and improves, the advantage of the two is carried out in conjunction with the defect that occurs when making up independent utility separately, but these present methods based on model exist for different batteries and the low problem of different operating state adaptive faculty.

Summary of the invention

The objective of the invention is to exist for different batteries and the low problem of different operating state adaptive faculty in order to solve these present methods based on model, the invention provides a kind of based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology.

Of the present invention based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it comprises the steps:

Step 1: the capacity data of on-line measurement lithium battery to be measured, save data also carries out pre-service to described data;

Step 2: the parameter of determining the lithium ion battery state-space model based on the EKF method:

According to lithium ion battery experience degradation model and AR Construction of A Model lithium ion battery state-space model, utilize pretreated data and according to the EKF method, determine the parameter of described lithium ion battery state-space model; The sequence of observations after the prediction output valve of described AR model and observation noise stack is the observed reading of the battery capacity of described lithium ion battery state-space model, and described AR model is to utilize pretreated the data to merge the AR model that the autoregressive coefficient acquiring method is determined;

Step 3: the lithium ion battery state-space model of setting up according to step 2 carries out state estimation to lithium ion battery to be measured, utilize the output of described AR model to carry out the state renewal of lithium ion battery to be measured, described lithium ion battery state-space model obtains the battery capacity data of each charge and discharge cycles, and the failure threshold of described data and lithium ion battery to be measured is relatively obtained to the lithium ion battery residual life.

The invention has the advantages that, the present invention utilizes the prediction of EKF method and AR model modeling, and the long-term degradation trend of battery capacity is predicted, obtains the long-term forecasting result and it is upgraded to the observed reading true value input of link.The feature that the lithium ion battery state-space model feature of this method and data itself embody is carried out combination, has promoted the adaptability of this method for different batteries, has reduced the dependence of RUL prediction algorithm for the experience degradation model.Method of the present invention possesses good status tracking ability, described method increases for the adaptability between different battery cells, NASA PCoE battery is tested, NASA PCoE battery experiment RUL prediction effect obviously improves, the RUL Relative Error on average reduces by 14% left and right, and the capacity predict relative error on average reduces by 1.65% left and right.

The accompanying drawing explanation

Fig. 1 is the schematic flow sheet based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology of the present invention.

Fig. 2 is for adopting the described method of this law to carry out the predicting residual useful life experiment of No. 5 batteries in NASA PCoE center, for 60 modelings in early stage, the schematic diagram of 1～10 rank AR model AIC result of calculation.

Fig. 3 tests for the predicting residual useful life that adopts the described method of this law to carry out No. 5 batteries in NASA PCoE center, for 80 modelings in mid-term, and the schematic diagram of 1～10 rank AR model AIC result of calculation.

Fig. 4 tests for the predicting residual useful life that adopts the described method of this law to carry out No. 5 batteries in NASA PCoE center, for later stage 100 modelings, and the schematic diagram of 1～10 rank AR model AIC result of calculation.

Embodiment

Embodiment one: in conjunction with Fig. 1, present embodiment is described, present embodiment is described based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, and it comprises the steps:

Step 1: the capacity data of on-line measurement lithium battery to be measured, save data also carries out pre-service to described data;

Step 2: the parameter of determining the lithium ion battery state-space model based on the EKF method:

According to lithium ion battery experience degradation model and AR Construction of A Model lithium ion battery state-space model, utilize pretreated data and according to the EKF method, determine the parameter of described lithium ion battery state-space model; The sequence of observations after the prediction output valve of described AR model and observation noise stack is the observed reading of the battery capacity of described lithium ion battery state-space model, and described AR model is to utilize pretreated the data to merge the AR model that the autoregressive coefficient acquiring method is determined;

Step 3: the lithium ion battery state-space model of setting up according to step 2 carries out state estimation to lithium ion battery to be measured, utilize the output of described AR model to carry out the state renewal of lithium ion battery to be measured, described lithium ion battery state-space model obtains the battery capacity data of each charge and discharge cycles, and the failure threshold of described data and lithium ion battery to be measured is relatively obtained to the lithium ion battery residual life.

Embodiment two: present embodiment is to the described further restriction based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology of embodiment one,

In described step 1, described data being carried out to pretreated method is:

For point unusual in described data, reject, for the excessive capacity orthogenesis of amplitude, carry out the level and smooth of trend.

Described unusual point comprises data and the wrong data of larger measuring error, and the excessive capacity orthogenesis of described amplitude is in curve, to show as several capacity rising parts in whole downtrending, i.e. burr part in decline curve.

Embodiment three: present embodiment is to the described further restriction based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology of embodiment one,

In step 2, described according to lithium ion battery experience degradation model and AR Construction of A Model lithium ion battery state-space model, utilize pretreated data and determine that according to the EKF method method of the parameter of described lithium ion battery state-space model comprises the steps:

Steps A: according to lithium ion battery experience degradation model

Construct the state-space model of the parameter estimation of described degradation model:

$\left\{\begin{array}{cc}{a}_k=a_{k-1}+w_a& w_a~N(0,Q_a)\\ b_k=b_{k-1}+w_b& w_b~N(0,Q_b)\\ c_k=c_{k-1}+w_c& w_c~N(0,Q_c)\\ C_{k+1}=a_k{C}_k+b_k{e}^{(-c_k)}+v_k& v_k~N(0,R)\end{array}\right.$

Wherein $\left\{\begin{array}{cc}{a}_k=a_{k-1}+w_a& w_a~N(0,Q_a)\\ b_k=b_{k-1}+w_b& w_b~N(0,Q_b)\\ c_k=c_{k-1}+w_c& w_c~N(0,Q_c)\end{array}\right.$ For state transition equation, $C_{k+1}=a_k{C}_k+b_k{e}^{(-c_k)}+v_k$ For observation equation, a _k, b _kAnd c _kBe respectively the enclosed pasture efficiency eta in current k described experience degradation model of the moment _{C, k}, the regenerated capacity parameter beta _{1, k}With the regenerated capacity parameter beta _{2, k}Estimated value;

C _kFor the discharge capacity constantly of k in the degradation in capacity process of lithium battery to be measured, C _K+1For the discharge capacity constantly of k+1 in the degradation in capacity process of lithium battery to be measured, η _{C, k}For the enclosed pasture efficiency in charging and discharging lithium battery process to be measured;

For lithium battery to be measured at standing time of having a rest section △ t _kThe capacity of interior regeneration; w _a, w _bAnd w _cBe respectively the white Gaussian noise that parameter a, b and c comprise, Q _a, Q _bAnd Q _cBe respectively w _a, w _bAnd w _cVariance, noise w _a, w _bAnd w _cMeet respectively N (0, Q _a), N (0, Q _b) and N (0, Q _c) Gaussian distribution; R is real number; v _kFor the observation noise of lithium battery to be measured, v _kThe obedience average is 0, v _kVariance be the Gaussian distribution of R; Step B: utilize pretreated data, employing EKF method is carried out linearization, state estimation and state renewal to the state-space model of the parameter estimation of described degradation model, determines the current K parameter a constantly of described state-space model _k, b _kAnd c _k

Step C: according to the current K parameter a constantly of the state-space model of the parameter estimation of described degradation model _k, b _kAnd c _k, try to achieve current k constantly under condition estimates of parameters be the probability P of parameter true value, namely the estimated value constantly measured of current k is that the probability of parameter true value is P; According to described probability P, be weighted on average, try to achieve current k a_s, b_s and c_s constantly:

$m\_s=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}m\left(i\right)\·\frac{P\left(i\right)}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}P\left(i\right)}m=a,b,c$

Wherein, N is the length of the capacity data of on-line measurement lithium battery to be measured; M (i) is i the corresponding parameter a of discharge cycles _k, b _kOr c _kPerhaps c, P (i) is the parameter a to i discharge cycles _k, b _kOr c _kThe result of estimating is the probability of the current k parameter actual value constantly of state-space model;

Step D: the a_s that will obtain, b_s and c_s, as the parameter of lithium ion battery state-space model, obtain described lithium ion battery state-space model:

$\left\{\begin{array}{cc}{C}_{k+1}=a\_s\·C_k+b\_s\·e^{(-c\_s)}+w_k& w_k~N(0,Q)\\ y_k=C_k+v_k& v_k~N(0,R)\end{array}\right.$

Wherein, w _kFor the process noise of lithium battery to be measured, obeying average is 0, and variance is the Gaussian distribution of Q, and Q is rational number, y _kFor the systematic perspective measured value.

Construct in the present embodiment the state-space model of the parameter estimation of described degradation model

$\left\{\begin{array}{cc}{a}_k=a_{k-1}+w_a& w_a~N(0,Q_a)\\ b_k=b_{k-1}+w_b& w_b~N(0,Q_b)\\ c_k=c_{k-1}+w_c& w_c~N(0,Q_c)\\ C_{k+1}=a_k{C}_k+b_k{e}^{(-c_k)}+v_k& v_k~N(0,R)\end{array}\right.$ The time,

By lithium ion battery experience degradation model

Capacity regeneration is regarded constant as and is processed, therefore required obtain be

The final calculation result of part, therefore in order to simplify calculating, by △ t _kTurn to constant 1, can reduce one and propose data and pretreated process, to improve the counting yield of algorithm.

Based on this probability P, be weighted on average in the present embodiment, the P value is larger, illustrates that corresponding parameter prediction result is more near real parameter value, therefore should have higher weight, and namely its confidence level is higher.

Embodiment four: present embodiment is to the described further restriction based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology of embodiment one,

In described step 2, utilize the method that pretreated the data merges the definite AR model of autoregressive coefficient acquiring method to comprise the steps:

Step e:

Utilize pretreated data and ask for the AR model according to AIC criterion

Model order p;

Step F: utilize pretreated data, ask for respectively the autoregressive coefficient of described AR model according to Yulle-Wallker method and Burg method, the final autoregressive coefficient of method output that adopts dynamic linears to merge two autoregressive coefficients of trying to achieve

Step G: according to the model order p of step e acquisition and the final autoregressive coefficient of step F acquisition Determine the AR model.

The acquiring method of AR model order has a lot, as Final prediction error criterion, average information criterion etc., these methods are all the AR model of each order to be carried out to the calculating of certain judgment criterion, and the corresponding model order of the minimum value in result of calculation is carried out to follow-up modeling and forecasting as best order.In the present embodiment, adopt average information criterion (Average Information Criterion, AIC) to judge model order.

Embodying suc as formula shown in (3-3) of AIC criterion.

$\mathrm{AIC}\left(p\right)=N\ln {\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="20131033187171000031.png,HDA00003609024500022.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+2p---(3-3)$

Wherein N is the sequential element number,

For p rank prediction error variance, the model order of p for determining.Usually, the order of AR model can not surpass 10 times, if surpass 10 times, not only bad for improving precision of prediction, precision of prediction is descended, and cause phenomenon consuming time in the algorithm implementation, that committed memory is larger.So in concrete order deterministic process, present embodiment is calculated the traversal formula that 1 ~ 10 rank AR model carries out the AIC result, and the order of therefrom choosing AIC result of calculation minimum is as the final modeling order of present embodiment.

Utilize formula (3-3) to calculate the corresponding AIC value of p=1 ~ 10 different order AR model, and judgement is big or small, AIC value hour corresponding model order p is the optimum AR model order for current modeling data.Concrete implementation method is as follows:

A) the capacity data F that extracts for training modeling inputs as the raw data of order judgement;

B) F is carried out to standardization:

Zero-mean: ask for the average Fmean of training modeling data F, can obtain the sequence f=F-Fmean of zero-mean;

Variance criterion: the standard deviation sigma of asking for the modeling data f after zero-mean _f, obtain standardized data Y=f/ σ _f

C) whether the modeling data after criterion is suitable for setting up the AR model, namely coefficient of autocorrelation and PARCOR coefficients truncation characteristic is judged:

0 step autocovariance: ${\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="20131033187171000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_0=\underset{i=1}{\overset{L1}{\mathrm{\&Sigma;}}}\frac{Y^2\left(i\right)}{L1}---(3-9)$

1 ~ 20 step autocovariance: $R\left(k\right)=\underset{i=k+1}{\overset{L1}{\mathrm{\&Sigma;}}}\frac{Y\left(i\right)\&CenterDot;Y(i-k)}{L1}(k=\mathrm{1,2},...,20)---(3-10)$

Coefficient of autocorrelation: x=R/R ₀(3-11)

According to result of calculation, draw the coefficient of autocorrelation curve, judgement truncation characteristic, if truncation is suitable for the MA modeling.

Partial correlation coefficient: solve the Yule-Wallker equation, according to solving result, draw the partial correlation coefficient curve, judgement truncation characteristic, if truncation is suitable for the AR modeling.

Research shows, the MA model can be similar to by the AR model of high-order, therefore, if data are suitable for the MA modeling, also just illustrate and can carry out the prediction of AR model modeling to it.

D) AIC calculates:

By coefficient of autocorrelation, calculate: S=[R ₀, R (1), R (2), R (3)] and (3-12)

Calculate the Toeplitz matrix: G=toeplitz (S) (3-13)

Calculating parameter: W=G ^-1[R (1), R (2), R (3), R (4)] ^T(3-14)

Model residual error variance is calculated: ${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="20131033187171000031.png,HDA00003609024500022.png"\; state="\{\{state\}\}">p</figure-callout>}}^2=\frac{1}{L1-p}\underset{t=p+1}{\overset{L1}{\mathrm{\&Sigma;}}}{[Y\left(t\right)-\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}W\left(i\right)\&CenterDot;Y(t-i)]}^2---(3-15)$

AIC calculates suc as formula (3-3).

E) model order p corresponding to judgement AIC minimum value, be Optimal order.

F) each modeling data sample of each battery data collection is carried out respectively to the asking for of best model order under AIC criterion, for follow-up modeling.

Special needs to be pointed out is, in algorithm principle introductory section present embodiment, the coefficient of AR model is merged to the estimation of way, each step merges need to carry out the stack of p to coefficient, and calculated amount is larger.So in actual applications, the method that present embodiment adopts estimated parameter respectively and predicts, obtain respectively prediction capacity separately, and capacity data is carried out to dynamic superpose, reduced the number of times of superposition, reduces calculated amount.But the two is identical in itself, is the different implementation methods of same thinking.Described Yule-Wallker method and Burg method:

(1) Yule-Wallker method

The Yule-Wallker method claims again correlation method, by the Yule-Wallker equation, solves, and the Yule-Wallker equation is as follows:

Matrix form is as follows:

In calculating process, utilize the parameter of AR (0) and AR (1) as starting condition, to ask for the parameter of AR (2), again according to the parameter of the parametric solution AR (3) of gained, by Recursive Solution, go out the parameter of AR (p), recursion completes the parameter that can obtain the AR model.

(2) Burg method

The Burg method is utilized filtering error f forward _n,tFiltering error b backward _n,t, obtain and guarantee that filtering error power is minimum

According to the Levinson algorithm, calculate again

Forward filtering error, backward filtering error and the filtering error power definition as follows:

${\mathrm{<figure-callout\; id="2"\; label="e\; n"\; filenames="20131033187171000031.png,HDA00003609024500022.png"\; state="\{\{state\}\}">e</figure-callout>}}_n^{}=\frac{1}{2(N-n)}(\underset{t=n+1}{\overset{N}{\mathrm{\&Sigma;}}}{f}_{n,\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="20131033187171000031.png,HDA00003609024500022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+\underset{t=N-(n+1)}{\overset{1}{\mathrm{\&Sigma;}}}{b}_{n,t}^2)---(3-8)$

Order

Can solve and guarantee filtering error power minimum

The way of asking for of autoregressive coefficient has a variety ofly, and enough in large situation, the coefficient that distinct methods obtains is close for sample.But for the such small sample data set of battery capacity data, the number of data is less, a kind of independent method ask for the real features that result is difficult to reflect exactly data.Therefore, in present embodiment, select Yulle-Wallker method and Burg method independently to ask for respectively model coefficient, then carry out the final coefficient results of method output of simple dynamic linear combination.Concrete parameter acquiring method is as follows:

Use Matlab to carry AR model modeling function arburg.m and aryule.m, utilize respectively identical historical modeling data computation model autoregressive coefficient, obtain independently coefficient and ask for result

With

Initial fusion coefficients P is set ₁And P ₂

Along with the increase of prediction step, dynamically adjust fusion coefficients: P ₁=P ₁-f (i), P ₂=P ₂+ f (i), wherein i is prediction step.It is pointed out that f in the actual prediction process (i) needs constantly to attempt adjusting, but for the same class battery, in case determined that the concrete form of f (i) just no longer changes.That is to say, for a class battery characteristics, construct a kind of dynamic fusion coefficient, to a certain extent, this dynamic fusion coefficient has also represented the degenerative character of a certain battery;

Fusion coefficients is calculated:

Using the coefficient of this coefficient as final AR model in order to capacity long-term degradation trend prediction.

Determined model order and model parameter, AR(p) model has just been set up.Then, utilize pretreated data, before the input current time, p state value constantly is as initial condition data (p is the AR model order), substitution

Shown model, can obtain current status predication result.According to the continuous iterative computation of such step, just can obtain current K battery capacity prediction result constantly, also just obtained degradation in capacity long-term forecasting output data set ARpredict.

Embodiment five: present embodiment is to the described further restriction based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology of embodiment three,

In described step B: utilize pretreated data, employing EKF method is carried out linearization, state estimation and state renewal to the state-space model of the parameter estimation of described degradation model, determines the current K parameter a constantly of described state-space model _k, b _kAnd c _kMethod be:

Step B1: the state-space model to the parameter estimation of described degradation model carries out linearization:

State transition equation input state transition matrix F to the state-space model of the parameter estimation of described degradation model _kDescribed F _kFor:

$F_k=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right];$

To the observation equation of the state-space model of the parameter estimation of described degradation model, carry out the Taylor expansion and utilize the one exponent part to carry out the linearization of nonlinear equation approximate, obtain the matrix H of the observation equation after linearization _k:

$H_k=[C_k,e^{-c_k},-b\&CenterDot;e^{-c_k}];$

Step B2: the current K parameter constantly of the state-space model of the parameter estimation of the described degradation model after adopting kalman filter method to linearization is carried out state estimation and renewal:

By the state transition equation after linearization, the current K parameter constantly of described model is estimated, is obtained the estimated value of current k parameter constantly:

[a _k ^-,b _k ^-,c _k ^-]=[a _k-1 ⁺,b _k-1 ⁺,c _k-1 ⁺]

$P_k^{-}=F_k{P}_{k-1}^{+}{F}_k^T+W_k{Q}_k{W}_k^T$

Wherein, a _k ^-, b _k ^-And c _k ^-Represent respectively k parameter a constantly _k, b _kAnd c _kEstimated value, a _K-1 ⁺, b _K-1 ⁺And c _K-1 ⁺Represent respectively k-1 parameter a constantly _k, b _kAnd c _kThe renewal value,

For the k estimated value of the state covariance matrix of lithium battery to be measured constantly,

1 is the k-1 renewal value of the state covariance matrix of lithium battery to be measured constantly, W _kFor the process noise matrix of coefficients of lithium battery to be measured, Q _kVariance for described process noise;

The estimated value of described current k parameter constantly is brought in the observation equation of state-space model of parameter estimation of degradation model, obtains the estimated value of battery capacity observed reading

The observed reading true value of the estimated value of described battery capacity observed reading and battery capacity is compared and obtains measuring remaining poor covariance

And obtain the optimum kalman gain that described estimated value is proofreaied and correct $K_k=P_k^{-}{H}_k^T{S}_k^{-1},$ Utilize formula ${{[a}_k}^{+},{b_k}^{+},{c_k}^{+}]=[{a_k}^{-},{b_k}^{-},{c_k}^{-}]+K_k(C_k-C_k^{~})$ And formula Estimated value to each parameter constantly of state-space model carries out upgrading based on the state under the minimum variance principle, obtains each parameter a constantly of described state-space model surely _k, b _kAnd c _k,

Wherein,

Be based on the discharge capacity in k the cycle that estimated parameter calculates, C _K-1For the discharge capacity in k-1 cycle of on-line measurement lithium battery to be measured, S _kTo measure remaining poor covariance matrix, H _kFor the observing matrix of lithium battery to be measured,

For the k renewal value of the state covariance matrix of lithium battery to be measured constantly, V _kFor the observation noise matrix of coefficients of lithium battery to be measured, R _kFor the variance of the observation noise of lithium battery to be measured, a _k ⁺, b _k ⁺And c _k ⁺Represent respectively k parameter a constantly _k, b _kAnd c _kThe renewal value, I is unit matrix.

In linearizing process, the process noise of lithium battery to be measured and observation noise are the linear superposition noise, therefore linearization process noise and observation noise matrix of coefficients are arranged suc as formula shown in (2-18), (2-19).

$W_k=\left[\begin{array}{ccc}\frac{{\&PartialD;f}_a}{{\&PartialD;w}_a}& \frac{{\&PartialD;f}_a}{{\&PartialD;w}_b}& \frac{{\&PartialD;f}_a}{{\&PartialD;w}_c}\\ \frac{{\&PartialD;f}_b}{{\&PartialD;w}_a}& \frac{{\&PartialD;f}_b}{{\&PartialD;w}_b}& \frac{{\&PartialD;f}_b}{{\&PartialD;w}_c}\\ \frac{{\&PartialD;f}_c}{{\&PartialD;w}_a}& \frac{{\&PartialD;f}_c}{{\&PartialD;w}_b}& \frac{{\&PartialD;f}_c}{{\&PartialD;w}_c}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]---(2-18)$

$V_k=\frac{\&PartialD;h}{\&PartialD;v}=1---(2-19)$

Because each noise is independent mutually, lithium battery process noise covariance matrix Q to be measured is arranged suc as formula (2-20).

$Q=\left[\begin{array}{ccc}{Q}_{a,a}& Q_{a,b}& Q_{a,c}\\ Q_{b,a}& Q_{b,b}& Q_{b,c}\\ Q_{c,a}& Q_{c,b}& Q_{c,c}\end{array}\right]=\left[\begin{array}{ccc}{Q}_a& 0& 0\\ 0& {\mathrm{<figure-callout\; id="0"\; label="Q\; b"\; filenames="20131033187171000031.png"\; state="\{\{state\}\}">Q</figure-callout>}}_b& 0\\ 0& 0& Q_c\end{array}\right]---(2-20)$

Cycle life of lithium ion battery Forecasting Methodology of the present invention, be exactly by the capacity long-term degradation prediction output valve ARpredict of the AR model of clear data driving, using the observed reading true value input under Kalman filtering capacity predict framework after ARpredict and white Gaussian noise stack, replace and upgrade the link formula

In

Like this, state based on the model prediction Output rusults upgrades the state renewal that link just replaces to based on data driving prediction Output rusults, utilize the characteristic information of data itself to upgrade the capacity estimation value based on the experience degradation model, model information and data message are carried out to combination.

Method based on EKF method and the fusion of AR model in the present invention is before based on Kalman filtering algorithm, battery capacity being predicted to link, need to carry out AR model modeling and ARpredict prediction output procedure, and obtain on this basis the true observation input of upgrading link, replace in simple EKF algorithm based on model and use

Carry out the process of state renewal, as follows based on the embodiment of EKF method and the fusion of AR model:

1. obtaining of state transition equation: utilize known modeling training dataset, the extension-based Kalman filtering algorithm upgrades through state equation being carried out to linearization, state estimation and state, realization is carried out dynamic estimation to experience degradation model parameter, and based on prediction probability, the model parameter that status tracking obtains is carried out to the parameter weighting mean value computation, determine the model parameter of using in the later stage forecasting process.

2. observe obtaining of true value:

(1) utilize historical modeling data collection to carry out the modeling feasibility analysis: to modeling data, to carry out standardization, calculate partial autocorrelation and coefficient of autocorrelation, judge its truncation characteristic, if the PARCOR coefficients truncation, be suitable for the AR model modeling, if the coefficient of autocorrelation truncation, be suitable for the MA model modeling, and is as can be known by preliminary analysis, the MA model can be similar to by high-order AR model, therefore, if the coefficient of autocorrelation truncation also can judge that data sample is suitable for the AR modeling.

(2) through type (3-12), (3-13), (3-14), (3-15), (3-3) carry out 1-10 rank AR model AIC calculating, and based on AIC criterion, judgement is for the best AR model order of current training sample.

(3) utilize Burg method and Yule-Wallker method to carry out the calculating of AR model coefficient and respective volume prediction output, adopt performance coeffcient to merge two kinds of methods, obtain fusion forecasting output ARpredict.

3. through 1 and 2, can obtain the lithium ion battery state-space model

$\left\{\begin{array}{cc}{C}_{k+1}=a\_s\&CenterDot;C_k+b\_{s\&CenterDot;e}^{(-c\_s)}+w_k& w_k~N(0,Q)\\ y_k=C_k+v_k& v_k~N(0,R)\end{array}\right.,$ Can carry out pattern of fusion RUL forecasting process:

(1) state estimation: utilize the lithium ion battery experience degradation model that obtains in 1 and upper predicting the outcome constantly, carry out $C_k^{-}=a\_s\&CenterDot;C_{k-1}^{+}+b\_s\&CenterDot;e^{(-c\_s)}$ With $P_k^{-}=F_k{P}_{k-1}^{+}{F}_k^T+Q_k$ The estimation of shown current time battery capacity.

(2) pattern of fusion state renewal process: in this link, utilize based on data in 2 to drive capacity long-term degradation that algorithm the obtains ARpredict structure observation true value sequence that predicts the outcome, and carry out the state renewal:

(a) determine observation true value sequence:

C_real=ARpredict+a _t (3-16)

Wherein ARpredict is AR model prediction output sequence, and with the modeling data unique characteristics, this feature and lithium battery model to be measured are irrelevant, only are conceived to the variation characteristic of data self.a _tFor obeying variance, be W, average is 0 white Gaussian noise, i.e. observation noise a _t～N (0, W).Two parts stack has namely formed upgrades the sequence of observations of link with observation noise.

(b) utilize formula

The remaining poor covariance of computation and measurement, and through type on this basis

Calculate optimum kalman gain, then utilize following formula to carry out the renewal process of state:

$C_k^{+}=C_k^{-}+K_k[C\_\mathrm{real}-C_k^{-}]---(3-17)$

In formula, C_real is the observed reading true value sequence that the based on data of determining in step (a) drives algorithm, all the other parameter definition and formulas

Identical.In this step, realized data-driven algorithm and fusion based on model method, utilize the long-term forecasting Output rusults that the data-driven algorithm obtains to upgrade the state estimation result of obtaining based on model algorithm.That is to say, utilize the data characteristics of capacity data itself the capacity predict result that represents lithium battery interior state transitions feature to be measured of obtaining based on the experience degradation model is upgraded and proofreaied and correct.Like this, at the algorithm based on model, incorporated the characteristic information of data itself, realized the fusion of algorithm, the predicated error of bringing for experience degradation model bad adaptability plays certain correcting action.

(3) based on the capacity estimation in previous step and renewal, the battery capacity of each charge and discharge cycles after the prediction starting point is made prediction, obtain the prediction output sequence of the battery capacity under the fusion forecasting algorithm.

4. so far complete the prediction of battery capacity, by comparing of failure threshold and capacity predict result, can provide corresponding RUL predicted value, can analyze the error of capacity predict and RUL prediction simultaneously, with technical requirement, compare.

in concrete confirmatory experiment, utilize the open battery data collection of NASA PCoE, selected certain battery testing data sample is as the capacity data of on-line measurement residual life lithium battery to be measured, it is the data of L2 that the length of described data sample is divided into to data and the length that length is L1, length is the capacity data that in the digital simulation actual application of L1, on-line measurement is obtained, for determining lithium ion battery state-space model training data, length is that the data of L2 belong to unknown data in the online life prediction process of reality, namely need to utilize prediction algorithm to its data of predicting, this part data are for verifying lithium ion battery predicting residual useful life effect in concrete experiment, the separation of L1 and L2 is the prediction starting point, for same data sample, carry out equally the contrast experiment of different prediction starting points, still select 30% of data total length, 50% and 70%(i.e. early stage, mid-term and later stage) as the model training data set, the checking prediction algorithm is for the adaptive faculty of the training data of same battery sample different length.Meanwhile, select 6 independently the battery testing sample carry out respectively prognostic experiment, the Generalization Ability of verification algorithm between different cells.

One, NASA PCoE lithium ion battery RUL prognostic experiment

The present invention utilizes normal 5,6, No. 18 batteries of degenerating of NASA normal temperature to carry out the checking of algorithm.In the experimental verification process, according to NASA PCoE battery testing condition, delimiting 1.38Ah is the battery capacity failure threshold, be roughly 70% of rated capacity, to each data sample, for this data length, predict that starting point is in the prognostic experiment of the different reference positions in the early stage of whole life cycle (30%), mid-term (50%) and later stage (70%), data before the prediction starting point are in order to simulate the battery capacity data of actual online acquisition, different samples are launched to experiment, observe the prediction effect of algorithm.

Below as an example of No. 5, NASA PCoE center battery example, the model and forecast process is described in detail.

1. remove: remove all variablees in work space, Close All the Windows;

2. raw data imports: by being written into data and data being carried out to pre-service, import the capacity data for modeling:

(1) by the load function, be written into the B0005.mat file, and extract the battery capacity data Capacity in discharge cycles;

(2) normal capacity threshold value U_MAX=1.85 is set, U_MIN=1.20, reject the singular point that peels off, and supplement corresponding capacity data according to the capability value of previous step;

(3) for orthogenesis visibility point too, the average in adopting between proximity replaces the former data of this point, avoids excessive capacity regeneration effect algorithm convergence.

3. parameter setting: dividing data, training modeling data length is still L ₁=60,80,100, U=1.38Ah is failure threshold;

4. the model parameter estimation of extension-based Kalman filtering algorithm: by being written into data and data being carried out to pre-service, import the capacity data for modeling, lithium battery state to be measured is followed the tracks of, and is carried out parameter estimation according to training data set experience degradation model:

(1) definition observation equation h is suc as formula the d formula in (2-12) with by the equation linearization process, obtain the partial derivative matrix H of observation equation _kShown in (2-17);

(2) filtering initialization, define the constant matrices that occurs in algorithm.

Lithium battery state to be measured (parameter) initial value: [a ₀; b ₀; c ₀]=[1; 10; 10]

Status predication covariance matrix initial value: $P=\left[\begin{array}{ccc}10& 0& 0\\ 0& 10& 0\\ 0& 0& 10\end{array}\right]$

Constant matrices in lithium battery state model to be measured: $F=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right];$ V=1； $W=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

Lithium battery noise parameter to be measured: $Q=\left[\begin{array}{ccc}0.0001& 0& 0\\ 0& 0.0001& 0\\ 0& 0& 0.0001\end{array}\right];$ R=0.0001

(3) input state tracking section concept of reality measured value is true capacity data Y _ real=Capacity (1:L ₁);

(4) initialization space of matrices: the space MM of stored parameter estimated value, the space PP of storage covariance matrix value, the space Cappredict of the capability value that the storage estimated parameter calculates;

(5) EKF parameter estimation procedure, carry out state estimation and state renewal to model parameter value, namely utilizes expanded Kalman filtration algorithm to carry out the battery status tracking.

State estimation: suc as formula [a _k ^-, b _k ^-, c _k ^-]=[a _K-1 ⁺, b _K-1 ⁺, c _K-1 ⁺],

Based on die sinking in upper a period of time shape parameter predicted value and state transition equation, carry out the estimation of current time model parameter value;

State upgrades: suc as formula (2-23)～(2-27), carry out the state renewal process, obtain based on the parameter renewal value after the correction of observation true value;

The capacity estimation value: $C_k^{~}=a_k^{-}{C}_{k-1}+b_k^{-}{e}^{(-c_k^{-})}---(2-23)$

Measure remaining poor covariance: $S_k=H_k{P}_k^{-}{H}_k^T+V_k{R}_k{V}_k^T---(2-24)$

Kalman gain: $K_k=P_{k|}^{-}{H}_k^T{S}_k^{-1}---(2-25)$

State upgrades: $[{a_k}^{+},{b_k}^{+},{c_k}^{+}]=[{a_k}^{-},{b_k}^{-},{c_k}^{-}]+K_k(C_k-C_k^{~})---(2-26)$

$P_k^{+}=(I-K_k{H}_k)P_k^{+}---(2-27)$

Result is preserved into default space of matrices: MM, PP and Cappredic.

(6) according to current estimates of parameters, be the prediction probability P of parameter true value,

According to formula

M=a, b, it is average that c carries out parameter weighting, obtains the required model parameter a_s of capacity predict link, b_s and c_s.

5.AR model modeling and forecasting process:

(1) according to the prediction starting point, extract historical modeling data, and historical data is carried out to standardization, making the average of the capacity data after processing is 0, and variance is 1, and detailed process is shown in the step that model order is asked for;

(2) calculate coefficient of autocorrelation and partial correlation coefficient, draw respective graphical, judgement truncation characteristic, if the partial correlation coefficient truncation meets AR modeling condition, detailed process is shown in the step that model order is asked for;

(3) utilize AIC criterion, carrying out the AIC value of 1-10 rank AR model calculates, step is suc as formula shown in (3-12)～(3-15), select the minimum order of AIC value as the best order p of modeling, and by the applicability of white noise test and judge model, even between white noise, related coefficient is namely approximate separate close to 0, can think that model is applicable;

(4) by Yule-Wallker and Burg method, carry out respectively AR model modeling and prediction, obtain respectively the capacity predict value under the different parameters computing method, the Mobile state additive fusion of going forward side by side.By continuous test, can obtain, for NASA PCoE battery data, f in fusion coefficients (i)=0.0011 √ i (i=1,2, ...), determine this factor and be applied to the forecasting process of NASA PCoE center all batteries sample, finally obtain volume output sequence A Rpredict, as the observed reading true value of subsequent step, use;

6. the battery capacity prediction process under the pattern of fusion prediction framework:

(1) definition status equation of transfer: h is suc as formula a formula in (2-29), and model parameter is obtained by the 4th step;

(2) filtering initialization: F=a_s; H=1; Q=0.0001; R=0.0001;

(3) actual value of input capacity predicted portions observed reading, consist of the capacity long-term degradation trend prediction value ARpredict of resulting AR model in step 5 and white Gaussian noise stack, i.e. C_real=ARpredict+a _t, a wherein _tFor the single-point white Gaussian noise.

(4) original state setting, adopt last capability value of historical training modeling data as the original state value, and this is also unique known true capacity value in forecasting process, and the setting of covariance is identical with (2) in 2.3.2.1 step 4;

(5) space of matrices setting: the space MM of stored parameter estimated value, the space PP of storage covariance matrix value, the space Cappredict of the capability value that the storage estimated parameter calculates;

(6) state estimation: based on upper moment status predication value and a state transition equation, carry out the estimation that the current state value is battery capacity value suc as formula (2-30), (2-31);

$C_k^{-}=a\_s\&CenterDot;C_{k-1}^{+}+b\_s\&CenterDot;e^{(-c\_s)}---(2-30)$

$P_k^{-}=F_k{P}_{k-1}^{+}{F}_k^T+Q_k---(2-31)$

(7) state upgrades: suc as formula (2-32), (2-33), (2-35) with (3-17), carry out calculating based on the remaining poor optimum kalman gain of observation, realize the data-driven algorithm and based on the fusion of model algorithm;

$S_k=H_k{P}_k^{-}{H}_k^T+R_k---(2-32)$

$K_k=P_k^{-}{H}_k^T{S}_k^{-1}---(2-33)$

$C_k^{+}=C_k^{-}+K_k[C\_\mathrm{real}-C_k^{-}]---(2-34)$

$P_k^{+}=(I-K_k{H}_k)P_k^{-}---(2-35)$

(8) residual life output: by the find function, find in forecasting sequence less than the index position of failure threshold U, its minimum value deducts 1 and is the RUL value, can calculate true residual life RUL ₁With prediction residual life RUL ₂

7. error is calculated: according to formula (2-7), (2-8) with (2-9) calculate respectively the absolute error that absolute average error, root-mean-square error and the RUL of battery capacity prediction predict, algorithm is carried out to quantitatively evaluating, in addition the relative error of calculated capacity prediction and RUL prediction, compare with technical indicator;

The capacity predict mean absolute error: $\mathrm{MAE}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}|Y\_\mathrm{real}\left(i\right)-Y\_m\left(i\right)|---(2-7)$

The capacity predict root-mean-square error: $\mathrm{RMSE}=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(Y\_\mathrm{real}\left(i\right)-Y\_m\left(i\right))}^2}---(2-8)$

Life prediction absolute error: errul=|RUL ₂-RUL ₁| (2-9)

8. Output rusults, judge whether to meet technical requirement.

By above-mentioned modeling flow process, carry out the predicting residual useful life experiment of No. 5 batteries in NASA PCoE center, for 60 modelings in early stage, 1～10 rank AR model AIC result of calculation as shown in Figure 2, AIC minimum value AICmin=-0.9875, the best order p=1 of corresponding modeling.Sequence of observations input fusion forecasting algorithm frame by after the long-term forecasting output of AR model and noise stack, can obtain RUL and predict the outcome.

For 80 modelings in mid-term of No. 5 batteries, 1～10 rank AR model AIC result of calculation as shown in Figure 2, AIC minimum value AICmin=-117.1, the best order p=1 of corresponding modeling.Sequence of observations input fusion forecasting algorithm frame by after the long-term forecasting output of AR model and noise stack, can obtain RUL and predict the outcome.

For 100 modelings of NASA5 battery later stage, 1～10 rank AR model AIC result of calculation as shown in Figure 4, AIC minimum value AICmin=-174.9, the best order p=1 of corresponding modeling.Sequence of observations input fusion forecasting algorithm frame by after the long-term forecasting output of AR model and noise stack, can obtain RUL and predict the outcome.

This method adopts same method to merge modeling and the RUL prognostic experiment under framework to No. PCoE6, NASA and No. 18 battery capacity data, and parameter adjustment is with above-mentioned consistent.And then obtain No. 6, No. 18 battery RUL and predict the outcome.The numerical result of AIC minimum value and corresponding best modeled order is as follows:

NASA PCoE6 battery AIC result of calculation:

The early stage 60 modeling: AICmin=-25.29; Best order p=1.

Mid-term 80 modeling: AICmin=-113.7; Best order p=1.

Later stage 100 modeling: AICmin=-201.1; Best order p=1.

NASA PCoE18 battery AIC result of calculation:

The early stage 30 modeling: AICmin=-7.936; Best order p=1.

Mid-term 50 modeling: AICmin=-2.847; Best order p=1.

Later stage 70 modeling: AICmin=-40.51; Best order p=1.

By 3 battery samples based on difference prediction starting point predicting the outcome and the quantization error result gathers, concrete result of calculation is as shown in table 1.

Table 1NASA Battery experimental result gathers

By prediction curve intuitively, can find out, the prediction degradation trend is obviously more identical with true degradation trend, and precision of prediction promotes to some extent.The introducing of this explanation data characteristics, promoted the adaptability of algorithm for different battery samples, can predict better the different degenerative characters of different battery samples.

By the quantization error data in table 1, can find out, no matter for different battery samples or for the different modeling data collection of same battery sample, predicting the outcome of battery capacity can meet the error requirements of expection, predicated error scope 2% left and right, left and right to 18%, and precision of prediction is higher.For the predicated error of battery RUL, the absolute value of error is less, is generally 10 below charge and discharge cycles.For the experiment sample of the overwhelming majority, the relative error of RUL can meet the setting requirement, but the early stage of indivedual samples as No. 6 battery later stages, No. 18 batteries arranged, and Relative Error has surpassed 40%.Can find out, the prediction effect of RUL promotes to some extent, but can't meet the demands fully.For different battery individualities, the otherness of prediction effect reduces, and adaptability improves.This explanation, the introducing of data-driven algorithm makes moderate progress to the poor problem of Model suitability, by data characteristics, aspect of model correction has been played to certain improved action.

Yet, for the prognostic experiment of the different modeling data samples of same battery, still showing some differences, the Relative Error ratio of some battery different times has even reached 10 times of left and right, and algorithm is still poor for the adaptability of different times.This is because no matter is state transitions relation or the feature of data own the period of degenerating in difference, all there will be larger difference, the data-driven algorithm be still for early stage modeling data predict, the data characteristics of introducing is also the information from early stage, modeling data comprised.Therefore be difficult to dope the variation of the degradation in capacity feature in the later stage degenerative process.That is to say, the introducing of data-driven algorithm is difficult to the predictive ability that boosting algorithm itself changes the different times degradation trend.

Claims (5)

1. based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it is characterized in that,

It comprises the steps:

Step 1: the capacity data of on-line measurement lithium battery to be measured, save data also carries out pre-service to described data;

Step 2: the parameter of determining the lithium ion battery state-space model based on the EKF method:

According to lithium ion battery experience degradation model and AR Construction of A Model lithium ion battery state-space model, utilize pretreated data and according to the EKF method, determine the parameter of described lithium ion battery state-space model; The sequence of observations after the prediction output valve of described AR model and observation noise stack is the observed reading of the battery capacity of described lithium ion battery state-space model, and described AR model is to utilize pretreated the data to merge the AR model that the autoregressive coefficient acquiring method is determined;

Step 3: the lithium ion battery state-space model of setting up according to step 2 carries out state estimation to lithium ion battery to be measured, utilize the output of described AR model to carry out the state renewal of lithium ion battery to be measured, described lithium ion battery state-space model obtains the battery capacity data of each charge and discharge cycles, and the failure threshold of described data and lithium ion battery to be measured is relatively obtained to the lithium ion battery residual life.

2. according to claim 1ly based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it is characterized in that, in described step 1, described data carried out to pretreated method and be:

For point unusual in described data, reject, for the excessive capacity orthogenesis of amplitude, carry out the level and smooth of trend.

3. according to claim 1 based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it is characterized in that, in step 2, described according to lithium ion battery experience degradation model and AR Construction of A Model lithium ion battery state-space model, utilize pretreated data and determine that according to the EKF method method of the parameter of described lithium ion battery state-space model comprises the steps:

Steps A: according to lithium ion battery experience degradation model

Construct the state-space model of the parameter estimation of described degradation model:

Wherein

For state transition equation,

For observation equation, a _k, b _kAnd c _kBe respectively the enclosed pasture efficiency eta in current k described experience degradation model of the moment _{C, k}, the regenerated capacity parameter beta _{1, k}With the regenerated capacity parameter beta _{2, k}Estimated value;

C _kFor the discharge capacity constantly of k in the degradation in capacity process of lithium battery to be measured, C _K+1For the discharge capacity constantly of k+1 in the degradation in capacity process of lithium battery to be measured, η _{C, k}For the enclosed pasture efficiency in charging and discharging lithium battery process to be measured;

For lithium battery to be measured at standing time of having a rest section △ t _kThe capacity of interior regeneration; w _a, w _bAnd w _cBe respectively the white Gaussian noise that parameter a, b and c comprise, Q _a, Q _bAnd Q _cBe respectively w _a, w _bAnd w _cVariance, noise w _a, w _bAnd w _cMeet respectively N (0, Q _a), N (0, Q _b) and N (0, Q _c) Gaussian distribution; R is real number; v _kFor the observation noise of lithium battery to be measured, v _kThe obedience average is 0, v _kVariance be the Gaussian distribution of R; Step B: utilize pretreated data, employing EKF method is carried out linearization, state estimation and state renewal to the state-space model of the parameter estimation of described degradation model, determines the current k parameter a constantly of described state-space model _k, b _kAnd c _k

Step C: according to the current k parameter a constantly of described state-space model _k, b _kAnd c _k, try to achieve current k constantly under condition estimates of parameters be the probability P of parameter true value, according to described probability P, be weighted on average, try to achieve a_s, b_s and the c_s in the current k moment:

Wherein, N is the length of the capacity data of on-line measurement lithium battery to be measured; M (i) is i the corresponding parameter a of discharge cycles _k, b _kOr c _k, P (i) is the parameter a to i discharge cycles _k, b _kOr c _kThe result of estimating is the probability of the current k parameter actual value constantly of state-space model;

Step D: the a_s that will obtain, b_s and c_s, as the parameter of lithium ion battery state-space model, obtain described lithium ion battery state-space model:

Wherein, w _kFor the process noise of lithium battery to be measured, obeying average is 0, and variance is the Gaussian distribution of Q, and Q is rational number, y _kFor the systematic perspective measured value.

4. according to claim 1 based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it is characterized in that, in described step 2, utilize the method that pretreated the data merges the definite AR model of autoregressive coefficient acquiring method to comprise the steps:

Step e:

Utilize pretreated data and ask for the AR model according to AIC criterion

Model order p;

Step F: utilize pretreated data, ask for respectively the autoregressive coefficient of described AR model according to Yulle-Wallker method and Burg method, the final autoregressive coefficient of method output that adopts dynamic linears to merge two autoregressive coefficients of trying to achieve

Step G: according to the model order p of step e acquisition and the final autoregressive coefficient of step F acquisition

Determine the AR model.

5. according to claim 3 based on EKF method and AR model pattern of fusion cycle life of lithium ion battery Forecasting Methodology, it is characterized in that, in described step B: utilize pretreated data, employing EKF method is carried out linearization, state estimation and state renewal to the state-space model of the parameter estimation of described degradation model, determines the current K parameter a constantly of described state-space model _k, b _kAnd c _kMethod be:

Step B1: the state-space model to the parameter estimation of described degradation model carries out linearization:

State transition equation input state transition matrix F to the state-space model of the parameter estimation of described degradation model _kDescribed F _kFor:

To the observation equation of the state-space model of the parameter estimation of described degradation model, carry out the Taylor expansion and utilize the one exponent part to carry out the linearization of nonlinear equation approximate, obtain the matrix H of the observation equation after linearization _k:

Step B2: the current K parameter constantly of the state-space model of the parameter estimation of the described degradation model after adopting kalman filter method to linearization is carried out state estimation and renewal:

By the state transition equation after linearization, the current K parameter constantly of described model is estimated, is obtained the estimated value of current k parameter constantly:

[a _k ^-,b ^k-,c _k ^-]=[a _k-1 ⁺,b _k-1 ⁺,c _k-1 ⁺]

Wherein, a _k ^-, b _k ^-And c _k ^-Represent respectively k parameter a constantly _k, b _kAnd c _kEstimated value, a _K-1 ⁺, b _K-1 ⁺And c _K-1 ⁺Represent respectively k-1 parameter a constantly _k, b _kAnd c _kThe renewal value,

For the k estimated value of the state covariance matrix of lithium battery to be measured constantly,

For the k-1 renewal value of the state covariance matrix of lithium battery to be measured constantly, W _kFor the process noise matrix of coefficients of lithium battery to be measured, Q _kVariance for described process noise;

The estimated value of described current k parameter constantly is brought in the observation equation of state-space model of parameter estimation of degradation model, obtains the estimated value of battery capacity observed reading:

The observed reading true value of the estimated value of described battery capacity observed reading and battery capacity is compared and obtains measuring remaining poor covariance

And obtain the optimum kalman gain that described estimated value is proofreaied and correct

Utilize formula And formula Estimated value to the current K parameter constantly of state-space model carries out upgrading based on the state under the minimum variance principle, obtains the current K parameter a constantly of described state-space model surely _k, b _kAnd c _k,

Wherein,

Be based on the discharge capacity in k the cycle that estimated parameter calculates, C _K-1For the discharge capacity in k-1 cycle of on-line measurement lithium battery to be measured, S _kTo measure remaining poor covariance matrix, H _kFor the observing matrix of lithium battery to be measured,

For the k renewal value of the state covariance matrix of lithium battery to be measured constantly, V _kFor the observation noise matrix of coefficients of lithium battery to be measured, R _kFor the variance of the observation noise of lithium battery to be measured, a _k ⁺, b _k ⁺And c _k ⁺Represent respectively k parameter a constantly _k, b _kAnd c _kThe renewal value, I is unit matrix.

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