CN104778337B - Method for predicting remaining service life of lithium battery based on FPCA (functional principal component analysis) and Bayesian updating - Google Patents

Abstract

The invention discloses a method for predicting remaining service life of a lithium battery based on FPCA (functional principal component analysis) and Bayesian updating. The method comprises the following steps of utilizing FPCA to build a lithium battery non-parameter degrading model, predicting the remaining service life of the lithium battery based on the degrading model, and analyzing the influence of different amount of modeling data on the predicting accuracy. The method has the advantages that an empirical Bayesian method is provided for updating the lithium battery degrading model in real time; the lithium battery degrading model is corrected in real time by the Bayesian method, so as to obtain the more accurate lithium battery degrading model; the distributing of the remaining service life of the lithium battery is calculated by a parameter bootstrap method, and the confidence interval is calculated.

Description

A kind of lithium battery residual life based on function type principal component analysiss and Bayesian updating Forecasting Methodology

Technical field

The present invention relates to the technical field of lithium battery predicting residual useful life, and in particular to a kind of based on function type main constituent point Analysis and the lithium battery method for predicting residual useful life of Bayesian updating.

Background technology

With the development of lithium ion battery, the research about lithium ion battery biometry originates in the eighties in 20th century. Effectively battery life predicting can not only predict potential risks, so as to provide effectively guidance for using for battery, and The associated loss that battery failure causes can be reduced.

Have many methods at present with regard to battery life predicting, wherein be all based on mostly model and based on data-driven Forecasting Methodology.The existing life-span prediction method based on model can be divided into the method based on electrochemical model, based on equivalent electric The method on road, the method based on performance and the method based on analytical model.Electrochemical model is theoretical based on porous electrode and receives What meter Li Xue set up, the model describe the physical deformation of battery polarization process and inside battery specific components.Equivalent circuit mould Type Jing is modeled to battery frequently with equivalent circuit, and estimates model parameter using many technologies.Electrochemical model and equivalent Circuit model has good effect in some specific cases, however, due to reasons such as technology, design and materials, these Model applicability is poor.Based on the relation that the model of performance needs to set up between degeneration factor and battery performance, however, it is contemplated that Influencing each other between many environmental variables, the relation between degeneration factor and battery performance are needed by under different operating situation Battery simulation can just obtain with a large amount of accelerated life tests.Analytical model can pass through particle filter, Unscented Kalman Filter Set up etc. method.When model is set up it is accurate when, the model accurately can be predicted the outcome.However, accurate model parameter Often it is difficult to obtain.These four battery models are compared, the elder generation of any cell degradation mechanism is not needed based on the method for data-driven Test knowledge and physical chemistry equation.This model applicability is strong, it is possible to realize real-time biometry.In recent years, it is based on The battery life predicting method of data-driven is extensively paid close attention to by researcher.Many service life of lithium battery Forecasting Methodologies based on data-driven It is suggested.However, the service life of lithium battery Forecasting Methodology for being mostly based on data-driven at present needs to carry out feature to battery data Extract, and inappropriate Feature Selection may appreciable impact battery life predicting precision.Meanwhile, big multi-method can only be given The point estimation of battery life, it is impossible to provide its confidence interval and residual life distribution when battery capacity reaches failure threshold.

The content of the invention

The present invention proposes a kind of based on function type principal component analysiss (Functional Principal Component Analysis, FPCA) with the service life of lithium battery Forecasting Methodology of Bayesian updating.The life-span prediction method need not extract any battery Degenerative character, not only can realize service life of lithium battery point estimation, and can provide the residual life distribution of battery.FPCA is one The statistical method of functional data analysis is planted, the most prominent features being hidden in initial data can be captured.Meanwhile, numerous studies Show, when data set is considered continuous function, the information provided by FPCA methods is carried than traditional discrete data analytic process For information it is more valuable.Therefore, the present invention sets up the nonparametric degradation model of battery using FPCA methods.Additionally, for reality The real-time update of existing lithium battery degradation model, invention introduces bayes method, is degenerated to lithium battery by bayes method Model is corrected in real time, can obtain more accurate lithium battery degradation model.On here basis, using parameter Bootstrap methods, realize the distribution of lithium battery residual life and the calculating of confidence interval.

The technical solution used in the present invention is：A kind of lithium battery based on function type principal component analysiss with Bayesian updating is remained Remaining life-span prediction method, the method step are as follows：

Step one, using function type principal component analysiss (functional principal component analysis, FPCA lithium battery nonparametric degradation model is built), lithium battery residual life is predicted based on this degradation model, and is analyzed Impact of the modeling data of varying number to precision of prediction；

Step 2, the real-time update in order to realize lithium battery nonparametric degradation model, by bayes method to lithium battery Degradation model is corrected in real time, can obtain more accurate lithium battery degradation model；

Step 3, the distribution of lithium battery residual life is calculated using parameter bootstrap method, and calculate its confidence interval.

Further, in step one, it is essentially non-ginseng based on the lithium ion battery Life Prediction Model of FPCA Exponential model, utilizes the field data of the degraded data and prediction object of known same type sample during prediction, is moved back Change model training, and the biometry of lithium battery is realized based on the degradation model for establishing, detailed process is as follows：

(1) assume that prediction starting point is t₀, identifying object is in moment t₀All capacity datas in the past are The capacity data of same type other lithium batteries isTwo parts data are combined, for setting up nonparametric degeneration Model；

(2) data set in conjunction with after, sets up nonparametric degradation model using FPCA methods, and estimates mean value function u (t), principal component scores ξ_ikAnd weighting function φ_k(t_ij)；

(3) according to the degradation model set up, the time serieses in future are providedThe capacity of its corresponding time point ValueIt is expected that such as moment t_l,d, the capability value S at the moment_l(t_l,d) can be estimated as follows：

Further, in step 2, the real-time update of degradation model is realized using bayes method, it is assumed that in moment t= {t₁,t₂,…,t_mObtain new observation, t_mIt it is the observation termination time, it is assumed that the prior distribution of principal component scores is normal state Distribution, mean value function u (t) and characteristic function φ_k(t), k=1,2 ..., K is all fixed, it is assumed that lithium battery degradation model isPrior distribution ξ_ikObey ξ_ik～N (0, λ_k), wherein ξ₁,ξ₂,...,ξ_KIt is uncorrelated, ε (t) clothes From ε (t)～N (0, σ²), wherein σ²It is fixed, then the Posterior distrbutionp of principal component scores can be calculated as follows：

WhereinAnd

S (t)=(S (t₁),S(t₂),…,S(t_m)) ', u (t)=(u (t₁),u(t₂),…,u(t_m)) ',

Λ=diag (λ₁,λ₂,…,λ_K),

Using eigenvalue λ_k, k=1,2 ..., K, principal component scores can be calculated and be distributed, and eigenvalue λ_kK=1,2 ..., K and characteristic vector φ_k, k=1,2 ..., K can be obtained by carrying out FPCA to history degeneration degradation in capacity data, therefore, update Principal component scoresK=1,2 ..., K its Posterior distrbutionp can pass through Matrix C and characteristic vector d is obtained, meanwhile, renewal Mean value function can be expressed as：

Further, in step 3, on the basis of degradation model Posterior distrbutionp updates, using parameter bootstrap side Method, calculates battery in t preset time^*RLD, and calculate confidence level be α confidence interval, the estimation procedure of confidence interval is such as Under：

(1) sampled from the function type principal component scores normal distribution for updating

(2) each value for b, obtains an analogue signal as follows：

(3) take T_b=inf_t∈[0,T]{S_b(t)≤D}

By obtaining sample value T₁,T₂,...,T_B, the RLD of lithium battery, remaining battery of the confidence interval for 1- α can be obtained Life-span can be drawn by below equation：

P(L≤T′-t^*≤U|S^*(·),T′≥t^*)=1- α

Calculating in view of L and U is relatively difficult, using an approximate 1- α confidence intervalTo be estimated, its Inα/2 and quantile sampled value T of (1- α)/2₁,T₂,...,T_BCalculated.

Advantages of the present invention with good effect is：

(1) the inventive method regards battery capacity data as continuous function with regard to cycle-index, and adopts function type number Lithium battery capacity data are analyzed according to the method for analysis, can be extracted more compared to traditional discrete data analysis method Many information, the cell degradation model set up are more accurate；

(2) the inventive method is without the need for carrying out feature extraction to lithium battery data, it is to avoid inappropriate Feature Selection is to electricity The impact that pond life prediction precision is caused；

(3) the inventive method fully combines the degradation information and individual specimen degradation information of population sample, is set up Degradation model has the higher suitability；

(4) the inventive method need not be predicted the complicated degradation mechanism of battery and set up accurate mathematical model；

(5) the inventive method not only can provide the point estimation of lithium battery residual life, while can provide lithium battery remaining Remaining life-span distribution and confidence interval；

Description of the drawings

Fig. 1 is the degradation in capacity curve of 4 lithium batteries；

Fig. 2 is the equal function and characteristic function schematic diagram estimated with non-parametric estmation method, wherein, it is the equal of estimation to scheme (a) FunctionFigure (b) is the characteristic function φ for estimating₁(t)；Figure (c) is the characteristic function φ for estimating₂(t)；

Fig. 3 is battery #5, the actual measured value of #6, #7 and reconstruct datagram, wherein, it is (a) the actual measurement of battery #5 Value and reconstruct datagram, (b) be battery #6 actual measured value and reconstruct datagram, (c) for battery #7 actual measured value and Reconstruct datagram；

Fig. 4 predicts the outcome schematic diagram for the capacity of battery #18；

Fig. 5 predicts the outcome schematic diagram for the capacity of battery #5；

Fig. 6 predicts the outcome schematic diagram for the capacity of battery #6；

Fig. 7 is the schematic diagram that predicts the outcome of battery #5 when field data amount is different, wherein, figure (a) field data is the 1st～ 30 circulation volume data, figure (b) field data are the 1st～60 circulation volume data, and figure (c) field data is that 1～90 circulation is held Amount data, figure (d) field data are 1～120 circulation volume data；

Fig. 8 is the asynchronous battery predictive RMSE of field data and prediction error value, wherein, figure (a) is battery predictive RMSE value, figure (b) is battery predictive error amount；

Fig. 9 be cell degradation model the 100th cycle, the 110th cycle, the 120th cycle be updated the RLD values of prediction and Empirical cumulative distribution function schematic diagram, wherein, figure (a), figure (b) are respectively cell degradation model and are updated in the 100th cycle The RLD values of prediction and empirical cumulative distribution function, figure (c), figure (d) are respectively cell degradation model and carry out more in the 110th cycle The RLD values and empirical cumulative distribution function of new prediction, figure (e), figure (f) are respectively cell degradation model and carry out in the 120th cycle Update the RLD values and empirical cumulative distribution function of prediction；

Figure 10 is the estimation normal density function schematic diagram of different prediction starting points.

Figure 11 is a kind of lithium battery method for predicting residual useful life based on function type principal component analysiss and Bayesian updating Flow chart schematic diagram.

Specific embodiment

Below in conjunction with the accompanying drawings and specific embodiment further illustrates the present invention.

1. what the present invention was provided is a kind of pre- with the lithium battery residual life of Bayesian updating based on function type principal component analysiss Survey method, comprises the following steps that：

The 1.1 lithium ion battery degradation models based on FPCA

1.1.1 degradation in capacity model

Performance of lithium ion battery declines process and can be considered a potential stochastic process.Meanwhile, the life cycle of battery can Regard the function with regard to the time as.The life-span that lithium battery degradation model is set up to realize battery first with existing capacity data is pre- Survey.As function type principal component analysiss (FPCA) are the extensions of traditional principal component analysiss (PCA), can provide and more stable estimate Evaluation simultaneously avoids introducing higher-dimension covariance matrix, meanwhile, the different pieces of information collection for giving process, FPCA can be extracted comprising him Common trait more information.Therefore the present invention builds lithium battery degradation model using FPCA.

Make S_i(t_ij) it is capacity observation of i-th piece of battery in the time, tij is the cycle period of i-th piece of battery.Consider The observation error of observation, S_i(t_ij) can express with the following methods：

S_i(t_ij)=X_i(t_ij)+ε_ij(t),0≤t_ij≤T；J=1,2 ..., m_i

X_ijIt is primary signal, u (t) is mean value function, cov (X (s), X (t))=G (s, t) is covariance function, and T is for most Long out-of-service time, m_iFor the points of measurement of i-th piece of battery.Assume ε_ijFor independent identically distributed random error, standard normal is obeyed Distribution N (0, σ²).G (s, t) can be according to characteristic vector φ_kAnd eigenvalue λ_kExpress according to below equation：

G (s, t)=∑ λ_kφ_k(s)φ_k(t),0≤s,t≤T

In classical FPCA methods, it will be assumed that i-th curve X_i(t_ij) can describe according to equation below：

X_i(t_ij)=u (t_ij)+∑ξ_ikφ_k(t_ij)

Wherein u (t_ij) for smooth function, φ_k(t_ij) for k-th characteristic function.ξ_ikFor principal component scores, and have following Property：

E[ξ_ik]=0；

In actual applications, K main constituent before Jing is often selected represents X_i(t_ij).Therefore X_i(t_ij) can be expressed as：

Therefore, the degradation model of lithium ion battery can be expressed as：

1.1.2 the non-parametric estmation of lithium ion degradation model

Most of remaining battery life forecast models are all parameter models, need to assume its parametric form.At this In modeling method, it is assumed that mean value function u (t) and covariance function cov (X (s), X (t)) are non-parameterized, i.e., we are to which Parametric form does not do any hypothesis.The main u (t) of this part content and the estimation technique of covariance function cov (X (s), X (t)).

(1) mean value function is estimated

We estimate mean value function u (t using kernel estimates method_ij), estimated using the data after all individual merging Value function u (t_ij), that is, solve following this minimization problem：

WhereinFor kernel function, gaussian kernel function, h are usually chosen to_uRepresent and estimate u (t_ij) selected by window width, Then the estimated value of u (t) is

Wherein：

Kernel function estimation method is relevant with the window width size chosen to the quality of the smooth estimation effect of mean value function, Wo Menke Suitable window width is selected with using the cross validation of leave-out-one-curve.Under normal circumstances, rule of thumb determine Window width size ensures that preferable effect.

(2) estimation of covariance function

Assume covariance function C_X(s, t)=cov (X (s), X (t))=G (s, t), 0≤s, t≤T.Notice cov (S_ij, S_il|T_ij,T_il)=cov (X (T_ij),X(T_il))+δ_jlσ², the δ if j=l_jl=1, on the contrary δ_jl=0.OrderThen E [G_i(T_ij,T_il)|T_ij,T_il]≈cov(X(T_ij),X(T_il))+δ_jlσ².Only As j ≠ l, G_i(T_ij,T_il) can just be used to estimate covariance function.As s ≠ t, G (s, t) can be by following minimum Problem is obtained：

WhereinRepresent certain binary kernel function, h_GRepresent the window width used by estimation G (s, t).Therefore, it is right In s ≠ t, the estimated value of G (s, t) is：

Wherein：

Equally, window width h_GDesired value can be selected using the cross validation of leave-out-one-curve, to obtain more preferably Estimation effect.

Method above is estimated in the case of s ≠ t to covariance function.Because covariance function is in diagonal Side reaches up to maximum, and is used up the approximate shapes that local secondary fitting goes out than local linear fitting in Vertical Diagonal line side It is better, so adopting local linear fitting in the diagonal directions, Vertical Diagonal line direction uses quadratic fit.Note concrete When implementing fitting, coordinate axess need to be turned clockwise π/4, then solve minimization problem again：

Wherein：

So obtain：

Obviously nowInformation not comprising random error, G_i(T_ij,T_il) as initial data, using local linear Fitting, obtainsObviouslyCovariance function G (t, t), the also variances sigma comprising random error are included not only², can be with ByTo obtain variances sigma²Estimation.In order to eliminate boundary effect, we remove two end points in interval.Order | T |=T, T₁=[inf { x:x∈T}+|T|/4,sup{x:X ∈ T }-| T |/4], then

For eigenfunctionAnd characteristic rootWe are by solving characteristic equation：

WhereinAndWe first willDiscretization, then with polynary point The method of analysis is obtained

1.2 capacity based on degradation model are predicted

Lithium ion battery Life Prediction Model based on FPCA is essentially nonparametric model, during prediction Using the field data of the degraded data and prediction object of known same type sample, degradation model training is carried out, process is as follows：

(1) assume that prediction starting point is t₀, identifying object is in moment t₀All capacity datas in the past are The capacity data of same type other lithium batteries isTwo parts data are combined, for setting up nonparametric degeneration Model.

(2) data set in conjunction with after, sets up nonparametric degradation model using FPCA methods, and estimates mean value function u (t), principal component scores ξ_ikAnd weighting function φ_k(t_ij)。

(3) according to the degradation model set up, the time serieses in future are providedThe capacity of its corresponding time point ValueCan predict.Such as moment t_l,d, the capability value S at the moment_l(t_l,d) can be estimated as follows：

1.3 residual lifes based on Bayesian updating are estimated

1.3.1 degradation model updates

In order to realize the real-time update of degradation model, the present invention proposes bayes method.Assume in moment t={ t₁, t₂,…,t_mObtain new observation, t_mIt is the observation termination time.We assume that the prior distribution of principal component scores is normal state Distribution, mean value function u (t) and characteristic function φ_k(t), k=1,2 ..., K is all fixed.Assume that lithium battery degradation model isPrior distribution ξ_ikObey ξ_ik～N (0, λ_k), wherein ξ₁,ξ₂,...,ξ_KIt is uncorrelated, ε (t) clothes From ε (t)～N (0, σ²), wherein σ²It is fixed.So the Posterior distrbutionp of principal component scores can be calculated as follows：

WhereinAnd

S (t)=(S (t₁),S(t₂),…,S(t_m)) ', u (t)=(u (t₁),u(t₂),…,u(t_m)) ',

Λ=diag (λ₁,λ₂,…,λ_K),

Using eigenvalue λ_k, k=1,2 ..., K, principal component scores can be calculated and be distributed, and eigenvalue λ_kK=1,2 ..., K and characteristic vector φ_k, k=1,2 ..., K can be obtained by carrying out FPCA to history degeneration degradation in capacity data.Therefore, update Principal component scoresK=1,2 ..., K its Posterior distrbutionp can pass through Matrix C and characteristic vector d is obtained.Meanwhile, renewal Mean value function can be expressed as：

1.3.2 residual life distribution estimating

Most of service life of lithium battery Forecasting Methodologies are only capable of providing a point estimation.However, lithium battery in actual applications RLD is even more important.This part content of the invention is on the basis of the renewal of degradation model Posterior distrbutionp, it is proposed that one is based on parameter Bootstrap methods, calculate battery in t preset time^*RLD, and calculate confidence level be α confidence interval.Confidence interval Estimation procedure is as follows：

(1) sampled from the function type principal component scores normal distribution for updating

(2) each value for b, obtains an analogue signal as follows：

(3) take T_b=inf_t∈[0,T]{S_b(t)≤D}

By obtaining sample value T₁,T₂,...,T_B, the RLD of lithium battery, remaining battery of the confidence interval for 1- α can be obtained Life-span can be drawn by below equation：

P(L≤T′-t^*≤U|S^*(·),T′≥t^*)=1- α

Calculating in view of L and U is relatively difficult, and we adopt an approximate 1- α confidence intervalTo be estimated Meter, whereinα/2 and quantile sampled value T of (1- α)/2₁,T₂,...,T_BCalculated.

2. analysis of cases

The description of 2.1 NASA li-ion battery experiment data

Lithium ion battery Life Cycle experimental data of this research using NASA PCoE research centers.This research selects electricity Pond #5, #6, #7 and #18 verify the effectiveness of the method.Such as table 1, AT, CC, DC, EOD and EOLC represent ambient temperature respectively, fill Electric current, discharge current, final discharging voltage, discharge off criterion.

Lithium ion battery, continues straight with constant-voltage charge first with 1.5A constant-current charges after cell voltage reaches 4.2V 20mA is dropped to charging current.Discharge regime lithium battery tests stopping when cell voltage reaches EOD with 2A constant-current discharges. In the experiment, EOLC refers to battery maximum charge electricity (MCC) and drops to the 70% of rated capacity.Therefore, lithium battery failure valve Value is 1.38Ah.Fig. 1 shows the degradation in capacity curve of 4 lithium ion batteries.In view of battery #7 capacity always greater than pre- If fault threshold 1.38Ah, therefore battery #7 is not adopted in subsequent authentication as identifying object.

Typical data under 1 different operating modes of table

2.2 nonparametric degradation models

We using battery #18 as identifying object, and assume battery #18 field data be it is front 70 circulation capacity numbers According to.Then, we utilize battery #5, the field data of all told degraded data and battery #18 of #6, #7 to build nonparametric and move back Change model, and model parameter is estimated with non-parametric estmation method.Estimated equal function is as shown in Figure 2 with characteristic function.

In order to verify the accuracy of lithium battery degradation model, using the equal function estimatedPrincipal component scores { ξ₁,ξ₂}、 Characteristic function φ₁(t)、φ₂T () reconstructs cell degradation data, and the accuracy of degradation model is verified with root-mean-square error.Fig. 3 shows Battery #5, actual capacity curve and the reconstruct curve of #6, #7 are shown.Corresponding battery reconstruct RMSE value is given in table 2.From table In as can be seen that RMSE value all very littles, this also demonstrates the high degree of accuracy of nonparametric degradation model.

2 battery #5 of table, #6, #7 reconstruct RMSE

2.3 capacity based on degradation model are predicted

After nonparametric degradation model is set up, battery #18 is chosen as identifying object, predict the maximum of its future circulation Charge capacity and confidence interval.Fig. 4 predicts the outcome for battery #18's, and confidence level is 1- α=0.95.

Equally, using battery #5 and battery #6 as identifying object.Field data is assumed to be the appearance of front 70 circulations of battery Amount data.The degradation model of battery is built using all energy datums of identifying object field data and other batteries.Fig. 5 and Tu 6 predict the outcome for capacity, and confidence interval is 0.5 to 0.95.

The 2.4 service life of lithium battery predictions based on given failure threshold values

Based on estimated lithium battery maximum discharge electricity amount value, failure threshold is given, the remaining use of lithium battery can be obtained Life-span.In our current research, fault threshold is 1.38Ah, i.e. the 70% of rated capacity.Meanwhile, service life of lithium battery confidence interval is set to 1- α=0.95.The 1st～10 circulation, the 1st～110 circulation of the 1st～20 circulation ..., the capacity of the 1st～120 circulation is respectively adopted Degraded data is predicted to service life of lithium battery as field data, to verify the field data of varying number to cell degradation mould The impact of type accuracy.This research is using battery #5 as identifying object.Fig. 7 show using battery #5 the 1st～30, the 1st～ Capacity data the predicting the outcome as field data of the 60, the 1st～90, the 1st～120 circulation.Battery capacity RMSE value and prediction Error is used for the accuracy for estimating this institute extracting method, as shown in table 3 and Fig. 8.

When 3 field data amount of table is different, battery #5's predicts the outcome

As shown in table 3 and Fig. 8, with the growth of field data quantity, the RMSE value of capacity data shows becoming for decline Gesture, bimetry are become closer in actual life, can make nonparametric degeneration mould using more field data training patterns Type has higher accuracy.From table 3 it is observed that optimal bimetry result is the 133rd circulation, minimum forecast error Circulate for 6.

2.5 RLD based on Bayesian updating are calculated

This part content realizes lithium battery degradation model real-time update using empirical Bayes method, and uses bootstrap Method calculates the residual life distribution of lithium ion battery and confidence interval.The contents of the section is still right as verifying using battery #5 As.The field data of hypothesis battery #5 is the capacity data in front 80 cycles, with field data and the degradation in capacity of other batteries Data set up cell degradation model.The sampling number of Bootstrap methods is set to B=1000.Whenever the new capacity data of acquisition, Just the parameter in cell degradation model is updated, so as to obtain the lithium battery residual life for updating distribution.From the 81st to 120 circulations, often measure a new data and just perform and once update, and total carries out 40 times.Fig. 9 shows cell degradation model 100th, the residual life distribution and corresponding empirical cumulative distribution function (CDF) obtained by 110,120 circulations are updated, in figure Curve is the normal density function estimated.For the ease of comparing, three curves are put in a figure, as shown in Figure 10.

4 predicting the outcome based on Bayesian updating of table

Can be seen that with the rear shifting for updating time point from Fig. 9 and Figure 10, the center of RLD becomes closer to actual electricity The pond life-span.Meanwhile, the distributed area on time shafts becomes narrow, and peak value is uprised, and is indicated the uncertainty for predicting the outcome and is diminished, accurate Exactness is improved, this is because as the data for Bayesian updating increase, degradation model contains more individual informations, because This can obtain more accurately forecast model.

Claims (3)

1. a kind of lithium battery method for predicting residual useful life based on function type principal component analysiss and Bayesian updating, its feature exist In：The method step is as follows：

Step one, using function type principal component analysiss (functional principal component analysis, FPCA) Lithium battery nonparametric degradation model is built, lithium battery residual life is predicted based on this degradation model, and is analyzed difference Impact of the modeling data of quantity to precision of prediction；

Step 2, the real-time update in order to realize lithium battery nonparametric degradation model, are degenerated to lithium battery by bayes method Model is corrected in real time, can obtain more accurate lithium battery degradation model；

Step 3, lithium battery residual life distribution (distribution of the are calculated using parameter bootstrap method Remaining lifetime, RLD), and calculate its confidence interval；

In step one, it is essentially nonparametric based on the lithium ion battery Life Prediction Model of function type principal component analysiss Model, utilizes the field data of the degraded data and prediction object of known same type sample during prediction, enters row degradation Model training, and the biometry of lithium battery is realized based on the degradation model for establishing, detailed process is as follows：

(1) assume that prediction starting point is t₀, identifying object is in moment t₀All capacity datas in the past areIt is similar The capacity data of type other lithium batteries isTwo parts data are combined, for setting up nonparametric degradation model；

(2) data set in conjunction with after, sets up nonparametric degradation model using function type principal component analytical method, and estimates equal Value function u (t), principal component scores ξ_ikAnd characteristic function φ_k(t)；

(3) according to the degradation model set up, the time serieses in future are providedThe capability value of its corresponding time pointIt is expected that for moment t_l,d, the capability value S at the moment_l(t_l,d) can be estimated as follows：

$E\[S_l\left(t_{l,d}\right)\]=\hat{u}\left(t_{l,d}\right)+\underset{k=1}{\overset{K}{\Σ}}{\widehat{\mathrm{\ξ}}}_k*\widehat{\mathrm{\φ}}\left(t_{l,d}\right).$

2. a kind of lithium battery residual life based on function type principal component analysiss and Bayesian updating according to claim 1 Forecasting Methodology, it is characterised in that：In step 2, the real-time update of degradation model is realized using bayes method, it is assumed that in moment t ={ t₁,t₂,…,t_mObtain new observation, t_mIt it is the observation termination time, it is assumed that the prior distribution of principal component scores is for just State distribution, mean value function u (t) and characteristic function φ_k(t), k=1,2 ..., K is all fixed, it is assumed that lithium battery degradation model ForPrior distribution ξ_ikObey ξ_ik～N (0, λ_k), wherein ξ₁,ξ₂,...,ξ_KIt is uncorrelated, ε (t) Obey ε (t)～N (0, σ²), wherein σ²It is fixed, then the Posterior distrbutionp of principal component scores can be calculated as follows：

${({\mathrm{\ξ}}_{i1}^{*},{\mathrm{\ξ}}_{i2}^{*},\·\·\·,{\mathrm{\ξ}}_{\mathrm{iK}}^{*})}^{\′}~N(\mathrm{Cd},C),$

WhereinAnd

S (t)=(S (t₁),S(t₂),…,S(t_m)) ', u (t)=(u (t₁),u(t₂),…,u(t_m)) ',

Λ=diag (λ₁,λ₂,…,λ_K),

Using eigenvalue λ_k, k=1,2 ..., K, principal component scores can be calculated and be distributed, and eigenvalue λ_k, k=1,2 ..., K and Characteristic function φ_k, k=1,2 ..., K can be obtained by carrying out FPCA to history degeneration degradation in capacity data, therefore, renewal Principal component scoresK=1,2 ..., K its Posterior distrbutionp can pass through Matrix C and characteristic vector d and obtain, meanwhile, renewal it is equal Value function can be expressed as：

$u^{*}\left(t\right)=u\left(t\right)+\underset{k=1}{\overset{K}{\Σ}}E\[{\mathrm{\ξ}}_k^{*}\]\×{\mathrm{\φ}}_k\left(t\right).$

3. a kind of lithium battery residual life based on function type principal component analysiss and Bayesian updating according to claim 2 Forecasting Methodology, it is characterised in that：In step 3, on the basis of degradation model Posterior distrbutionp updates, using parameter bootstrap Method, calculates residual life distribution of the battery in t* preset time, and calculates the confidence interval that confidence level is α, confidence interval Estimation procedure is as follows：

(1) sampled from the function type principal component scores normal distribution for updating

(2) each value for b, obtains an analogue signal as follows：

$S_b=u\left(t\right)+\underset{k=1}{\overset{K}{\Σ}}{\mathrm{\ξ}}_k^b{\mathrm{\φ}}_k\left(t\right),k=1,...,K$

(3) take T_b=inf_t∈[0,T]{S_b(t)≤D}

By obtaining sample value T₁,T₂,...,T_B, the residual life distribution of lithium battery, electricity of the confidence interval for 1- α can be obtained Pond residual life can be drawn by below equation：

P(L≤T′-t^*≤U|S^*(·),T′≥t^*)=1- α

Calculating in view of L and U is relatively difficult, using an approximate 1- α confidence intervalTo be estimated, whereinα/2 and quantile sampled value T of (1- α)/2₁,T₂,...,T_BCalculated.