CN102968573A - Online lithium ion battery residual life predicting method based on relevance vector regression - Google Patents

Online lithium ion battery residual life predicting method based on relevance vector regression Download PDF

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Publication number
CN102968573A
CN102968573A CN2012105437010A CN201210543701A CN102968573A CN 102968573 A CN102968573 A CN 102968573A CN 2012105437010 A CN2012105437010 A CN 2012105437010A CN 201210543701 A CN201210543701 A CN 201210543701A CN 102968573 A CN102968573 A CN 102968573A
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new
rvm
prediction
lithium ion
ion battery
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周建宝
刘大同
马云彤
彭宇
彭喜元
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

The invention discloses an online lithium ion battery residual life predicting method based on relevance vector regression, belongs to the technical field of lithium ion battery life prediction, and solves the problem that the residual life of the existing lithium ion battery is predicted by an offline method with low precision. The method comprises the following steps: firstly selecting original samples, performing phase-space reconstruction to construct a training sample set; initializing the model parameters of RVM (relevance vector machine); performing RVM training to obtain a RVM prediction model; comparing the obtained prediction value with ynew, if yes, the constructed novel training set WS equal to WSUINS, retraining RVM, and updating the RVM prediction model; otherwise, keeping the RVM prediction model stable; performing recurrence prediction until the prediction value is smaller than the invalid threshold value U, and finishing the online prediction of the residual life of the predicted lithium ion battery. The method is suitable for prediction of the lithium ion battery residual life.

Description

The method of the on-line prediction lithium ion battery residual life that returns based on associated vector
Technical field
The present invention relates to a kind of method of the on-line prediction lithium ion battery residual life that returns based on associated vector, belong to lithium ion battery forecasting technique in life span field.
Background technology
Lithium ion battery with its superior performance be applied to we the life in every field, expanded to gradually at present the fields such as Aeronautics and Astronautics, such as satellite in orbit, space station etc.Along with the carrying out of charge and discharge cycles, lithium ion battery internal resistance increases, and the life-span reduces.Use for the inaccessible space of the mankind, the fault of lithium ion battery or the lost of life usually cause critical failure, lost efficacy such as U.S. Mars Global Surveyor aircraft, exactly because battery failures causes a series of mistakes of computer system, cause battery system to be faced directly and shine upon to cause the overheated mission failure that causes security system to lose efficacy and cause.As seen, the lithium ion battery predicting residual useful life is very important, the lithium ion battery used of space particularly, and its residual life on-line prediction is even more important.
At present, method for predicting residual useful life can be divided into based on model and data-driven two classes.Model-based methods is set up the battery equivalent-circuit model from the electrochemical reaction of inside battery, and precision of prediction relies on the accuracy of model, and practical application is difficult to accurately set up battery model.Data-driven method mainly comprises neural network, support vector machine, particle filter method and Method Using Relevance Vector Machine method.Neural net prediction method does not need the mathematical model of the system that sets up and has extremely strong non-linear mapping capability, but when training needs the mass data sample.Support vector machine method has clear superiority for small sample, nonlinear problem, has been widely used in the prediction field, but its major defect is to provide the single-point predicted value.Particle filter method is the prediction of probabilistic type, and present research is more, and its major defect is to rely on empirical model to set up state transition equation.With the similar Method Using Relevance Vector Machine of support vector machine (Relevance Vector Machine, RVM) be the algorithm model of the sparse Bayesian theories of learning of the Based on Probability study that proposed by U.S. doctor Tipping 2000.Based on the Method Using Relevance Vector Machine of kernel function, not only can reflect the probabilistic information of Output rusults, and have the advantage that strong, the fixing super parameter of generalization ability, learning algorithm are simple and easy to realize, begun for the prediction field.Its major advantage be provide can also prediction of output result when predicting the outcome fiducial interval, this has more directive significance for the user.
At present, be off-line method mostly for the various Forecasting Methodologies of lithium ion battery residual life, i.e. an off-line forecast model setting up of per sample historical data.Off-line model no longer upgrades once just setting up, but when using online because its load behavior acute variation, the forecast model adaptability of off-line is relatively poor, precision of prediction is lower.
At present, the lithium ion battery method for predicting residual useful life that returns based on associated vector does not still have effective on-line prediction strategy to realize online, fast prediction.
Summary of the invention
The present invention adopts off-line method prediction residual life in order to solve existing lithium ion battery, and the problem that precision of prediction is low provides a kind of method of the on-line prediction lithium ion battery residual life that returns based on associated vector.
The method of the on-line prediction lithium ion battery residual life that returns based on associated vector of the present invention, it may further comprise the steps:
Step 1: choose capacity of lithium ion battery data I S=(C to be predicted 1, C 2... C n) as original sample, C iBe battery capacity, unit is Ah, i=1, and 2 ..., n, n are positive integer;
Carry out phase space reconfiguration structure training sample set: set and embed dimension l=5, delay d=1, obtain training sample set { (x 1, y 1), (x 2, y 2) ..., (x N-l, y N-l), x wherein j=(C j, C J+1..., C J+l-1), y j=C J+l, j=1,2 ... n-l, wherein x=(x 1, x 2..., x N-l) be Method Using Relevance Vector Machine RVM mode input data, y=(y 1, y 2..., y N-l) be the output data of Method Using Relevance Vector Machine RVM model;
Step 2: initialization Method Using Relevance Vector Machine RVM model parameter:
The mathematic(al) representation of Method Using Relevance Vector Machine RVM model is y=Φ ω+ε,
ω=(ω wherein 0..., ω N-l) TBe the weights of model,
ε=(ε 1, ε 2... ε N-l) be Gaussian noise, and ε j~N (0, σ 2), σ 2Be the noise variance of RVM model output data y,
Φ is the matrix of n * (n+1), and Φ=[φ 1, φ 2φ N-l] T,
φ j=[1,K(x j,x 1),…,K(x j,x j)…K(x j,x n-1)]
K (x j, x N-1) be kernel function:
K ( x j , x n - l ) = exp ( - | | x j - x n - l | | 2 η 2 ) ,
η is nuclear parameter;
Set nuclear parameter η=3, maximum iteration time iter=1000,
{ α k}=0.1, k=0,1 ... n-l, α kBe weights ω kSuper parameter,
σ 2=var(y)*0.1;
Step 3: RVM training:
Step 3 one: the covariance ∑ and the average μ that calculate ω:
∑=(σ -2Φ TΦ+A) -1,μ=σ -2∑Φ Ty T
Wherein, ∑ is the matrix of (n-l+1) * (n-l+1), and μ is the column vector of (n-l+1) * 1,
μ=(μ 0,μ 1,…,μ n-1) T,A=diag(α 0,α 1,…,α n-l);
Step 3 two: use iteration algorithm to calculate new α kAnd σ 2, be designated as 2) New:
α k new = γ k μ k 2 , ( σ 2 ) new = | | y - Φμ | | n - l - Σ k = 0 n - l γ k ,
γ wherein k=1-α kKk, μ kBe ω kAverage, ∑ KkK diagonal entry for the covariance ∑;
Set iterations parameter L=1;
Step 3 three:
Will 2) NewBring in the formula of step 3 one, repeating step 31 and step 3 two are upgraded μ and ∑, make L=L+1, repeat this step 3 three, until L>and iteration finishes the (σ when iteration finishes during iter 2) NewBe designated as
Step 4: after iteration finishes in the step 3, deletion and ω kX among=0 corresponding x j, residue x jBe called associated vector RVs, all associated vector RVs form associated vector collection IS RV, obtain thus the RVM forecast model y ~ n + h = μ T φ n + h , H is prediction step, and variance is σ n + h 2 = σ MP 2 + ( φ n + h ) T Σ φ n + h , And obtain working set WS, WS=IS RV
Step 5: will increase sample set INS=[x newly New, y New] middle x NewBe input to the RVM forecast model, obtain predicted value Will With y NewCompare, if Then construct new training set WS=WS ∪ INS, again train RVM, upgrade the RVM forecast model; Otherwise keep the RVM forecast model constant;
PEB is the predicated error limit,
y ^ new = μ T φ new , σ new 2 = σ MP 2 + φ new T Σ φ new , σ new 2 Variance for predicted value;
Step 6: repeating step three carries out stepwise predict to step 5, until predicted value less than failure threshold U time prediction finish, thereby realize the on-line prediction of lithium ion battery residual life to be predicted.
Predicated error limit PEB=0.1.
Described failure threshold U=1.38Ah.
Advantage of the present invention is: in the inventive method during on-line prediction, along with the renewal forecast model of sample needs online training to upgrade, and then improve predictablity rate.Also have in the existing on-line prediction method adopt similar in forecasting process the method for new samples more, in having now with class methods, increasing gradually its counting yield and will significantly reduce along with sample size, it needs a large amount of storage spaces, these running environment for on-line prediction are had higher requirement, the running environment that obvious online running environment, particularly space are used is restricting the application of on-line Algorithm.The computation complexity of Method Using Relevance Vector Machine algorithm is O (M 3), storage space is O (M 2), wherein M is the number of basis function, and M=N+1 during initial training, N are the training sample number, and along with training is carried out, M quantity reduces gradually.The online training algorithm of traditional increment type, the original training set of at first online maintenance, along with the renewal of online sample data, the online data collection will increase gradually, and consequently the M value increases gradually, causes storage space and computation complexity to increase.The increment type support vector machine method that the present invention will hang down calculated amount is incorporated into Method Using Relevance Vector Machine, has effectively overcome defects.The increment type Method Using Relevance Vector Machine algorithm (Incremental Optimized Relevance Vector Machine, IP-RVM) of a kind of optimization that the present invention proposes is used for solving online lithium ion battery predicting residual useful life problem.The sample data of IP-RVM algorithm is comprised of associated vector (Relevance vectors, RVs) and new online sample, because Method Using Relevance Vector Machine is very sparse, namely the associated vector number is much smaller than initial sample set, so the M value of online training is very little.Therefore, the speed of on-line prediction is fast, efficient is high, storage space and computation complexity are low, has realized the accurately predicting to the lithium ion battery residual life.
Description of drawings
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is for adopting experimental verification the present invention whether can effectively realize in the process of life prediction of lithium ion battery the degradation in capacity conditional curve figure of four batteries of acquisition; 1 is that the degradation in capacity curve, 2 of Battery#05 is the degradation in capacity curve of Battery#18 for the degradation in capacity curve of Battery#07,4 for the degradation in capacity curve of Battery#06,3 among the figure;
Fig. 3 is Battery#5 battery capacity degenerated curve and the RUL correlation curve figure that predicts the outcome, and the initial time of prediction is 60cycle.
Embodiment
Embodiment one: below in conjunction with Fig. 1 present embodiment is described, the method for the described on-line prediction lithium ion battery residual life that returns based on associated vector of present embodiment, it may further comprise the steps:
Step 1: choose capacity of lithium ion battery data I S=(C to be predicted 1, C 2... C n) as original sample, C iBe battery capacity, unit is Ah, i=1, and 2 ..., n, n are positive integer;
Carry out phase space reconfiguration structure training sample set: set and embed dimension l=5, delay d=1, obtain training sample set { (x 1, y 1), (x 2, y 2) ..., (x N-l, y N-l), x wherein j=(C j, C J+1..., C J+l-1), y j=C J+l, j=1,2 ... n-l, wherein x=(x 1, x 2..., x N-l) be Method Using Relevance Vector Machine RVM mode input data, y=(y 1, y 2..., y N-l) be the output data of Method Using Relevance Vector Machine RVM model;
Step 2: initialization Method Using Relevance Vector Machine RVM model parameter:
The mathematic(al) representation of Method Using Relevance Vector Machine RVM model is y=Φ ω+ε,
ω=(ω wherein 0..., ω N-l) TBe the weights of model,
ε=(ε 1, ε 2... ε N-l) be Gaussian noise, and ε j~N (0, σ 2), σ 2Be the noise variance of RVM model output data y,
Φ is the matrix of n * (n+1), and Φ=[φ 1, φ 2φ N-l] T,
φ j=[1,K(x j,x 1),…,K(x j,x j)…K(x j,x n-l)]
K (x j, x N-l) be kernel function:
K ( x j , x n - l ) = exp ( - | | x j - x n - l | | 2 η 2 ) ,
η is nuclear parameter;
Set nuclear parameter η=3, maximum iteration time iter=1000,
{ α k}=0.1, k=0,1 ... n-l, α kBe weights ω kSuper parameter,
σ 2=var(y)*0.1;
Step 3: RVM training:
Step 3 one: the covariance ∑ and the average μ that calculate ω:
∑=(σ -2Φ TΦ+A) -1,μ=σ -2∑Φ Ty T
Wherein, ∑ is the matrix of (n-l+1) * (n-l+1), and μ is the column vector of (n-l+1) * 1,
μ=(μ 0,μ 1,…,μ n-l) T,A=diag(α 0,α 1,…,α n-l);
Step 3 two: use iteration algorithm to calculate new α kAnd σ 2, be designated as 2) New:
α k new = γ k μ k 2 , ( σ 2 ) new = | | y - Φμ | | n - l - Σ k = 0 n - l γ k ,
γ wherein k=1-α kKk, μ kBe ω kAverage, ∑ KkK diagonal entry for the covariance ∑;
Set iterations parameter L=1;
Step 3 three:
Will 2) NewBring in the formula of step 3 one, repeating step 31 and step 3 two are upgraded μ and ∑, make L=L+1, repeat this step 3 three, until L>and iteration finishes the (σ when iteration finishes during iter 2) NewBe designated as
Step 4: after iteration finishes in the step 3, deletion and ω kX among=0 corresponding x j, residue x jBe called associated vector RVs, all associated vector RVs form associated vector collection IS RV, obtain thus the RVM forecast model y ~ n + h = μ T φ n + h , H is prediction step, and variance is σ n + h 2 = σ MP 2 + ( φ n + h ) T Σ φ n + h , And obtain working set WS, WS=IS RV
Step 5: will increase sample set INS=[x newly New, y New] middle x NewBe input to the RVM forecast model, obtain predicted value Will With y NewCompare, if Then construct new training set WS=WS ∪ INS, again train RVM, upgrade the RVM forecast model; Otherwise keep the RVM forecast model constant;
PEB is the predicated error limit,
y ^ new = μ T φ new , σ new 2 = σ MP 2 + φ new T Σ φ new , σ new 2 Variance for predicted value;
Step 6: repeating step three carries out stepwise predict to step 5, until predicted value less than failure threshold U time prediction finish, thereby realize the on-line prediction of lithium ion battery residual life to be predicted.
In the step 5 of present embodiment, INS=[x New, y New] and { (x 1, y 1), (x 2, y 2) ..., (x N-l, y N-l) implication is identical, all is the battery capacity data, it is along with the producing of prediction, as newly-increased (x New, y New) time need to carry out RVM forecast model adaptability checking, be about to x NewBe input to the RVM forecast model, obtain predicted value
Embodiment two: present embodiment is for to the further specifying of embodiment one, predicated error limit PEB=0.1 in the present embodiment.
Embodiment three: below in conjunction with Fig. 1 to Fig. 3 present embodiment is described, present embodiment is for further specifying the U=1.38Ah of failure threshold described in the present embodiment to embodiment one or two.
The lithium ion battery method for predicting residual useful life of data-driven all is off-line mostly, and its ability that dynamically updates is low, precision of prediction is low, and the counting yield of online again training is low, particularly the Method Using Relevance Vector Machine algorithm is directly used in online model and forecast.Simultaneously, because the sparse property of Method Using Relevance Vector Machine algorithm and the challenge aspect the residual life long-term forecasting, the Method Using Relevance Vector Machine algorithm of off-line is difficult to acquisition and predicts the outcome accurately.Therefore, the again training of the renewal of sample, model and be very important in the predicting residual useful life process with the dynamic perfromance of sample online updating.Off-line Method Using Relevance Vector Machine method is that the batch off-line data is trained Forecasting Methodology or the model that obtains off-line, and its model just remains unchanged once acquisition, and the batch off-line data often can not reflect the random character of online degenerative process.The degradation trend of complexity when lithium ion battery is used online, a small amount of cell degradation data set and sparse forecast model are difficult to obtain accurately long-term forecasting result when causing the Method Using Relevance Vector Machine method to be used online.So research lithium ion battery residual life on-line prediction strategy is very significant.
In order to verify whether the present invention can realize the life prediction of lithium ion battery effectively, the Battery Data Set experimental data that the below adopts NASA to provide is carried out experimental verification.
Data analysis:
Following data set derives from the lithium ion battery test envelope of building in the NASAPCoE research centre, the battery experiment: charging, discharge and impedance measurement move down 25 ℃ of room temperatures:
Be to charge under the pattern of 1.5A at steady current, until cell voltage reaches 4.2V;
Be to discharge under the pattern of 2A at steady current, until cell voltage drops to 2.5V;
Measure battery impedance by EIS, the scope of frequency sweeping is from 0.1Hz to 5kHz.
Analyze by data and experiment condition to each Battery pack, the presentation of data of finding the 3rd Battery pack goes out obvious degenerative character, because these group data are to test at ambient temperature acquisition, actual working conditions closer to most of lithium ion battery, with it the inventive method is verified to have better representativeness, the degradation in capacity process of Battery#05, Battery#06, Battery#07, Battery#18 battery is shown in the curve among Fig. 2.
Transverse axis is the charge and discharge cycles cycle of lithium ion battery among Fig. 3, and unit is cycle (cycle), and the longitudinal axis is battery capacity value, and unit is ampere-hour (Ah).As we know from the figure, the capacity of battery is an index degenerated curve generally, and the local energy orthogenesis is obvious, and sample size is few.When battery reaches the standard of end-of-life (End OfLife, EOL), namely the charging capacity of battery is to about 70% of rated capacity, and experiment stops.The capacity threshold U of circulating battery end in serviceable life is made as 1.38Ah in this experiment, Battery#05, Battery#06 battery sample data are 168, the life-span T1=123cycle of Battery#05 battery, the life-span T2=112123cycle of Battery#06 battery.Battery#18 battery sample data is 132, the life-span T3=100123cycle of Battery#18 battery.Select the Battery#5 battery to set forth experimentation and analyze experimental result as standard among the present invention, adopt the validity of Battery#5 and Battery#18 checking prediction algorithm framework.
Experimental result and analysis:
The gaussian kernel function that the kernel parameter selection of RVM is commonly used, nuclear parameter has certain impact to the performance of RVM, and through experimental verification, it is 3 more suitable that nuclear parameter is elected as.Noise variance σ 2=var (y) * 0.1.Maximum cycle and pruning threshold value are got respectively iter=1000, α Max=1e5.When initial, the super parameter that all basis functions are corresponding be set to { α }=(ones (1, N+1) * 0.1), use simultaneously and have bias (1,1 ... 1) TBasis function.
Adopt respectively 40,60,80 samples to carry out modeling as training data during the forecast model training, then adopt prediction flow process of the present invention to predict, employing process interruption root-mean-square error (RMS), RUL error and relative error are estimated, and it predicts the outcome as shown in table 1.
Table 1Battery#5 lithium ion battery predicts the outcome
Simultaneously RVM (Retraining RVM) method of the RVM method (RVM) of IP-RVM method and off-line, again training has been carried out the prediction effect comparative analysis, such as table 2 and shown in Figure 3.
The quantitative result of the different Forecasting Methodologies of table 2 (Battery#5)
From above-mentioned form and figure as can be known, Forecasting Methodology of the present invention is fine to long-term results and RUL prediction effect, particularly the capacity predict value in the forecasting process and actual value are substantially identical.
In order to verify adaptability and the validity of this paper institute extracting method, adopt respectively Battery#6 battery and Battery#18 battery to verify.Its result is shown in table 3 and table 4.
The quantitative result of the different Forecasting Methodologies of table 3 (Battery#18)
The quantitative result of the different Forecasting Methodologies of table 4 (Battery#6)
On-line operation efficient and the additive method of the inventive method compare, and be as shown in table 5.
To sum up experimental result is described, and the present invention improves obviously than the Forecasting Methodology RVM precision of prediction of off-line;
The IP-RVM method that the present invention proposes is suitable with Retraining RVM method precision of prediction; But the IP-RVM method is carried out efficient than Retraining RVM method and can be improved more than 14%;
Adopt different lithium ion batteries to verify the adaptability of IP-RVM algorithm in the present embodiment.
Therefore, the present invention has preferably application prospect aspect the lithium ion battery predicting residual useful life.

Claims (3)

  1. One kind based on the relevant on-line prediction lithium that returns with amount from ten thousand methods of remaining battery life, it is characterized in that: it may further comprise the steps:
    Step 1: choose capacity of lithium ion battery data I S=(C to be predicted 1, C 2... C n) as original sample, C iBe battery capacity, unit is Ah, i=1, and 2 ..., n, n are positive integer;
    Carry out phase space reconfiguration structure training sample set: set and embed dimension l=5, delay d=1, obtain training sample set { (x 1, y 1), (x 2, y 2) ..., (x N-l, y N-l), x wherein j=(C j, C J+1..., C J+l-1), y j=C J+l, j=1,2 ... n-l, wherein x=(x 1, x 2..., x N-l) be Method Using Relevance Vector Machine RVM mode input data, y=(y 1, y 2..., y N-l) be the output data of Method Using Relevance Vector Machine RVM model;
    Step 2: initialization Method Using Relevance Vector Machine RVM model parameter:
    The mathematic(al) representation of Method Using Relevance Vector Machine RVM model is y=Φ ω+ε,
    ω=(ω wherein 0..., ω N-l) TBe the weights of model,
    ε=(ε 1, ε 2... ε N-l) be Gaussian noise, and ε j~N (0, σ 2), σ 2Be the noise variance of RVM model output data y,
    Φ is the matrix of n * (n+1), and Φ=[φ 1, φ 2φ N-l] T,
    φ j=[1,K(x j,x 1),…,K(x j,x j)…K(x j,x n-l)]
    K (x j, x N-l) be kernel function:
    K ( x j , x n - l ) = exp ( - | | x j - x n - l | | 2 η 2 ) ,
    η is nuclear parameter;
    Set nuclear parameter η=3, maximum iteration time iter=1000,
    { α k}=0.1, k=0,1 ... n-l, α kBe weights ω kSuper parameter,
    σ 2=var(y)*0.1;
    Step 3: RVM training:
    Step 3 one: the covariance ∑ and the average μ that calculate ω:
    ∑=(σ -2Φ TΦ+A) -1,μ=σ -2∑Φ Ty T
    Wherein, ∑ is the matrix of (n-l+1) * (n-l+1), and μ is the column vector of (n-l+1) * 1,
    μ=(μ 0,μ 1,…,μ n-l) T,A=diag(α 0,α 1,…,α n-l);
    Step 3 two: use iteration algorithm to calculate new α kAnd σ 2, be designated as 2) New:
    α k new = γ k μ k 2 , ( σ 2 ) new = | | y - Φμ | | n - l - Σ k = 0 n - l γ k ,
    γ wherein k=1-α kKk, μ kBe ω kAverage, ∑ KkK diagonal entry for the covariance ∑;
    Set iterations parameter L=1;
    Step 3 three:
    Will 2) NewBring in the formula of step 3 one, repeating step 31 and step 3 two are upgraded μ and ∑, make L=L+1, repeat this step 3 three, until L>and iteration finishes the (σ when iteration finishes during iter 2) NewBe designated as
    Step 4: after iteration finishes in the step 3, deletion and ω kX among=0 corresponding x j, residue x jBe called associated vector RVs, all associated vector RVs form associated vector collection IS RV, obtain thus the RVM forecast model H is prediction step, and variance is And obtain working set WS, WS=IS RV
    Step 5: will increase sample set INS=[x newly New, y New] middle x NewBe input to the RVM forecast model, obtain predicted value Will With y NewCompare, if Then construct new training set WS=WS ∪ INS, again train RVM, upgrade the RVM forecast model; Otherwise keep the RVM forecast model constant;
    PEB is the predicated error limit,
    y ^ new = μ T φ new , σ new 2 = σ MP 2 + φ new T Σ φ new , σ new 2 Variance for predicted value;
    Step 6: repeating step three carries out stepwise predict to step 5, until predicted value less than failure threshold U time prediction finish, thereby realize the on-line prediction of lithium ion battery residual life to be predicted.
  2. 2. the method for the on-line prediction lithium ion battery residual life that returns based on associated vector according to claim 1 is characterized in that: predicated error limit PEB=0.1.
  3. 3. the method for the on-line prediction lithium ion battery residual life that returns based on associated vector according to claim 1 and 2 is characterized in that: described failure threshold U=1.38Ah.
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