CN107479000B - A kind of lithium-ion-power cell RUL prediction technique based on Box-Cox transformation and Monte-Carlo Simulation - Google Patents

A kind of lithium-ion-power cell RUL prediction technique based on Box-Cox transformation and Monte-Carlo Simulation Download PDF

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CN107479000B
CN107479000B CN201710706002.6A CN201710706002A CN107479000B CN 107479000 B CN107479000 B CN 107479000B CN 201710706002 A CN201710706002 A CN 201710706002A CN 107479000 B CN107479000 B CN 107479000B
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coefficient
battery
rul
offline
power battery
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CN107479000A (en
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熊瑞
张永志
何洪文
孙逢春
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Beijing University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/392Determining battery ageing or deterioration, e.g. state of health
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367Software therefor, e.g. for battery testing using modelling or look-up tables
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04Ageing analysis or optimisation against ageing

Abstract

The present invention proposes a kind of power battery RUL prediction technique based on Box-Cox transformation and Monte-Carlo Simulation, it converts battery capacity using Box-Cox transformation, construct the linear model between capacity transformed value and cycle-index, and model parameter and model uncertainty are recognized using least-squares algorithm, the uncertainty application Monte-Carlo Simulation of remaining life generates.The algorithm can reduce online aging data needed for accurate predicting residual useful life, and when there is offline aging data, minimum online data amount required for accurate predicting residual useful life is only the 30% of battery complete attenuation data volume.

Description

A kind of lithium-ion-power cell RUL based on Box-Cox transformation and Monte-Carlo Simulation Prediction technique
Technical field
The present invention relates to the prognostics and health management fields of power battery, more particularly to establish the prediction of power battery With health status administrative model, and the power battery management system based on established model.
Background technique
Lithium-ion-power cell can pass through its remaining life (Remaining useful in application on site Life:RUL) prediction cut-off service life (End of Life:EOL).Under normal conditions, when the capacity attenuation of lithium battery holds to initial Amount 80% when, that is, be considered the cut-off service life of lithium battery.Existing lithium-ion-power cell RUL prediction mainly has based on model Method and method based on data-driven.Wherein, it usually using non-linear Ageing Model and is combined based on the method for model Advanced particle filter technology such as particle filter technology predicts RUL, but on service life of lithium battery latter stage capacity attenuation slope When spending very little, the accuracy of RUL prediction result is lower.It is dynamic to lithium ion that method based on data-driven is based primarily upon machine learning Power cell degradation data carry out data mining, so that online URL fallout predictor is obtained, however this method is that acquisition is higher accurate Degree, it usually needs a large amount of offline aging data.
Summary of the invention
For technical problem present in above-mentioned this field, the present invention provides one kind to be converted and be covered based on Box-Cox The power battery RUL prediction technique of special Caro emulation, method includes the following steps:
Step 1 selects the lithium-ion-power cell of same size to carry out accelerated aging based on the condition that actually works online Experiment, using the data of acquisition as the offline aging data of lithium-ion-power cell;
Step 2 carries out Box-Cox transformation to the offline aging data in step 1, obtains different dynamic battery Offline transformation coefficient and capability value linear model;
The offline transformation coefficient of different dynamic battery in step 2 is averaged, and exists as power battery by step 3 The online transformation coefficient is applied to the capacity data observation that part obtains online, and recognizes step 2 by line transformation coefficient The model coefficient of the capability value linear model of middle acquisition and the variance of the model coefficient.
Step 4, coefficient and the variance according to the model recognized in step 3, is calculated based on Monte Carlo Method is emulated, and predicts the probability distribution of power battery RUL and RUL.
Further, the Box-Cox transformation carried out in the step 2, using following expression:
For C > 0
Wherein, C represents battery capacity observation, and λ represents the offline transformation coefficient of power battery.
Further, the capability value linear model of the power battery in the step 2, meet C (λ)~N (K β, σ2) hypothesis, it may be assumed that
Wherein, C (λ)=(C1(λ),C2(λ),…,Cn(λ))T, λ represents the offline transformation coefficient of power battery, and K is design Matrix meets K=(K1,K2,…,Kn)T, and Ki=(1, ki), β=(β01)T, n is size, kiBattery is represented to follow Number of rings, β01Representative model coefficient, εiFor the independent random error for meeting normal distribution, mean value 0, variance σ2
Further, the offline transformation coefficient of the power battery is obtained using maximum likelihood estimate, is taken so that following Offline transformation coefficient λ of the maximum λ of formula intermediate value as power battery:
Wherein L*(λ) represents log-likelihood function,Expression formula is as follows:
Expression formula it is as follows:
It willAndExpression formula bring expression formula (3) into, that is, acquire corresponding λ value.
Further, the online transformation coefficient is applied to the capacity that part obtains online described in the step 3 Data, and the model coefficient of the capability value linear model obtained in step 2 and the variance of the model coefficient are recognized, It specifically includes:
Based on the offline transformation coefficient λ of the power battery obtained in the step 2 to the capacity partially obtained online Data observation value is converted, and utilizes least square method computation model factor beta01:
Wherein
Model coefficient β01Variance are as follows:
Wherein s2Representative errors item variances sigma2Estimated value: s2=SSR/ (n-2);SSR is the quadratic sum of residual error, expression formula It is as follows:
Further, it is emulated in the step 4 based on Monte Carlo EGS4 method, predicts power battery RUL and RUL Probability distribution, specifically include: multistep forward prediction carried out to the capability value linear model, for each simulation sample, When the capacity transformed value of prediction is less than defined stale value, that is, think that battery reaches the cut-off service life, to export RUL;By institute It states all RUL values that emulation obtains and carries out probability statistics acquisition RUL prediction and its probability distribution.
Based on method provided by aforementioned present invention, have following many utility model has the advantages that it can effectively eliminate battery declines Subtract the lesser capacity attenuation situation of the latter stage gradient, is obviously improved the precision of prediction of battery RUL.Model is based on relative to existing Or the method for data-driven, online data amount needed for constructing accurate linear Ageing Model and initialization Ageing Model from Line data volume is all substantially reduced.
Detailed description of the invention
Fig. 1 is the RUL prediction principle figure of method provided by the present invention
Fig. 2 is lithium-ion-power cell accelerated life test data
Fig. 3 is the RUL prediction result of the battery A based on preceding 30% aging data
Specific embodiment
Method provided by the present invention is made with reference to the accompanying drawing and further illustrates and explains in detail.
As shown in Figure 1, a kind of power battery RUL based on Box-Cox transformation and Monte-Carlo Simulation of the invention is pre- Survey method, method includes the following steps:
Step 1 selects the lithium-ion-power cell of same size to carry out accelerated aging based on the condition that actually works online Experiment, using the data of acquisition as the offline aging data of lithium-ion-power cell;
Step 2 carries out Box-Cox transformation to the offline aging data in step 1, obtains different dynamic battery Offline transformation coefficient and capability value linear model;
The offline transformation coefficient of different dynamic battery in step 2 is averaged, and exists as power battery by step 3 The online transformation coefficient is applied to the capacity data observation that part obtains online, and recognizes step 2 by line transformation coefficient The model coefficient of the capability value linear model of middle acquisition and the variance of the model coefficient.
Step 4, coefficient and the variance according to the model recognized in step 3, is calculated based on Monte Carlo Method is emulated, and predicts the probability distribution of power battery RUL and RUL.
In the preferred embodiment of the application, the Box-Cox carried out in the step 2 is converted, using as follows Expression formula:
For C > 0
Wherein, C represents battery capacity observation, and λ represents the offline transformation coefficient of power battery.
In the preferred embodiment of the application, the linear mould of capability value of the power battery in the step 2 Type meets C (λ)~N (K β, σ2) hypothesis, it may be assumed that
Wherein, C (λ)=(C1(λ),C2(λ),…,Cn(λ))T, λ represents the offline transformation coefficient of power battery, and K is design Matrix meets K=(K1,K2,…,Kn)T, and Ki=(1, ki), β=(β01)T, n is size, kiBattery is represented to follow Number of rings, β01Representative model coefficient, εiFor the independent random error for meeting normal distribution, mean value 0, variance σ2
In the preferred embodiment of the application, the offline transformation coefficient of the power battery uses maximal possibility estimation Method obtains, and takes so that offline transformation coefficient λ of the maximum λ of following formula intermediate value as power battery:
Wherein L*(λ) represents log-likelihood function,Expression formula is as follows:
Expression formula it is as follows:
It willAndExpression formula bring expression formula (3) into, that is, acquire corresponding λ value.
In the preferred embodiment of the application, the online transformation coefficient is applied to described in the step 3 The capacity data that part obtains online, and recognize model coefficient and the institute of the capability value linear model obtained in step 2 The variance for stating model coefficient, specifically includes:
Based on the offline transformation coefficient λ of the power battery obtained in the step 2 to the capacity partially obtained online Data observation value is converted, and utilizes least square method computation model factor beta01:
Wherein
Model coefficient β01Variance are as follows:
Wherein s2Representative errors item variances sigma2Estimated value: s2=SSR/ (n-2);SSR is the quadratic sum of residual error, expression formula It is as follows:
It in the preferred embodiment of the application, is emulated, is predicted based on Monte Carlo EGS4 method in the step 4 The probability distribution of power battery RUL and RUL, specifically include: multistep forward prediction is carried out to the capability value linear model, it is right In each simulation sample, when the capacity transformed value of prediction is less than defined stale value, that is, think that battery reaches the cut-off service life, To export RUL;All RUL values that the emulation obtains are subjected to probability statistics and obtain RUL prediction and its probability distribution.
Fig. 2 and Fig. 3 show the power battery RUL based on the condition that actually works online to predict example.Fig. 2 is selected lithium The experimental data of ion battery, experiment condition are as follows: experimental temperature is 25 DEG C;Constant current constant voltage is full of, i.e. constant current 0.5C fills The supreme blanking voltage of electricity, then constant-voltage charge is until cut-off current 0.05C;Constant current 1C is discharged to lower blanking voltage, then with 0.5C size is discharged to lower blanking voltage again, and all capability values released are added the capability value as each cycle battery.Four A battery number is respectively battery A, battery A1, battery A2, battery A3, and wherein battery A is the battery to work online, battery A1- A3 is as the battery to work offline.It can be seen that battery A is smaller in the capacity attenuation gradient of end of lifetime.Table 1 shows four batteries Transformation coefficient λ value,
Battery A A1 A2 A3
λ -6.534 -5.987 -6.612 -6.185
The λ value of battery A is the smallest in 4 batteries.Battery A1-A3 be offline battery, λ value be it is known that battery A be Line working battery, since battery A only has part aging data it is known that therefore its λ value is unknown, estimated value is other three batteries The mean value of λ, i.e. the λ estimated value of battery A are -6.113, and 0.421. bigger than the true λ value of battery A assumes that battery A only has 30% For aging data it is known that being now to predict its remaining life, Fig. 3 shows the battery obtained based on preceding 30% aging data The remaining life estimation condition of A, the lesser capacity attenuation of the end of lifetime gradient have avoided.λ of the capacity conversion value based on battery A Estimated value converts to obtain to its capacity observation as Box-Cox, and preceding 30% data (150 circulations) are as the capacity acquired Value, capacity predicted value are to carry out linear fit based on known capacity change data to obtain, it is seen that the mistake of predicted value and conversion value Difference is smaller, and battery EOL predicted value is 512 circulations, more 12 circulations of than true value 500 circulations, so RUL is predicted at this time Error is only -12 circulations, and the confidence interval of EOL prediction 95% is [502,522], it is shown that higher prediction accuracy and essence Degree.
It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding And modification, the scope of the present invention is defined by the appended.

Claims (3)

1. a kind of power battery RUL prediction technique based on Box-Cox transformation and Monte-Carlo Simulation, it is characterised in that: tool Body the following steps are included:
Step 1 selects the lithium-ion-power cell of same size to carry out accelerated life test based on the condition that actually works online, Using the data of acquisition as the offline aging data of lithium-ion-power cell;
Step 2 carries out Box-Cox transformation to the offline aging data in step 1, obtains the offline of different dynamic battery Transformation coefficient and capability value linear model;
The offline transformation coefficient of different dynamic battery in step 2 is averaged, and becomes online as power battery by step 3 Coefficient is changed, the online transformation coefficient is applied to the capacity data observation that part obtains online, and recognize in step 2 and obtain The model coefficient of the capability value linear model taken and the variance of the model coefficient;
Step 4, coefficient and the variance according to the model recognized in step 3, based on Monte Carlo EGS4 method into Row emulation, predicts the probability distribution of power battery RUL and RUL;
The Box-Cox transformation carried out in the step 2, using following expression:
For C > 0
Wherein, C represents battery capacity observation, and λ represents the offline transformation coefficient of power battery;
The capability value linear model of the power battery in the step 2 meets C (λ)~N (K β, σ2) hypothesis, it may be assumed that
Wherein, C (λ)=(C1(λ),C2(λ),…,Cn(λ))T, λ represents the offline transformation coefficient of power battery, and K is design matrix, Meet K=(K1,K2,…,Kn)T, and Ki=(1, ki), β=(β01)T, n is size, kiCirculating battery number is represented, β01Representative model coefficient, εiFor the independent random error for meeting normal distribution, mean value 0, variance σ2
The online transformation coefficient is applied to the capacity data that part obtains online described in the step 3, and recognizes step The model coefficient of the capability value linear model obtained in rapid two and the variance of the model coefficient, specifically include:
Based on the offline transformation coefficient λ of the power battery obtained in the step 2 to the capacity data partially obtained online Observation is converted, and utilizes least square method computation model factor beta01:
Wherein
Model coefficient β01Variance are as follows:
Wherein s2Representative errors item variances sigma2Estimated value: s2=SSR/ (n-2);SSR is the quadratic sum of residual error, and expression formula is as follows:
2. the method as described in claim 1, it is characterised in that: the offline transformation coefficient of the power battery uses maximum likelihood The estimation technique obtains, and takes so that offline transformation coefficient λ of the maximum λ of following formula intermediate value as power battery:
Wherein L*(λ) represents log-likelihood function,Expression formula is as follows:
Expression formula it is as follows:
It willAndExpression formula bring expression formula (8) into, that is, acquire corresponding λ value.
3. the method as described in claim 1, it is characterised in that: it is emulated in the step 4 based on Monte Carlo EGS4 method, The probability distribution for predicting power battery RUL and RUL, specifically includes: it is pre- forward to carry out multistep to the capability value linear model It surveys, when the capacity transformed value of prediction is less than defined stale value battery, which reaches cut-off, to be thought for each simulation sample Service life, to export RUL;All RUL values that the emulation obtains are subjected to probability statistics and obtain RUL prediction and its probability point Cloth.
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