CN106055775A - Prediction method for life of secondary battery based on particle filter and mechanism model - Google Patents
Prediction method for life of secondary battery based on particle filter and mechanism model Download PDFInfo
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Abstract
Provided is a prediction method for life of a secondary battery based on particle filter and a mechanism model. The invention is aimed at solving the problem in the prior art that the prediction for life of a secondary battery is totally based on data drive and does not take the defect of an object mechanism so that a prediction result for the life of an electrochemical power source has poor accuracy.In a training stage, a particle filter method is utilized for tracking the actual value of internal state variables for the battery such that a regression equation of state variables varying with charge-discharge cycle frequency changes is obtained as a new state equation. In a prediction stage, the new state equation is utilized for calculating estimation values of state variables during unknown charge-discharge circulation in order to generate multiple particles. Multiple estimation values for capacity observation values are taken into an observation equation such that medians of estimation values for multiple capacity observation value are utilized for predicting the battery capacity in the future during the charge-discharge circulation. When the pre-set battery capacity reaches the lower limit, difference value between cycle numbers corresponding to the capacity observation value and cycle numbers used in the training stage is used as the residual number of cycles available for the battery.
Description
Technical field
The present invention relates to a kind of by secondary cell (including lithium ion battery, lead-acid battery, hereinafter referred to as battery) mechanism mould
The battery life predicting new method that type emulation technology combines with particle filter algorithm.Belong to equipment dependability field.
Background technology
In recent years, the secondary rechargeable battery such as lead-acid battery and lithium ion battery obtains in the field such as electric automobile, intelligent grid
Obtained extensive application.From the angle used, the life problems of battery has become as restriction electric automobile, the bottle of intelligent grid development
Neck problem.
In the life-span of Accurate Prediction battery, be the basic demand of battery system based on state maintenance, for improving battery system
The reliability, cost-effective most important of system.The life-span prediction method of battery can be divided three classes: " based on agine mechaism ", needs
It is to be understood that cause the such as catalyst effective area of cell degradation to reduce, can use the reduction of conductive ion concentration, electrode passivation film to increase
The aging mechanism such as long, and be modeled it, the modeling of single aging mechanism is the most extremely complex, phase again between various aging modes
Mutual coupling, so life-span prediction method based on agine mechaism is difficult to；" based on data-driven ", according to going through of battery capacity
History data variation trend, in conjunction with nonlinear regression, Kalman filtering, particle filter scheduling algorithm, is predicted battery performance, this
The method of kind ignores physical significance and the battery object of data, is difficult to the precision of prediction obtained；" feature based ", in conjunction with reflection
The feature the surveyed prediction battery life of battery life, usual this feature is relatively difficult to choose, and characteristic quantity and battery capacity
Between contact be difficult to quantify.
The thought of particle filter is based on monte carlo method, and it is to utilize particle collection to represent probability, can be used in any
On the state-space model of form.Its core concept is to carry out expression status by the random manner particle of extraction from posterior probability
Variable is distributed, and is a kind of order importance sampling method.In simple terms, particle filter method refers to by finding one group empty in state
Between the random sample propagated probability density function is approximated, replace integral operation with sample average, thus obtain state
The process of little variance distribution.Here sample i.e. refers to particle, can be to approach any form when sample size levels off to infinity
Probability density distribution.Particle filter has the feature of imparametrization, break away from understand by no means linear filtering problem time random quantity must
The restriction of Gauss distribution must be met, can widely be distributed by expression ratio Gauss model, also the nonlinear characteristic of variable parameter is had
Higher modeling ability.Therefore, particle filter can relatively accurately be expressed posterior probability based on observed quantity and controlled quentity controlled variable and divided
Cloth, it is possible to obtain more accurate system state estimation result.
Summary of the invention
The present invention be in order to solve tradition service life of secondary cell based on particle filter prediction be based entirely on data-driven, neglect
Depending on predicting the defect of object Characteristics, the problem of the poor accuracy that causes battery life is predicted the outcome.A kind of grain is now provided
The service life of secondary cell Forecasting Methodology that son filtering combines with mechanism model.
The service life of secondary cell Forecasting Methodology that a kind of particle filter combines with mechanism model, it includes herein below:
Step one, the mechanism model of structure secondary cell, the mechanism model of described secondary cell can simulate any electric current
The charging/discharging voltage of battery time dependent curve during condition；
Step 2, training stage: the secondary cell in step one is carried out aging a period of time under normal applying working condition,
The charging and discharging curve in dynamic operation condition off-line measurement secondary cell ageing process is utilized at interval of fixing charge and discharge cycles number of times,
The voltage now obtained is actual secondary cell output voltage U,
Emulate, to the mechanism model of secondary cell, the dynamic operation condition electric current that input is same, export with model emulationGo simulation
Secondary cell, at the actual output U of different ageing steps, utilizes genetic algorithm or method of least square, and it is right to realize according to object function
The identification of secondary cell model parameter collection P, multiple parameter set P of each ageing step of secondary cell identification obtained are as instruction
Practice data,
Select from multiple parameter set P of training L the mechanism model parameter relevant to ageing process as state to
Amount X, wherein, L is positive integer, using battery capacity Q under actual load current conditions as observed quantity, same load current conditions
Under battery mechanism model emulation and conversion capacity estimation valueProcess as observational equation, utilize particle filter algorithm to make always
The estimated value of the state vector in each stage during changeClose to actual value X；
Step 3, prediction process: use the state vector estimation during particle filter algorithm is trained in step 2
Value sequence, by the method for polynomial regression, obtains the state vector X regression equation about cycle-index k, in this, as new shape
State equation, when k is certain charge and discharge cycles number of times following, obtains the estimated value of state vector by new state equationSubstitution equation:
In formula, k is cycle-index, XP,i,jK () represents the i-th component of jth particle, obey average and beSide
Difference is σw,iNormal distribution, 1≤i≤L, 1≤j≤M, wiFor the systematic procedure noise of state variable Xi,
Obtain the multiple particles meeting Gauss distribution, multiple particles are substituted in the observational equation in step 2, to obtain
The median of multiple observed quantity estimated values, as the predictive value to following battery capacity, when prediction capacity reaches to preset
Battery capacity lower limit time, in corresponding cycle-index and step 2, the difference of cycle-index used by the training stage is that battery can
Cycles left number of times, thus realize prediction to secondary cell residual life.
The invention have the benefit that in the training stage, utilize particle filter method to follow the tracks of inside battery state vector
Actual value, and be new state equation with the state vector that obtains with the regression equation that charge and discharge cycles number of times changes.In prediction
Stage, the estimated value of state variable when utilizing new state equation to calculate unknown charge and discharge cycles, generate many on this basis
Individual particle, substitutes into the estimated value obtaining multiple capacity observed quantities in observational equation, respectively with in multiple capacity observation estimated values
Figure place is as to the prediction of battery capacity during certain charge and discharge cycles following, when the predictive value of battery capacity reaches set in advance
During battery capacity lower limit, this cycle-index corresponding to capacity predictive value is electricity with the difference of the cycle-index used by the training stage
The cycles left number of times of Chi Keyong.It is for being predicted the life-span of electrochemical power source.
First mechanism electrochemical model is combined with particle filter algorithm, be applied to the biometry of secondary cell, adopt
The biometry result phase predicting the outcome with using existing method to obtain secondary cell of service life of secondary cell is obtained by the method
Reduce within 10% than forecast error.The method breaches traditional particle filter biometry being based entirely on data-driven
Method.The method is using mechanism model simulated program as observer, with the mechanism model ginseng regularly changing with cell degradation
Conventional particle filter forecasting method, as state variable, is improved by number.Comparing conventional particle filtering method, this method has
Observational equation precision is high, the feature of state variable explicit physical meaning, it is possible to realize the Accurate Prediction to remaining battery life.Can
Biometry for the secondary cell of different principle.
Accompanying drawing explanation
Fig. 1 is that the service life of secondary cell that a kind of particle filter described in detailed description of the invention one combines with mechanism model is pre-
The flow chart of survey method；
Fig. 2 is certain lead-acid battery DST operating mode current curve diagram；
Fig. 3 is certain lead-acid battery DST operating mode voltage curve.
Detailed description of the invention
Detailed description of the invention one: illustrate present embodiment referring to figs. 1 through Fig. 3, a kind of grain described in present embodiment
The son service life of secondary cell Forecasting Methodology that combines with mechanism model of filtering, it includes herein below:
Step one, the mechanism model of structure secondary cell, the mechanism model of described secondary cell can simulate any electric current
The charging/discharging voltage of battery time dependent curve during condition；
Step 2, training stage: the secondary cell in step one is carried out aging a period of time under normal applying working condition,
The charging and discharging curve in dynamic operation condition off-line measurement secondary cell ageing process is utilized at interval of fixing charge and discharge cycles number of times,
The voltage now obtained is actual secondary cell output voltage U,
Emulate, to the mechanism model of secondary cell, the dynamic operation condition electric current that input is same, export with model emulationGo simulation
Secondary cell, at the actual output U of different ageing steps, utilizes genetic algorithm or method of least square, and it is right to realize according to object function
The identification of secondary cell model parameter collection P, multiple parameter set P of each ageing step of secondary cell identification obtained are as instruction
Practice data,
Select from multiple parameter set P of training L the mechanism model parameter relevant to ageing process as state to
Amount X, wherein, L is positive integer, using battery capacity Q under actual load current conditions as observed quantity, same load current conditions
Under battery mechanism model emulation and conversion capacity estimation valueProcess as observational equation, utilize particle filter algorithm to make always
The estimated value of the state vector in each stage during changeClose to actual value X；
Step 3, prediction process: use the state vector estimation during particle filter algorithm is trained in step 2
Value sequence, by the method for polynomial regression, obtains the state vector X regression equation about cycle-index k, in this, as new shape
State equation, when k is certain charge and discharge cycles number of times following, obtains the estimated value of state vector by new state equationSubstitution equation:
In formula, k is cycle-index, XP,i,jK () represents the i-th component of jth particle, obey average and beVariance
For σw,iNormal distribution, 1≤i≤L, 1≤j≤M, wiFor the systematic procedure noise of state variable Xi,
Obtain the multiple particles meeting Gauss distribution, multiple particles are substituted in the observational equation in step 2, to obtain
The median of multiple observed quantity estimated values, as the predictive value to following battery capacity, when prediction capacity reaches to preset
Battery capacity lower limit time, in corresponding cycle-index and step 2, the difference of cycle-index used by the training stage is that battery can
Cycles left number of times, thus realize prediction to secondary cell residual life.
In present embodiment, for secondary cell, the aging time is such as 20 circulations.Secondary cell uses normal
Carry out aging a period of time at interval of fixing charge and discharge cycles number of times under operating mode, according to object function, measure repeatedly discharge and recharge
Many groups parameter set under Xun Huan, selects several groups of minimum parameter sets as training data, uses particle filter algorithm to make this training
State vector estimated value in dataClose to actual value X after experiencing repeatedly cycle charge-discharge；Employing particle filter algorithm is instructed
State vector estimated value sequence during white silk, by the method for polynomial regression, obtains L new mechanism model parameter through too much
State equation X (k) after secondary circulation.
One, electrochemical mechanism modeling
Electrochemical mechanism model herein refers to the charge or discharge electricity that its performance simulation model, i.e. mode input are battery
Stream, model is output as the time dependent curve of terminal voltage of correspondence.
Electrochemical model includes battery electrode thermodynamics reversible voltage (open-circuit voltage), liquid phase diffusion and migration, solid phase
The mathematical description of the processes such as diffusion, electrochemical reaction kinetics, is usually expressed as partial differential equation and boundary condition, initial value bar
The form of part, can be iterated solving by finite difference method.The input of model, output relation can be expressed as:
U (t)=f [I (t), P (k)] (1)
Wherein, Function Mapping f () is given electric current I (t) and parameter set P (k), mechanism model calculate the number of terminal voltage
Value simulation process, describes under specific operation voltage U with the change of discharge and recharge time；K is charge and discharge cycles number of times, it is believed that parameter
Collection P changes with the increase of discharge and recharge number of times.
Because the input of performance simulation model is present battery status and applying working condition, it is output as outside voltage-measurable, because of
This can be as the observational equation of battery system.In problem of aging, the observed quantity of cell degradation is usually capacity, can be at electricity
Formula (1) artificial battery discharge voltage profile under the conditions of actual load is passed through, according to discharge voltage under conditions of completely filling in pond
Cut-off point determine electric discharge cut-off time, from electric discharge start to electric discharge cut-off, integrated current over time (ampere-hour integration method) is obtained
Obtain the capacity of battery.The calculating process of capacity can be described as
Q (k)=q [I (t), P (k)] (2)
Wherein, Q (k) is the estimated value of capacity, and I (t) is by measuring the electric current that capacity is used, and P (k) is model parameter collection, q
[] represents according to the process calculating discharge curve and discharge time discharge capacity.
Two, training data is prepared
In order to obtain the battery parameter set in the different ageing steps, the different ageing steps at battery are needed to test battery
Charging and discharging curve.The operating mode of test charging and discharging curve can select ambulatory stress test operating mode DST (DynamicStress
Test), this operating mode contain reflection the various process of battery situation, it is thus achieved that voltage, electric current, electric quantity data collection abundant information,
The robustness of parameter identification result is stronger.Typical case's DST operating mode current curve and certain lead-acid battery voltage curve such as Fig. 2 of correspondence
Shown in Fig. 3.
The target of parameter identification is to select one group of parameter set, when inputting same electric current so that mechanism model emulation electricity
Pressure outputAnd the error between actual cell voltage output U is minimum, shown in object function such as formula (3).
Wherein, I (t) is load current；P is parameter set to be identified；S is the search volume of parameter set；N is the voltage taken
The data changed on curve are counted.
Parameter identification can realize with genetic algorithm or method of least square.
Three, some concepts of particle filter algorithm
(1) state variable
Parameter set according to the training stage and change thereof, select and aging closely-related L mechanism model parameter conduct
State variable, is designated as state vector X.Other parameter fixes the meansigma methods taking repeatedly identification.
Wherein, X1～XLFor in model parameter collection P, ageing-related L parameter.
(2) observed quantity
The capacity that observed quantity is battery used, measured value is Q, and estimated value is
(3) observational equation
Battery terminal voltage simulation process formula (1) and calculation of capacity process formula (2) are combined, it is thus achieved that specific discharge and recharge
The estimated value of the observed quantity under operating mode I (t)This observation process represents at observational equation formula (5) middle h [].Additionally,
The calculating of observation it is also contemplated that plus observation noise, it may be assumed that
Wherein, k is cycle-index, and v is observation noise, and obedience average is 0, variance is σvGauss distribution.
(4) state equation
In the training stage, the rule of unclear state variable change how, and state equation can be regarded as following recursion
Relational expression:
In formula, k is cycle-index；For kth time circulation to state variable XiEstimated value；Wi is state variable Xi's
Systematic procedure noise, obedience average is 0, variance is σw,iGauss distribution.
Detailed description of the invention two: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, in present embodiment, in step one, and the machine of secondary cell
Reason model is:
U (t)=f [I (t), P (k)] (formula 2),
In formula, I (t) is given electric current, and f is Function Mapping, and P (k) is the parameter set of secondary cell, and k is charge and discharge cycles
Number of times, parameter set P changes with the increase of discharge and recharge number of times k, and U (t) is the outside voltage-measurable of secondary cell.
Detailed description of the invention three: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, and in present embodiment, in step 2, object function is:
In formula, I (t) is given electric current, and P is parameter set to be identified, and S is the search volume of parameter set, and N is the voltage taken
The data changed on curve are counted,For mechanism model simulation data voltage, U is actual battery output voltage.
Detailed description of the invention four: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, and in present embodiment, in step 2, state vector X is:
In formula, X1～XLFor in model parameter collection P, ageing-related L parameter.
Detailed description of the invention five: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, in present embodiment, in step 2, battery capacity Q
Equation is:
Q (k)=q [I (t), P (k)] (formula 5),
In formula, I (t) is by measuring the electric current that capacity is used, and P (k) is model parameter collection, and q [] represents according to electric discharge song
Line and discharge time calculate the process of discharge capacity；
In step 2, observational equation is:
In formula,For the estimated value of the observed quantity under specific discharge and recharge operating mode I (t), k is charge and discharge cycles number of times, and v is for seeing
Surveying noise, obedience average is 0, variance is σvGauss distribution.
Detailed description of the invention six: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, and in present embodiment, in step 2, utilizes particle filter
Algorithm makes the estimated value of the state vector in each stage in ageing processDetailed process close to actual value X is:
Step A1, particle filter algorithm is utilized to carry out particle initialization: state vector X is setiProcess-noise variance
σw,i, 1≤i≤L；Observation noise variances sigma is setv；Population M is set；
During step A2, kth secondary charge and discharge cycles, state vector is according to a preliminary estimate: according to formula:
Realize being obtained state vector when kth time circulates by the final estimated value recursion of state vector during-1 circulation of kth
It is worth according to a preliminary estimate,
In formula,For kth time circulation to state variable XiEstimated value；wiFor state variable XiSystematic procedure make an uproar
Sound, obedience average is 0, variance is σw,iGauss distribution；
Particle sampler during the secondary charge and discharge cycles of step A3, kth: state vector correspondence M particle during each circulation, root
According to formula 1, determine particle during kth time charge and discharge cycles；
Step A4, calculating importance weight: bring M particle into observational equation in formula 6 respectively, obtain seeing capacity
M the estimated value measuredWherein,V～N (0, σv), Xp,jK () is jth
Particle,For the observed quantity estimated value that jth particle is corresponding, 1≤j≤M,
According to M estimated valueWith actual measurement observed quantity Q (k) error, according to formula:
Obtain the importance weight of different particle,
In formula, WjK () is the importance weight of jth particle, σvIt is σ for variancevGauss distribution；
Step A5, weights normalization: according to formula:
By the importance weight of each particle divided by the sum of all particle importance weight, it is achieved each particle importance is weighed
The normalization of value,
In formula,For the importance weight after normalization；
Step A6, particle resampling: particle is carried out resampling, make each particle be returned equal to it by the probability of resampling
One importance weight changed；
Step A7, particle update: according to formula:
The meansigma methods of M each dimension of particle after resampling as corresponding states vector final estimated value,
Training stage, for each charge and discharge cycles, repeat the above steps A2 to step A7, make the estimated value to state vector more and more
Close to its actual value.
In present embodiment, for convenience, all using k to represent the index of observation data sequence, Q represents observed quantity, w table
Show that process noise, v represent observation noise, σwRepresent process-noise variance, σvRepresent observation noise variance.Particle sampler: according to shape
State equation, from M state variable particle of kth-1 time, M state variable particle of recursion kth time.
Calculate importance weight: bring quantity of state corresponding for each particle into observational equation, obtain the estimation to observed quantity
ValueAccording to respective and actual measurement observed quantity Q error, it is thus achieved that the importance weight of different particles.
The importance weight of each particle is divided by the sum of all particle importance weight, it is achieved each particle importance weight
Normalization.
Detailed description of the invention seven: present embodiment is to a kind of particle filter described in detailed description of the invention one and mechanism mould
The service life of secondary cell Forecasting Methodology that type combines is described further, in present embodiment, in step 3, it was predicted that the tool of process
Body process is:
Step B1, state equation update: last in the training stage, become according to the change of historic state vector estimated value
Gesture, obtains they recurrence polynomial equations with charge and discharge cycles number of times k change, adds systematic procedure error, updated
After state equation, the state equation after renewal is:
X (k)=fregression(k)+w (k), w～N (0, σw) (formula 11),
In formula, fregressionK () represents the quantity of state regression equation about k, w (k) is systematic procedure noise；
Step B2, observed quantity update: by estimating of state vector X (k) after the kth obtained in step B1 time charge and discharge cycles
This estimated value, as initial value, is substituted in formula 1, it is thus achieved that M particle by evaluation, substitutes in formula 6 by this M particle, it is thus achieved that M
The estimated value of observation, using the median of the estimated value of M observation as to capacity pre-during following kth time charge and discharge cycles
Measured value；
Step B3, predicting residual useful life: by the predictive value of capacity during kth time charge and discharge cycles and battery set in advance
Low capacity compares, along with the increase of charge and discharge cycles number of times, when predicting that capacity starts less than setting capacity, the reality of battery
In cycle-index k corresponding to the observed quantity of border and step 2 the difference of cycle-index used by the training stage be battery can surplus
Remaining cycle-index, thus obtain secondary cell residual life.
Claims (7)
1. the service life of secondary cell Forecasting Methodology that a particle filter combines with mechanism model, it is characterised in that it include with
Lower content:
Step one, the mechanism model of structure secondary cell, the mechanism model of described secondary cell can simulate any current condition
Time battery the time dependent curve of charging/discharging voltage；
Step 2, training stage: the secondary cell in step one is carried out aging a period of time under normal applying working condition, every
Charging and discharging curve in fixing charge and discharge cycles number of times utilizes dynamic operation condition off-line measurement secondary cell ageing process, now
The voltage obtained is actual secondary cell output voltage U,
Emulate, to the mechanism model of secondary cell, the dynamic operation condition electric current that input is same, export with model emulationGo to simulate secondary
Battery, at the actual output U of different ageing steps, utilizes genetic algorithm or method of least square, realizes secondary according to object function
The identification of battery model parameter set P, multiple parameter set P of each ageing step of secondary cell identification obtained are as training number
According to,
Select from multiple parameter set P of training L the mechanism model parameter relevant to ageing process as state vector X,
Wherein, L is positive integer, using battery capacity Q under actual load current conditions as observed quantity, under same load current conditions
Battery mechanism model emulation and conversion capacity estimation valueProcess as observational equation, utilize particle filter algorithm to make aging mistake
The estimated value of the state vector in each stage in journeyClose to actual value X；
Step 3, prediction process: use the state vector estimated value sequence during particle filter algorithm is trained in step 2
Row, by the method for polynomial regression, obtain the state vector X regression equation about cycle-index k, in this, as new state side
Journey, when k is certain charge and discharge cycles number of times following, obtains the estimated value of state vector by new state equationGeneration
Enter equation:
In formula, k is cycle-index, XP,i,jK () represents the i-th component of jth particle, obey average and beVariance is
σw,iNormal distribution, 1≤i≤L, 1≤j≤M, wiFor the systematic procedure noise of state variable Xi,
Obtain the multiple particles meeting Gauss distribution, multiple particles are substituted in the observational equation in step 2, many to obtain
The median of individual observed quantity estimated value, as the predictive value to following battery capacity, when prediction capacity reaches electricity set in advance
During tankage lower limit, in corresponding cycle-index and step 2 the difference of cycle-index used by the training stage be battery can
Cycles left number of times, thus realize the prediction to secondary cell residual life.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step one, the mechanism model of secondary cell is:
U (t)=f [I (t), P (k)] (formula 2),
In formula, I (t) is given electric current, and f is Function Mapping, and P (k) is the parameter set of secondary cell, and k is charge and discharge cycles number of times,
Parameter set P changes with the increase of discharge and recharge number of times k, and U (t) is the outside voltage-measurable of secondary cell.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step 2, object function is:
In formula, I (t) is given electric current, and P is parameter set to be identified, and S is the search volume of parameter set, and N is by the voltage that taken at any time
Between data on change curve count,For mechanism model simulation data voltage, U is actual battery output voltage.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step 2, state vector X is:
In formula, X1～XLFor in model parameter collection P, ageing-related L parameter.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step 2, the equation of battery capacity Q is:
Q (k)=q [I (t), P (k)] (formula 5),
In formula, I (t) is by measuring the electric current that used of capacity, and P (k) is model parameter collection, q [] represent according to discharge curve and
Calculate the process of discharge capacity discharge time；
In step 2, observational equation is:
In formula,For the estimated value of the observed quantity under specific discharge and recharge operating mode I (t), k is charge and discharge cycles number of times, and v is that observation is made an uproar
Sound, obedience average is 0, variance is σvGauss distribution.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step 2, utilize particle filter algorithm to make the estimated value of the state vector in each stage in ageing process
Detailed process close to actual value X is:
Step A1, particle filter algorithm is utilized to carry out particle initialization: state vector X is setiProcess-noise variance σw,i, 1≤i
≤L；Observation noise variances sigma is setv；Population M is set；
During step A2, kth secondary charge and discharge cycles, state vector is according to a preliminary estimate: according to formula:
When realizing being obtained kth time circulation by the final estimated value recursion of state vector during kth-1 time circulation, state vector is preliminary
Estimated value,
In formula,For kth time circulation to state variable XiEstimated value；wiFor state variable XiSystematic procedure noise, clothes
From average be 0, variance be σw,iGauss distribution；
Particle sampler during the secondary charge and discharge cycles of step A3, kth: state vector correspondence M particle during each circulation, according to public affairs
Formula 1, determines particle during kth time charge and discharge cycles；
Step A4, calculating importance weight: bring M particle into observational equation in formula 6 respectively, obtain capacity observed quantity
M estimated valueWherein,Xp,jK () is jth grain
Son,For the observed quantity estimated value that jth particle is corresponding, 1≤j≤M,
According to M estimated valueWith actual measurement observed quantity Q (k) error, according to formula:
Obtain the importance weight of different particle,
In formula, WjK () is the importance weight of jth particle, σvIt is σ for variancevGauss distribution；
Step A5, weights normalization: according to formula:
By the importance weight of each particle divided by the sum of all particle importance weight, it is achieved each particle importance weight
Normalization,
In formula,For the importance weight after normalization；
Step A6, particle resampling: particle is carried out resampling, make each particle by the probability of resampling equal to its normalization
Importance weight；
Step A7, particle update: according to formula:
The meansigma methods of M each dimension of particle after resampling is as the final estimated value of corresponding states vector, in training
In the stage, for each charge and discharge cycles, repeat the above steps A2 to step A7, make the estimated value to state vector the most close
Its actual value.
The service life of secondary cell Forecasting Methodology that a kind of particle filter the most according to claim 1 combines with mechanism model,
It is characterized in that, in step 3, it was predicted that the detailed process of process is:
Step B1, state equation update: last in the training stage, according to the variation tendency of historic state vector estimated value,
To them with the recurrence polynomial equation of charge and discharge cycles number of times k change, add systematic procedure error, the shape after being updated
State equation, the state equation after renewal is:
X (k)=fregression(k)+w (k), w～N (0, σw) (formula 11),
In formula, fregressionK () represents the quantity of state regression equation about k, w (k) is systematic procedure noise；
Step B2, observed quantity update: the estimated value of state vector X (k) after the kth time charge and discharge cycles that will obtain in step B1
As initial value, this estimated value is substituted in formula 1, it is thus achieved that M particle, this M particle is substituted in formula 6, it is thus achieved that M observation
The estimated value of value, using the median of the estimated value of M observation as the prediction of capacity during charge and discharge cycles secondary to following kth
Value；
Step B3, predicting residual useful life: the predictive value of capacity during kth time charge and discharge cycles is held with battery minimum set in advance
Amount compares, along with the increase of charge and discharge cycles number of times, when predicting that capacity starts less than setting capacity, the actual sight of battery
The difference of cycle-index k corresponding to measurement and the cycle-index used by the training stage in step 2 be battery can residue follow
Ring number of times, thus obtain secondary cell residual life.
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