CN109932656A - A kind of service life of lithium battery estimation method based on IMM-UPF - Google Patents

Abstract

The service life of lithium battery estimation method based on IMM-UPF that the invention discloses a kind of, using a kind of new Fusion Model interactive multi-model, for different attenuation model fusion calculations.Consider that there are biggish errors using Kalman filtering for lithium battery decaying presentation non-gaussian and nonlinear trend, each model is filtered using no mark particle filter, on the one hand it solves the problems, such as particle filter particle degeneracy during resampling, has on the other hand obtained more accurate prediction result than Kalman filtering again.The IMM-UPF method of proposition is verified by the method that simulation result and experimental data compare, the results showed that this method can be promoted to service life of lithium battery forecasting accuracy.

Description

A kind of service life of lithium battery estimation method based on IMM-UPF

Technical field

The present invention relates to technical field of lithium batteries more particularly to a kind of service life of lithium battery estimation methods based on IMM-UPF.

Background technique

With the rapid development of electric car, lithium battery is then concerned as its mainstream power resources.Health status (SOH) be lithium battery one of key parameter, be user assess the present battery service life direct parameter.

Service life of lithium battery is predicted at present mainly to carry out lithium electricity using the method based on physical principle modeling and data modeling The prediction of tankage decaying.However, for complicated dynamical system, especially with the system of uncertain noise, it is difficult to establish Accurate analysis model.Method based on data modeling, which can capture, to be presented in the internal relation in data and learning data It is excessively complicated to avoid exploitation without the concrete knowledge to material property, structure, inefficacy mechanism etc. for variation tendency Physical model, common single empirical model may obtain good prediction effect in different phase, but can not be good The variation tendency of the entire life cycle of lithium battery is described.

Summary of the invention

The object of the invention is to remedy the disadvantages of known techniques, provides a kind of service life of lithium battery based on IMM-UPF Estimation method.

The present invention is achieved by the following technical solutions:

Interactive multi-model and the service life of lithium battery combined without mark particle filter algorithm are used the invention proposes a kind of Estimation method describes lithium battery based on physical property degradation using multinomial model, biexponential model, integrated model first Then three models are used no mark particle filter algorithm to be filtered, finally by filter by empirical model respectively in IMM model The result of wave makes accurate prediction to the SOH of lithium battery.

A kind of service life of lithium battery estimation method based on IMM-UPF, the specific steps are as follows:

(1) it is charged first using the battery of four same models with constant 1.1A electric current, until voltage reaches charge cutoff 4.2 volts of voltage, then with 4.2 volts of constant voltage chargings, after charging current is down to cut-off current 0.05A or less, terminate to fill Electricity；The rated capacity of battery is 1.1Ah.Charge-discharge test is carried out at room temperature, and record is each time after complete charge and discharge process Discharge capacity obtains battery capacity attenuation curve, sets the failure threshold of battery as 0.88Ah；

(2) four cell set capacity data are had collected by carrying out charge-discharge test to four batteries, passes through observation Attenuation curve finds that the 4th group of data and first three groups gap are big, therefore is used to determine each single model parameter for first three groups data The data that 4th battery obtains capacity are used as the verifying of forecasting accuracy by initial value；

(3) use is by Least Square Method battery capacity C_lSecond order polynomial regression equation followed to describe lithium battery At ring number l times with the maximum capacity C that can store_lBetween relationship, be denoted as model one, polynomial expression formula is

C_l=a₁l²+b₁l+c₁

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₁,b₁And c₁All it is constant related with discharge current and temperature, its value is determined by the mode of curve matching；

Second model that the empirical model for using double exponential equations to indicate is decayed as battery capacity, expression formula is such as Under: C_l=a₂·exp(b₂·l)+c₂·exp(d₂·l)

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₂And b₂It is constant related with internal driving, parameter c₂And d₂It is constant related with aging rate of the battery, parameter a₂,b₂,c₂ And d₂Value by way of curve matching determine；

The integrated model for using polynomial empirical model and exponential model to combine is as the third model, and expression formula is such as Under: C_l=a₃·exp(-b₃·l)+c₃·l^2+d₃

C in formula_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₃,b₃,c₃And d₃The mode of curve matching is determining, parameter a₃And b₃It is constant related with internal driving, parameter c₃And d₃It is and electric The related constant of pond rate of ageing.

Then parameter fitting is carried out to three single models respectively using the data of first three groups battery, respectively obtains first three groups Battery correspond to the parameter of each single model.Assuming that obtained fit parameter values are credible, obtained based on different groups of data The initial basic confidence distribution of parameter value is determined by following formula:

Wherein a_1,v,a_2,v, a_3,v, b_1,v,b_2,v, b_3,v, c_1,v,c_2,v, c_3,v, d_2,v, d_3,vFor each model parameter, parameter a_1,v, a_2,v, a_3,vAnd b_1,v, b_2,v, b_3,vIt is constant related with internal driving, parameter c_1,v, c_2,v, c_3,vAnd d_2,v, d_3,vIt is old with battery Change the related constant of rate, h is battery sample number, and v indicates v-th of model, it follows that the 4th battery corresponds to each model The initial value of parameter

M indicates the confidence level of each single model parameter.

(4) in order to realize that Interactive Multiple-Model (IMM) to the reciprocation of input quantity, needs the quantity of state by three models equal It is set as battery capacity C_l, establish corresponding state equation and observational equation.

The corresponding state equation of first model:

Observational equation:

The corresponding state equation of second model；

Observational equation:

Third model state equation:

Observational equation:

Wherein x_kIndicate that the battery when cycle period is k can use maximum capacity predicted value, that is, state vector, Z_kIndicate circulation Maximum capacity measured value when period is k measures vector,Indicate that mean value is 0 and standard deviation is σ Gaussian noise, a₁,b₁,c₁,a₂,b₂,c₂,d₂,a₃,b₃,c₃,d₃Initial value by X_M1,X_M2,X_M3It provides；

(5) each single model uses no mark particle filter algorithm (UPF) respectively to predict the remaining longevity of the 4th battery Life.

(6) it is filtered using data of the interactive multi-model to the 4th battery and parameter updates, three models are every The quantity of state and covariance in a period are realized in IMM outputs and inputs interaction, is realized using IMMUPF algorithm to remaining battery The prediction in service life.The present invention is imitative to measure using the standard deviation of absolute error and remaining life probability density function (RULPDF) The Stability and veracity of true result, uses preceding 300 groups of data as training data (Training Data), failure threshold (Failure Threshold) is 0.8, i.e. battery capacity C_l=0.88Ah, battery actual life are 665.Work as C_l=0.88Ah When, the 4th circulating battery number is 665 times corresponding.

The UPF algorithm specifically:

1) it initializes first

For system:

Wherein x indicates state vector, and Z indicates measurement vector, parameter W_k-1Indicate process noise, V_kExpression measurement noise, two Person is white Gaussian noise vector that is mutually indepedent and being zero-mean；F_k-1Indicate state-transition matrix, H_kIndicate observing matrix, It is assumed that observed quantity Z_kIndependently of given current quantity of state x_kOther states；

The equation that period is k is

θ_k-1Indicate the error amount of k-1 moment state estimation,Indicate the state estimation at k-1 moment, P_k-1Indicate k-1 The error co-variance matrix at moment, E are expectation of a random variable, Q_k-1Indicate the covariance matrix of process noise, R_k-1It indicates The covariance matrix of observation noise, T representing matrix transposition；

If k=0, and make particle collectionK is sample number, that is, population, if It indicates original state mean value, state primary condition is augmented:

p(x₀) indicate prior distribution,Indicate the original state amount of i-th of particle after being augmented,Expression is augmented The error covariance of the original state amount of i-th of particle afterwards；

2) Sigma sampling and weight computing

Sigma sampled point obtains:

λ=α²(n_x+κ)-n_x

Wherein,Indicate the state variable after being augmented,Indicate the error covariance after being augmented, λ is scaling Coefficient, κ are parameter to be selected, are usually taken to be 3-n_x, n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise, n_xIt indicates The dimension of state vector, n_u=n_x+n_V+n_WIt indicates state vector, measures the sum of noise and the dimension of process noise；

Calculate the weight of sampled point:

Wherein, y is the weight of mean value, and z is the weight of covariance, and f indicates which sampled point, α indicatePeriphery Sigma point distribution situation, β are constant related with the prior distribution of x, and γ is typically set to 0 or 3-n as scale parameter, works as ε Measurement noise Gaussian distributed is indicated when=3-n；

3) update of anticipation function

Corresponding Sigma point particle collection can be expressed as when period is kIndicate sampling number, Wherein for particle collectionWithRespectively indicate n before particle collection_xDimensional vector, n_x+ 1 dimension arrives n_x+n_WDimensional vector And n_x+n_W+ 1 dimension arrives n_x+n_V+n_WDimensional vector；n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise, Indicate the k+1 moment to the predicted state value of Sigma point set,Indicate that the k+1 moment adds the predicted state value of Sigma point set The predicted value for the system mode that power summation obtains, P_i,(k+1|k)Indicate the k+1 moment to the error covariance square of system state variables Battle array, P_VV,(k+1|k)Indicate the error co-variance matrix to observational equation at prediction k+1 moment, P_xV,(k+1|k)Indicate that the k+1 moment mutually assists Variance matrix, Z_i,(k+1|k)Indicate the k+1 moment to the observation of the prediction of Sigma point particle collection,Indicate the k+1 moment pair The system prediction value that the observed value weighting of the prediction of Sigma point particle collection is summed,It is nonlinear state side Eikonal number,It is non-Systems with Linear Observation equation functions；

P_i,(k+1|k+1)=P_i,(k+1|k)-G(k+1)P_VV,(k+1|k)G^T(k+1)

G (k+1) is Kalman filtering gain matrix,Indicate the shape of etching system when by measuring the k+1 for updating and obtaining State value, P_i,(k+1|k+1)It indicates to measure the error co-variance matrix for updating the obtained k+1 moment, Z_k+1Indicate that etching system is practical when k+1 Observation；

4) weight computing and resampling

Each particle is updated to obtain the estimated value and mistake of the particle at current time using Unscented kalman filtering algorithm Poor covariance value, to obtain suggestion distributionWhereinFor the probability of Gaussian distributed Then density function is predicted final result with particle filter (PF) algorithm, if reference distribution is prior distribution, it may be assumed that

q(x_i,k|x_i,(0:k-1),Z_0:k)=p (x_i,k|x_i,k-1)

x_i,kIndicate i-th of particle shape state value of k moment, x_i,(0:k-1)It indicates from 0 to k-1 moment, i-th of particle shape state value Set, Z_0:kIndicate the set from 0 to k moment measuring value, x_i,k-1Indicate i-th of particle shape state value of k-1 moment；

The weighted value of each particle is determined by following formula:

Weight standardization:

Resampling: work as N_effValue be less than setting threshold value N_thWhen, to particle collectionResampling is carried out, is obtained new Particle collectionThreshold value N_thIt is typically set to N_th=2K/3；N_effIt is calculated by following:

N_effThe number for indicating effective particle, by comparing the threshold value N of itself and setting_thSize determines whether to be adopted again Sample；

Output state amount and the estimation of corresponding covariance are as follows:

For the estimated value of quantity of state, P_i,kThe estimated value of covariance is corresponded to for quantity of state；

5) as k < L, L is observation sample number, enables k=k+1, repeats step 2), 3), 4), otherwise terminates.

The thought of IMMUPF is at each moment, it is assumed that some model passes through mixing under the conditions of present moment is effective Whether there is or not mark particle filters to estimate that obtained battery capacity prediction value matches to obtain with this particular model for previous moment institute The primary condition without mark particle filter, then each mold sync is filtered, finally with Model Matching likelihood function Based on update model probability, and whether there is or not the revised battery capacity prediction values of mark particle filter to be weighted to obtain most to institute Whole battery capacity prediction value.By analyzing and comparing each model in the absolute error and probability density letter of predicting residual useful life Several standard deviation sizes judges the stability and accuracy of prediction result.

The IMMUPF algorithm specifically:

1)) input interaction

By state estimationWith the model probability of filter each in previous stepObtain hybrid estimationAnd association VarianceUsing hybrid estimation as the original state of previous cycle；

For model g, when the period is k:

The prediction probability of model g:M is Number of Models, π_sgIt indicates

Transition probability of the model s to model g；

Prediction probability of the model s to model g:

The admixture of model g is estimated:

The mixing covariance of model g is estimated:

2) it) filters

For model g, particle will be filtered with UPF, utilize the particle collection of period kWithObtain next week The state of phase k+1 and its estimator of covarianceWithResidual error and its covariance are

3)) model probability updates

Original probability will be updated, and new mixing probability will be calculated according to its likelihood function, for model g, Likelihood function is write as:

WhereinIndicate that the density function of Gaussian distributed, new model mixing probability are expressed as:

Alphabetical o is normaliztion constant；

4)) output interaction: being based on model probability, weights and merges to each filter estimated result, obtains total state and estimate Meter and covariance estimation；

The particle collection of expression state and its covariance will be realized by lower array function and be interacted:

Final state amount and its covariance export in the following manner:

The invention has the advantages that the 1, present invention has used interactive multi-model, has made during estimating service life of lithium battery It obtains prediction result and not only realizes and the accuracy dependency degree of each model initial parameter is declined, improve efficiency in actual use With the effect reduced costs.

2, the present invention reduces prediction error, and remaining battery life without mark particle filter algorithm using Interactive Multiple-Model Probability distribution it is narrower, i.e., prediction result is more stable.

Detailed description of the invention

Tetra- cell set capacity data attenuation curve of Fig. 1.

Fig. 2 Interactive Multiple-Model estimates battery life flow chart without mark particle filter algorithm.

Fig. 3 training data be 300 when model one using no mark particle filter algorithm prediction result.

Fig. 4 training data be 300 when model two using no mark particle filter algorithm prediction result.

Fig. 5 training data be 300 when model three using no mark particle filter algorithm prediction result.

Interactive Multiple-Model use is without mark particle filter algorithm prediction result when Fig. 6 training data is 300.

Specific embodiment

A kind of service life of lithium battery estimation method based on IMM-UPF, the specific steps are as follows:

(1) it is charged first using the battery of four same models with constant 1.1A electric current, until voltage reaches charge cutoff 4.2 volts of voltage, then with 4.2 volts of constant voltage chargings, after charging current is down to cut-off current 0.05A or less, terminate to fill Electricity；The rated capacity of battery is 1.1Ah.Charge-discharge test is carried out at room temperature, and record is each time after complete charge and discharge process Discharge capacity obtains battery capacity attenuation curve, sets the failure threshold of battery as 0.88Ah；As shown in Figure 1.

(2) four cell set capacity data are had collected by carrying out charge-discharge test to four batteries, passes through observation Attenuation curve finds that the 4th group of data and first three groups gap are big, therefore is used to determine each single model parameter for first three groups data The data that 4th battery obtains capacity are used as the verifying of forecasting accuracy by initial value；

(3) use is by Least Square Method battery capacity C_lSecond order polynomial regression equation followed to describe lithium battery At ring number l times with the maximum capacity C that can store_lBetween relationship, be denoted as model one, polynomial expression formula is

C_l=a₁l²+b₁l+c₁

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₁,b₁And c₁All it is constant related with discharge current and temperature, its value is determined by the mode of curve matching；

Second model that the empirical model for using double exponential equations to indicate is decayed as battery capacity, expression formula is such as Under: C_l=a₂·exp(b₂·l)+c₂·exp(d₂·l)

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₂And b₂It is constant related with internal driving, parameter c₂And d₂It is constant related with aging rate of the battery, parameter a₂,b₂,c₂ And d₂Value by way of curve matching determine；

The integrated model for using polynomial empirical model and exponential model to combine is as the third model, and expression formula is such as Under: C_l=a₃·exp(-b₃·l)+c₃·l^2+d₃

C in formula_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₃,b₃,c₃And d₃The mode of curve matching is determining, parameter a₃And b₃It is constant related with internal driving, parameter c₃And d₃It is and electric The related constant of pond rate of ageing；

Then parameter fitting is carried out to three single models respectively using the data of first three groups battery, respectively obtains first three groups Battery correspond to the parameter of each single model.Assuming that obtained fit parameter values are credible, obtained based on different groups of data The initial basic confidence distribution of parameter value is determined by following formula:

Wherein a_1,v,a_2,v, a_3,v, b_1,v,b_2,v, b_3,v, c_1,v,c_2,v, c_3,v, d_2,v, d_3,vFor each model parameter, parameter a_1,v, a_2,v, a_3,vAnd b_1,v, b_2,v, b_3,vIt is constant related with internal driving, parameter c_1,v, c_2,v, c_3,vAnd d_2,v, d_3,vIt is old with battery Change the related constant of rate, h is battery sample number, and v indicates v-th of model, it follows that the 4th battery corresponds to each model The initial value of parameter

M indicates the confidence level of each single model parameter.

(4) in order to realize that Interactive Multiple-Model (IMM) to the reciprocation of input quantity, needs the quantity of state by three models equal It is set as battery capacity C_l, establish corresponding state equation and observational equation.

The corresponding state equation of first model:

Observational equation:

The corresponding state equation of second model:

Observational equation:

Third model state equation:

Observational equation:

Wherein x_kIndicate that the battery when cycle period is k can use maximum capacity predicted value, that is, state vector, Z_kIndicate circulation Maximum capacity measured value when period is k measures vector, Indicate the Gaussian noise that mean value is 0 and standard deviation is σ, a₁, b₁, c₁, a₂, b₂, c₂, d₂, a₃, b₃, c₃, d₃Initial value by X_M1, X_M2, X_M3It provides.

(5) each single model uses no mark particle filter algorithm respectively to predict the remaining life of the 4th battery.Such as Shown in Fig. 3,4,5.

(6) as shown in Fig. 2, being carried out using data of the interactive multi-model to the 4th battery without mark particle filter and parameter It updates, quantity of state and covariance of three models in each period are realized in IMM outputs and inputs interaction, is calculated using IMMUPF Method realizes the prediction to remaining battery life.The present invention uses absolute error and remaining life probability density function (RULPDF) Standard deviation measures the Stability and veracity of simulation result.As shown in Figure 6.

When training data is 300, the absolute error of the prediction result of Fig. 3 model one and Fig. 5 model three is respectively 241 Hes 135, RULPDF standard deviation is respectively 48 and 42；The absolute error of the prediction result of Fig. 4 model two is the mark of 41, RULPDF Quasi- deviation is 37.The standard deviation that the absolute error of the prediction result of Fig. 6 Interactive Multiple-Model is 10, RULPDF is 19, thus table Bright IMM-UPF algorithm reduces the error of prediction, has preferable precision, i.e. stability is more preferable.

The UPF algorithm specifically:

1) it initializes first

For system:

Wherein x indicates state vector, and Z indicates measurement vector, parameter W_k-1Indicate process noise, V_kExpression measurement noise, two Person is white Gaussian noise vector that is mutually indepedent and being zero-mean；F_k-1Indicate state-transition matrix, H_kIndicate observing matrix, It is assumed that observed quantity Z_kIndependently of given current quantity of state x_kOther states；

The equation that period is k is

θ_k-1Indicate the error amount of k-1 moment state estimation,Indicate the state estimation at k-1 moment, P_k-1Indicate k-1 The error co-variance matrix at moment, E are expectation of a random variable, Q_k-1Indicate the covariance matrix of process noise, R_k-1It indicates The covariance matrix of observation noise, T representing matrix transposition；

If k=0, and make particle collectionK is sample number, that is, population, if It indicates original state mean value, state primary condition is augmented:

p(x₀) indicate prior distribution,Indicate the original state amount of i-th of particle after being augmented,Expression is augmented The error covariance of the original state amount of i-th of particle afterwards；

2) Sigma sampling and weight computing

Sigma sampled point obtains:

λ=α²(n_x+κ)-n_x

Wherein,Indicate the state variable after being augmented,Indicate the error covariance after being augmented, λ is scaling Coefficient, κ are parameter to be selected, are usually taken to be 3-n_x, n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise, n_xIt indicates The dimension of state vector, n_u=n_x+n_V+n_WIt indicates state vector, measures the sum of noise and the dimension of process noise；

Calculate the weight of sampled point:

Wherein, y is the weight of mean value, and z is the weight of covariance, and f indicates which sampled point, α indicatePeriphery Sigma point distribution situation, β are constant related with the prior distribution of x, and γ is typically set to 0 or 3-n as scale parameter, works as ε Measurement noise Gaussian distributed is indicated when=3-n；

3) update of anticipation function

Corresponding Sigma point particle collection can be expressed as when period is kIndicate sampling number, Wherein for particle collectionWithRespectively indicate nx dimensional vector before particle collection, nx+1 dimension to n_x+n_WDimensional vector And n_x+n_W+ 1 dimension arrives n_x+n_V+n_WDimensional vector；n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise, Indicate the k+1 moment to the predicted state value of Sigma point set,Indicate that the k+1 moment adds the predicted state value of Sigma point set The predicted value for the system mode that power summation obtains, P_i,(k+1|k)Indicate the k+1 moment to the error covariance square of system state variables Battle array, P_VV,(k+1|k)Indicate the error co-variance matrix to observational equation at prediction k+1 moment, P_xV,(k+1|k)Indicate that the k+1 moment mutually assists Variance matrix, Z_i,(k+1|k)Indicate the k+1 moment to the observation of the prediction of Sigma point particle collection,Indicate the k+1 moment pair The system prediction value that the observed value weighting of the prediction of Sigma point particle collection is summed,It is nonlinear state side Eikonal number,It is non-Systems with Linear Observation equation functions；

P_i,(k+1|k+1)=P_i,(k+1|k)-G(k+1)P_VV,(k+1|k)G^T(k+1)

G (k+1) is Kalman filtering gain matrix,Indicate the shape of etching system when by measuring the k+1 for updating and obtaining State value, P_i,(k+1|k+1)It indicates to measure the error co-variance matrix for updating the obtained k+1 moment, Z_k+1Indicate that etching system is practical when k+1 Observation；

4) weight computing and resampling

Each particle is updated to obtain the estimated value and mistake of the particle at current time using Unscented kalman filtering algorithm Poor covariance value, to obtain suggestion distributionWhereinFor the probability of Gaussian distributed Then density function is predicted final result with particle filter (PF) algorithm, if reference distribution is prior distribution, it may be assumed that

q(x_i,k|x_i,(0:k-1),Z_0:k)=p (x_i,k|x_i,k-1)

x_i,kIndicate i-th of particle shape state value of k moment, x_i,(0:k-1)It indicates from 0 to k-1 moment, i-th of particle shape state value Set, Z_0:kIndicate the set from 0 to k moment measuring value, x_i,k-1Indicate i-th of particle shape state value of k-1 moment；

The weighted value of each particle is determined by following formula:

Weight standardization:

Resampling: work as N_effValue be less than setting threshold value N_thWhen, to particle collectionResampling is carried out, is obtained new Particle collectionThreshold value N_thIt is typically set to N_th=2K/3；N_effIt is calculated by following:

N_effThe number for indicating effective particle, by comparing the threshold value N of itself and setting_thSize determines whether to be adopted again Sample；

Output state amount and the estimation of corresponding covariance are as follows:

For the estimated value of quantity of state, P_i,kThe estimated value of covariance is corresponded to for quantity of state；

5) as k < L, L is observation sample number, enables k=k+1, repeats step 2), 3), 4), otherwise terminates.

The IMMUPF algorithm specifically:

1)) input interaction

By state estimationWith the model probability of filter each in previous stepObtain hybrid estimationAnd association VarianceUsing hybrid estimation as the original state of previous cycle；

For model g, when the period is k:

The prediction probability of model g:M is Number of Models, π_sgIt indicates

Transition probability of the model s to model g；

Prediction probability of the model s to model g:

The admixture of model g is estimated:

The mixing covariance of model g is estimated:

2) it) filters

For model g, particle will be filtered with UPF, utilize the particle collection of period kWithObtain next week The state of phase k+1 and its estimator of covarianceWithResidual error and its covariance are

3)) model probability updates

Original probability will be updated, and new mixing probability will be calculated according to its likelihood function, for model g, Likelihood function is write as:

WhereinIndicate that the density function of Gaussian distributed, new model mixing probability are expressed as:

Alphabetical o is normaliztion constant；

4)) output interaction: being based on model probability, weights and merges to each filter estimated result, obtains total state and estimate Meter and covariance estimation；

The particle collection of expression state and its covariance will be realized by lower array function and be interacted:

Final state amount and its covariance export in the following manner:

Claims (3)

1. a kind of service life of lithium battery estimation method based on IMM-UPF, it is characterised in that: specific step is as follows:

(1) first using the battery of four same models with constant current charging, until voltage reaches charge cutoff voltage, then With constant voltage charging, after charging current is down to cut-off current, terminate charging；Charge-discharge test is carried out at room temperature, is remembered Discharge capacity after recording complete charge and discharge process each time, obtains battery capacity attenuation curve, sets the failure threshold of battery；

(2) four cell set capacity data are had collected by carrying out charge-discharge test to four batteries, is decayed by observation Curve finds that the 4th group of data and first three groups gap are big, therefore is used to determine the initial of each single model parameter for first three groups data The data that 4th battery obtains capacity are used as the verifying of forecasting accuracy by value；

(3) use is by Least Square Method battery capacity C_lSecond order polynomial regression equation come describe lithium battery circulation time At number l time and the maximum capacity C that can store_lBetween relationship, be denoted as model one, polynomial expression formula is

C_l=a₁l²+b₁l+c₁

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₁,b₁ And c₁All it is constant related with discharge current and temperature, its value is determined by the mode of curve matching；

Second model that the empirical model for using double exponential equations to indicate is decayed as battery capacity, expression formula are as follows: C_l= a₂·exp(b₂·l)+c₂·exp(d₂·l)

In formula, C_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₂With b₂It is constant related with internal driving, parameter c₂And d₂It is constant related with aging rate of the battery, parameter a₂,b₂,c₂And d₂ Value by way of curve matching determine；

The integrated model for using polynomial empirical model and exponential model to combine is as the third model, and expression formula is as follows: C_l =a₃·exp(-b₃·l)+c₃·l^2+d₃

C in formula_lIndicate maximum battery capacity of the lithium battery in cycle-index l, l indicates lithium battery cycle-index, parameter a₃,b₃, c₃And d₃The mode of curve matching is determining, parameter a₃And b₃It is constant related with internal driving, parameter c₃And d₃It is old with battery Change the related constant of rate；

Then parameter fitting is carried out to three single models respectively using the data of first three groups battery, respectively obtains the electricity of first three groups Pond corresponds to the parameter of each single model, it is assumed that obtained fit parameter values are credible, the parameter obtained based on different groups of data The initial basic confidence distribution of value is determined by following formula:

Wherein a_1,v,a_2,v,a_3,v,b_1,v,b_2,v,b_3,v,c_1,v,c_2,v,c_3,v,d_2,v,d_3,vFor each model parameter,

Parameter a_1,v, a_2,v, a_3,vAnd b_1,v, b_2,v, b_3,vIt is constant related with internal driving, parameter c_1,v, c_2,v, c_3,vAnd d_2,v, d_3,vIt is constant related with aging rate of the battery, h is battery sample number, and v indicates v-th of model, it follows that the 4th battery The initial value of corresponding each model parameter M indicates the confidence level of each single model parameter；

(4) in order to realize that the quantity of state of three models to the reciprocation of input quantity, is set as battery and held by Interactive Multiple-Model IMM Measure C_l, establish corresponding state equation and observational equation；

The corresponding state equation of first model: x_k=x_k-1+a₁·(2·k-1)+b₁+W_1,k-1,

Observational equation: Z_k=x_k+V_1,k,

The corresponding state equation of second model；

x_k=x_k-1+a₂·exp(b₂·k)[1-exp(-b₂)]+c₂·exp(d₂·k)[1-exp(-d₂)]+W_2,k-1,

Observational equation: Z_k=x_k+V_2,k,

Third model state equation:

x_k=x_k-1+a₃·exp(b₃·k)[1-exp(-b₃)]+c₃·(2·k-1)+W_3,k-1,

Observational equation: Z_k=x_k+V_3,k,

Wherein x_kIndicate that the battery when cycle period is k can use maximum capacity predicted value, that is, state vector, Z_kIndicate cycle period Maximum capacity measured value when for k measures vector,Indicate that mean value is 0 and standard deviation is σ Gaussian noise, a₁,b₁,c₁,a₂,b₂,c₂,d₂,a₃,b₃,c₃,d₃Initial value by X_M1, X_M2, X_M3It provides；

(5) each single model uses no mark particle filter algorithm respectively to predict the remaining life of the 4th battery；

(6) update without mark particle filter and parameter using data of the interactive multi-model to the 4th battery, three models It is realized in IMM in the quantity of state and covariance in each period and outputs and inputs interaction, realized using IMMUPF algorithm to battery The prediction of remaining life.

2. a kind of service life of lithium battery estimation method based on IMM-UPF according to claim 1, it is characterised in that: described Without mark particle filter algorithm specifically:

1) it initializes first

For system:

Wherein x_kIndicate state vector, Z_kIndicate measurement vector, parameter W_k-1Indicate process noise, V_kIndicate measurement noise, the two It is white Gaussian noise vector that is mutually indepedent and being zero-mean；F_k-1Indicate state-transition matrix, H_kIndicate observing matrix, it is false Determine observed quantity Z_kIndependently of given current quantity of state x_kOther states；

The equation that period is k is

θ_k-1Indicate the error amount of k-1 moment state estimation,Indicate the state estimation at k-1 moment, P_k-1Indicate the k-1 moment Error co-variance matrix, E is expectation of a random variable, Q_k-1Indicate the covariance matrix of process noise, R_k-1Indicate observation The covariance matrix of noise, T representing matrix transposition；

If k=0, and make particle collectionK is sample number, that is, population, ifIt indicates The original state mean value of i-th of particle, is augmented state primary condition:

p(x₀) indicate prior distribution,Indicate the original state amount of i-th of particle after being augmented,Expression is augmented rear i-th The error covariance of the original state amount of a particle；

2) Sigma sampling and weight computing

Sigma sampled point obtains:

λ=α²(n_x+κ)-n_x

Wherein,Indicate the state variable after being augmented,Indicate the error covariance after being augmented, λ is scaling coefficient, κ For parameter to be selected, it is usually taken to be 3-n_x, n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise, n_xExpression state to The dimension of amount, n_u=n_x+n_V+n_WIt indicates state vector, measures the sum of noise and the dimension of process noise；

Calculate the weight of sampled point:

Wherein, y is the weight of mean value, and z is the weight of covariance, and f indicates which sampled point, α indicate the sigma point on the periphery x Distribution situation, β are constant related with the prior distribution of x, and γ is typically set to 0 or 3-n as scale parameter, as ε=3-n Indicate measurement noise Gaussian distributed；

3) update of anticipation function

Corresponding Sigma point particle collection can be expressed as when period is kSampling number is indicated, wherein right In particle collectionWithRespectively indicate n before particle collection_xDimensional vector, n_x+ 1 dimension arrives n_x+n_WDimensional vector and n_x+n_W+ 1 dimension arrives n_x+n_V+n_WDimensional vector；n_WIndicate the dimension of process noise, n_VIndicate the dimension of observation noise,When indicating k+1 The predicted state value to Sigma point set is carved,Indicate that the k+1 moment obtains the predicted state value weighted sum of Sigma point set The predicted value of the system mode arrived, P_i,(k+1|k)Indicate the k+1 moment to the error co-variance matrix of system state variables, P_VV,(k+1|k)Indicate the error co-variance matrix to observational equation at prediction k+1 moment, P_xV,(k+1|k)Indicate the k+1 moment mutual side of association Poor matrix, Z_i,(k+1|k)Indicate the k+1 moment to the observation of the prediction of Sigma point particle collection,Indicate the k+1 moment pair The system prediction value that the observed value weighting of the prediction of Sigma point particle collection is summed,It is nonlinear state side Eikonal number,It is non-Systems with Linear Observation equation functions；

P_i,(k+1|k+1)=P_i,(k+1|k)-G(k+1)P_VV,(k+1|k)G^T(k+1)

G (k+1) is Kalman filtering gain matrix,Indicate the state value of etching system when by measuring the k+1 for updating and obtaining, P_i,_(k+1|k+1)It indicates to measure the error co-variance matrix for updating the obtained k+1 moment, Z_k+1Indicate etching system actual sight when k+1 Measured value；

4) weight computing and resampling

Each particle is updated to obtain estimated value and the error association of the particle at current time using Unscented kalman filtering algorithm Variance yields, to obtain suggestion distributionWhereinFor the probability density letter of Gaussian distributed Number, then predicts final result with particle filter algorithm, if reference distribution is prior distribution, it may be assumed that

q(x_i,k|x_i,(0:k-1),Z₀:_k)=p (x_i,k|x_i,k-1)

x_i,kIndicate i-th of particle shape state value of k moment, x_i,(0:k-1)Indicate the set from 0 to i-th of particle shape state value of k-1 moment, Z_0:kIndicate the set from 0 to k moment measuring value, x_i,k-1Indicate i-th of particle shape state value of k-1 moment；

The weighted value of each particle is determined by following formula:

Weight standardization:

Resampling: work as N_effValue be less than setting threshold value N_thWhen, to particle collectionResampling is carried out, new particle is obtained Collection Threshold value N_thIt is typically set to N_th=2K/3；N_effIt is calculated by following:

N_effThe number for indicating effective particle, by comparing the threshold value N of itself and setting_thSize come determine whether carry out resampling；

Output state amount and the estimation of corresponding covariance are as follows:

For the estimated value of quantity of state, P_i,kThe estimated value of covariance is corresponded to for quantity of state；

(5) as k < L, L is observation sample number, enables k=k+1, repeats step 2), 3), 4), otherwise terminates.

3. a kind of service life of lithium battery estimation method based on IMM-UPF according to claim 2, it is characterised in that: described IMMUPF algorithm specifically:

1)) input interaction

By state estimationWith the model probability of filter each in previous stepObtain hybrid estimationAnd covarianceUsing hybrid estimation as the original state of previous cycle；

For model g, when the period is k:

The prediction probability of model g:M is Number of Models, π_sgIndicate model s to mould The transition probability of type g；

Prediction probability of the model s to model g:

The admixture of model g is estimated:

The mixing covariance of model g is estimated:

2) it) filters

For model g, particle will be filtered with UPF algorithm, utilize the particle collection of period kWithObtain next week The state of phase k+1 and its estimator of covarianceWithResidual error and its covariance are

3)) model probability updates

Original probability will be updated, and new mixing probability will be calculated according to its likelihood function, for model g, likelihood Function is write as:

WhereinIndicate that the density function of Gaussian distributed, new model mixing probability are expressed as:

Alphabetical o is normaliztion constant；

4)) output interaction: being based on model probability, weights and merges to each filter estimated result, obtain total state estimation and Covariance estimation；

The particle collection of expression state and its covariance will be realized by lower array function and be interacted:

Final state amount and its covariance export in the following manner: