CN109932656A - A Lithium Battery Life Estimation Method Based on IMM-UPF - Google Patents

Abstract

The invention discloses a lithium battery life estimation method based on IMM-UPF, which adopts a new fusion model interactive multi-model for fusion calculation of different attenuation models. The method has the advantages that the trend that the attenuation of the lithium battery is non-Gaussian and non-linear is considered, the Kalman filtering has larger errors, and unscented particle filtering is used for filtering each model, so that the problem that particles are deficient in the resampling process of the particle filtering is solved, and more accurate prediction results are obtained compared with the Kalman filtering. The IMM-UPF method is verified by a simulation result and experimental data comparison method, and the result shows that the method can improve the lithium battery service life prediction accuracy.

Description

A Lithium Battery Life Estimation Method Based on IMM-UPF

technical field

The invention relates to the technical field of lithium batteries, in particular to a method for estimating the life of a lithium battery based on IMM-UPF.

Background technique

With the rapid development of electric vehicles, lithium batteries have attracted much attention as their mainstream power source. State-of-health (SOH) is one of the key parameters of lithium batteries, and it is a direct parameter for users to evaluate the current battery life.

At present, the life prediction of lithium battery mainly adopts the method based on physical principle modeling and data modeling to predict the capacity decay of lithium battery. However, for complex dynamic systems, especially those with uncertain noise, it is difficult to establish an accurate analytical model. The method based on data modeling can capture the internal relationship in the data and learn the changing trend presented in the data, without the need for specific knowledge of material properties, structure, failure mechanism, etc., avoiding the development of overly complex physical models, commonly used The single empirical model of can achieve good prediction results in different stages, but it cannot describe the change trend of the whole life cycle of lithium batteries well.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for estimating the life of a lithium battery based on IMM-UPF in order to make up for the defects of the prior art.

The present invention is achieved through the following technical solutions:

The present invention proposes a lithium battery life estimation method using the combination of interactive multi-model and unscented particle filtering algorithm. First, a polynomial model, a double exponential model and an integrated model are used to describe an empirical model of the lithium battery based on physical performance degradation. The three models are filtered by the unscented particle filter algorithm in the IMM model, and finally the SOH of the lithium battery is accurately predicted through the filtering results.

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

(1) First, use four batteries of the same type to charge at a constant 1.1A current until the voltage reaches the charging cut-off voltage of 4.2 volts, and then charge at a constant voltage of 4.2 volts until the charging current drops below the cut-off current of 0.05A, then end charging; The rated capacity of the battery is 1.1 Ah. The charge-discharge experiment was carried out at room temperature, the discharge capacity after each complete charge-discharge process was recorded, and the battery capacity decay curve was obtained, and the failure threshold of the battery was set to 0.88Ah;

(2) Four groups of battery capacity data were collected by charging and discharging the four batteries described above. By observing the decay curve, it was found that the fourth group of data had a large gap with the first three groups. Therefore, the first three groups of data were used to determine each single The initial value of the model parameters, the data of the obtained capacity of the fourth battery is used as a verification of the prediction accuracy;

(3) Use the second-order polynomial regression equation to estimate the battery capacity C _l by the least squares method to describe the relationship between the lithium battery when the number of cycles is l and the maximum capacity C _l that can be stored, denoted as model 1, the expression of polynomial The formula is

C _l =a ₁ l ² +b ₁ l+c ₁

In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, l represents the number of cycles of the lithium battery, and the parameters a ₁ , b ₁ and c ₁ are all constants related to the discharge current and temperature, which are fitted by the curve. way to determine its value;

The empirical model expressed by the double exponential equation is used as the second model of battery capacity fading, and its expression is as follows: C _l =a ₂ ·exp(b ₂ ·l)+c ₂ ·exp(d ₂ ·l)

In the formula, C _l represents the maximum battery capacity of the lithium battery at the number of cycles l, l represents the number of cycles of the lithium battery, the parameters a ₂ and b ₂ are constants related to the internal impedance, and the parameters c ₂ and d ₂ are related to the battery aging rate. Relevant constants, the values of parameters a ₂ , b ₂ , c ₂ and d ₂ are determined by curve fitting;

An ensemble model combining an empirical model of a polynomial and an exponential model is used as the third model, and the expression is as follows: C _l =a ₃ ·exp(-b ₃ ·l)+c ₃ ·l^2+d ₃

In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, and l represents the number of cycles of the lithium battery. The parameters a ₃ , b ₃ , c ₃ and d ₃ are determined by curve fitting, and the parameters a ₃ and b ₃ are Constants related to internal impedance, parameters _c3 and _d3 are constants related to the battery aging rate.

Then use the data of the first three groups of batteries to fit the parameters of the three single models respectively, and obtain the parameters of the first three groups of batteries corresponding to each single model. Assuming that the obtained fitted parameter values are credible, the initial basic confidence distribution of the parameter values obtained based on different sets of data is determined by the following formula:

where 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,v are model parameters, parameters a _1,v , a _2,v , a _3,v and b _1,v , b _2,v , b _3,v are constants related to internal impedance, parameter c _1,v , c _2,v , c _3,v and d _2,v , d _3,v is a constant related to the aging rate of the battery, h is the number of battery samples, and v represents the vth model, which leads to the Four batteries correspond to the initial values of each model parameter

M represents the confidence of each single model parameter.

(4) In order to realize the interaction of the interactive multi-model (IMM) on the input quantity, it is necessary to set the state quantity of the three models as the battery capacity C _l , and establish the corresponding state equation and observation equation.

The equation of state corresponding to the first model:

Observation equation:

The state equation corresponding to the second model;

Observation equation:

The third model equation of state:

Observation equation:

where x _k represents the predicted value of the maximum battery capacity available when the cycle period is k, that is, the state vector, and Z _k represents the maximum capacity measurement value when the cycle period is k, that is, the measurement vector, Represents Gaussian noise with mean 0 and standard deviation σ, the initial values of a ₁ , b ₁ , c ₁ , a ₂ , b ₂ , c ₂ , d ₂ , a ₃ , b ₃ , c ₃ , d ₃ are determined by X _M1 , X _M2 , X _{M3 are} given;

(5) Each single model uses the Unscented Particle Filter (UPF) algorithm to predict the remaining life of the fourth battery.

(6) Use the interactive multi-model to filter and update the parameters of the data of the fourth battery. The state quantities and covariances of the three models in each cycle realize the input and output interaction in the IMM, and use the IMMUPF algorithm to realize the battery remaining Prediction of lifespan. The present invention uses the absolute error and the standard deviation of the remaining life probability density function (RULPDF) to measure the accuracy and stability of the simulation results, uses the first 300 groups of data as training data, and the failure threshold (Failure Threshold) is 0.8, That is, the battery capacity C _l =0.88Ah, and the actual battery life is 665. That is, when C _l =0.88Ah, the fourth battery cycle number corresponds to 665 times.

The UPF algorithm is specifically:

1) First initialize

For the system:

where x represents the state vector, Z represents the measurement vector, the parameter W _k-1 represents the process noise, and V _k represents the measurement noise, both of which are independent Gaussian white noise vectors with zero mean; F _k-1 represents the state transition matrix , H _k represents the observation matrix, assuming that the observation quantity Z _k is independent of other states given the current state quantity x _k ;

The equation with period k is

θ _k-1 represents the error value of state estimation at time k-1, Represents the state estimate value at time k-1, P _k-1 represents the error covariance matrix at time k-1, E is the expected value of the random variable, Q _k-1 represents the covariance matrix of process noise, R _k-1 represents the observation Covariance matrix of noise, T represents matrix transpose;

Set k = 0, and make a particle set K is the number of samples, that is, the number of particles, set Represents the mean value of the initial state, and expands the initial condition of the state:

p(x ₀ ) represents the prior distribution, represents the initial state quantity of the ith particle after dimension expansion, Represents the error covariance of the initial state quantity of the ith particle after dimension expansion;

2) Sigma sampling and weight calculation

Sigma sampling point acquisition:

λ=α ² (n _x +κ)-n _x

in, represents the state variable after expansion, Represents the error covariance after dimension expansion, λ is the scaling factor, κ is the parameter to be selected, usually taken as 3-n _x , n _W represents the dimension of the process noise, n _V represents the dimension of the observation noise, and n _x represents the The dimension of the state vector, n _u =n _x +n _V +n _W represents the state vector, the sum of the dimensions of measurement noise and process noise;

Calculate the weights of the sampling points:

Among them, y is the weight of the mean, z is the weight of the covariance, f represents the number of sampling points, and α represents The distribution of surrounding sigma points, β is a constant related to the prior distribution of x, γ is usually set to 0 or 3-n as a scale parameter, and when ε=3-n, it means that the measurement noise obeys the Gaussian distribution;

3) Update of the prediction function

When the period is k, the corresponding Sigma point particle set can be expressed as represents the number of sampling points, where for the particle set and Represents the first n _x dimension column vector of the particle set, n _x +1 dimension to n _x +n _W dimension column vector and n _x +n _W +1 dimension to n _x +n _V +n _W dimension column vector; n _W represents the dimension of the process noise, n _V represents the dimension of the observation noise, Represents the predicted state value of the Sigma point set at time k+1, Represents the predicted value of the system state obtained by the weighted summation of the predicted state values of the Sigma point set at time k+1, P _i,(k+1|k) represents the error covariance matrix of the system state variable at time k+1, P _VV,(k+1|k) represents the error covariance matrix of the observation equation at time k+1, P _xV,(k+1|k) represents the cross-covariance matrix at time k+1, Z _{i,(k +1|k)} represents the predicted observation value of the Sigma point particle set at time k+1, Represents the system prediction value obtained by the weighted summation of the predicted observations of the Sigma point particle set at time k+1, is the nonlinear state equation function, is the nonlinear observation equation function;

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 the Kalman filter gain matrix, Represents the state value of the system at time k+1 obtained by measurement update, P _i,(k+1|k+1) represents the error covariance matrix at time k+1 obtained by measurement update, Z _k+1 represents k The actual observation value of the system at +1 time;

4) Weight calculation and resampling

For each particle, use the unscented Kalman filter algorithm to update the estimated value and error covariance value of the particle at the current moment, so as to obtain the proposed distribution in In order to obey the probability density function of the Gaussian distribution, and then use the particle filter (PF) algorithm to predict the final result, let the reference distribution be the prior distribution, namely:

q(x _i,k |x _i,(0:k-1) ,Z _0:k )=p(x _i,k |x _i,k-1 )

x _i,k represents the i-th particle state value at time k, x _i,(0:k-1) represents the set of i-th particle state values from 0 to k-1 time, Z _0:k represents from 0 to k The set of measurement values at time, x _i,k-1 represents the state value of the ith particle at time k-1;

The weight value of each particle is determined by the following formula:

Weight normalization:

Resampling: When the value of N _eff is less than the set threshold N _th , the particle set is Perform resampling to get a new set of particles The threshold N _th is usually set as N _th =2K/3; N _eff is calculated by the following:

N _eff represents the number of valid particles, and it is determined whether to perform resampling by comparing it with the set threshold N _th ;

The output state quantities and the corresponding covariance estimates are:

is the estimated value of the state quantity, and P _i,k is the estimated value of the covariance corresponding to the state quantity;

5) When k<L, L is the number of observation samples, let k=k+1, repeat steps 2), 3), 4), otherwise end.

The idea of IMMUPF is that at each moment, assuming that a certain model is valid at the present moment, by mixing the predicted value of battery capacity estimated by all the unscented particle filters at the previous moment to obtain a matching unscented model matching this particular model. The initial conditions of the particle filter, then synchronously filter each model, and finally update the model probability based on the model matching likelihood function, and weight all the battery capacity predictions corrected by the unscented particle filter to obtain the final battery. Capacity forecast. The stability and accuracy of the prediction results are judged by analyzing and comparing the absolute error of each model in the prediction of remaining life and the standard deviation of the probability density function.

The described IMMUPF algorithm is specifically:

1)) Input interaction

estimated by state with the model probability of each filter in the previous step get a mixed estimate and covariance Use the hybrid estimate as the initial state of the current loop;

For model g, with period k:

The predicted probability of model g: m is the number of models, π _sg represents

The transition probability from model s to model g;

Predicted probability from model s to model g:

Mixed state estimation for model g:

Mixed covariance estimate for model g:

2)) Filtering

For model g, the particles will be filtered with UPF, using the set of particles of period k and Get the state of the next cycle k+1 and its covariance estimator and The residuals and their covariances are

3)) Model probability update

The original probability will be updated, and the new mixed probability will be calculated according to its likelihood function. For model g, its likelihood function is written as:

in Represents a density function that obeys a Gaussian distribution, and the new model mixture probability is expressed as:

The letter o is a normalization constant;

4)) Output interaction: Based on the model probability, weighted and merged the estimation results of each filter to obtain the total state estimation and covariance estimation;

The set of particles representing states and their covariances will interact through the following functions:

The final state quantity and its covariance are output in the following way:

The advantages of the present invention are: 1. In the process of estimating the life of the lithium battery, the present invention uses an interactive multi-model, so that the prediction result not only reduces the accuracy dependence on the initial parameters of each model, but also improves the actual use. Efficiency and cost reduction effect.

2. The present invention uses the interactive multi-model unscented particle filtering algorithm to reduce the prediction error, and the probability distribution of the remaining battery life is narrower, that is, the prediction result is more stable.

Description of drawings

Figure 1. Four groups of battery capacity data decay curves.

Figure 2. Flowchart of the interactive multi-model unscented particle filter algorithm for estimating battery life.

Figure 3. The prediction results of model 1 using the unscented particle filter algorithm when the training data is 300.

Figure 4. The prediction results of model 2 using the unscented particle filter algorithm when the training data is 300.

Figure 5. The prediction results of model 3 using the unscented particle filter algorithm when the training data is 300.

Figure 6. When the training data is 300, the interactive multi-model uses the unscented particle filter algorithm to predict the results.

Detailed ways

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

(1) First, use four batteries of the same type to charge at a constant 1.1A current until the voltage reaches the charging cut-off voltage of 4.2 volts, and then charge at a constant voltage of 4.2 volts until the charging current drops below the cut-off current of 0.05A, then end charging; The rated capacity of the battery is 1.1 Ah. The charge-discharge experiment was carried out at room temperature, the discharge capacity after each complete charge-discharge process was recorded, and the battery capacity decay curve was obtained, and the battery failure threshold was set to 0.88Ah; as shown in Figure 1.

(2) Four groups of battery capacity data were collected by charging and discharging the four batteries described above. By observing the decay curve, it was found that the fourth group of data had a large gap with the first three groups. Therefore, the first three groups of data were used to determine each single The initial value of the model parameters, the data of the obtained capacity of the fourth battery is used as a verification of the prediction accuracy;

(3) Use the second-order polynomial regression equation to estimate the battery capacity C _l by the least squares method to describe the relationship between the lithium battery when the number of cycles is l and the maximum capacity C _l that can be stored, denoted as model 1, the expression of polynomial The formula is

C _l =a ₁ l ² +b ₁ l+c ₁

In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, l represents the number of cycles of the lithium battery, and the parameters a ₁ , b ₁ and c ₁ are all constants related to the discharge current and temperature, which are fitted by the curve. way to determine its value;

The empirical model expressed by the double exponential equation is used as the second model of battery capacity fading, and its expression is as follows: C _l =a ₂ ·exp(b ₂ ·l)+c ₂ ·exp(d ₂ ·l)

In the formula, C _l represents the maximum battery capacity of the lithium battery at the number of cycles l, l represents the number of cycles of the lithium battery, the parameters a ₂ and b ₂ are constants related to the internal impedance, and the parameters c ₂ and d ₂ are related to the battery aging rate. Relevant constants, the values of parameters a ₂ , b ₂ , c ₂ and d ₂ are determined by curve fitting;

An ensemble model combining an empirical model of a polynomial and an exponential model is used as the third model, and the expression is as follows: C _l =a ₃ ·exp(-b ₃ ·l)+c ₃ ·l^2+d ₃

In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, and l represents the number of cycles of the lithium battery. The parameters a ₃ , b ₃ , c ₃ and d ₃ are determined by curve fitting, and the parameters a ₃ and b ₃ are Constants related to the internal impedance, parameters c3 and _d3 are constants related to the battery aging rate _;

Then use the data of the first three groups of batteries to fit the parameters of the three single models respectively, and obtain the parameters of the first three groups of batteries corresponding to each single model. Assuming that the obtained fitted parameter values are credible, the initial basic confidence distribution of the parameter values obtained based on different sets of data is determined by the following formula:

where 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,v are model parameters, parameters a _1,v , a _2,v , a _3,v and b _1,v , b _2,v , b _3,v are constants related to internal impedance, parameter c _1,v , c _2,v , c _3,v and d _2,v , d _3,v is a constant related to the aging rate of the battery, h is the number of battery samples, and v represents the vth model, which leads to the Four batteries correspond to the initial values of each model parameter

M represents the confidence of each single model parameter.

(4) In order to realize the interaction of the interactive multi-model (IMM) on the input quantity, it is necessary to set the state quantity of the three models as the battery capacity C _l , and establish the corresponding state equation and observation equation.

The equation of state corresponding to the first model:

Observation equation:

The state equation corresponding to the second model:

Observation equation:

The third model equation of state:

Observation equation:

where x _k represents the predicted value of the maximum battery capacity available when the cycle period is k, that is, the state vector, and Z _k represents the maximum capacity measurement value when the cycle period is k, that is, the measurement vector, Represents Gaussian noise with mean 0 and standard deviation σ, the initial values of a ₁ , b ₁ , c ₁ , a ₂ , b ₂ , c ₂ , d ₂ , a ₃ , b ₃ , c ₃ , d ₃ are determined by X _M1 , X _M2 , X _{M3 are} given.

(5) Each single model uses the unscented particle filter algorithm to predict the remaining life of the fourth battery. As shown in Figures 3, 4 and 5.

(6) As shown in Figure 2, the interactive multi-model is used to perform unscented particle filtering and parameter update on the data of the fourth battery. The state quantities and covariances of the three models in each cycle are input and output in the IMM Interactively, use the IMMUPF algorithm to predict the remaining battery life. The present invention uses the absolute error and the standard deviation of the remaining life probability density function (RULPDF) to measure the accuracy and stability of the simulation results. As shown in Figure 6.

When the training data is 300, the absolute errors of the prediction results of Model 1 in Figure 3 and Model 3 in Figure 5 are 241 and 135, respectively, and the standard deviations of RULPDF are 48 and 42, respectively; the absolute error of the prediction results of Model 2 in Figure 4 is 41, The standard deviation of RULPDF is 37. Figure 6 The absolute error of the prediction results of the interactive multi-model is 10, and the standard deviation of RULPDF is 19, which shows that the IMM-UPF algorithm reduces the prediction error and has better accuracy, that is, better stability.

The UPF algorithm is specifically:

1) First initialize

For the system:

where x represents the state vector, Z represents the measurement vector, the parameter W _k-1 represents the process noise, and V _k represents the measurement noise, both of which are independent Gaussian white noise vectors with zero mean; F _k-1 represents the state transition matrix , H _k represents the observation matrix, assuming that the observation quantity Z _k is independent of other states given the current state quantity x _k ;

The equation with period k is

θ _k-1 represents the error value of state estimation at time k-1, Represents the state estimate value at time k-1, P _k-1 represents the error covariance matrix at time k-1, E is the expected value of the random variable, Q _k-1 represents the covariance matrix of process noise, R _k-1 represents the observation Covariance matrix of noise, T represents matrix transpose;

Set k = 0, and make a particle set K is the number of samples, that is, the number of particles, set Represents the mean value of the initial state, and expands the initial condition of the state:

p(x ₀ ) represents the prior distribution, represents the initial state quantity of the ith particle after dimension expansion, Represents the error covariance of the initial state quantity of the ith particle after dimension expansion;

2) Sigma sampling and weight calculation

Sigma sampling point acquisition:

λ=α ² (n _x +κ)-n _x

in, represents the state variable after expansion, Represents the error covariance after dimension expansion, λ is the scaling factor, κ is the parameter to be selected, usually taken as 3-n _x , n _W represents the dimension of the process noise, n _V represents the dimension of the observation noise, and n _x represents the The dimension of the state vector, n _u =n _x +n _V +n _W represents the state vector, the sum of the dimensions of measurement noise and process noise;

Calculate the weights of the sampling points:

Among them, y is the weight of the mean, z is the weight of the covariance, f represents the number of sampling points, and α represents The distribution of surrounding sigma points, β is a constant related to the prior distribution of x, γ is usually set to 0 or 3-n as a scale parameter, and when ε=3-n, it means that the measurement noise obeys the Gaussian distribution;

3) Update of the prediction function

When the period is k, the corresponding Sigma point particle set can be expressed as represents the number of sampling points, where for the particle set and Represents the nx-dimensional column vector before the particle set, nx+1-dimensional to n _x +n _W -dimensional column vector and n _x +n _W +1-dimensional to n _x +n _V +n _W -dimensional column vector; n _W represents process noise The dimension of , n _V represents the dimension of observation noise, Represents the predicted state value of the Sigma point set at time k+1, Represents the predicted value of the system state obtained by the weighted summation of the predicted state values of the Sigma point set at time k+1, P _i,(k+1|k) represents the error covariance matrix of the system state variable at time k+1, P _VV,(k+1|k) represents the error covariance matrix of the observation equation at time k+1, P _xV,(k+1|k) represents the cross-covariance matrix at time k+1, Z _{i,(k +1|k)} represents the predicted observation value of the Sigma point particle set at time k+1, Represents the system prediction value obtained by the weighted summation of the predicted observations of the Sigma point particle set at time k+1, is the nonlinear state equation function, is the nonlinear observation equation function;

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 the Kalman filter gain matrix, Represents the state value of the system at time k+1 obtained by measurement update, P _i,(k+1|k+1) represents the error covariance matrix at time k+1 obtained by measurement update, Z _k+1 represents k The actual observation value of the system at +1 time;

4) Weight calculation and resampling

For each particle, use the unscented Kalman filter algorithm to update the estimated value and error covariance value of the particle at the current moment, so as to obtain the proposed distribution in In order to obey the probability density function of the Gaussian distribution, and then use the particle filter (PF) algorithm to predict the final result, let the reference distribution be the prior distribution, namely:

q(x _i,k |x _i,(0:k-1) ,Z _0:k )=p(x _i,k |x _i,k-1 )

x _i,k represents the i-th particle state value at time k, x _i,(0:k-1) represents the set of i-th particle state values from 0 to k-1 time, Z _0:k represents from 0 to k The set of measurement values at time, x _i,k-1 represents the state value of the ith particle at time k-1;

The weight value of each particle is determined by the following formula:

Weight normalization:

Resampling: When the value of N _eff is less than the set threshold N _th , the particle set is Perform resampling to get a new set of particles The threshold N _th is usually set as N _th =2K/3; N _eff is calculated by the following:

N _eff represents the number of valid particles, and it is determined whether to perform resampling by comparing it with the set threshold N _th ;

The output state quantities and the corresponding covariance estimates are:

is the estimated value of the state quantity, and P _i,k is the estimated value of the covariance corresponding to the state quantity;

5) When k<L, L is the number of observation samples, let k=k+1, repeat steps 2), 3), 4), otherwise end.

The described IMMUPF algorithm is specifically:

1)) Input interaction

estimated by state with the model probability of each filter in the previous step get a mixed estimate and covariance Use the hybrid estimate as the initial state of the current loop;

For model g, with period k:

The predicted probability of model g: m is the number of models, π _sg represents

The transition probability from model s to model g;

Predicted probability from model s to model g:

Mixed state estimation for model g:

Mixed covariance estimate for model g:

2)) Filtering

For model g, the particles will be filtered with UPF, using the set of particles of period k and Get the state of the next cycle k+1 and its covariance estimator and The residuals and their covariances are

3)) Model probability update

The original probability will be updated, and the new mixed probability will be calculated according to its likelihood function. For model g, its likelihood function is written as:

in Represents a density function that obeys a Gaussian distribution, and the new model mixture probability is expressed as:

The letter o is a normalization constant;

4)) Output interaction: Based on the model probability, weighted and merged the estimation results of each filter to obtain the total state estimation and covariance estimation;

The set of particles representing states and their covariances will interact through the following functions:

The final state quantity and its covariance are output in the following way:

Claims (3)

1. a lithium battery life estimation method based on IMM-UPF, is characterized in that: concrete steps are as follows: (1) First, use four batteries of the same type to charge at a constant current until the voltage reaches the charge cut-off voltage, and then charge at a constant voltage until the charge current drops to the cut-off current, and then end the charge; conduct a charge-discharge experiment at room temperature and record The discharge capacity after each full charge and discharge process is obtained, and the battery capacity decay curve is obtained, and the failure threshold of the battery is set; (2) Four groups of battery capacity data were collected by charging and discharging the four batteries described above. By observing the decay curve, it was found that the fourth group of data had a large gap with the first three groups. Therefore, the first three groups of data were used to determine each single The initial value of the model parameters, the data of the obtained capacity of the fourth battery is used as a verification of the prediction accuracy; (3) Use the second-order polynomial regression equation to estimate the battery capacity C _l by the least squares method to describe the relationship between the lithium battery when the number of cycles is l and the maximum capacity C _l that can be stored, denoted as model 1, the expression of polynomial The formula is C _l =a ₁ l ² +b ₁ l+c ₁ In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, l represents the number of cycles of the lithium battery, and the parameters a ₁ , b ₁ and c ₁ are all constants related to the discharge current and temperature, which are fitted by the curve. way to determine its value; The empirical model expressed by the double exponential equation is used as the second model of battery capacity fading, and its expression is as follows: C _l =a ₂ ·exp(b ₂ ·l)+c ₂ ·exp(d ₂ ·l) In the formula, C _l represents the maximum battery capacity of the lithium battery at the number of cycles l, l represents the number of cycles of the lithium battery, the parameters a ₂ and b ₂ are constants related to the internal impedance, and the parameters c ₂ and d ₂ are related to the battery aging rate. Relevant constants, the values of parameters a ₂ , b ₂ , c ₂ and d ₂ are determined by curve fitting; An ensemble model combining an empirical model of a polynomial and an exponential model is used as the third model, and the expression is as follows: C _l =a ₃ ·exp(-b ₃ ·l)+c ₃ ·l^2+d ₃ In the formula, C _l represents the maximum battery capacity of the lithium battery when the number of cycles is l, and l represents the number of cycles of the lithium battery. The parameters a ₃ , b ₃ , c ₃ and d ₃ are determined by curve fitting, and the parameters a ₃ and b ₃ are Constants related to the internal impedance, parameters c3 and _d3 are constants related to the battery aging rate _; Then use the data of the first three groups of batteries to fit the parameters of the three single models, respectively, and obtain the parameters of the first three groups of batteries corresponding to each single model. The initial base confidence assignments for parameter values are determined by the following formula: where 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, v} are the model parameters, Parameters a _1,v , a _2,v , a _3,v and b _1,v , b _2,v , b _3,v are constants related to internal impedance, parameters c _1,v , c _2,v , c _3,v and d _2,v , d _3,v is a constant related to the battery aging rate, h is the number of battery samples, v represents the vth model, and the fourth battery corresponds to the initial value of each model parameter M represents the confidence of each single model parameter; (4) In order to realize the interaction of the interactive multi-model IMM on the input quantity, the state quantities of the three models are all set as the battery capacity C _l , and the corresponding state equation and observation equation are established; The state equation corresponding to the first model: x _k =x _k-1 +a ₁ ·(2·k-1)+b ₁ +W _1,k-1 , Observation equation: Z _k = x _k +V _1,k , The state equation corresponding to the second model; x _k =x _k-1 +a ₂ ·exp(b ₂ ·k)[1-exp(-b ₂ )]+c ₂ ·exp(d ₂ ·k)[1-exp(-d ₂ )]+ W _2,k-1 , Observation equation: Z _k =x _k +V _2,k , The third model equation of state: x _k =x _k-1 +a ₃ ·exp(b ₃ ·k)[1-exp(-b ₃ )]+c ₃ ·(2·k-1)+W _3,k-1 , Observation equation: Z _k =x _k +V _3,k , where x _k represents the predicted value of the maximum battery capacity available when the cycle period is k, that is, the state vector, and Z _k represents the maximum capacity measurement value when the cycle period is k, that is, the measurement vector, Represents Gaussian noise with mean 0 and standard deviation σ, the initial values of a ₁ , b ₁ , c ₁ , a ₂ , b ₂ , c ₂ , d ₂ , a ₃ , b ₃ , c ₃ , d ₃ are determined by X _M1 , X _M2 , X _{M3 are} given; (5) Each single model uses the unscented particle filter algorithm to predict the remaining life of the fourth battery; (6) Use the interactive multi-model to perform unscented particle filtering and parameter update on the data of the fourth battery. The state quantities and covariances of the three models in each cycle realize the input and output interaction in the IMM, and use the IMMUPF algorithm to achieve Prediction of remaining battery life. 2. a kind of lithium battery life estimation method based on IMM-UPF according to claim 1, is characterized in that: described unscented particle filter algorithm is specifically: 1) First initialize For the system: where x _k represents the state vector, Z _k represents the measurement vector, the parameter W _k-1 represents the process noise, and V _k represents the measurement noise, both of which are independent and zero-mean Gaussian white noise vectors; F _k-1 represents the state Transition matrix, H _k represents the observation matrix, assuming that the observation quantity Z _k is independent of other states given the current state quantity x _k ; The equation with period k is θ _k-1 represents the error value of state estimation at time k-1, Represents the state estimate value at time k-1, P _k-1 represents the error covariance matrix at time k-1, E is the expected value of the random variable, Q _k-1 represents the covariance matrix of process noise, R _k-1 represents the observation Covariance matrix of noise, T represents matrix transpose; Set k = 0, and make a particle set K is the number of samples, that is, the number of particles, set Represents the mean value of the initial state of the i-th particle, and expands the initial condition of the state: p(x ₀ ) represents the prior distribution, represents the initial state quantity of the ith particle after dimension expansion, Represents the error covariance of the initial state quantity of the ith particle after dimension expansion; 2) Sigma sampling and weight calculation Sigma sampling point acquisition: λ=α ² (n _x +κ)-n _x in, represents the state variable after expansion, Represents the error covariance after dimension expansion, λ is the scaling factor, κ is the parameter to be selected, usually taken as 3-n _x , n _W represents the dimension of the process noise, n _V represents the dimension of the observation noise, and n _x represents the The dimension of the state vector, n _u =n _x +n _V +n _W represents the state vector, the sum of the dimensions of measurement noise and process noise; Calculate the weights of the sampling points: Among them, y is the weight of the mean, z is the weight of the covariance, f is the number of sampling points, α is the distribution of sigma points around x, β is a constant related to the prior distribution of x, and γ is the ratio The parameter is usually set to 0 or 3-n, when ε=3-n, it means that the measurement noise obeys the Gaussian distribution; 3) Update of the prediction function When the period is k, the corresponding Sigma point particle set can be expressed as represents the number of sampling points, where for the particle set and Represents the first n _x dimension column vector of the particle set, n _x +1 dimension to n _x +n _W dimension column vector and n _x +n _W +1 dimension to n _x +n _V +n _W dimension column vector; n _W represents the dimension of the process noise, n _V represents the dimension of the observation noise, Represents the predicted state value of the Sigma point set at time k+1, Represents the predicted value of the system state obtained by the weighted summation of the predicted state values of the Sigma point set at time k+1, P _i,(k+1|k) represents the error covariance matrix of the system state variable at time k+1, P _VV,(k+1|k) represents the error covariance matrix of the observation equation at time k+1, P _xV,(k+1|k) represents the cross-covariance matrix at time k+1, Z _{i,(k +1|k)} represents the predicted observation value of the Sigma point particle set at time k+1, Represents the system prediction value obtained by the weighted summation of the predicted observations of the Sigma point particle set at time k+1, is the nonlinear state equation function, is the nonlinear observation equation function; 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 the Kalman filter gain matrix, Represents the state value of the system at time k+1 obtained by measurement update, P _i , _(k+1|k+1) represents the error covariance matrix at time k+1 obtained by measurement update, Z _k+1 represents k The actual observation value of the system at +1 time; 4) Weight calculation and resampling For each particle, use the unscented Kalman filter algorithm to update the estimated value and error covariance value of the particle at the current moment, so as to obtain the proposed distribution in In order to obey the probability density function of the Gaussian distribution, and then use the particle filter algorithm to predict the final result, let the reference distribution be the prior distribution, namely: q(x _i,k |x _i,(0:k-1) ,Z ₀ : _k )=p(x _i,k |x _i,k-1 ) x _i,k represents the i-th particle state value at time k, x _i,(0:k-1) represents the set of i-th particle state values from 0 to k-1 time, Z _0:k represents from 0 to k The set of measurement values at time, x _i,k-1 represents the state value of the ith particle at time k-1; The weight value of each particle is determined by the following formula: Weight normalization: Resampling: When the value of N _eff is less than the set threshold N _th , the particle set is Perform resampling to get a new set of particles The threshold N _th is usually set as N _th =2K/3; N _eff is calculated by the following: N _eff represents the number of valid particles, and it is determined whether to perform resampling by comparing it with the set threshold N _th ; The output state quantities and the corresponding covariance estimates are: is the estimated value of the state quantity, and P _i,k is the estimated value of the covariance corresponding to the state quantity; (5) When k<L, L is the number of observation samples, let k=k+1, repeat steps 2), 3), 4), otherwise end. 3. a kind of lithium battery life estimation method based on IMM-UPF according to claim 2, is characterized in that: described IMMUPF algorithm is specifically: 1)) Input interaction estimated by state with the model probability of each filter in the previous step get a mixed estimate and covariance Use the hybrid estimate as the initial state of the current loop; For model g, with period k: The predicted probability of model g: m is the number of models, and π _sg represents the transition probability from model s to model g; Predicted probability from model s to model g: Mixed state estimation for model g: Mixed covariance estimate for model g: 2)) Filtering For model g, the particles will be filtered with the UPF algorithm, using the set of particles of period k and Get the state of the next cycle k+1 and its covariance estimator and The residuals and their covariances are 3)) Model probability update The original probability will be updated, and the new mixed probability will be calculated according to its likelihood function. For model g, its likelihood function is written as: in Represents a density function that obeys a Gaussian distribution, and the new model mixture probability is expressed as: The letter o is a normalization constant; 4)) Output interaction: Based on the model probability, weighted and merged the estimation results of each filter to obtain the total state estimation and covariance estimation; The set of particles representing states and their covariances will interact through the following functions: The final state quantity and its covariance are output in the following way: