CN112485692A - Battery health state estimation and residual life prediction method based on sparrow search and least square support vector machine - Google Patents

Battery health state estimation and residual life prediction method based on sparrow search and least square support vector machine Download PDF

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CN112485692A
CN112485692A CN202011262204.4A CN202011262204A CN112485692A CN 112485692 A CN112485692 A CN 112485692A CN 202011262204 A CN202011262204 A CN 202011262204A CN 112485692 A CN112485692 A CN 112485692A
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李忠
陈媛
何怡刚
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Abstract

A battery state of health estimation and residual life prediction method based on sparrow search and a least square support vector machine relates to a method for parameterizing a least square support vector machine (LSSVR) model by a Sparrow Search Algorithm (SSA) and predicting the state of health (SOH) and residual life (RUL) of a battery by utilizing the model. The method comprises the following steps: firstly, an LSSVR model of the battery is established, and the LSSVR model is parameterized by SSA to obtain related parameters. When SOH estimation and RUL prediction are carried out, a method of predicting the next data by the first 3 data is adopted. The method has higher accuracy in SOH estimation and RUL prediction, and can solve the defects of PSO and ABC optimization.

Description

Battery health state estimation and residual life prediction method based on sparrow search and least square support vector machine
Technical Field
The invention relates to health state estimation in the field of battery management systems, in particular to a sparrow search algorithm for performing parameter optimization on a least square support vector machine (LSSVR) and training and testing battery capacity by using an LSSVR model to obtain SOH estimation and RUL prediction results of a battery.
Background
Battery state of health (SOH) is used to describe the state of health of a battery, the most intuitive manifestation being that as the battery capacity decays with use of the battery, the resistance increases. The Remaining Useful Life (RUL) is the number of charge and discharge cycles that pass from the current cycle to the end of life (EOL). The SOH estimated value represents the residual life predicted in a short term of the battery, and provides reference for predictability management such as optimization and maintenance of the lithium ion battery, the RUL prediction represents the residual life predicted in a long term of the battery, safety and stability in the whole life cycle of the lithium ion battery can be estimated, and whether the battery can meet the requirements of the driving years and the driving mileage of an automobile is judged.
SOH estimation and RUL prediction methods can be classified into a model-based prediction method and a data-driven prediction method, and a support vector machine is one of the data-driven prediction methods. Support Vector Machines (SVMs) are one of the most popular machine learning algorithms, primarily used for pattern recognition and classification. Current SOH estimation algorithms mainly use SVMs as regression tools, implementing a variant of the algorithm, called Support Vector Regression (SVR). The capacity data is trained and tested by adopting an SVR method, so that SOH estimation and RUL prediction of the battery can be realized.
The Sparrow Search Algorithm (SSA) is a novel swarm intelligence optimization algorithm inspired by sparrow foraging behavior and anti-predation behavior. The specific implementation of the SSA is close to that of the ABC algorithm, the basic structure is almost the same, only the search operator has certain difference, and the SSA can be said to be the ABC improved algorithm. The SSA algorithm is an optimization algorithm with simple principle, few parameters, high precision, high convergence rate, high adaptability and high search efficiency, and can solve various practical problems and obtain more accurate parameters.
Disclosure of Invention
The invention aims to provide a battery state of health estimation and residual life prediction method based on sparrow search and a least square support vector machine, aiming at improving the accuracy of the battery state of health estimation and residual life prediction.
The technical scheme adopted for solving the technical problems is as follows:
a battery state of health estimation and remaining life prediction method based on sparrow search and least square support vector machine comprises the following steps:
firstly, carrying out data processing on two groups of battery data sets subjected to algorithm verification;
step two, establishing a least square support vector regression model;
thirdly, obtaining the optimal parameters of the least square support vector machine model by applying a sparrow search algorithm;
and step four, substituting the processed data into an LSSVR model for training and testing to obtain the SOH estimation and RUL prediction of the battery.
Further, the first step comprises the following steps:
data processing is carried out, and it is noted that the rated capacity of the same battery is constant, the current capacity value and the SOH have the same variation trend, and the SOH estimation problem of the battery can be converted into the capacity estimation problem. The prediction starting points of B0005 and B0007 are set at the middle T stage of the degradation of the lithium ion batteryy84, the prediction starting point of CS35 and CS37 is Ty323. And dividing a training set and a test set according to the prediction starting point, and carrying out normalization processing on the data. The method for predicting the next day by adopting the data of the first three days comprises the following steps:
Figure BDA0002774998990000021
wherein the content of the first and second substances,
Figure BDA0002774998990000022
capacity corresponding to predicted nth cycle, Cn-1Is the actual capacity for n-1 cycles.
Further, the second step comprises the following steps:
the optimization problem of least squares support vector regression can be expressed as shown below.
Figure BDA0002774998990000031
s.t.yi＝wT·φ(xi)+b+ei i＝1,2,…,N
Wherein, { xiI ═ 1,2, …, N } is an input feature quantity, { yiI is 1,2, …, N is the output target value, C is the penaltyThe factor, e, is the regression error,
Figure BDA0002774998990000032
the characteristic vector after x is mapped is shown, w is a normal vector and determines the direction of the hyperplane, and b is a displacement item and determines the distance between the hyperplane and the origin.
The Lagrange multiplier method is adopted to convert the above formula into a maximum solving problem of alpha:
Figure BDA0002774998990000033
the partial derivatives are calculated to obtain:
Figure BDA0002774998990000034
introducing a kernel function omegaij＝φ(xi)Tφ(xj)＝K(xi,xj) And eliminate w and e from the above formulaiAnd simplified to obtain:
Figure BDA0002774998990000035
wherein α ═ α1,α2,…,αN]T，INIs an N-th order matrix, y ═ y1,y2,…,yN]T。
Solving b and α by the above formula:
Figure BDA0002774998990000036
substitution can obtain the LSSVR model:
Figure BDA0002774998990000037
further, the third step comprises the following steps:
firstly, algorithm initialization is carried out: giving the values of the sparrow number P, the iteration number M, the optimization parameter gamma and the kernel function parameter sigma; in the sparrow search algorithm, each sparrow has 3 possible behaviors: and (4) performing seeker, follower and alert investigation, wherein P sparrows with the best positions in the population are selected as seekers and the rest n-P sparrows are selected as followers in each generation.
The seeker with the better fitness value will get food first and find the food for a wider range, and the position update equation is shown in the following formula.
Figure BDA0002774998990000041
Wherein t is the current iteration number, and M is the maximum iteration number. Xi,jIndicates the position of the ith sparrow in the jth dimension, and alpha is [0-1 ]]Random numbers within the interval. R2For a warning value, R2∈[0,1]ST is a security value, and ST belongs to [0.5,1 ]]And Q is a random number following a normal distribution. L is a 1 × d matrix with 1 per element. If R is2< ST indicates no predators around, the seeker enters the Wide search mode if R2Gtst, indicating that some sparrows in the population found predators and raised an alarm, and all sparrows were about to fly to a safe place for food.
The location update description of the follower is shown in the following equation.
Figure BDA0002774998990000042
Wherein XPIs the best position, X, currently occupied by the searcherwIs the global worst position, A represents a 1 × d matrix whose elements are randomly assigned 1 or-1, A+＝AT(AAT)-1. When i is more than n/2, the fact that the ith follower with lower fitness does not obtain food and needs to fly to other places for foraging.
While sparrows are foraging, their part will be responsible for vigilance, and when danger is found, anti-predation will take place: the food is abandoned and moved to a new location. Sparrows at the periphery of the population are vulnerable to predators and need to be constantly repositioned, while sparrows in the center of the population will come closer to their adjacent partners, reducing their danger zones. In each generation, S individuals are randomly selected from the population for early warning. The position update formula is shown in the following formula.
Figure BDA0002774998990000051
Wherein XBThe current global optimal position is, beta is a step size control parameter, and is a random number which follows normal distribution with a mean value of 0 and a variance of 1. K is a random number and takes the value of [ -1,1]And in between, the direction in which the sparrows move. f. ofiIs the fitness of the current sparrow individuals. f. ofg、fwRespectively the current global best and worst fitness value. ξ is a very small constant that prevents the denominator from being 0. f. ofi＞fgMeaning that sparrows are at the periphery of the population and are vulnerable. f. ofi＝fgMeaning that the centrally located sparrow is aware of the danger and needs to be close to other sparrows.
And stopping iteration when the conditions are met, outputting the optimal parameters [ gamma, sigma ] of the LSSVR model, and training the model to obtain the results of SOH estimation and RUL prediction.
Further, in the fourth step, the input and output data of the training set are substituted into the training to obtain the LSSVR training model. And substituting the test data set for input and output to obtain a predicted capacity value. The EOL thresholds for the B0005 and B0007 battery capacity fade were set to 75% of the initial capacity, i.e., to 1.4Ah and 1.42 Ah. The EOL threshold for the degradation of the CS35, CS37 battery capacities was set to 80% of the initial capacity, i.e., both degraded to 0.90 Ah. The RUL prediction is performed based on the attenuation threshold setting and the estimated capacity value.
Wherein, the steps one to four are all completed in a computer MATLAB.
Compared with the existing simulation method, the method has the following advantages:
(1) and a least square support vector machine model (LSSVR) is adopted, so that the training efficiency and the convergence rate of solution are improved, and the precision is higher.
(2) A Sparrow Search Algorithm (SSA) is provided for parameterizing the LSSVR model, and the obtained parameters are high in precision, high in convergence speed and high in adaptability.
(3) The method is simple to implement, and compared with PSO-SVR and ABC-SVR algorithms, the method has the advantage that the accuracy is greatly improved when the SOH estimation and RUL prediction of the battery are carried out.
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Fig. 1 is a flow chart of a battery state of health estimation and remaining life prediction method based on sparrow search and a least square support vector machine according to the present invention.
FIG. 2 is a comparison of the estimation results of battery capacity according to the present invention with (a) B0005(B) B0007(c) CS35(d) CS 37.
FIG. 3 is a comparison of the error of the battery capacity estimation according to the present invention with the error of the battery capacity estimation shown in (a) B0005(B) B0007(c) CS35(d) CS 37.
FIG. 4 shows the RUL prediction comparison results of battery of the present invention (a) B0005(B) B0007(c) CS35(d) CS 37.
Table 1 shows the error values of the battery capacity estimation according to the present invention.
Table 2 shows the RUL prediction results of the battery of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings and embodiments.
To verify the accuracy of the method of the present invention, SOH and RUL estimation of the cells were performed using the CS35, CS37 cells of the university of Maryland and the B0005, B0007 cells of the NASA cell data set. It should be noted that the rated capacity of the same battery is constant, the current capacity value and the SOH have the same trend of change, and the SOH estimation problem of the battery can be converted into the capacity estimation problem.
Referring to fig. 1, the battery state of health estimation and remaining life prediction method based on sparrow search and least square support vector machine of the present invention includes the following steps:
1. battery capacity data processing: the prediction starting points of B0005 and B0007 are set at the middle T stage of the degradation of the lithium ion batteryy84, the prediction starting point of CS35 and CS37 is Ty323. And dividing a training set and a test set according to the prediction starting point, and carrying out normalization processing on the data. The method for predicting the next day by adopting the data of the first three days comprises the following steps:
Figure BDA0002774998990000061
wherein the content of the first and second substances,
Figure BDA0002774998990000062
capacity corresponding to predicted nth cycle, Cn-1Is the actual capacity for n-1 cycles.
2. Establishing an LSSVR model and obtaining optimal parameters through a sparrow search algorithm: firstly, algorithm initialization is carried out: the values of sparrow number P-20, iteration number M-10, optimization parameter γ, and kernel parameter σ are given. And dividing the population into an explorer and a follower, and updating the positions of the explorer and the follower according to corresponding formulas. And randomly selecting S individuals for early warning, and updating the positions of the S individuals according to a corresponding formula. And stopping iteration when the conditions are met, and outputting the optimal parameters [ gamma, sigma ] of the LSSVR model.
3. The training of the training set is performed by the SSA optimized LSSVR model, and the data of the test set is substituted to obtain the battery capacity estimation and the error as shown in fig. 2 and fig. 3. Fig. 2 shows the results of the battery capacity estimation, fig. 3 shows the battery capacity estimation error, and table 1 shows the error values of the battery capacity estimation.
The conclusions can be drawn from fig. 2, fig. 3 and table 1: the capacity estimated value obtained by the method of the invention changes along with the actual value, and the error is smaller. The PSO-SVR algorithm obtains a capacity estimation error MAE value of 0.013, an RMSE of 0.0164 and a MAPE value of 0.811%. ABC-SVR corresponds to values of 0.015, 0.0085 and 0.53%, SSA-LSSVR corresponds to values of 0.0069, 0.0135 and 0.495%. The precision of the SSA-LSSVR algorithm is higher than that of the ABC-SVR and PSO-SVR algorithms.
The EOL threshold for the B0005, B0007 battery capacity fade was set to 75% of the initial capacity, i.e., to 1.4Ah and 1.42 Ah. The EOL threshold for the degradation of the CS35, CS37 battery capacities was set to 80% of the initial capacity, i.e., both degraded to 0.90 Ah. Fig. 4 shows a comparison of the RUL prediction results for the battery, and table 2 shows the RUL prediction results for the battery.
As can be seen from FIG. 4 and Table 2, the RUL predicted value obtained by the method of the present invention is close to the actual RUL value, the difference is not large, the error between the RUL predicted value obtained by the PSO-SVR algorithm and the true value is the largest, and the SSA-LSSVR algorithm and the ABC-SVR algorithm have similar accuracy.
The method for estimating the state of health and predicting the residual life of the battery based on the sparrow search and the least square support vector machine can realize the prediction of the SOH and the RUL of the battery, is simple and effective, and has higher precision.
Various modifications and variations of the present invention may be made by those skilled in the art, and they are also within the scope of the present invention provided they are within the scope of the claims of the present invention and their equivalents.
What is not described in detail in the specification is prior art that is well known to those skilled in the art.
Figure 3
Figure BDA0002774998990000121
Figure BDA0002774998990000131

Claims (5)

1. A method for estimating the state of health and predicting the residual life of a battery based on sparrow search and a least square support vector machine is characterized by comprising the following steps:
firstly, carrying out data processing on two groups of battery data sets subjected to algorithm verification;
step two, establishing a least square support vector regression model;
thirdly, obtaining the optimal parameters of the least square support vector machine model by applying a sparrow search algorithm;
and step four, substituting the processed data into an LSSVR model for training and testing to obtain the SOH estimation and RUL prediction of the battery.
2. The method for estimating state of health and predicting remaining life of battery based on sparrow search and least squares support vector machine as claimed in claim 1, wherein the first step comprises the steps of:
data processing is carried out, and it is noted that the rated capacity of the same battery is constant, the current capacity value and the SOH have the same variation trend, and the SOH estimation problem of the battery can be converted into the capacity estimation problem. The prediction starting points of B0005 and B0007 are set at the middle T stage of the degradation of the lithium ion batteryy84, the prediction starting point of CS35 and CS37 is Ty323. And dividing a training set and a test set according to the prediction starting point, and carrying out normalization processing on the data. The method for predicting the next day by adopting the data of the first three days comprises the following steps:
Figure FDA0002774998980000011
wherein the content of the first and second substances,
Figure FDA0002774998980000012
capacity corresponding to predicted nth cycle, Cn-1Is the actual capacity for n-1 cycles.
3. The method for estimating the state of health and predicting the remaining life of the battery based on sparrow search and least square support vector machine according to claim 1, wherein the second step comprises the following steps:
the optimization problem of least squares support vector regression can be expressed as shown below.
Figure FDA0002774998980000021
s.t.yi＝wT·φ(xi)+b+eii＝1,2,…,N
Wherein, { xiI ═ 1,2, …, N } is an input feature quantity, { yiI is 1,2, …, N is the output target value, C is the penalty factor, e is the regression error,
Figure FDA0002774998980000022
the characteristic vector after x is mapped is shown, w is a normal vector and determines the direction of the hyperplane, and b is a displacement item and determines the distance between the hyperplane and the origin.
The Lagrange multiplier method is adopted to convert the above formula into a maximum solving problem of alpha:
Figure FDA0002774998980000023
the partial derivatives are calculated to obtain:
Figure FDA0002774998980000024
αi＝C·e,(wT·φ(xi))+b+ei-yi＝0
introducing a kernel function omegaij＝φ(xi)Tφ(xj)＝K(xi,xj) And eliminate w and e from the above formulaiAnd simplified to obtain:
Figure FDA0002774998980000025
wherein α ═ α1,α2,…,αN]T，INIs an N-th order matrix, y ═ y1,y2,…,yN]T。
Solving b and α by the above formula:
Figure FDA0002774998980000026
α＝(Ω+C-1IN)-1(y-1Nb)
substitution can obtain the LSSVR model:
Figure FDA0002774998980000027
4. the method for estimating state of health and predicting remaining life of battery based on sparrow search and least squares support vector machine as claimed in claim 1, wherein said step three comprises the steps of:
firstly, algorithm initialization is carried out: giving the values of the sparrow number P, the iteration number M, the optimization parameter gamma and the kernel function parameter sigma; in the sparrow search algorithm, each sparrow has 3 possible behaviors: and (4) performing seeker, follower and alert investigation, wherein P sparrows with the best positions in the population are selected as seekers and the rest n-P sparrows are selected as followers in each generation.
The seeker with the better fitness value will get food first and find the food for a wider range, and the position update equation is shown in the following formula.
Figure FDA0002774998980000031
Wherein t is the current iteration number, and M is the maximum iteration number. Xi,jIndicates the position of the ith sparrow in the jth dimension, and alpha is [0-1 ]]Random numbers within the interval. R2For a warning value, R2∈[0,1]ST is a security value, and ST belongs to [0.5,1 ]]And Q is a random number following a normal distribution. L is a 1 × d matrix with 1 per element. If R is2< ST indicates no predators around, the seeker enters the Wide search mode if R2gtoreq.ST, indicating that some sparrows in the population found predators and alarmedAll sparrows are flown to a safe place to find food.
The location update description of the follower is shown in the following equation.
Figure FDA0002774998980000032
Wherein XPIs the best position, X, currently occupied by the searcherwIs the global worst position, A represents a 1 × d matrix whose elements are randomly assigned 1 or-1, A+＝AT(AAT)-1. When i is more than n/2, the fact that the ith follower with lower fitness does not obtain food and needs to fly to other places for foraging.
While sparrows are foraging, their part will be responsible for vigilance, and when danger is found, anti-predation will take place: the food is abandoned and moved to a new location. Sparrows at the periphery of the population are vulnerable to predators and need to be constantly repositioned, while sparrows in the center of the population will come closer to their adjacent partners, reducing their danger zones. In each generation, S individuals are randomly selected from the population for early warning. The position update formula is shown in the following formula.
Figure FDA0002774998980000033
Wherein XBThe current global optimal position is, beta is a step size control parameter, and is a random number which follows normal distribution with a mean value of 0 and a variance of 1. K is a random number and takes the value of [ -1,1]And in between, the direction in which the sparrows move. f. ofiIs the fitness of the current sparrow individuals. f. ofg、fwRespectively the current global best and worst fitness value. ξ is a very small constant that prevents the denominator from being 0. f. ofi＞fgMeaning that sparrows are at the periphery of the population and are vulnerable. f. ofi＝fgMeaning that the centrally located sparrow is aware of the danger and needs to be close to other sparrows.
And stopping iteration when the conditions are met, outputting the optimal parameters [ gamma, sigma ] of the LSSVR model, and training the model to obtain the results of SOH estimation and RUL prediction.
5. The method for estimating the state of health and predicting the remaining life of a battery based on sparrow search and least square support vector machine as claimed in claim 1, wherein in the fourth step, the input and output data of the training set are substituted into the training to obtain the LSSVR training model. And substituting the test data set for input and output to obtain a predicted capacity value. The EOL thresholds for the B0005 and B0007 battery capacity fade were set to 75% of the initial capacity, i.e., to 1.4Ah and 1.42 Ah. The EOL threshold for the degradation of the CS35, CS37 battery capacities was set to 80% of the initial capacity, i.e., both degraded to 0.90 Ah. The RUL prediction is performed based on the attenuation threshold setting and the estimated capacity value.
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CN113124552A (en) * 2021-04-29 2021-07-16 苏州科技大学 Optimized control algorithm of chilled water system
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Application publication date: 20210312