CN112230154A - Lithium battery residual life prediction method - Google Patents
Lithium battery residual life prediction method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/396—Acquisition or processing of data for testing or for monitoring individual cells or groups of cells within a battery
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- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Abstract
The invention discloses a lithium battery residual life prediction method, which mainly adopts a life prediction method based on an Autoregressive (AR) time sequence and an extended Kalman particle filter algorithm (EKPF), and comprises two stages, namely an experience degradation model construction stage and a life prediction stage. The first stage, the degradation model construction stage, is to construct a battery capacity decline dual-exponential model based on coulomb's law, which describes the change relationship between the available capacity of the battery and time, and reflects the concentration polarization and the battery capacity loss caused by two-stage polarization. The form of the deformation adaptive state transfer equation is modified for the double-index model, so that a deformed experience degradation model is formed, the number of parameters of an original model is reduced, and the complexity of parameter training is reduced. And in the second stage, a life prediction stage, obtaining the parameters of the degradation empirical model and the autoregressive parameters through training, and acquiring a predicted value of the residual life of the lithium battery by adopting an EKPF algorithm to trend the electric quantity of the battery.
Description
Technical Field
The invention relates to the technical field of batteries, in particular to a lithium battery residual life prediction method based on an AR time sequence and extended Kalman particle filter.
Background
At present, the application of the battery in various fields is more and more extensive, and almost all the fields of daily life, production and scientific research of people are covered. Particularly, new energy vehicles, communication equipment and electronic equipment are rapidly developed at home and abroad, the battery demand is more and more large, further battery fault Prediction and Health Management (PHM) become important links, and the state of health (SOH) of the battery is directly related to the reliability of operation of each system.
The SOH reflects the capacity decline condition of the battery in multiple charge-discharge cycles, represents the long-term health condition of the battery, and the service life (RUL) of the battery is the most intuitive index reflecting the SOH of the battery. Therefore, predicting the RUL of the lithium battery in advance is an extremely important link in the PHM technology of the system.
The main research methods for predicting the RUL of the lithium battery are as follows: modeling methods, data-driven methods, and fusion-type methods based on various algorithms. The model-based RUL prediction method realizes prediction by depending on the chemical reaction mechanism in the battery, the material property of the battery and the load condition, and can be further divided into a model of a degradation mechanism, an equivalent circuit model and an empirical degradation model according to a modeling principle. For a system such as a lithium battery, the modeling difficulty is high due to the fact that the electrochemical reaction inside the system is very complex, a data driving method does not need to consider the reaction mechanism inside the battery, a large amount of historical data is used for mining the service life information of the battery, and the weakness that different models are required to be established for different batteries by a model method can be overcome to a certain extent. The data driving method mainly comprises the following steps: AR time series model, artificial neural network, support vector machine and Gaussian process regression and statistic random filtering algorithm. The fusion-type method is the research trend of the RUL prediction at present, namely, the defects of a single method are made up by fusing a plurality of methods. The common fusion types are two types, one is the fusion of a data driving method and a model method, and the most common is the combined use of an empirical degradation model and a statistical random filtering algorithm; and the other type is that a plurality of data driving methods are fused and complemented to improve the stability of the prediction result. The current research of multi-base fusion type algorithm has important practical value.
Disclosure of Invention
The invention aims to provide a method based on an autoregressive model (namely an AR time sequence model) and extended Kalman particle filtering, which can perform approximate real simulation on battery capacity degradation, simultaneously deform a battery degradation model, conform to a state transfer equation of the particle filtering, reduce the number of parameters and reduce the difficulty of parameter training. In order to reduce excessive dependence on the model, an autoregressive model is introduced to correct an observed value so as to improve the prediction accuracy, and an extended Kalman particle filter algorithm is adopted in order to enable the particle distribution to be closer to the real distribution.
The technical scheme provided by the invention is as follows: a method for predicting the residual life of a lithium battery comprises the following steps:
a degradation model construction stage: firstly, constructing a degradation model for describing the relation between the available capacity of the battery and the time variation, and acquiring degradation model parameters;
and a life prediction stage: and establishing an autoregressive model according to the parameters of the degradation model, and predicting the residual life of the battery by a Kalman particle filtering method.
The degradation model is obtained by the following steps:
Ck=a·exp(b·k)+c·exp(d·k) (1)
wherein a, b, C, d are coefficients, k is the number of cycles, one charge and discharge of the battery is a cycle, CkIs the battery capacity of the k-th cycle;
the model at time k-1 is Ck-1=a·exp[b·(k-1)]+c·exp[d·(k-1)]; (2)
Obtained by subtracting the above expressions:
Ck=Ck-1exp(b)+c·exp(d·k)[1-exp(b-d)]; (3)
due to exp (b) and c · [1-exp (b-d)]Are all constant terms, and the simplified degradation model can be Ck=α·Ck-1+β·exp(γ·k); (4)
The expressions of the parameters alpha, beta and gamma of the degradation model are as follows:
α=exp(b),β=c·[1-exp(b-d)],γ=d。
and the parameters alpha, beta and gamma of the degradation model are obtained by nonlinear least square fitting.
The life prediction phase comprises the following steps:
1) establishing an autoregressive model, namely the order and the autoregressive coefficient of the AR model, and constructing the AR model;
2) training an AR model by using input data to obtain the order p and the autoregressive coefficient of the AR modelObtaining a trained AR model;
3) initializing parameters of a particle filter algorithm;
4) constructing a state space equation which accords with a particle filter algorithm;
5) modifying an observation Z generated based on an observation equation with an observation generated based on a historical capacity value by a trained AR modelk;
6) Generating a suggested density function by utilizing an EKPF algorithm, executing a particle filter algorithm, and obtaining a predicted value of the battery capacity;
7) judging whether the predicted value of the battery capacity reaches a service life ending threshold value; and if the current battery life reaches the threshold value, the next step is carried out, otherwise, the step 4) is returned to until the life is attenuated to the battery life ending threshold value, the battery capacity probability density function distribution generated by the particle set is obtained, and finally the battery life is obtained.
The initialization of the parameters of the particle filter algorithm is as follows: the number of the sampling particles, the initial state value of the sampling particles, the covariance of process noise and observation noise, the particle regression resampling threshold value and the battery service life ending threshold value are set.
Data for training the AR model includes:
input values are as follows: battery capacity data { C over first N charge-discharge cyclesk}(k=1,2,…,N);
And (3) outputting a value: an estimate of the remaining life of the battery and a posterior probability density distribution of the prediction.
The state space equation is as follows:
the state transition equation: ck=α·Ck-1+β·exp(γ·k)+μk
The observation equation: zk=Ck+vk
Wherein, CkIs the actual capacity of the cell in the k-th cycle, ZkIs an observed value, mu, for an electric quantitykAnd vkThe method comprises the following steps of (1) respectively obeying zero-mean Gaussian distribution, namely process noise and observation noise; alpha, beta and gamma are degradation model parameters.
The proposed density function is a probability density function.
The battery life is the number of charge and discharge cycles of the battery.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the lithium battery RUL prediction algorithm based on the EKPF is based on an operation framework of the PF algorithm, an observed value is generated by an AR time series model, and a suggested density function closer to a real posterior probability density is generated by the EKF algorithm, so that the performance of the PF algorithm is improved, and the prediction accuracy is improved.
Drawings
FIG. 1 is a flow chart of a prediction method according to an embodiment of the present invention;
FIG. 2 shows RUL prediction curves according to an embodiment of the present invention;
FIG. 3 shows RUL prediction contrast curves according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The invention aims to provide a method for predicting the residual service life (RUL) of a lithium battery, which can accurately predict the residual service life of the battery and better improve the utilization rate of the battery.
A lithium battery residual life prediction method is divided into a degradation model construction stage and a life prediction stage.
And in the degradation model construction stage, firstly, a coulomb law-based dual-exponential model of battery capacity degradation is constructed, which describes the change relation between the available capacity of the battery and time and reflects the capacity loss of the battery caused by concentration polarization and two-stage polarization. The form of the deformation adaptive state transfer equation is modified for the double-index model, so that a deformed experience degradation model is formed, the number of parameters of an original model is reduced, and the complexity of parameter training is reduced.
The life prediction phase consists of the following steps:
input values are as follows: battery capacity data { C over first N charge-discharge cyclesk}(k=1,2,…,N)
And (3) outputting a value: posterior probability density distribution of estimated value and predicted result of battery residual life
Step 1, performing nonlinear least square fitting training on battery capacity data to obtain model parameters, and completing construction of a deformed dual-exponential regression empirical model;
step 3, training an AR (autoregressive) time sequence model by using the input data to obtain the order p of the AR model and an autoregressive coefficient related to the model
Step 4, when k is equal to 0, initializing related parameters of the PF algorithm, setting the number of sampling particles, the initial state value of the sampling particles, the covariance of process noise and observation noise, and a particle regression resampling threshold; initializing parameters of an EKF algorithm, and setting covariance of process noise and observation noise; setting initial values such as battery end-of-life threshold, and using prior probability density for i equal to 1, 2, …, Np(x0) Sampling particle setAnd let the weight of the particle set Representing the ith sample particle;representing the ith particle set weight. The particles of this example represent the battery capacity.
Step 5.AR _ predict (t): replacing the observation value generated based on the observation equation with an observation value generated based on a past capacity value by the AR time series model;
and 6, generating a suggested density function by an EKF (extended Kalman Filter) based on a framework of a PF (particle Filter), correcting an observed value by an AR (augmented reality) time series model, and acquiring a predicted value of the residual service life of the battery.
The prediction method is mainly divided into 2 stages, wherein the first stage is a model building stage, namely a degradation empirical model is built and model parameters are obtained, and the second stage is a prediction stage, namely the battery residual life is estimated by combining the empirical model and an AR + EKPF method, so that an accurate prediction value is obtained.
Fig. 1 is a flowchart of a method for predicting remaining life of a lithium battery according to an embodiment of the present invention.
Step 1, extracting battery capacity data from a large amount of collected battery data;
and 3, fitting main parameters of the double-exponential model by combining a nonlinear least square method, wherein the double-exponential model has the following form: ckA · exp (b · k) + c · exp (d · k); wherein a, b, c, d are coefficients, k is the number of cycles, and one charge and discharge cycle of the battery is one cyclePeriod C ofkFor the battery capacity of the k-th cycle, the model at the time k-1 is Ck-1=a·exp[b·(k-1)]+c·exp[d·(k-1)](ii) a Obtained by subtracting the above expressions, Ck=Ck-1exp(b)+c·exp(d·k)[1-exp(b-d)]. Due to exp (b) and c · [1-exp (b-d)]Are all constant terms, the model can be simplified to Ck=α·Ck-1+ β · exp (γ · k); exp denotes an exponential function.
Step 4, establishing an order and an autoregressive coefficient of the AR model according to a correlation criterion, and establishing the AR model;
step 5, when k is equal to 0, initializing related parameters of the PF algorithm, and setting initial values of sampling particle number, initial state values of sampling particles, covariance of process noise and observation noise, a particle regression resampling threshold value, a battery life ending threshold value and the like;
step 6, constructing a state space equation conforming to a PF algorithm so as to carry out a prediction stage at a later stage, wherein the form of the PF state space equation is as follows:
the state transition equation: ck=a·Ck-1+β·exp(γ·k)+μk
The observation equation: zk=Ck+vk
Wherein, CkIs the actual capacity of the cell in the k-th cycle, ZkIs an observed value, mu, for an electric quantitykAnd vkThe method comprises the following steps of (1) respectively obeying zero-mean Gaussian distribution, namely process noise and observation noise;
step 7 corrects the observation Z generated based on the observation equation for the observation generated based on the past volume value by the AR time series modelk;
Step 8, generating a suggested density function by utilizing an EKPF (extended Kalman particle Filter) algorithm so as to facilitate more accurate prediction in the execution process of a subsequent PF (particle Filter) algorithm;
step 9 is to execute PF algorithm;
step 10, obtaining a predicted value of the battery capacity through the algorithm;
step 11, whether the predicted value of the battery capacity reaches a service life ending threshold value or not is judged, the next step of result calculation is carried out after the predicted value of the battery capacity reaches the service life ending threshold value, and the algorithm is continuously executed until the service life is attenuated to the threshold value;
step 12, generating pdf (probability density function) distribution of battery capacity according to the last particle set by the battery, and finally obtaining a result (battery life, namely battery charge and discharge cycle number);
in this embodiment, the lithium battery remaining life prediction curve and the probability density function curve shown in fig. 2 can be obtained through the above steps, and meanwhile, the error comparison can also be performed without the AR and EKPF correction algorithm to obtain the remaining life comparison curve shown in fig. 3.
Claims (9)
1. A method for predicting the residual life of a lithium battery is characterized by comprising the following steps:
a degradation model construction stage: firstly, constructing a degradation model for describing the relation between the available capacity of the battery and the time variation, and acquiring degradation model parameters;
and a life prediction stage: and establishing an autoregressive model according to the parameters of the degradation model, and predicting the residual life of the battery by a Kalman particle filtering method.
2. The method for predicting the remaining life of a lithium battery as claimed in claim 1, wherein the degradation model is obtained by:
Ck=a·exp(b·k)+c·exp(d·k) (1)
wherein a, b, C, d are coefficients, k is the number of cycles, one charge and discharge of the battery is a cycle, CkIs the battery capacity of the k-th cycle;
the model at time k-1 is Ck-1=a·exp[b·(k-1)]+c·exp[d·(k-1)]; (2)
Obtained by subtracting the above expressions:
Ck=Ck-1exp(b)+c·exp(d·k)[1-exp(b-d)]; (3)
due to exp (b) and c · [1-exp (b-d)]Are all constant terms, and the simplified degradation model can be Ck=α·Ck-1+β·exp(γ·k); (4)
The expressions of the parameters alpha, beta and gamma of the degradation model are as follows:
α=exp(b),β=c·[1-exp(b-d)],γ=d。
3. the method for predicting the remaining life of a lithium battery as claimed in claim 1, wherein the degradation model parameters α, β, γ are obtained by nonlinear least squares fitting.
4. The method for predicting the remaining life of a lithium battery as claimed in claim 1, wherein the life prediction stage comprises the steps of:
1) establishing an autoregressive model, namely the order and the autoregressive coefficient of the AR model, and constructing the AR model;
2) training an AR model by using input data to obtain the order p and the autoregressive coefficient of the AR modelObtaining a trained AR model;
3) initializing parameters of a particle filter algorithm;
4) constructing a state space equation which accords with a particle filter algorithm;
5) modifying an observation Z generated based on an observation equation with an observation generated based on a historical capacity value by a trained AR modelk;
6) Generating a suggested density function by utilizing an EKPF algorithm, executing a particle filter algorithm, and obtaining a predicted value of the battery capacity;
7) judging whether the predicted value of the battery capacity reaches a service life ending threshold value; and if the current battery life reaches the threshold value, the next step is carried out, otherwise, the step 4) is returned to until the life is attenuated to the battery life ending threshold value, the battery capacity probability density function distribution generated by the particle set is obtained, and finally the battery life is obtained.
5. The method for predicting remaining life of lithium battery as claimed in claim 4, wherein the initializing the parameters of the particle filter algorithm is as follows: the number of the sampling particles, the initial state value of the sampling particles, the covariance of process noise and observation noise, the particle regression resampling threshold value and the battery service life ending threshold value are set.
6. The method of predicting remaining life of a lithium battery as claimed in claim 4, wherein training data of the AR model comprises:
input values are as follows: battery capacity data { C over first N charge-discharge cyclesk}(k=1,2,…,N);
And (3) outputting a value: an estimate of the remaining life of the battery and a posterior probability density distribution of the prediction.
7. The method for predicting the remaining life of a lithium battery as claimed in claim 4, wherein the state space equation is as follows:
the state transition equation: ck=α·Ck-1+β·exp(γ·k)+μk
The observation equation: zk=Ck+vk
Wherein, CkIs the actual capacity of the cell in the k-th cycle, ZkIs an observed value, mu, for an electric quantitykAnd vkThe method comprises the following steps of (1) respectively obeying zero-mean Gaussian distribution, namely process noise and observation noise; alpha, beta and gamma are degradation model parameters.
8. The method of predicting remaining life of a lithium battery as claimed in claim 4, wherein the suggested density function is a probability density function.
9. The method of predicting the remaining life of a lithium battery as claimed in claim 4, wherein the battery life is a number of battery charge and discharge cycles.
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CN113504473A (en) * | 2021-09-10 | 2021-10-15 | 四川大学 | RUL prediction method suitable for power lithium battery nonlinear regression process |
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CN114859231A (en) * | 2022-04-27 | 2022-08-05 | 电子科技大学 | Method for predicting remaining life of battery based on wiener process and extreme learning machine |
CN114859231B (en) * | 2022-04-27 | 2023-06-09 | 电子科技大学 | Battery remaining life prediction method based on wiener process and extreme learning machine |
CN115184831A (en) * | 2022-09-13 | 2022-10-14 | 南通云锦微电子科技有限公司 | Early warning method for echelon lithium battery pack |
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