CN110687450B - Lithium battery residual life prediction method based on phase space reconstruction and particle filtering - Google Patents

Lithium battery residual life prediction method based on phase space reconstruction and particle filtering Download PDF

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CN110687450B
CN110687450B CN201910802571.XA CN201910802571A CN110687450B CN 110687450 B CN110687450 B CN 110687450B CN 201910802571 A CN201910802571 A CN 201910802571A CN 110687450 B CN110687450 B CN 110687450B
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张永
陈廖格豪
李曦
付晓薇
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention discloses a lithium battery residual life prediction method based on phase space reconstruction and particle filtering, which comprises the following steps: firstly, extracting a voltage difference health index of equal time interval discharge on the basis of battery capacity, and using BCT to strengthen the linear correlation between the index and a capacitor; then, using a PSR algorithm to obtain the time delay and embedding dimension of a training set in the process of training the SVR model; and finally, substituting the predicted value of the SVR into the system state space model and updating the state by using the PF. The superiority of the method in the RUL prediction is proved by a NASA lithium ion battery data set.

Description

Lithium battery residual life prediction method based on phase space reconstruction and particle filtering
Technical Field
The invention belongs to the technical field of batteries, and relates to a hybrid prediction method for the residual life of a lithium iron phosphate battery based on a PSR-SVR-PF algorithm.
Background
In recent years, lithium ion batteries have been widely used as power sources for mobile phones, notebook computers and electric vehicles, and have been gradually expanded into the fields of military communication, aerospace and the like. The serious safety and economic consequences of the lithium ion battery caused by the failure of supplying the required power level are avoided, and the prediction of the residual service life (RUL) plays an important role. Therefore, the accurate prediction of the remaining life of the lithium ion battery plays an important role in lithium ion battery fault Prediction and Health Management (PHM), and the PHM can enable the health management function to have autonomy and reduce human intervention, thereby greatly reducing the cost. The PHM technology estimates the state of the lithium ion battery by detecting various indexes of the lithium ion battery, wherein the residual life performance index is the core, and the safety and the reliability of the lithium ion battery are greatly improved. The invention adopts a PSRSVR-PF algorithm, firstly extracts the equal time interval voltage difference health index, and utilizes BCT transformation to strengthen the linear relation between the index and the capacity. And Phase Space Reconstruction (PSR) is used for defining a training sample set to train the SVR model, updating the state of the system state space model by using the predicted value of the SVR through PF, and finally obtaining the capacity predicted value through a measurement equation.
Disclosure of Invention
The invention aims to provide a mixing method capable of accurately predicting the residual service life of a lithium iron phosphate battery.
In order to achieve the above purpose, the solution of the invention is:
the invention provides a lithium battery residual life prediction method based on phase space reconstruction and particle filtering.
The method comprises the following steps: the obtained NASA data set is firstly screened, and three groups B0005, B0006 and B0007 are correspondingly selected as experimental data sets. Two health factors of battery capacitance and discharge voltage difference at equal time intervals are extracted, and a training set and a test set are divided.
Step two: SVR part: before training the SVR model, in order to enhance the linear correlation between the equal time interval discharge voltage difference and the capacity, the equal time interval discharge voltage difference is subjected to BOX-COX conversion.
The BOX-COX transformation is as follows:
Figure GDA0002304488890000021
where y is the original data and y (λ) is the changed data. Different lambda is selected to be substituted into the formula, and the optimal parameter lambda is selected by calculating the correlation between the converted equal-time interval discharge voltage difference and the capacity.
Step three: in the training set, the time delay tau of the two processed health factors is respectively calculated by using a C-C method 1 ,τ 2 And embedding dimension m 1 ,m 2 Selecting tau = max (tau) 1 ,τ 2 ),m＝max(m 1 ,m 2 ) Performing multivariate phase space reconstruction:
Figure GDA0002304488890000022
the training sample defining SVR is (X) j ,Y j ) X is input and Y is output.
PF part: the state space model chosen here is as follows:
Figure GDA0002304488890000023
wherein x is k ＝[a k ,b k ,c k ,d k ]K denotes the number of cycles, x k Representing state model parameters, Q k An observed value, ω, representing the capacity k ，v k Representing state noise and observation noise, respectively.
The initial values of the model are estimated by a least square method by using a training set of three groups of batteries and are obtained by taking the mean value.
Step four: and (3) filtering process of the training set:
initialization k =0, setting parameters.
Sampling, from a prior probability distribution p (X) at k =0 0 ) Randomly extracting initialization particle sample state set
Figure GDA0002304488890000031
Setting initial weight of particles to
Figure GDA0002304488890000032
And importance sampling is divided into two steps of k moment prediction and weight value updating.
For i =1, n, at time k, sampled from the proposed distribution function,
Figure GDA0002304488890000033
and is provided with
Figure GDA0002304488890000034
For i =1, updating the weight, calculating the importance weight of each particle:
Figure GDA0002304488890000035
normalization processing weight:
Figure GDA0002304488890000036
resampling, and estimating the effective particle number if N eff ＞N threshold Then no resampling is needed, including:
Figure GDA0002304488890000037
Figure GDA0002304488890000038
otherwise, resampling is carried out to obtain a new particle set and a corresponding importance weight:
Figure GDA0002304488890000039
Figure GDA00023044888900000310
state estimation, posterior probability calculation is carried out through the output of the particle filter algorithm,
Figure GDA00023044888900000311
and judging whether the training set filtering process is finished, otherwise, enabling k = k +1, and repeating the filtering process until the training set filtering process is finished.
Step five: and predicting the future battery capacity by using the trained SVR model, updating the system state by using the predicted value by repeating the PF process, and obtaining the predicted value of the battery capacity by using a measurement equation.
If the predicted battery capacity reaches the battery failure threshold, the RUL is the time from this moment to the predicted starting point. And calculating prediction accuracy indexes such as RMSE, MAPE and RUL prediction errors between the predicted value and the real finger, and verifying the effectiveness of the method.
After the scheme is adopted, the battery capacitance and the voltage difference of the discharge at equal time intervals are extracted to be used as health factors, and the linear correlation between the health factors and the battery capacity is improved by performing BOX-COX conversion on the health factors. C-C method for obtaining time delay tau of health factor after treatment 1 ,τ 2 And embedding dimension m 1 ,m 2 Selecting τ = max (τ) 1 ,τ 2 ),m＝max(m 1 ,m 2 ) Performing multivariate phase space reconstruction; thereby defining the input in training the SVRInput and output. And estimating the training set of the three groups of batteries by using a least square method, taking the mean value to obtain an initial value of a system state space model, and then performing a filtering process on the training set by using PF (particle filter) to obtain the latest state of the system. And after the SVR model obtains a capacity predicted value, updating the system state by using the predicted value, finally obtaining a final predicted value of the battery capacity through a measurement equation, comparing the final predicted value with a previously defined threshold value, and finally estimating the residual service life of the lithium battery. The method and the device can accurately estimate the RUL of the lithium battery.
Reference documents
BOX-COX transformation [1] R.M.SAKIA.the Box-Cox transformation technique: a review [ J ]. Journal of Royal Statistical Society,1992,41 (2): 169-178.
C-C method [2] Kim H S, R.Eykholt, J.D.Salas. Nonlinear dynamics, delay times, and embedding windows [ J ]. Physica D-nonlinear Phenomena,1999,127 (1-2): 48-60.
Drawings
Fig. 1 is a graph of capacity decay curves and failure thresholds corresponding to three groups of lithium batteries used in the present invention.
FIG. 2 is a flow chart of PSR-SVR-PF used in the present invention.
FIG. 3a is a graph showing the result of the present invention using B05 battery data with a predicted starting point of 100
FIG. 3B is a graph of predicted capacitance distribution at the end of life for group B05 cells.
FIG. 4a is a graph showing the result of the B06 battery data prediction starting point of 100 used in the present invention
Fig. 4B is a predicted capacitance distribution for end-of-life point for group B06 cell data used in the present invention.
FIG. 5a is a graph showing the result of the present invention when the predicted starting point of the B07 set of battery data is 100
FIG. 5B is a predicted capacitance distribution for end-of-life for group B07 cell data used in the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with reference to the attached drawings. Simulation was performed on three sets of battery data, but only a comparison graph of the simulation effect is given here with 100 as the predicted starting point to verify the validity of the algorithm.
The overall process of the present invention is shown in FIG. 2.
Firstly, screening the obtained NASA data set, and correspondingly selecting three groups B0005, B0006 and B0007 as experimental data sets. Two health factors of battery capacitance and discharge voltage difference at equal time intervals are extracted, and a training set and a test set are divided.
As shown in FIG. 1, the invention carries out simulation experiments based on three groups of battery data of B0005, B0006 and B0007 in NASA, and verifies the effectiveness of the algorithm on the three groups of battery data.
SVR part: before training the SVR model, in order to enhance the linear correlation between the equal time interval discharge voltage difference and the capacity, the equal time interval discharge voltage difference is subjected to BOX-COX conversion.
A key parameter lambda exists in BOX-COX conversion, and the optimal parameter lambda is selected by calculating Pearson correlation coefficients of discharge voltage difference and capacity at equal time intervals.
In the training set, the time delay tau of the two processed health factors is respectively calculated by using a C-C method 1 ,τ 2 And embedding dimension m 1 ,m 2 Selecting tau = max (tau) 1 ,τ 2 ),m＝max(m 1 ,m 2 ) Performing multivariate phase space reconstruction:
Figure GDA0002304488890000061
the training sample defining SVR is (X) j ,Y j ) X is input and Y is output.
PF part: the state space model chosen here is as follows:
Figure GDA0002304488890000062
wherein x is k ＝[a k ,b k ,c k ,d k ]K denotes the number of cycles, x k Representing state model parameters, Q k An observed value, ω, representing the capacity k ，v k Representing state noise and observation noise, respectively.
The initial values of the model are estimated by a least square method by using a training set of three groups of batteries and are obtained by taking the mean value.
And (3) filtering process of the training set:
initialization k =0, setting parameters.
Sampling, from a prior probability distribution p (X) when k =0 0 ) Randomly drawing a set of initialization particle sample states
Figure GDA0002304488890000063
Setting initial weight of particles to
Figure GDA0002304488890000064
And importance sampling is divided into two steps of k moment prediction and weight value updating.
For i =1, at time k, sampled from the proposed distribution function,
Figure GDA0002304488890000065
and is provided with
Figure GDA0002304488890000066
For i =1, updating the weight, calculating the importance weight of each particle:
Figure GDA0002304488890000067
normalization processing weight:
Figure GDA0002304488890000071
resampling, and estimating the effective particle number if N eff ＞N threshold Then no resampling is needed, as follows:
Figure GDA0002304488890000072
Figure GDA0002304488890000073
otherwise, resampling is carried out to obtain a new particle set and a corresponding importance weight:
Figure GDA0002304488890000074
Figure GDA0002304488890000075
state estimation, posterior probability calculation is carried out through the output of the particle filter algorithm,
Figure GDA0002304488890000076
and judging whether the training set filtering process is finished, if not, enabling k = k +1, and repeating the filtering process until the training set filtering process is finished.
And predicting the future battery capacity by using the trained SVR model, updating the system state by repeating the PF process by using a predicted value, and obtaining a predicted value of the battery capacity by using a measurement equation.
Fig. 3a, 3b, 4a, 4b, 5a and 5b show graphs of the predicted results of three different batteries at 100 as the predicted starting point. It can be seen from the figure that the present invention has a higher accuracy and also gives an uncertain expression of the predicted end-of-life.
Table 1: the performance of the method of the present invention on the prediction of RUL is illustrated in terms of accuracy index.
Figure GDA0002304488890000077
Aiming at the problem of residual life prediction of the lithium iron phosphate battery, the invention provides a PSRSVR-PF algorithm, a simulation experiment is realized based on NASA lithium battery real discharge data, and the effectiveness of the PSR-SVR-PF algorithm is proved through the experiment.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (4)

1. The lithium battery residual life prediction method based on phase space reconstruction and particle filtering is characterized by comprising the following steps:
the method comprises the following steps: selecting battery capacity and equal time interval discharge voltage difference as two health factors, selecting T time as a prediction starting point, namely selecting a time sequence before the T time as a training set,
step two: in order to strengthen the linear relation between the discharge voltage difference of equal time intervals and the battery capacity, BOX-COX conversion is carried out on the discharge voltage difference,
step three: when training the SVR model, using phase space reconstruction PSR to respectively obtain the time delay and embedding dimension of two health factor time sequences, performing multivariate phase space reconstruction to define the input and output of the training SVR,
step four: selecting a dual-exponential degeneration model Z k ＝a k exp(b k ·k)+c k exp(d k K) as a particle filter measurement equation with state x k ＝[a k ，b k ，c k ，d k ]The system's equation of state is x k+1 ＝x k +v k Wherein v is k In order to process noise, a particle filter PF is used for carrying out a filtering process in a training set to obtain the latest state x of the system T-1 And when the calculation of the predicted value of the SVR is finished, updating the system state by using the predicted value, finally obtaining the final predicted value of the battery capacity through a particle filter measurement equation, and if the predicted capacity reaches the failure threshold value, the residual service life RUL is the time from the moment k to the failure threshold value point.
2. The lithium battery residual life prediction method based on phase space reconstruction and particle filtering according to claim 1, characterized in that:
the selected lithium battery capacity data is NASA data set,
three groups of B0005, B0006 and B0007 in the NASA data set are selected as experimental data sets, for different data sets, different initial prediction points are selected, data before the initial prediction points are used as training sets, and a regression model is trained to predict the future battery capacity.
3. The lithium battery residual life prediction method based on phase space reconstruction and particle filtering according to claim 1, characterized in that:
in the fourth step: the specific flow of the particle filter PF algorithm is as follows:
(1) Set the number of particles to N, particle set initialization, k =0,
(2) Sampling, from a prior probability distribution p (X) when k =0 0 ) Randomly extracting initialization particle sample state set
Figure FDA0003712239310000021
Setting initial weight of particles to
Figure FDA0003712239310000022
(3) At time k, the sample is taken from the proposed distribution function,
Figure FDA0003712239310000023
and is provided with
Figure FDA0003712239310000029
Wherein i represents the ith particle;
(4) Updating the weight, calculating the importance weight of each particle:
Figure FDA0003712239310000024
wherein the content of the first and second substances,
Figure FDA0003712239310000025
is the weight value, Y, corresponding to the particle at the time k 1：k Is the observed value from time 1 to time k,
(5) Normalization processing weight:
Figure FDA0003712239310000026
(6) Resampling, estimating effective particle number, if N eff ＞N threshold Then no resampling is needed, including:
Figure FDA0003712239310000027
otherwise, resampling is carried out to obtain a new particle set and a corresponding importance weight:
Figure FDA0003712239310000028
(7) State estimation, posterior probability calculation is carried out through the output of the particle filter algorithm,
Figure FDA0003712239310000031
(8) Judgment of
Figure FDA0003712239310000032
If the failure threshold is reached, otherwise let k = k +1, and repeat steps (3) - (7).
4. The method for predicting the remaining life of a lithium battery based on phase space reconstruction and particle filtering according to claim 1, wherein:
in the third step, the time delay and embedding dimension of two health indexes after noise reduction are solved by using a C-C method, and multivariate phase space reconstruction is carried out, so that the input and the output during SVR training are defined, wherein the selected SVR kernel function is a radial basis kernel function, and the specific expression is as follows:
Figure FDA0003712239310000033
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