CN112415414A - Method for predicting remaining service life of lithium ion battery - Google Patents

Method for predicting remaining service life of lithium ion battery Download PDF

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CN112415414A
CN112415414A CN202011072777.0A CN202011072777A CN112415414A CN 112415414 A CN112415414 A CN 112415414A CN 202011072777 A CN202011072777 A CN 202011072777A CN 112415414 A CN112415414 A CN 112415414A
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value
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rpf
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李祖欣
郑晋辉
周哲
蔡志端
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Hangzhou Dianzi University
Huzhou University
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Huzhou University
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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
    • 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
    • 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]
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Abstract

The invention discloses a method for predicting the remaining service life of a lithium ion battery, which comprises the following specific steps: extracting capacity data from a lithium battery data set, decomposing the capacity data into a high-frequency component representing a capacity regeneration phenomenon and a low-frequency component representing a capacity general degradation trend by adopting an empirical mode decomposition method, respectively predicting subcomponents of EMD decomposition by utilizing an ARIMA model, and finally adding prediction results of the components to obtain a comprehensive prediction result; taking the capacity predicted value of the previous step as an observed value of the regularized particle filter model, and adjusting and updating the capacity predicted value in each iteration process of the regularized particle filter model so as to obtain more accurate residual service life; the EMD-ARIMA predicted value is used as an observation value of the RPF algorithm model, so that the problem that the particle filter algorithm excessively depends on an empirical degradation model is solved, meanwhile, the RPF is introduced to make up the single-point estimation problem of the prediction result of the EMD-ARIMA method, more detailed PDF interval expression can be provided, the uncertainty expression capability of the particle filter is improved due to the introduction of the regularized particle filter, and the method can be widely applied to prediction of the residual service life of the lithium battery.

Description

Method for predicting remaining service life of lithium ion battery
Technical Field
The invention relates to the technical field of testing the electrical condition of a battery, in particular to a method for predicting the remaining service life of a lithium ion battery.
Technical Field
The lithium ion battery has the advantages of high energy density, environmental protection, no memory effect, low self-discharge rate, long service life and the like, and is widely applied and developed in the fields of electric automobiles, portable electronic equipment, aerospace and the like. However, as the number of battery charge and discharge cycles increases, the performance of the lithium battery gradually degrades, as indicated by an increase in internal resistance and a decrease in capacity. The performance degradation of the lithium battery can affect the function of the equipment, reduce the reliability of the system, increase the maintenance cost and even cause great loss in the aspects of personnel, facilities and the like. Therefore, it is necessary to accurately predict the remaining service life (RUL) of a lithium ion battery. The RUL of a battery is defined as the number of charge and discharge cycles remaining before its operating state deteriorates to a fault threshold. The state of degradation of the battery may be characterized by Health Indicators (HI), such as current, voltage, impedance, and capacity. Capacity is the most widespread indicator of battery health, and it is generally accepted that a battery reaches its end-of-life (EOL) threshold when its capacity degrades to 70% of its rated capacity.
Researchers have now performed a great deal of research work in RU prediction of lithium ion batteries. The battery prediction method may be roughly classified into a model-based method, a data-driven method, and a hybrid method. Model-based approaches rely on analysis of the lithium-ion battery degradation process and failure mechanisms, and then build correct parametric models to predict the degradation process of the system. Data-driven based prediction methods rely solely on historical data, extract significant feature information from monitored data, such as current, voltage, impedance, and capacity, use statistical and machine learning techniques to track degradation trends and estimate RUL. The prediction accuracy of the data-driven approach depends on the quantity and quality of the modeling sample data. The prediction method based on data driving and the prediction method based on the model have respective limitations when applied to the prediction of the lithium ion battery, so that the fusion prediction becomes a research hotspot for improving the prediction performance of the RUL.
The existing EMD-ARIMA can obtain a more accurate long-term prediction result of the battery capacity as a data-driven prediction method, but the prediction result is a single-point estimation of a prediction value, and a more detailed probability density function PDF expression of the prediction result cannot be given in practical application.
Disclosure of Invention
Aiming at the problems that the prediction result in the prior art depends on an empirical degradation model excessively, the adaptability to different data is poor, the prediction result is a single-point estimation of an RUL prediction value, and a more detailed probability density function expression of the prediction result cannot be given in practical application, the invention provides a method for predicting the remaining service life of a lithium ion battery based on the fusion of an EMD-ARIMA algorithm and a Regularized Particle Filter (RPF) algorithm, which comprises the following specific steps:
step 1, collecting battery capacity data and preprocessing the capacity data. Selecting a prediction starting point T from the capacity data, taking data before the prediction starting point T as training data, taking data after T as test data, and setting a battery capacity failure threshold CapEOL；
Step 2, decomposing the training data set by adopting an EMD algorithm, predicting each component obtained by decomposition by adopting an ARIMA algorithm, and finally summing the predicted values of each component to obtain a comprehensive prediction result, which is expressed as an EMD-ARIMApre, wherein the specific implementation steps are as follows:
step 2.1, using the training data set as an original signal x (t), further decomposing the original data x (t) into a set of sub-signals IMFs and residual signals, and finally, the original signal x (t) can be represented as:
Figure BDA0002715677920000021
wherein r isn(t) denotes a residual component, hi(t) a natural modal component;
step 2.2, adopting ABC-SVM to predict two ends of the signal before EMD decomposition processing is carried out on the signal;
step 2.3, ARIMA is adopted to predict the decomposed components respectively, and the flow is as follows:
judging whether the time sequence is stable, if not, executing difference to make the time sequence stable; after the stabilization treatment, selecting a corresponding model and presetting corresponding AR and MA orders according to the characteristics of the autocorrelation function and the partial autocorrelation function; according to different ARIMA (p, d, q) models formed by parameter combination, adopting an AIC Chichi information criterion to compare the AIC values of the models, and taking the model with the minimum AIC value as a final model; finally, estimating model parameters by adopting a least square method;
step 2.4, adding the prediction results of the ARIMA on the components to obtain a comprehensive prediction result EMD-ARIMApre;
step 3, establishing a state space equation based on the lithium battery empirical degradation model, estimating the system state by adopting a Regularized Particle Filter (RPF) algorithm, taking the comprehensive prediction result in the step 2 as an observed value, and updating and adjusting the prediction capacity value of the lithium battery in each iteration of the RPF algorithm;
step 4, judging whether the predicted capacity value reaches a capacity failure threshold value, namely a battery capacity failure threshold value CapEOLAnd setting the prediction result and the corresponding probability density function PDF of the RUL to be 70%, if the threshold is reached, and returning to the step 3 if the threshold is not reached.
As an optimized design: the specific way to perform the difference smoothing the time series in step 2.3 is to convert the non-smoothed time series into a smoothed time series using a d-order difference, representing d difference of y (t) as ^dyt(ii) a Thus, the ARIMA (p, d, q) model can be described as:
wt＝φ1wt-1+φ2wt-2+...+φpwt-p+εt-θ1εt-1-θ2εt-2-...-θpεt-pformula 2
Wherein, wtIs a time sequence of ∈tIs a mean value of zero and a variance of σ2White noise and zero mean. p is the order of the AR model, q is the order of the MA model, phiiAnd thetaiParameters of the AR model and MA model, respectively. w is at＝▽dytAnd d is the order of the difference.
As an optimized design: the state space equation of the empirical degradation model of the lithium battery in the step 3 is defined as shown in formula 3:
Figure BDA0002715677920000022
in the formula, CkIs the capacity value at the time of k cycles, ηcIs coulombic efficiency, beta1And beta2For the parameter to be estimated, Δ tkFor the rest time of adjacent cycles, wkAnd vkProcess noise and observation noise, respectively;
according to the state space equation constructed by the formula 3, the training data is tracked by adopting an RPF algorithm to further determine an unknown parameter beta in the state space equation1And beta2And setting initialization parameters of RPF algorithm, including the number of particles N and the initial state of capacity C0The covariance R of the process noise, and the covariance Q of the observation noise;
the specific process of iteratively updating the particles by adopting the RPF algorithm and outputting a predicted capacity value comprises the following steps:
a. initializing particles: from a priori probability p (x)0) Generating a collection of particles
Figure BDA0002715677920000031
All the particles have a weight of
Figure BDA0002715677920000032
b. Starting an iterative process: acquiring a prior estimated value of the battery capacity at the moment k according to the formula 3;
c. importance sampling, namely calculating an observed value corresponding to the prior estimated value by using formula 3 in an importance sampling stage, comparing the observed value with the comprehensive prediction result EMD-ARIMAPRE obtained in the step 2, correcting the observed value to obtain the posterior estimation of the capacity, and further updating the weight of the particles;
d. resampling; the RPF algorithm resamples the continuous distribution by continuously approximating the discrete distribution, and resamples the continuous approximated distribution according to equation 4 to obtain particles:
Figure BDA0002715677920000033
in formula 4, Kh(. h) is a new kernel function rescaled from the symmetric kernel density function K (·); h is>0 is nuclear bandwidth, nxIs the dimension of the state vector x; the kernel density function satisfies the condition shown in equation 5:
Figure BDA0002715677920000034
e. and (5) repeatedly executing the steps by taking k as k +1, iteratively updating the battery capacity according to the state space model, and outputting a predicted capacity value capout (k) in each loop.
The invention has the beneficial effects that:
because the closer the center point of the probability density function is to the actual life threshold value and the narrower the PDF distribution interval is, the higher the uncertainty precision of the prediction result is, after the RPF algorithm is introduced into the EMD-ARIMA, the final prediction result has the capability of uncertain expression, and thus the prediction result has higher reliability and scientificity. The fusion algorithm can fully exert the advantages of respective methods, make up for the defects and effectively improve the overall performance of the RUL prediction of the lithium ion battery.
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FIG. 1 is a schematic view of the overall process of the present invention.
Fig. 2 is a graph showing the relationship of capacity degradation of a lithium ion battery.
Fig. 3 is a diagram of a prediction result of the remaining service life of the lithium ion battery.
Detailed Description
The following clearly and completely describes the capacity degradation data of the lithium battery No. B0005 by taking the example in combination with the technical scheme in the embodiment of the present invention.
TABLE 1B 0005 lithium ion batteries
Constant current charging current/A Charge cut-off voltage/V Discharge current/A Discharge cut-off voltage/V Rated capacity/Ah
1.5 4.2 2.0 2.7 2.0
Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the like or similar elements throughout.
As shown in fig. 1, according to the embodiment of the present invention, the method for predicting the remaining service life of a lithium ion battery based on EMD-ARIMA and RPF includes three basic steps.
Step 1, extracting battery capacity data from a battery database and performing preprocessing 100. Setting a prediction starting point T101 from the capacity data, and using the data before the prediction starting point T as training data and the data after T as test dataData and set a battery capacity failure threshold CapEOL。
And 2, training and parameter estimation 103 by using an EMD-ARIMA model, specifically decomposing a training data set by using an EMD algorithm, predicting each component obtained by decomposition by using an ARIMA algorithm, and finally summing predicted values of each component to obtain a comprehensive prediction result, which is expressed as EMD-ARIMApre 105. The concrete implementation steps are as follows:
step 2.1, using the training data set as an original signal x (t), further decomposing the original data x (t) into a set of sub-signals IMFs and residual signals, and finally, the original signal x (t) can be represented as:
Figure BDA0002715677920000041
wherein r isn(t) denotes a residual component, hi(t) a natural modal component.
Step 2.2, adopting ABC-SVM to predict two ends of the signal before EMD decomposition processing is carried out on the signal;
step 2.3, the flow of predicting the decomposed components by using ARIMA respectively comprises the following steps;
step (1), judging whether the time sequence is stable, if not, executing difference to make the time sequence stable;
and (2) after the stabilization treatment, judging a prediction model and estimating the value of the correlation parameter through the trailing and truncation characteristics of the autocorrelation function and the partial autocorrelation function. The prediction model is shown in the following table 2 in functional relationship.
TABLE 2 prediction model and functional relationship
Figure BDA0002715677920000042
If both the autocorrelation function and the partial autocorrelation function are smeared, an ARMA model is established (ARIMA (p, d, q)).
After the model is determined and p and q parameters are obtained through prediction, different ARIMA (p, d and q) models are synthesized according to the parameters, the AIC values of the ARIMA (p, d and q) models are compared according to an AIC (information criterion of the Chichi pool), and the model with the minimum AIC value is taken as a final model.
AIC＝(n-d)logσ2+2(p+q+1)log n
In the formula: n is the number of samples, σ2To fit the average sum of residuals, p, d and q are the undetermined parameters.
And (5) checking whether the residual sequence of the final model is a pure random sequence, and if so, determining that the model is qualified. Otherwise, adjusting the number p of autoregressive terms and the number q of moving average terms until a qualified ARIMA prediction model is obtained.
Estimating model parameters by adopting a least square method; maximum likelihood estimation, Yule-Walker, Burg, etc. may also be employed.
The specific way to perform the difference smoothing the time series in step 2.3 is to convert the non-smoothed time series into a smoothed time series using a d-order difference, representing d difference of y (t) as ^dyt(ii) a Thus, the ARIMA (p, d, q) model can be described as:
wt＝φ1wt-1+φ2wt-2+...+φpwt-p+εt-θ1εt-1-θ2εt-2-...-θpεt-pformula 2
Wherein, wtIs a time sequence of ∈tIs a mean value of zero and a variance of σ2White noise and zero mean. p is the order of the AR model, q is the order of the MA model, phiiAnd thetaiParameters of the AR model and MA model, respectively. w is at＝▽dytAnd d is the order of the difference.
Step 3, establishing a state space equation of the empirical model aiming at the lithium battery empirical degradation model:
Ck+1＝ηcCk+β1exp(-β2/Δtk)+wk
yk＝Ck+vkformula 3
In formula 3, CkIs the capacity value at the time of k cycles, ηcFor coulombic efficiency, beta1And beta2For the parameter to be estimated, Δ tkFor the rest time of adjacent cycles, wkAnd vkProcess noise and observation noise, respectively.
First, the parameter β in the state space equation of equation 3 is determined1And beta2Then, the RPF algorithm is adopted to estimate the system state, the comprehensive prediction result in step 2 is used as an observation value, the particles are updated in each iteration of the RPF algorithm, and the predicted capacity value capout (k) of the lithium ion battery is adjusted, which is specifically described below.
After determining the prediction starting point T101, defining training data and test numbers, identifying 102 parameters by using an empirical model, i.e. an empirical degradation model of the lithium battery is used, and determining 104 parameters in the empirical model. Namely, the RPF algorithm is adopted to track the training data so as to determine the unknown parameter beta in the state space equation1And beta2。
First, an initialization particle set X is obtained0106. I.e. by a prior probability p (x)0) Generating a collection of particles
Figure BDA0002715677920000051
All the particles have a weight of
Figure BDA0002715677920000052
The particles 107 are then iteratively updated by the state transition equations, with the particular iterative process being the prior estimation of the battery capacity at time k being obtained according to the state transition equations of equation 3. Then enter importance sampling correction observations and update particle weights 108: calculating an observation value corresponding to the prior estimation by using an observation equation in the formula 3, comparing the observation value with the comprehensive prediction result EMD-ARIMApre obtained in the step 2, correcting the prior estimation value, namely updating the observation value to obtain the posterior estimation of the capacity, and further updating the weight of the particles; then resample 109:
the RPF algorithm resamples the continuous distribution by continuously approximating the discrete distribution according to formula (4) to obtain particles:
Figure BDA0002715677920000061
in formula 4, Kh(. h) is a new kernel function rescaled from the symmetric kernel density function K (·); h is>0 is nuclear bandwidth, nxIs the dimension of the state vector x; the kernel density function satisfies the condition shown in equation 5:
Figure BDA0002715677920000062
and (5) repeatedly executing the steps by taking k as k +1, iteratively updating the battery capacity according to the state space model, and outputting an estimated state capout (k) in each loop.
Step 4, judging whether Capout (k) reaches a capacity threshold CapEOLAnd 110, if the capacity threshold is reached, outputting the cycle number k at the moment, and then the predicted remaining service life value RUL of the lithium ion battery is k. And calculating the probability density function PDF111 of the RUL according to the PDF distribution of the battery capacity and the corresponding relation between the capacity and the battery cycle service life. And if the capacity does not reach the threshold value, returning to the state transition equation to update the particles in an iterative manner.
Compared with the resampling step of the standard PF method, the resampling of the RPF algorithm is mainly a sampling process from the kernel density. Therefore, the RPF algorithm does not vary significantly in computational complexity. Under the condition that the diversity of the particles is poor seriously, the estimation precision of the RPF algorithm is superior to that of the standard PF algorithm, and the reliability of a prediction result can be well guaranteed.
The invention selects a B0005 battery capacity data set as an experimental object, and predicts a starting point T as 80 cycles. The failure threshold for the B0005 battery was set to 70% of the rated capacity of the battery, i.e., 1.4 Ah. In this example, as shown in the battery capacity-cycle number relationship diagram of fig. 2, the relationship between the capacity and the cycle period in the B0005 data set is extracted, and the data is preprocessed.
The relationship between the discharge capacity and the cycle period is shown in fig. 3. And selecting the predicted starting point T as 80, and using the first 80 data as a training data set.Coulomb efficiency ηc0.997, the RPF algorithm tracks the determined parameter β1＝-0.3，β20.5. The initialization parameters of the RPF algorithm are set, the number of particles N is 500, the initial state of the capacity (the battery capacity C0 when T is 80 is 1.5649), the covariance R of the process noise is 0.001, the covariance Q of the observation noise is 0.001, and the like.
Compared with the resampling step of the standard PF method, the resampling of the RPF algorithm is mainly a sampling process from the kernel density. Therefore, the RPF algorithm does not vary significantly in computational complexity. Under the condition that the diversity of the particles is poor seriously, the estimation precision of the RPF algorithm is superior to that of the standard PF algorithm, and the reliability of a prediction result can be well guaranteed.
In order to quantitatively analyze the accuracy of the prediction result, evaluation indexes such as Absolute Error (AE) and Root Mean Square Error (RMSE) are defined:
Figure BDA0002715677920000071
Figure BDA0002715677920000072
RULkis the true value of the instant of the k-cycle,
Figure BDA0002715677920000073
is a predicted value of the k-cycle time. M is the length of the prediction data, x (i) is the test data,
Figure BDA0002715677920000074
is a capacity prediction value.
TABLE 2 prediction results
Predicting a starting point True RUL (cycle) Prediction of RUL (cycle) Absolute error (Cycle) RMSE
80 45 42 3 0.0242
In this patent, the threshold of the B5 battery is set to 1.4Ah, the actual threshold charge-discharge cycle is 125 cycles, when the starting point start is 80 cycles, the actual RUL is 125-80 cycles 45 cycles, the predicted RUL is 122-80 cycles 42 cycles, and the RUL predicted absolute error AE is 45-42 cycles 3 cycles.
In conclusion, the invention discloses a lithium ion battery residual service life prediction method based on EMD-ARIMA and regularized particle filter RPF, belongs to the field of new energy electric vehicle lithium ion battery service life prediction, and on one hand, the introduction of the EMD-ARIMA algorithm solves the problems that the prediction result excessively depends on an empirical degradation model and the adaptability to different data is poor when the RUL of the lithium battery is predicted based on the RPF algorithm. On the other hand, the RUL of the lithium battery can be predicted for a long time based on the EMD-ARIMA model, but the prediction result is a point estimation value, and the reliability is poor. The introduction of the RPF algorithm enables the final prediction result to have the capability of uncertain expression, and the prediction result is qualitatively or quantitatively analyzed and has higher reliability and scientificity. The fusion algorithm can fully exert the advantages of respective methods, make up for the defects and effectively improve the overall performance of the RUL prediction of the lithium ion battery. The method can be applied to the service life prediction of the lithium ion battery of the new energy electric vehicle, and can effectively predict the performance degradation process of the lithium ion battery.
The foregoing has described the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are given by way of illustration of the principles of the present invention, and that various changes and modifications may be made without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (3)

1. A method for predicting the remaining service life of a lithium ion battery is characterized by comprising the following steps:
step 1, collecting battery capacity data and preprocessing the capacity data; selecting a prediction starting point T from the capacity data, taking data before the prediction starting point T as training data, taking data after T as test data, and setting a battery capacity failure threshold CapEOL；
Step 2, decomposing the training data set by adopting an EMD algorithm, predicting each component obtained by decomposition by adopting an ARIMA algorithm, and finally summing the predicted values of each component to obtain a comprehensive prediction result, which is expressed as an EMD-ARIMApre, wherein the specific implementation steps are as follows:
step 2.1, using the training data set as an original signal x (t), further decomposing the original data x (t) into a set of sub-signals IMFs and residual signals, and finally, the original signal x (t) can be represented as:
Figure FDA0002715677910000011
wherein r isn(t) denotes a residual component, hi(t) a natural modal component;
step 2.2, adopting ABC-SVM to predict two ends of the signal before EMD decomposition processing is carried out on the signal;
step 2.3, ARIMA is adopted to predict the decomposed components respectively, and the flow is as follows:
judging whether the time sequence is stable, if not, executing difference to make the time sequence stable; after the stabilization treatment, selecting a corresponding model and presetting corresponding AR and MA orders according to the characteristics of the autocorrelation function and the partial autocorrelation function; according to different ARIMA (p, d, q) models formed by parameter combination, adopting an AIC Chichi information criterion to compare the AIC values of the models, and taking the model with the minimum AIC value as a final model; finally, estimating model parameters by adopting a least square method;
step 2.4, adding the prediction results of the ARIMA on the components to obtain a comprehensive prediction result EMD-ARIMApre;
step 3, establishing a state space equation based on the lithium battery empirical degradation model, estimating the system state by adopting a Regularized Particle Filter (RPF) algorithm, taking the comprehensive prediction result in the step 2 as an observed value, and updating and adjusting the prediction capacity value of the lithium battery in each iteration of the RPF algorithm;
and 4, judging whether the predicted capacity value reaches a capacity failure threshold value, if so, calculating a prediction result of the RUL and a corresponding probability density function PDF, and if not, returning to the step 3.
2. The method for predicting the remaining service life of a lithium ion battery according to claim 1, wherein: the specific way to perform the difference in step 2.3 to smooth the time sequence is to convert the non-smooth time sequence into a smooth time sequence using a d-order difference, where the d-order difference of y (t) is expressed as
Figure FDA0002715677910000012
Thus, the ARIMA (p, d, q) model can be described as:
wt＝φ1wt-1+φ2wt-2+...+φpwt-p+εt-θ1εt-1-θ2εt-2-...-θpεt-pformula 2
Wherein, wtIs a time sequence，εtIs a mean value of zero and a variance of σ2White noise and zero mean. p is the order of the AR model, q is the order of the MA model, phiiAnd thetaiParameters of the AR model and MA model, respectively.
Figure FDA0002715677910000013
d is the order of the difference.
3. The method for predicting the remaining service life of a lithium ion battery according to claim 1, wherein: the state space equation of the empirical degradation model of the lithium battery in the step 3 is shown as the formula 3:
Figure FDA0002715677910000021
in the formula, CkIs the capacity value at the time of k cycles, ηcIs coulombic efficiency, beta1And beta2For the parameter to be estimated, Δ tkFor the rest time of adjacent cycles, wkAnd vkProcess noise and observation noise, respectively;
according to the state space equation constructed by the formula 3, the training data is tracked by adopting an RPF algorithm to further determine an unknown parameter beta in the state space equation1And beta2And setting initialization parameters of RPF algorithm, including the number of particles N and the initial state of capacity C0The covariance R of the process noise, and the covariance Q of the observation noise;
the specific process of iteratively updating the particles by adopting the RPF algorithm and outputting a predicted capacity value comprises the following steps:
a. initializing particles: from a priori probability p (x)0) Generating a collection of particles
Figure FDA0002715677910000022
All the particles have a weight of
Figure FDA0002715677910000023
b. Starting an iterative process: acquiring a prior estimated value of the battery capacity at the moment k according to the formula 3;
c. importance sampling, namely calculating an observed value corresponding to the prior estimated value by using formula 3 in an importance sampling stage, comparing the observed value with the comprehensive prediction result EMD-ARIMAPRE obtained in the step 2, correcting the observed value to obtain the posterior estimation of the capacity, and further updating the weight of the particles;
d. resampling; the RPF algorithm resamples the continuous distribution by continuously approximating the discrete distribution, and resamples the continuous approximated distribution according to equation 4 to obtain particles:
Figure FDA0002715677910000024
in formula 4, Kh(. h) is a new kernel function rescaled from the symmetric kernel density function K (·); h is>0 is nuclear bandwidth, nxIs the dimension of the state vector x; the kernel density function satisfies the condition shown in equation 5:
Figure FDA0002715677910000025
e. and (5) repeatedly executing the steps by taking k as k +1, iteratively updating the battery capacity according to the state space model, and outputting a predicted capacity value capout (k) in each loop.
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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
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