CN113791351B - Lithium battery life prediction method based on transfer learning and difference probability distribution - Google Patents

Lithium battery life prediction method based on transfer learning and difference probability distribution Download PDF

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CN113791351B
CN113791351B CN202111090229.5A CN202111090229A CN113791351B CN 113791351 B CN113791351 B CN 113791351B CN 202111090229 A CN202111090229 A CN 202111090229A CN 113791351 B CN113791351 B CN 113791351B
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lithium battery
capacity degradation
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capacity
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顾博瑞
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University of Electronic Science and Technology of China
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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
    • 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
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
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    • G06N20/00—Machine learning

Abstract

The invention discloses a lithium battery service life prediction method based on transfer learning and difference probability distribution, which is characterized in that the service life experiment of a lithium battery is accelerated to obtain the degradation amount of the capacity of the lithium battery at different moments; then, obtaining a correction factor of a predicted value based on the transfer learning and the historical data of the lithium battery capacity degradation amount, and further estimating the probability distribution parameter of the correction factor by using normal distribution; then, predicting the capacity degradation amount of the lithium battery to be tested in real time by using transfer learning, and correcting the predicted value by using a correction factor; and finally, judging the residual life of the lithium battery according to the obtained correction predicted value, and having the characteristics of high prediction precision, high prediction speed and the like.

Description

Lithium battery life prediction method based on transfer learning and difference probability distribution
Technical Field
The invention belongs to the technical field of lithium battery reliability analysis, and particularly relates to a lithium battery service life prediction method based on transfer learning and difference probability distribution.
Background
The lithium battery is an important and widely applied energy storage device and has the advantages of high efficiency, long service life, convenience in carrying, quickness in charging and the like. The method is widely applied to various key fields of electronic products, new energy carriers, aerospace and the like. The lithium battery is taken as a core part of the system, the reliability affects the operation stability of the whole system equipment, and the research on the prediction technical method of the residual Life (RUL) of the lithium battery module becomes necessary, and the method has the following important significance: (1) as an important way for obtaining the reliability information of the lithium battery module, the method can further provide a basis for realizing the on-line monitoring and health management of the system; (2) the accelerated aging test can be better designed to obtain more accurate aging data, so that reminding and early warning can be made in advance; (3) the maintenance can be realized according to the situation, so that the terminal user can obtain more service life information of the lithium battery module to reduce the investment on system maintenance; (4) as a prediction idea, the method can be analogized to other similar fields, and the prediction efficiency effect of other fields is improved.
The remaining service life of the lithium battery refers to the number of charge-discharge cycles required for the maximum available capacity of the battery to be attenuated to a specified failure threshold value after a certain charge-discharge process, and the existing lithium battery life prediction methods mainly comprise three categories, namely data driving-based and fusion algorithm-based. The model-based prediction method usually adopts a certain type of specific model to predict the residual life of the lithium battery, and has certain precision. However, the built RUL prediction model is only suitable for a specific system, and the model parameters are difficult to estimate. The prediction method based on data driving does not need to know the aging mechanism and the extension rule, does not establish a specific physical model, and establishes a statistical model or a machine learning model based on data. The data-driven model is more easily applied to different occasions and does not depend on a specific physical model.
For data-driven based prediction methods, the accuracy is indeed improved to some extent by using the powerful computational power of the machine. But the accuracy of prediction is related to the amount of training data, and therefore, the method often depends on a huge data base. The probability statistics-based method describes the degradation trend of the lithium battery by using a probability statistics model, can well depict uncertainty in the degradation process of the lithium battery, but the probability density function of the residual life of the lithium battery is difficult to solve.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a lithium battery life prediction method based on transfer Learning and difference probability distribution.
In order to achieve the above object, the present invention provides a lithium battery life prediction method based on transfer learning and difference probability distribution, which is characterized by comprising the following steps:
(1) calculating the capacity degradation of the lithium battery
Setting capacity degradation data of N lithium batteries at different sampling moments, and using each lithium batterySubtracting the capacity value of the lithium battery at the starting moment from the capacity degradation data at different sampling moments to obtain the capacity degradation amounts of the N groups of lithium batteries at different sampling moments; the capacity degradation of the ith lithium battery is recorded as
Figure BDA0003267107460000021
Wherein i is 1, 2, 3.. N,
Figure BDA0003267107460000022
indicates the initial capacity degradation amount of the ith lithium battery,
Figure BDA0003267107460000023
the capacity degradation amount of the ith lithium battery at the sampling time T is represented, wherein T is 1, 2, 3.. T, and T is the total number of the sampling times;
(2) calculating probability distribution of prediction correction factor by using capacity degradation amount of lithium battery
(2.1) capacity degradation amount of first group lithium battery
Figure BDA0003267107460000024
Performing single-step prediction based on transfer learning;
setting the current time as T, wherein T is less than T; taking the volume degradation
Figure BDA0003267107460000025
The data of the first t times (j is 2,3, …, N) are respectively calculated by XjAnd X1Euclidean distance of Oj：
Figure BDA0003267107460000026
Selecting the minimum OjCorresponding capacity degradation XjThen X is addedjAs a training set;
in the training set, the pass window length is NEExtracting input data by a sliding window with the step length of 1, and then training an input data with the length of NEAn extreme learning machine ELM with an output of 1;
will be provided with
Figure BDA0003267107460000027
Middle and last NEData of a person
Figure BDA0003267107460000028
Inputting the data into a trained extreme learning machine ELM, and predicting a first group of lithium batteries X at the t +1 moment by using the extreme learning machine ELM1Amount of capacity degradation of
Figure BDA0003267107460000029
Calculating the actual capacity degradation amount of the first group of lithium batteries at the moment of t +1
Figure BDA0003267107460000031
And predicting the amount of capacity degradation
Figure BDA0003267107460000032
Difference of difference
Figure BDA0003267107460000033
Memo
Figure BDA0003267107460000034
Is a correction factor;
Figure BDA0003267107460000035
(2.2) mixing
Figure BDA0003267107460000036
Instead of in step (2.1)
Figure BDA0003267107460000037
And repeating the step (2.1) to obtain N correction factors at the t +1 moment:
Figure BDA0003267107460000038
(2.3) calculating N correction factors
Figure BDA0003267107460000039
Mean value of (a)Δ,t+1Sum variance
Figure BDA00032671074600000310
Figure BDA00032671074600000311
Figure BDA00032671074600000312
(2.4) after the time prediction is finished, replacing the current time T in the step (2.1) with the time T +1, T +2, … and T-1 in sequence, and repeating the steps (2.1) and (2.2) to obtain N correction factors of the subsequent time
Figure BDA00032671074600000313
And corresponding mean value muΔ,t+2,μΔ,t+3,…,μΔ,TThe sum of the variances
Figure BDA00032671074600000314
(2.5) respectively obtaining the mean values [ mu ]Δ,t+1,μΔ,t+2,…,μΔ,TThe sum of the variances
Figure BDA00032671074600000315
To obtain the overall mean value mu of the correction factorΔSum variance
Figure BDA00032671074600000316
And obey normal distribution
Figure BDA00032671074600000317
(3) Extreme learning machine ELM training based on transfer learning
(3.1) setting the capacity degradation amount of the lithium battery to be tested at the current t moments as X ═{x0,x1,…,xt}；
(3.2) capacity degradation data of existing N lithium batteries
Figure BDA00032671074600000318
Selecting one of the lithium batteries to be tested and setting the capacity degradation amount of the lithium battery to be tested as X ═ X0,x1,…,xtThe most similar group, note as
Figure BDA00032671074600000319
(3.3) the method according to step (2.1), using
Figure BDA00032671074600000324
Training an input data length of NEAn extreme learning machine ELM with an output of 1;
(3.4) converting X to { X ═ X0,x1,…,xtThe last N inEData of a person
Figure BDA00032671074600000320
Inputting the data into an extreme learning machine ELM so as to predict the degradation amount of the lithium battery to be tested at the t +1 moment
Figure BDA00032671074600000321
(4) Single step prediction correction of extreme learning machine ELM
(4.1) calculating the capacity degradation amount of the existing N lithium batteries at the t +1 moment
Figure BDA00032671074600000322
Mean value of (a)x,t+1Sum variance
Figure BDA00032671074600000323
(4.2) setting the capacity degradation amount of N lithium batteries at the t +1 moment
Figure BDA0003267107460000041
Obey normal distribution
Figure BDA0003267107460000042
Amount of degradation is determined
Figure BDA0003267107460000043
To normal distribution
Figure BDA0003267107460000044
Distance p of centert+1：
Figure BDA0003267107460000045
(4.3) binding correction factor distribution
Figure BDA0003267107460000046
And a distance pt+1To find a predicted value
Figure BDA0003267107460000047
Corresponding correction factor
Figure BDA0003267107460000048
Figure BDA0003267107460000049
(4.4) the predicted value of the corrected capacity degradation amount of the lithium battery to be tested at the t +1 moment:
Figure BDA00032671074600000410
(5) prediction of remaining life of lithium battery to be tested
(5.1) mixing
Figure BDA00032671074600000411
As the input of the ELM, obtaining the predicted value of the capacity degradation amount of the lithium battery to be measured at the time of t +2
Figure BDA00032671074600000412
Then according to the method pair in the step (4.4)
Figure BDA00032671074600000413
Correcting to obtain the corrected predicted value
Figure BDA00032671074600000414
(5.2) judging the predicted value
Figure BDA00032671074600000415
Whether the threshold value omega is larger than a given failure threshold value omega is judged, if so, the lithium battery is judged to be failed, and the algorithm is ended; otherwise, it will
Figure BDA00032671074600000416
Adding into ELM input, and continuing prediction according to the method of step (5.1), and repeating the steps until obtaining corrected predicted value
Figure BDA00032671074600000417
And when the current value is larger than the given failure threshold omega, recording the time n corresponding to the degradation of the lithium battery to be tested to the failure threshold, thereby obtaining the residual life of the lithium battery to be tested after the time t.
The invention aims to realize the following steps:
the lithium battery life prediction method based on the transfer learning and the difference probability distribution obtains the degradation amount of the capacity of the lithium battery at different moments by accelerating the life experiment of the lithium battery; then, obtaining a correction factor of a predicted value based on the transfer learning and the historical data of the lithium battery capacity degradation amount, and further estimating the probability distribution parameter of the correction factor by using normal distribution; then, predicting the capacity degradation amount of the lithium battery to be tested in real time by using transfer learning, and correcting the predicted value by using a correction factor; and finally, judging the residual life of the lithium battery according to the obtained correction predicted value, and having the characteristics of high prediction precision, high prediction speed and the like.
Meanwhile, the lithium battery service life prediction method based on the transfer learning and the difference probability distribution further has the following beneficial effects:
(1) the prediction result is corrected by using the transfer learning technology based on the Euclidean distance and utilizing the difference probability distribution, so that the self-adaptive selection of the optimal training data and the error improvement of the prediction result are realized, and the prediction precision of the model is improved;
(2) the transfer learning technology based on the Euclidean distance is adopted when the training data is selected, and compared with the traditional ELM training method, the method has strong self-adaptive capacity for training data selection, avoids the influence of bad data on the ELM training process, and improves the efficiency and performance of ELM training;
(3) and the correction of the prediction result is realized by using the correction factor based on the difference probability, so that the prediction error is reduced and the prediction precision of the residual life is improved compared with the traditional ELM.
Drawings
FIG. 1 is a flow chart of a lithium battery life prediction method based on transfer learning and difference probability distribution according to the present invention;
FIG. 2 is degradation data of 6 groups of lithium battery capacity obtained from accelerated life tests;
FIG. 3 is a diagram of a prediction result of a method for predicting remaining life of a lithium battery based on transfer learning and difference probability distribution according to the present invention;
fig. 4 shows the results of the prediction of the remaining life of the lithium battery by the two prediction models.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a lithium battery life prediction method based on transfer learning and difference probability distribution according to the present invention.
In this embodiment, as shown in fig. 1, a lithium battery life prediction method based on transfer learning and difference probability distribution according to the present invention includes the following steps:
(1) calculating the capacity degradation of the lithium battery
Setting capacity degradation data of N lithium batteries at different sampling moments, and subtracting the capacity value of the lithium battery at the starting moment from the capacity degradation data of each lithium battery at the different sampling moments to obtain the capacity degradation amounts of the N groups of lithium batteries at the different sampling moments; the capacity degradation of the ith lithium battery is recorded as
Figure BDA0003267107460000051
Wherein i is 1, 2, 3.. N,
Figure BDA0003267107460000052
indicates the initial capacity degradation amount of the ith lithium battery,
Figure BDA0003267107460000061
the capacity degradation amount of the ith lithium battery at the sampling time T is represented, wherein T is 1, 2, 3.. T, and T is the total number of the sampling times;
(2) calculating probability distribution of prediction correction factor by using capacity degradation amount of lithium battery
(2.1) capacity degradation amount of first group lithium battery
Figure BDA0003267107460000062
Performing single-step prediction based on transfer learning;
setting the current time as T, wherein T is less than T; taking the volume degradation
Figure BDA0003267107460000063
The data of the first t times (j is 2,3, …, N) are respectively calculated by XjAnd X1Euclidean distance of Oj：
Figure BDA0003267107460000064
Selecting the minimum OjCorresponding capacity degradationQuantity XjThen X is addedjAs a training set;
in the training set, the pass window length is NEExtracting input data by a sliding window with the step length of 1, and then training an input data with the length of NEAn extreme learning machine ELM with an output of 1;
will be provided with
Figure BDA0003267107460000065
Middle and last NEData of a person
Figure BDA0003267107460000066
Inputting the data into a trained extreme learning machine ELM, and predicting a first group of lithium batteries X at the t +1 moment by using the extreme learning machine ELM1Amount of capacity degradation of
Figure BDA0003267107460000067
Calculating the actual capacity degradation amount of the first group of lithium batteries at the moment of t +1
Figure BDA0003267107460000068
And predicting the amount of capacity degradation
Figure BDA0003267107460000069
Difference of difference
Figure BDA00032671074600000610
Memo
Figure BDA00032671074600000611
Is a correction factor;
Figure BDA00032671074600000612
(2.2) mixing
Figure BDA00032671074600000613
Instead of in step (2.1)
Figure BDA00032671074600000614
And repeating the step (2.1) to obtain N correction factors at the t +1 moment:
Figure BDA00032671074600000615
(2.3) calculating N correction factors
Figure BDA00032671074600000616
Mean value of (a)Δ,t+1Sum variance
Figure BDA00032671074600000617
Figure BDA00032671074600000618
Figure BDA00032671074600000619
(2.4) after the time prediction is finished, replacing the current time T in the step (2.1) with the time T +1, T +2, … and T-1 in sequence, and repeating the steps (2.1) and (2.2) to obtain N correction factors of the subsequent time
Figure BDA00032671074600000620
And corresponding mean value muΔ,t+2,μΔ,t+3,…,μΔ,TThe sum of the variances
Figure BDA00032671074600000621
(2.5) respectively obtaining the mean values [ mu ]Δ,t+1,μΔ,t+2,…,μΔ,TThe sum of the variances
Figure BDA0003267107460000071
To obtain the overall mean value mu of the correction factorΔSum variance
Figure BDA0003267107460000072
And obey normal distribution
Figure BDA0003267107460000073
(3) Extreme learning machine ELM training based on transfer learning
(3.1) setting the capacity degradation amount of the lithium battery to be tested at the current t moments as X ═ X0,x1,…,xt}；
(3.2) capacity degradation data of existing N lithium batteries
Figure BDA0003267107460000074
Selecting one of the lithium batteries to be tested and setting the capacity degradation amount of the lithium battery to be tested as X ═ X0,x1,…,xtThe most similar group, note as
Figure BDA0003267107460000075
(3.3) the method according to step (2.1), using
Figure BDA0003267107460000076
Training an input data length of NEAn extreme learning machine ELM with an output of 1;
(3.4) converting X to { X ═ X0,x1,…,xtThe last N inEData of a person
Figure BDA0003267107460000077
Inputting the data into an extreme learning machine ELM so as to predict the degradation amount of the lithium battery to be tested at the t +1 moment
Figure BDA0003267107460000078
(4) Single step prediction correction of extreme learning machine ELM
(4.1) calculating the capacity degradation amount of the existing N lithium batteries at the t +1 moment
Figure BDA0003267107460000079
Mean value of (a)x,t+1Sum variance
Figure BDA00032671074600000710
(4.2) setting the capacity degradation amount of N lithium batteries at the t +1 moment
Figure BDA00032671074600000711
Obey normal distribution
Figure BDA00032671074600000712
Amount of degradation is determined
Figure BDA00032671074600000713
To normal distribution
Figure BDA00032671074600000714
Distance p of centert+1：
Figure BDA00032671074600000715
(4.3) binding correction factor distribution
Figure BDA00032671074600000716
And a distance pt+1To find a predicted value
Figure BDA00032671074600000717
Corresponding correction factor
Figure BDA00032671074600000718
Figure BDA00032671074600000719
(4.4) the predicted value of the corrected capacity degradation amount of the lithium battery to be tested at the t +1 moment:
Figure BDA00032671074600000720
(5) prediction of remaining life of lithium battery to be tested
(5.1) mixing
Figure BDA00032671074600000721
As the input of the ELM, obtaining the predicted value of the capacity degradation amount of the lithium battery to be measured at the time of t +2
Figure BDA00032671074600000722
Then according to the method pair in the step (4.4)
Figure BDA00032671074600000723
Correcting to obtain the corrected predicted value
Figure BDA00032671074600000724
(5.2) judging the predicted value
Figure BDA0003267107460000081
Whether the threshold value omega is larger than a given failure threshold value omega is judged, if so, the lithium battery is judged to be failed, and the algorithm is ended; otherwise, it will
Figure BDA0003267107460000082
Adding into ELM input, and continuing prediction according to the method of step (5.1), and repeating the steps until obtaining corrected predicted value
Figure BDA0003267107460000083
And when the current value is larger than the given failure threshold omega, recording the time n corresponding to the degradation of the lithium battery to be tested to the failure threshold, thereby obtaining the residual life of the lithium battery to be tested after the time t.
In order to illustrate the technical effect of the invention, 5 groups of lithium battery degradation data CS2-33, CS2-34, CS2-35, CS2-36 and CS2-38 are selected as historical degradation data, and lithium batteries CS2-37 are selected as implementation objects of the invention, so that the prediction of the residual life of the lithium batteries under the real-time working state is simulated. Fig. 2 is data of the amount of degradation of the capacity of 6 groups of lithium batteries obtained by the experiment.
In the calculation of the probability distribution of the correction factor, the current time is selectedAt 400, the distribution obeyed by correction factors estimated by using the degradation data of 5 groups of lithium batteries is as follows:
Figure BDA0003267107460000084
predicting the residual life of the battery according to the methods in the steps (3) and (4), and predicting the residual life of the battery once every 10 cycles to obtain a result as shown in fig. 3, wherein one curve is a predicted value of the residual life of the lithium battery based on transfer learning and difference probability distribution; the other curve is the real residual life value of the lithium battery to be measured, and the average absolute error of the residual life prediction obtained by the method is about 25 cycles by comparing the difference values at the same moment.
For quantitative comparison and measurement of prediction performance, fig. 4 shows the prediction results of the method and the ELM network on the remaining life of the lithium battery CS2-37, wherein the first curve is the predicted value of the remaining life of the lithium battery based on the transfer learning and the difference probability distribution; the second curve is a predicted value of the residual life of the lithium battery based on an Extreme Learning Machine (ELM); the third curve is the real residual life of the lithium battery to be tested; through the prediction results of different types of models in fig. 4 on the RUL of the lithium battery, it can be found that the residual life prediction accuracy of the invention is much higher than that of a general ELM model because the invention corrects the prediction data of the ELM network by using the correction factor on the basis of the transfer learning model. Table 1 gives the mean prediction error for the present model and the ELM model.
The invention ELM
Mean error 25cycle 49cycle
TABLE 1
The prediction results shown in table 1 show that the accuracy of the residual life prediction result of the model is much higher than that of a general ELM model, which directly illustrates the advantages of the residual life prediction model of the lithium battery based on the transfer learning and the difference probability distribution.
The experimental result shows that compared with the existing neural network prediction model, the lithium battery residual life prediction model based on the migration learning and difference probability distribution conditions, which is constructed by the invention, has higher prediction precision, so that the method is more suitable for the requirement of lithium battery residual life prediction in actual engineering.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (1)

1. A lithium battery life prediction method based on transfer learning and difference probability distribution is characterized by comprising the following steps:
(1) calculating the capacity degradation of the lithium battery
Setting capacity degradation data of N lithium batteries at different sampling moments, and subtracting the capacity value of the lithium battery at the starting moment from the capacity degradation data of each lithium battery at the different sampling moments to obtain the capacity degradation amounts of the N groups of lithium batteries at the different sampling moments; the capacity degradation of the ith lithium battery is recorded as
Figure FDA0003506993360000011
Wherein i is 1, 2, 3.. N,
Figure FDA0003506993360000012
indicates the initial capacity degradation amount of the ith lithium battery,
Figure FDA0003506993360000013
the capacity degradation amount of the ith lithium battery at the sampling time T is represented, wherein T is 1, 2, 3.. T, and T is the total number of the sampling times;
(2) calculating probability distribution of prediction correction factor by using capacity degradation amount of lithium battery
(2.1) capacity degradation amount of first group lithium battery
Figure FDA0003506993360000014
Performing single-step prediction based on transfer learning;
setting the current time as T, wherein T is less than T; taking the volume degradation
Figure FDA0003506993360000015
The data of the first t times (j is 2,3, …, N) are respectively calculated by XjAnd X1Euclidean distance of Oj：
Figure FDA0003506993360000016
Selecting the minimum OjCorresponding capacity degradation XjThen X is addedjAs a training set;
in the training set, the pass window length is NEExtracting input data by a sliding window with the step length of 1, and then training an input data with the length of NEAn extreme learning machine ELM with an output of 1;
will be provided with
Figure FDA0003506993360000017
Middle and last NEData of a person
Figure FDA0003506993360000018
Inputting the data into a trained extreme learning machine ELM, and predicting a first group of lithium batteries X at the t +1 moment by using the extreme learning machine ELM1Amount of capacity degradation of
Figure FDA0003506993360000019
Calculating the actual capacity degradation amount of the first group of lithium batteries at the moment of t +1
Figure FDA00035069933600000110
And predicting the amount of capacity degradation
Figure FDA00035069933600000111
Difference of difference
Figure FDA00035069933600000112
Memo
Figure FDA00035069933600000113
Is a correction factor;
Figure FDA00035069933600000114
(2.2) mixing
Figure FDA00035069933600000115
Instead of in step (2.1)
Figure FDA00035069933600000116
And repeating the step (2.1) to obtain N correction factors at the t +1 moment:
Figure FDA00035069933600000117
(2.3) calculating N correction factors
Figure FDA00035069933600000118
Mean value of (a)Δ,t+1Sum variance
Figure FDA00035069933600000119
Figure FDA0003506993360000021
Figure FDA0003506993360000022
(2.4) when the prediction of the time T is finished, replacing the current time T in the step (2.1) with the times T +1, T +2, … and T-1 in sequence, and repeating the steps (2.1) and (2.2) to obtain N correction factors of the subsequent time
Figure FDA0003506993360000023
And corresponding mean value muΔ,t+2,μΔ,t+3,…,μΔ,TThe sum of the variances
Figure FDA0003506993360000024
(2.5) respectively obtaining the mean values [ mu ]Δ,t+1,μΔ,t+2,…,μΔ,TThe sum of the variances
Figure FDA0003506993360000025
To obtain the overall mean value mu of the correction factorΔSum variance
Figure FDA0003506993360000026
And obey normal distribution
Figure FDA0003506993360000027
(3) Extreme learning machine ELM training based on transfer learning
(3.1) setting the capacity degradation amount of the lithium battery to be tested at the current t moments as X ═ X0,x1,…,xt}；
(3.2) capacity degradation data of existing N lithium batteries
Figure FDA0003506993360000028
Selecting one of the lithium batteries to be tested and setting the capacity degradation amount of the lithium battery to be tested as X ═ X0,x1,…,xtThe most similar group, note as
Figure FDA0003506993360000029
(3.3) the method according to step (2.1), using
Figure FDA00035069933600000210
Training an input data length of NEAn extreme learning machine ELM with an output of 1;
(3.4) converting X to { X ═ X0,x1,…,xtThe last N inEData of a person
Figure FDA00035069933600000211
Inputting the data into an extreme learning machine ELM so as to predict the degradation amount of the lithium battery to be tested at the t +1 moment
Figure FDA00035069933600000212
(4) Single step prediction correction of extreme learning machine ELM
(4.1) calculating the capacity degradation amount of the existing N lithium batteries at the t +1 moment
Figure FDA00035069933600000213
Mean value of (a)x,t+1Sum variance
Figure FDA00035069933600000214
(4.2) setting the capacity degradation amount of N lithium batteries at the t +1 moment
Figure FDA00035069933600000215
Obey normal distribution
Figure FDA00035069933600000216
Amount of degradation is determined
Figure FDA00035069933600000217
To normal distribution
Figure FDA00035069933600000218
Distance p of centert+1：
Figure FDA00035069933600000219
(4.3) binding correction factor distribution
Figure FDA00035069933600000220
And a distance pt+1To find a predicted value
Figure FDA00035069933600000221
Corresponding correction factor
Figure FDA00035069933600000222
Figure FDA00035069933600000223
(4.4) the predicted value of the corrected capacity degradation amount of the lithium battery to be tested at the t +1 moment:
Figure FDA0003506993360000031
(5) prediction of remaining life of lithium battery to be tested
(5.1) mixing
Figure FDA0003506993360000032
As the input of the ELM, obtaining the predicted value of the capacity degradation amount of the lithium battery to be measured at the time of t +2
Figure FDA0003506993360000033
Then according to the method pair in the step (4.4)
Figure FDA0003506993360000034
Correcting to obtain the corrected predicted value
Figure FDA0003506993360000035
(5.2) judging the predicted value
Figure FDA0003506993360000036
Whether the threshold value omega is larger than a given failure threshold value omega is judged, if so, the lithium battery is judged to be failed, and the algorithm is ended; otherwise, it will
Figure FDA0003506993360000037
Adding into ELM input, and continuing prediction according to the method of step (5.1), and repeating the steps until obtaining corrected predicted value
Figure FDA0003506993360000038
And when the current value is larger than the given failure threshold omega, recording the time n corresponding to the degradation of the lithium battery to be tested to the failure threshold, thereby obtaining the residual life of the lithium battery to be tested after the time t.
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