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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

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2018 Impact Factor: 1.701

Front. Energy    2024, Vol. 18 Issue (4) : 447-462    https://doi.org/10.1007/s11708-023-0906-4
Two-phase early prediction method for remaining useful life of lithium-ion batteries based on a neural network and Gaussian process regression
Zhiyuan WEI1, Changying LIU1, Xiaowen SUN1, Yiduo LI1, Haiyan LU2()
1. College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130021, China
2. College of Chemistry, Jilin University, Changchun 130012, China; Changsha Automobile Innovation Research Institute of Jilin University, Changsha 410006, China
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Abstract

Lithium-ion batteries (LIBs) are widely used in transportation, energy storage, and other fields. The prediction of the remaining useful life (RUL) of lithium batteries not only provides a reference for health management but also serves as a basis for assessing the residual value of the battery. In order to improve the prediction accuracy of the RUL of LIBs, a two-phase RUL early prediction method combining neural network and Gaussian process regression (GPR) is proposed. In the initial phase, the features related to the capacity degradation of LIBs are utilized to train the neural network model, which is used to predict the initial cycle lifetime of 124 LIBs. The Pearson coefficient’s two most significant characteristic factors and the predicted normalized lifetime form a 3D space. The Euclidean distance between the test dataset and each cell in the training dataset and validation dataset is calculated, and the shortest distance is considered to have a similar degradation pattern, which is used to determine the initial Dual Exponential Model (DEM). In the second phase, GPR uses the DEM as the initial parameter to predict each test set’s early RUL (ERUL). By testing four batteries under different working conditions, the RMSE of all capacity estimation is less than 1.2%, and the accuracy percentage (AP) of remaining life prediction is more than 98%. Experiments show that the method does not need human intervention and has high prediction accuracy.

Keywords lithium-ion batteries      RUL prediction      double exponential model      neural network      Gaussian process regression (GPR)     
Corresponding Author(s): Haiyan LU   
About author:

Chunqi Yang contributed equally to this work.

Online First Date: 01 December 2023    Issue Date: 31 July 2024
 Cite this article:   
Zhiyuan WEI,Changying LIU,Xiaowen SUN, et al. Two-phase early prediction method for remaining useful life of lithium-ion batteries based on a neural network and Gaussian process regression[J]. Front. Energy, 2024, 18(4): 447-462.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-023-0906-4
https://academic.hep.com.cn/fie/EN/Y2024/V18/I4/447
Fig.1  Capacity degradation of 124 LFP/graphite cells.
Fig.2  Results of feature factor extraction.
Notation Feature name Details of extracted features
F1 DeltaYmax dQ/dV, the maximum value of the y-axis on the IC curve between the 2nd and 100th cycles
F2 DeltaXmax dQ/dV max (V), the maximum value of the x-axis on the IC curve between the 2nd and 100th cycles
F3 DeltaQvar Variance = log? (|1 p1 i=1p(ΔQ(V)ΔQ ¯(V) )2|)
F4 DeltaQmin log(|min(?Q(V))|)
F5 CapFadeCycle2Slope Slope of discharge curve, cycles 2 to 100 = first value in vector b* as in Eq. (5), where d = 99
F6 AvgChargeTime Average charge time = 1 5 i=26Charg? e Tim e i
F7 MinIR Minimum internal resistance = minn? IR(n)
F8 IRDiff2And100 Internal resistance, cycle 100 – cycle 2 = IR(n=100) IR(n= 2)
F9 IntegralTemp Temperature integral, cycles 2 to 100 = t2 t100T(t) dt
Tab.1  Extraction of feature factors
Fig.3  Distribution of feature factors.
Fig.4  Structure of neural network.
Fig.5  Flowchart of proposed methodology.
RMSE/cycles MAPE/%
Train_data Val_data Test_data Train_data Val_data Test_data
Severson et al.[20] 51 91 173 5.6 13 8.6
Ma et al. [48] 51 90 160 5.1 10 11.7
This study 1 80 194 0.09 8.08 14.25
Tab.2  RMSE and MAPE results
Fig.6  Comparison of actual cycle life of training, validation, and test data sets with predicted cycle life.
Fig.7  Capacity degradation data of overall test data set.
Test LIBs DEM parameters
LIB-C1 [–1.2013e–05, 0.0088, 1.0865, –4.8361e–05]
LIB-C9 [–3.0073e-04, 0.0063, 1.0847, –2.4610e-05]
LIB-C25 [–1.0910e–04, 0.0036, 1.0855, –1.2848e–05]
LIB-C30 [–9.2455e-04, 0.0068, 1.0896, –2.2405e-05]
Tab.3  DEM parameters
Fig.8  Fitting curves of four chosen LIBs.
Fig.9  Predicted capacities.
LIBs EOM Phase 1 prediction Phase 2 prediction Actual RUL AE AP TS RMSE MAPE
C1 200 1186 999 ± 3 1008 9 ± 3 99.1071% ± 0.3968% 0.0093 0.84% 0.6559%
300 1002 ± 3 6 ± 3 99.4048% ± 0.3968% 0.0086 0.73% 0.5596%
400 1005 ± 3 3 ± 3 %99.7024 ± 0.3968% 0.0077 0.61% 0.4617%
C9 200 1008 1025 ± 3 1038 13 ± 3 98.7476% ± 0.288% 0.0123 1.11% 0.7863%
300 1028 ± 3 10 ± 3 99.0366% ± 0.288% 0.0119 1.01% 0.6934%
400 1032 ± 3 6 ± 3 99.4220% ± 0.288% 0.0112 0.88% 0.5919%
C25 200 1361 1020 ± 2 1027 7 ± 2 99.3184% ± 0.194% 0.0080 0.72% 0.5966%
300 1021 ± 2 6 ± 2 99.4158% ± 0.194% 0.0079 0.67% 0.5587%
400 1024 ± 2 3 ± 2 99.7079% ± 0.194% 0.0083 0.66% 0.5471%
C30 200 778 718 ± 3 730 12 ± 3 98.3562% ± 0.1370% 0.0071 0.61% 0.4070%
300 719 ± 3 11 ± 3 98.4932% ± 0.2740% 0.0070 0.54% 0.3707%
400 725 ± 3 5 ± 3 99.3151% ± 0.2740% 0.0079 0.36% 0.2702%
Tab.4  Evaluation index of EOM cycle
Method RMSE AE Time/s
This study 0.84% 3 0.607085
SVR 2.51% 16 0.092757
LSTM 4.15% 0.418334
MLP 3.93% 33 0.019167
Tab.5  Comparison of Cell1 statistical error and prediction results
Fig.10  Comparison of algorithm results.
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