Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

The state of health (SOH) of lithium-ion batteries is a crucial parameter for assessing battery degradation. The aim of this study is to solve the problems of single extraction of health features (HFs) and redundancy of information between features in the SOH estimation. This article develops an SOH estimation method for lithium-ion batteries based on multifeature fusion and Bayesian optimization (BO)-bidirectional gated recurrent unit (BiGRU) model. First, a total of eight HFs in three categories, namely, time, energy, and probability, can be extracted from the charging data to accurately describe the aging mechanism of the battery. The Pearson and Spearman analysis method verified the strong correlation between HFs and SOH. Second, the multiple principal components obtained by kernel principal component analysis (KPCA) can eliminate the redundancy of information between HFs. The principal component with the highest correlation with SOH is selected by bicorrelation analysis to be defined as the fused HF. Finally, to improve SOH estimation accuracy, the BO-BiGRU model is proposed. The proposed method is validated using battery datasets from NASA. The results show that the SOH estimation accuracy of the BO-BiGRU model proposed in this article is high, while mean absolute error (MAE) is lower than 1.2%. In addition, the SOH of the lithium battery is estimated using different proportions of test sets, and the results show that the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE) of the SOH remain within 3%, with high estimation accuracy and robustness.

References

1.
He
,
Z.
,
Ni
,
X.
,
Pan
,
C.
,
Li
,
W.
, and
Han
,
S.
,
2024
, “
Power Batteries State of Health Estimation of Pure Electric Vehicles for Charging Process
,”
ASME J. Electrochem. Energy Convers. Storage
,
21
(
3
), p.
031007
.
2.
Yang
,
F.
,
Xu
,
Y.
,
Su
,
L.
,
Yang
,
Z.
,
Feng
,
Y.
,
Zhang
,
C.
, and
Shao
,
T.
,
2024
, “
State of Charge and State of Health Estimation of Lithium-Ion Battery Packs With Inconsistent Internal Parameters Using Dual Extended Kalman Filter
,”
ASME J. Electrochem. Energy Convers. Storage
,
21
(
1
), p.
011004
.
3.
Lu
,
J.
,
Xiong
,
R.
,
Tian
,
J.
,
Wang
,
C.
, and
Sun
,
F.
,
2023
, “
Deep Learning to Estimate Lithium-Ion Battery State of Health Without Additional Degradation Experiments
,”
Nat. Commun.
,
14
(
1
), p.
2760
.
4.
Peng
,
S.
,
Zhang
,
D.
,
Dai
,
G.
,
Wang
,
L.
,
Jiang
,
Y.
, and
Zhou
,
F.
,
2025
, “
State of Charge Estimation for LiFePO4 Batteries Joint by PID Observer and Improved EKF in Various OCV Ranges
,”
Appl. Energy
,
377
, p.
124435
.
5.
Peng
,
S.
,
Miao
,
Y.
,
Xiong
,
R.
,
Bai
,
J.
, and
Pecht
,
M.
,
2024
, “
State of Charge Estimation for a Parallel Battery Pack Jointly by Fuzzy-PI Model Regulator and Adaptive Unscented Kalman Filter
,”
Appl. Energy
,
360
, p.
122807
.
6.
Peng
,
S.
,
Zhu
,
J.
,
Wu
,
T.
,
Tang
,
A.
,
Kan
,
J.
, and
Pecht
,
M.
,
2024
, “
SOH Early Prediction of Lithium-Ion Batteries Based on Voltage Interval Selection and Features Fusion
,”
Energy
,
308
, p.
132993
.
7.
Pang
,
H.
,
Chen
,
K.
,
Geng
,
Y.
,
Wu
,
L.
,
Wang
,
F.
, and
Liu
,
J.
,
2024
, “
Accurate Capacity and Remaining Useful Life Prediction of Lithium-Ion Batteries Based on Improved Particle Swarm Optimization and Particle Filter
,”
Energy
,
293
, p.
130555
.
8.
Fang
,
D.
,
Wu
,
W.
,
Li
,
J.
,
Yuan
,
W.
,
Liu
,
T.
,
Dai
,
C.
,
Wang
,
Z.
, and
Zhao
,
M.
,
2023
, “
Performance Simulation Method and State of Health Estimation for Lithium-Ion Batteries Based on Aging-Effect Coupling Model
,”
Green Energy Intell. Transp.
,
2
(
3
), p.
100082
.
9.
Yu
,
Q.
,
Nie
,
Y.
,
Peng
,
S.
,
Miao
,
Y.
,
Zhai
,
C.
,
Zhang
,
R.
,
Han
,
J.
, and
Pecht
,
M.
,
2023
, “
Evaluation of the Safety Standards System of Power Batteries for Electric Vehicles in China
,”
Appl. Energy
,
349
, p.
121674
.
10.
Waseem
,
M.
,
Amir
,
M.
,
Lakshmi
,
G. S.
,
Harivardhagini
,
S.
, and
Ahmad
,
M.
,
2023
, “
Fuel Cell-Based Hybrid Electric Vehicles: An Integrated Review of Current Status, Key Challenges, Recommended Policies, and Future Prospects
,”
Green Energy Intell. Transp.
,
2
(
6
), pp.
100121
.
11.
Liu
,
Y.
,
Wang
,
L.
,
Li
,
D.
, and
Wang
,
K.
,
2023
, “
State-of-Health Estimation of Lithium-Ion Batteries Based on Electrochemical Impedance Spectroscopy: A Review
,”
Prot. Control Mod. Power Syst.
,
8
(
3
), pp.
1
17
.
12.
Li
,
Y.
,
Luo
,
Y.
,
Jiang
,
C.
,
Wang
,
F.
,
Ma
,
T.
,
Park
,
J. W.
,
Wu
,
S.
,
Xu
,
D.
,
Xie
,
K.
, and
Wei
,
M.
,
2021
, “
Study of the Test Conditions and Thermostability of an Overcharge Test for Large Capacity Lithium-Ion Batteries.
,”
ASME J. Electrochem. Energy Convers. Storage
,
18
(
2
), p.
020907
.
13.
Chen
,
L.
,
Bao
,
X.
,
Lopes
,
A. M.
,
Xu
,
C.
,
Wu
,
X.
,
Kong
,
H.
, and
Huang
,
J.
,
2023
, “
State of Health Estimation of Lithium-Ion Batteries Based on Equivalent Circuit Model and Data-Driven Method
,”
J. Energy Storage
,
73
, p.
109195
.
14.
Dong
,
M.
,
Li
,
X.
,
Yang
,
Z.
,
Chang
,
Y.
,
Liu
,
W.
,
Luo
,
Y.
,
Lei
,
W.
,
Ren
,
M.
, and
Zhang
,
C.
,
2024
, “
State of Health (SOH) Assessment for LIBs Based on Characteristic Electrochemical Impedance
,”
J. Power Sources
,
603
, p.
234386
.
15.
Li
,
C.
,
Yang
,
L.
,
Li
,
Q.
,
Zhang
,
Q.
,
Zhou
,
Z.
,
Meng
,
Y.
,
Zhao
,
X.
, et al
,
2024
, “
SOH Estimation Method for Lithium-Ion Batteries Based on an Improved Equivalent Circuit Model via Electrochemical Impedance Spectroscopy
,”
J. Energy Storage
,
86
, p.
111167
.
16.
Horstkötter
,
I.
, and
Bäker
,
B.
,
2023
, “
An Application-Oriented Lithium-ion Battery Degradation Modelling Framework for Ageing Prediction
,”
J. Energy Storage
,
60
, p.
106640
.
17.
Fan
,
Y.
,
Xiao
,
F.
,
Li
,
C.
,
Yang
,
G.
, and
Tang
,
X.
,
2020
, “
A Novel Deep Learning Framework for State of Health Estimation of Lithium-Ion Battery
,”
J. Energy Storage
,
32
, p.
101741
. .1016/j.est.2020.101741
18.
Peng
,
S.
,
Sun
,
Y.
,
Liu
,
D.
,
Yu
,
Q.
,
Kan
,
J.
, and
Pecht
,
M.
,
2023
, “
State of Health Estimation of Lithium-Ion Batteries Based on Multi-Health Features Extraction and Improved Long Short-Term Memory Neural Network
,”
Energy
,
282
, p.
128956
.
19.
Zhang
,
C.
,
Luo
,
L.
,
Yang
,
Z.
,
Zhao
,
S.
,
He
,
Y.
,
Wang
,
X.
, and
Wang
,
H.
,
2023
, “
Battery SOH Estimation Method Based on Gradual Decreasing Current, Double Correlation Analysis and GRU
,”
Green Energy Intell. Transp.
,
2
(
5
), pp.
100108
.
20.
Ma
,
Y.
,
Li
,
J.
,
Gao
,
J.
, and
Chen
,
H.
,
2024
, “
State of Health Prediction of Lithium-Ion Batteries Under Early Partial Data Based on IWOA-BiLSTM With Single Feature
,”
Energy
,
295
, p.
131085
.
21.
Chen
,
K.
,
Li
,
J.
,
Liu
,
K.
,
Bai
,
C.
,
Zhu
,
J.
,
Gao
,
G.
,
Wu
,
G.
, and
Laghrouche
,
S.
,
2024
, “
State of Health Estimation for Lithium-Ion Battery Based on Particle Swarm Optimization Algorithm and Extreme Learning Machine
,”
Green Energy Intell. Transp.
,
3
(
1
), p.
100151
.
22.
Ma
,
Y.
,
Shan
,
C.
,
Gao
,
J.
, and
Chen
,
H.
,
2022
, “
A Novel Method for State of Health Estimation of Lithium-Ion Batteries Based on Improved LSTM and Health Indicators Extraction
,”
Energy
,
251
, pp.
123973
.
23.
Ling
,
M.
,
Hu
,
H.
,
Chen
,
J.
,
Zhao
,
J.
,
Qu
,
K.
, and
Lei
,
J.
,
2023
, “
Online State-of-Health Estimation Method for Lithium-Ion Battery Based on CEEMDAN for Feature Analysis and RBF Neural Network
,”
IEEE J. Emerging Sel. Top. Power Electron.
,
11
(
1
), pp.
187
200
.
24.
Wang
,
C.
, and
Min
,
Y.
,
2023
, “
SOH Estimation of Lithium-Ion Batteries Based on Capacity Increment Curve and GWO-GPR
,”
Energy Storage Sci. Technol.
,
12
(
11
), pp.
3508
3518
.
25.
He
,
Y.
,
Bai
,
W.
,
Wang
,
L.
,
Wu
,
H.
, and
Ding
,
M.
,
2024
, “
SOH Estimation for Lithium-Ion Batteries: An Improved GPR Optimization Method Based on the Developed Feature Extraction
,”
J. Energy Storage
,
83
, p.
110678
.
26.
Zhang
,
L.
,
Zhang
,
J.
,
Gao
,
T.
,
Lyu
,
L.
,
Wang
,
L.
,
Shi
,
W.
,
Jiang
,
L.
, and
Cai
,
G.
,
2023
, “
Improved LSTM Based State of Health Estimation Using Random Segments of the Charging Curves for Lithium-Ion Batteries
,”
J. Energy Storage
,
74
, p.
109370
.
27.
Xue
,
J.
,
Ma
,
W.
,
Feng
,
X.
,
Guo
,
P.
,
Guo
,
Y.
,
Hu
,
X.
, and
Chen
,
B.
,
2023
, “
Stacking Integrated Learning Model via ELM and GRU With Mixture Correntropy Loss for Robust State of Health Estimation of Lithium-Ion Batteries
,”
Energy
,
284
, pp.
129279
.
28.
She
,
D.
, and
Jia
,
M.
,
2021
, “
A BiGRU Method for Remaining Useful Life Prediction of Machinery
,”
Measurement
,
167
, p.
108277
.
29.
Yu
,
Z.
,
Zhang
,
Z.
,
Jiang
,
Q.
, and
Yan
,
X.
,
2024
, “
Neural Network-Based Hybrid Modeling Approach Incorporating Bayesian Optimization With Industrial Soft Sensor Application
,”
Knowl. Based Syst.
,
301
, pp.
112341
.
30.
Zhang
,
Y.
,
Zeng
,
W.
,
Chang
,
C.
,
Wang
,
Q.
, and
Xu
,
S.
,
2022
, “
Lithium-Ion Battery State of Health Estimation Based on Improved Deep Extreme Learning Machine.
,”
ASME J. Electrochem. Energy Convers. Storage
,
19
(
3
), p.
030904
.
31.
Saha
,
B.
,
Goebel
,
K.
, and
Poll
,
S.
,
2008
, “
Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework
,”
IEEE Trans. Instrum. Meas.
,
58
(
2
), pp.
291
296
.
32.
Shen
,
D.
,
Yang
,
D.
,
Lyu
,
C.
,
Hinds
,
G.
,
Wang
,
L.
, and
Bai
,
M.
,
2023
, “
Detection and Quantitative Diagnosis of Micro-Short-Circuit Faults in Lithium-Ion Battery Packs Considering Cell Inconsistency
,”
Green Energy Intell. Transp.
,
2
(
5
), p.
100109
.
33.
Lin
,
Z.
,
Hu
,
H.
,
Liu
,
W.
,
Zhang
,
Z.
,
Zhang
,
Y.
,
Geng
,
N.
, and
Liao
,
Q.
,
2023
, “
State of Health Estimation of Lithium-Ion Batteries Based on Remaining Area Capacity
,”
J. Energy Storage
,
63
, p.
107078
.
34.
Peng
,
S.
,
Zhu
,
J.
,
Wu
,
T.
,
Yuan
,
C.
,
Cang
,
J.
,
Zhang
,
K.
, and
Pecht
,
M.
,
2024
, “
Prediction of Wind and PV Power by Fusing the Multi-Stage Feature Extraction and a PSO-BiLSTM Model
,”
Energy
,
298
, p.
131345
.
35.
Zhang
,
J.
,
Chen
,
J.
,
He
,
L.
,
Liu
,
D.
,
Yang
,
K.
, and
Liu
,
Q.
,
2024
, “
State of Charge Estimation of Lithium-Ion Battery Based on IDRSN and BiGRU
,”
ASME J. Electrochem. Energy Convers. Storage
,
21
(
3
), p.
031001
.
36.
Tang
,
S.
,
Zhu
,
Y.
, and
Shou
,
Y.
,
2022
, “
Intelligent Fault Diagnosis of Hydraulic Piston Pump Based on Deep Learning and Bayesian Optimization
,”
ISA Trans.
,
129
, pp.
555
563
.
37.
Pang
,
Z.
,
Yang
,
K.
,
Song
,
Z.
,
Niu
,
P.
,
Chen
,
G.
, and
Meng
,
J.
,
2023
, “
A New Method for Determining SOH of Lithium Batteries Using the Real-Part Ratio of EIS Specific Frequency Impedance
,”
J. Energy Storage
,
72
, p.
108693
.
38.
Mazzi
,
Y.
,
Sassi
,
H. B.
, and
Errahimi
,
F.
,
2024
, “
Lithium-Ion Battery State of Health Estimation Using a Hybrid Model Based on a Convolutional Neural Network and Bidirectional Gated Recurrent Unit
,”
Eng. Appl. Artif. Intell.
,
127
, p.
107199
.
You do not currently have access to this content.