State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine
Abstract
:1. Introduction
- (1)
- To balance the interpretability of the aging mechanism and the performance of the estimated model during LIBs aging, this paper proposes HFs that fuse ECM with DRT characteristics, which also utilize the random forest (RF) for screening the effectiveness of the HFs.
- (2)
- The KELM is used as an estimation model with three radial basis function (RBF) kernel functions and two regularization parameters, which enable to capture of the complex nonlinear relationships of the HFs and battery SOH from multiple scales.
- (3)
- The SSA is used to optimize the parameters of the KELM model to automate the algorithm configuration. The algorithm automatically adjusts the parameters of the model, reducing human effort and avoiding expert experience.
2. EIS-Based HFs Extraction
2.1. HFs Extraction and Selection
2.1.1. ECM-Based HFs
2.1.2. DRT-Based HFs
2.2. Feature Selection Using Random Forest
3. SOH Estimation with KELM
3.1. Extreme Learning Machine with Multi-Kernel Functions
3.2. Parameter Optimization Using the Sparrow Search Algorithm
4. Results and Discussion
4.1. Battery Dataset
4.2. Results
4.3. Comparison of Estimation Results for Different Input Features
4.3.1. Comparison for Different Input Features
4.3.2. Comparison of Different Estimation Models
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
SOH | State of health |
LIBs | Lithium-ion batteries |
EIS | Electrochemical impedance spectroscopy |
ECM | Equivalent circuit model |
DRT | Distribution of relaxation times |
MS-KELM | Multi-scale kernel extreme learning machine |
SSA | Sparrow Search Algorithm |
MAE | Mean absolute error |
RMSE | Root mean square error |
SVR | Support vector regression |
GPR | Gaussian process regression |
EVs | Electric vehicles |
BMS | Battery management system |
ICA | Incremental capacity analysis |
DVA | Differential voltage analysis |
EIR | Equivalent internal resistance |
RUL | Remaining useful life |
SEI | Solid electrolyte interface |
HFs | Health features |
ANN | Artificial Neural Networks |
LSSVR | Least square support vector regression |
HIs | Health indicators |
ARD | Automatic relevance determination |
MRMR | Minimum Redundancy Maximum Relevance |
KELM | Kernel extreme learning machine |
RF | Random forest |
RBF | Radial basis function |
SSA-MS-KELM | Multi-scale kernel extremum learning machine by the sparrow search algorithm |
CPE | Constant phase elements |
PH | Peak Height |
PP | Peak Position |
VH | Valley Height |
VP | Valley Position |
HPA | Half Peak Area |
PPR | Peak to Total Peak Ratio |
VVR | Valley to Total Valley Ratio |
CC | constant current |
CV | constant voltage |
STL | Seasonal and Trend decomposition using Loess |
SSA-SVR | support vector machine model optimized by the sparrow search algorithm |
MLM-GPR | Gaussian regression model optimized by the maximized marginal likelihood |
SSA-RF | random forest model optimized by the sparrow search algorithm |
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References | Feature Selection | Model | Advantage | Disadvantage |
---|---|---|---|---|
[15] | EIS data | GPR | Easy to obtain features | It may have limited feature interpretability and involve some redundant computations. |
[16] | ANN, SVR | Easy to apply | It may have limited feature interpretability. | |
[26] | Six key health features from EIS data | GPR | High accuracy | It may introduce relatively high complexity. |
[25] | Battery modeling identification parameters | LSSVR | Interpretable features | The method could be relatively resource-intensive. |
[29] | Six key health features from DRT curves | GPR | Robust | It may face challenges in feature interpretability and computational complexity. |
proposed | Nine key health features from ECM and DRT | SSA-MS-KELM | Balanced features, low complexity | / |
DRT Peaks | ||||||
---|---|---|---|---|---|---|
Peak 1 | Peak 2 | Peak 3 | Peak 4 | Peak 5 | Peak 6 | |
Physical process | Electric and magnetic effects | SEI Growth/decomposition; Li plating | Cathode charge transfer/CEI | Cathode charge transfer | Graphite degradation | Diffusion processes |
Main reason | Particle–particle and particle–collector interactions | SEI layer of graphite | Cathode | Anode charge transfer | Kinetic slow down |
Category | Features | |||
---|---|---|---|---|
Height of the four peaks | PH 1 | PH 2 | PH 3 | PH 4 |
Location of the four peaks | PP 1 | PP 2 | PP 3 | PP 4 |
Height of the four valleys | VH 1 | VH 2 | VH 3 | VH 4 |
Location of the four valleys | VP 1 | VP 2 | VP 3 | VP 4 |
Half-peak area of the four peaks | HPA 1 | HPA 2 | HPA 3 | HPA 4 |
The ratio of four peak heights to the sum of peak heights | PPR 1 | PPR 2 | PPR 3 | PPR 4 |
The ratio of four valley heights to the sum of valley heights | VVR 1 | VVR 2 | VVR 3 | VVR 4 |
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Peng, J.; Gao, Y.; Cai, L.; Zhang, M.; Sun, C.; Liu, H. State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine. World Electr. Veh. J. 2025, 16, 224. https://doi.org/10.3390/wevj16040224
Peng J, Gao Y, Cai L, Zhang M, Sun C, Liu H. State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine. World Electric Vehicle Journal. 2025; 16(4):224. https://doi.org/10.3390/wevj16040224
Chicago/Turabian StylePeng, Jichang, Ya Gao, Lei Cai, Ming Zhang, Chenghao Sun, and Haitao Liu. 2025. "State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine" World Electric Vehicle Journal 16, no. 4: 224. https://doi.org/10.3390/wevj16040224
APA StylePeng, J., Gao, Y., Cai, L., Zhang, M., Sun, C., & Liu, H. (2025). State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine. World Electric Vehicle Journal, 16(4), 224. https://doi.org/10.3390/wevj16040224