# State of Health Estimation Method for Lithium-Ion Batteries via Generalized Additivity Model and Transfer Component Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feature Extraction

#### 2.1. Definition of SOH

#### 2.2. ICS Feature Vector Extraction

#### 2.3. ICS Feature Transfer

## 3. Methodology of SOH Estimation

#### 3.1. GAM Method

#### 3.2. TCA-Based SOH Estimation Methodology

## 4. Experiments and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, S.; Zhang, X. A comparative study of different online model parameters identification methods for lithium-ion battery. Sci. China Technol. Sci.
**2021**, 64, 2312–2327. [Google Scholar] [CrossRef] - Chen, T.; Huo, M.; Yang, X.; Wen, R. A Fast Lithium-Ion Battery Impedance and SOC Estimation Method Based on Two-Stage PI Observer. World Electr. Veh. J.
**2021**, 12, 108. [Google Scholar] [CrossRef] - Noura, N.; Boulon, L.; Jemeï, S. A Review of Battery State of Health Estimation Methods: Hybrid Electric Vehicle Challenges. World Electr. Veh. J.
**2020**, 11, 66. [Google Scholar] [CrossRef] - Farmann, A.; Waag, W.; Marongiu, A.; Sauer, D.U. Critical review of on-board capacity estimation techniques for lithium-ion batteries in electric and hybrid electric vehicles. J. Power Sources
**2015**, 281, 114–130. [Google Scholar] [CrossRef] - Wei, J.; Dong, G.; Chen, Z. Remaining Useful Life Prediction and State of Health Diagnosis for Lithium-Ion Batteries Using Particle Filter and Support Vector Regression. IEEE Trans. Ind. Electron.
**2018**, 65, 5634–5643. [Google Scholar] [CrossRef] - Shu, X.; Li, G.; Shen, J.; Lei, Z.; Chen, Z.; Liu, Y. A uniform estimation framework for state of health of lithium-ion batteries considering feature extraction and parameters optimization. Energy
**2020**, 204, 117957. [Google Scholar] [CrossRef] - Li, Y.; Liu, K.; Foley, A.M.; Zülke, A.; Berecibar, M.; Nanini-Maury, E.; Van Mierlo, J.; Hoster, H.E. Data-driven health estimation and lifetime prediction of lithium-ion batteries: A review. Renew. Sustain. Energy Rev.
**2019**, 113, 109254. [Google Scholar] [CrossRef] - Zheng, Y.; Ouyang, M.; Han, X.; Lu, L.; Li, J. Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles. J. Power Sources
**2017**, 377, 161–188. [Google Scholar] [CrossRef] - Hu, X.; Che, Y.; Lin, X.; Deng, Z. Health Prognosis for Electric Vehicle Battery Packs: A Data-Driven Approach. IEEE/ASME Trans. Mechatron.
**2020**, 25, 2622–2632. [Google Scholar] [CrossRef] - Li, X.; Wang, Z.; Zhang, L.; Zou, C.; Dorrell, D.D. State-of-health estimation for Li-ion batteries by combing the incremental capacity analysis method with grey relational analysis. J. Power Sources
**2019**, 410, 106–114. [Google Scholar] [CrossRef] - Wu, B.; Yufit, V.; Merla, Y.; Martinez-Botas, R.F.; Brandon, N.P.; Offer, G.J. Differential thermal voltammetry for tracking of degradation in lithium-ion batteries. J. Power Sources
**2015**, 273, 495–501. [Google Scholar] [CrossRef] - Lin, M.; Yan, C.; Meng, J.; Wang, W.; Wu, J. Lithium-ion batteries health prognosis via differential thermal capacity with simulated annealing and support vector regression. Energy
**2022**, 250, 123829. [Google Scholar] [CrossRef] - Tian, J.; Xiong, R.; Shen, W. State-of-Health Estimation Based on Differential Temperature for Lithium Ion Batteries. IEEE Trans. Power Electron.
**2020**, 35, 10363–10373. [Google Scholar] [CrossRef] - Lin, M.; Wu, D.; Meng, J.; Wu, J.; Wu, H. A multi-feature-based multi-model fusion method for state of health estimation of lithium-ion batteries. J. Power Sources
**2022**, 518, 230774. [Google Scholar] [CrossRef] - Wu, J.; Wang, Y.; Zhang, X.; Chen, Z. A novel state of health estimation method of Li-ion battery using group method of data handling. J. Power Sources
**2016**, 327, 457–464. [Google Scholar] [CrossRef] - Lin, M.; Zeng, X.; Wu, J. State of health estimation of lithium-ion battery based on an adaptive tunable hybrid radial basis function network. J. Power Sources
**2021**, 504, 230063. [Google Scholar] [CrossRef] - Li, K.; Wang, Y.; Chen, Z. A comparative study of battery state-of-health estimation based on empirical mode decomposition and neural network. J. Energy Storage
**2022**, 54, 105333. [Google Scholar] [CrossRef] - Wang, Y.; Li, K.; Chen, Z. Battery Full Life Cycle Management and Health Prognosis Based on Cloud Service and Broad Learning. IEEE/CAA J. Autom. Sin.
**2022**, 9, 1540–1542. [Google Scholar] [CrossRef] - Deng, Z.; Lin, X.; Cai, J.; Hu, X. Battery health estimation with degradation pattern recognition and transfer learning. J. Power Sources
**2022**, 525, 231027. [Google Scholar] [CrossRef] - Wang, Y.-X.; Chen, Z.; Zhang, W. Lithium-ion battery state-of-charge estimation for small target sample sets using the improved GRU-based transfer learning. Energy
**2022**, 244, 123178. [Google Scholar] [CrossRef] - Shu, X.; Shen, J.; Li, G.; Zhang, Y.; Chen, Z.; Liu, Y. A Flexible State-of-Health Prediction Scheme for Lithium-Ion Battery Packs with Long Short-Term Memory Network and Transfer Learning. IEEE Trans. Transp. Electrif.
**2021**, 7, 2238–2248. [Google Scholar] [CrossRef] - Blitzer, J.; Mcdonald, R.T.; Pereira, F. Domain adaptation with structural correspondence learning. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, Sydney, Australia, 22–23 July 2006; pp. 120–128. [Google Scholar]
- Wang, D.; Nie, F.; Huang, H. Learning task relational structure for multi-task feature learning. In Proceedings of the IEEE International Conference on Data Mining, Barcelona, Spain, 12–15 December 2016; IEEE: New York, NY, USA, 2016; pp. 1239–1244. [Google Scholar]
- Si, S.; Tao, D.; Geng, B. Bregman Divergence-Based Regularization for Transfer Subspace Learning. IEEE Trans. Knowl. Data Eng.
**2010**, 22, 929–942. [Google Scholar] [CrossRef] - Pérez-Cruz, F. Kullback-Leibler divergence estimation of continuous distributions. In Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, 6–11 July 2008; IEEE: New York, NY, USA, 2008; pp. 1666–1670. [Google Scholar]
- Gretton, A.; Borgwardt, K.; Rasch, M.; Schölkopf, B.; Smola, A. A kernel method for the two-sample problem. Adv. Neural Inf. Process. Syst.
**2006**, 19, 513–520. [Google Scholar] - Pan, S.J.; Tsang, I.W.; Kwok, J.T.; Yang, Q. Domain Adaptation via Transfer Component Analysis. IEEE Trans. Neural Netw.
**2011**, 22, 199–210. [Google Scholar] [CrossRef] [Green Version] - Birkl, C.R. Diagnosis and Prognosis of Degradation in Lithium-Ion Batteries. Ph.D. Thesis, Department of Engineering Science, University of Oxford, Oxford, UK, 2017. [Google Scholar] [CrossRef]
- Dai, H.; Zhao, G.; Lin, M.; Wu, J.; Zheng, G. A Novel Estimation Method for the State of Health of Lithium-Ion Battery Using Prior Knowledge-Based Neural Network and Markov Chain. IEEE Trans. Ind. Electron.
**2019**, 66, 7706–7716. [Google Scholar] [CrossRef] - Thompson, A.H. Electrochemical Potential Spectroscopy: A New Electrochemical Measurement. J. Electrochem. Soc.
**1979**, 126, 608–616. [Google Scholar] [CrossRef] - Gao, Y.; Dahn, J.R. Synthesis and characterization of LiMnO for Li-ion battery applications. J. Electrochem. Soc.
**1996**, 143, 100–114. [Google Scholar] [CrossRef] - Hu, X.; Jiang, J.; Cao, D.; Egardt, B. Battery Health Prognosis for Electric Vehicles Using Sample Entropy and Sparse Bayesian Predictive Modeling. IEEE Trans. Ind. Electron.
**2016**, 63, 2645–2656. [Google Scholar] [CrossRef] - Hastie, T.J.; Tibshirani, R.J. Generalized Additive Models; Chapman & Hall: London, UK, 1990. [Google Scholar]
- Vilsen, S.B.; Stroe, D.-I. Battery state-of-health modelling by multiple linear regression. J. Clean. Prod.
**2021**, 290, 125700. [Google Scholar] [CrossRef] - Li, Y.; Li, K.; Liu, X.; Wang, Y.; Zhang, L. Lithium-ion battery capacity estimation—A pruned convolutional neural network approach assisted with transfer learning. Appl. Energy
**2021**, 285, 116410. [Google Scholar] [CrossRef]

**Figure 4.**SOH estimation results before and after feature transfer on the Oxford battery dataset: (

**a**,

**c**,

**e**,

**g**,

**i**,

**k**,

**m**) are the SOH prediction curves of cell 1 to cell 7; (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**,

**n**) are the predicted error curves of cell 1 to cell 7.

**Figure 5.**SOH estimation results of different models on the Oxford battery dataset: (

**a**,

**c**,

**e**,

**g**,

**i**,

**k**,

**m**) are the SOH prediction curves of cell 1 to cell 7; (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**,

**n**) are the predicted error curves of cell 1 to cell 7.

Cell | MAE | RMSE | ||
---|---|---|---|---|

TCA + GAM | GAM | TCA + GAM | GAM | |

Cell 1 | 0.92% | 1.95% | 1.12% | 2.41% |

Cell 2 | 1.72% | 7.37% | 2.31% | 10.86% |

Cell 3 | 0.93% | 1.54% | 1.17% | 2.22% |

Cell 4 | 1.55% | 3.47% | 1.90% | 4.46% |

Cell 5 | 1.16% | 1.95% | 1.74% | 2.48% |

Cell 6 | 1.10% | 3.29% | 1.73% | 4.30% |

Cell 7 | 0.97% | 3.97% | 1.42% | 5.28% |

Cell | MAE | RMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

TCA + GAM | SVR | NN | LR | CNN | TCA + GAM | SVR | NN | LR | CNN | |

Cell 1 | 0.89% | 2.34% | 2.24% | 2.98% | 7.03% | 1.06% | 3.12% | 2.83% | 3.14% | 9.65% |

Cell 2 | 1.74% | 3.09% | 3.26% | 3.71% | 5.97% | 2.31% | 3.73% | 4.01% | 4.24% | 7.38% |

Cell 3 | 0.92% | 2.03% | 2.06% | 2.57% | 6.49% | 1.15% | 2.41% | 2.61% | 2.73% | 7.52% |

Cell 4 | 1.53% | 1.95% | 2.90% | 2.15% | 10.52% | 1.88% | 2.88% | 3.67% | 2.34% | 11.25% |

Cell 5 | 1.16% | 2.19% | 1.85% | 2.00% | 8.51% | 1.73% | 2.85% | 2.34% | 2.18% | 10.65% |

Cell 6 | 1.08% | 2.48% | 2.25% | 1.68% | 8.38% | 1.71% | 2.77% | 2.98% | 1.91% | 10.48% |

Cell 7 | 0.97% | 1.74% | 2.81% | 1.58% | 7.98% | 1.42% | 2.23% | 3.44% | 1.73% | 9.62% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lin, M.; Yan, C.; Zeng, X.
State of Health Estimation Method for Lithium-Ion Batteries via Generalized Additivity Model and Transfer Component Analysis. *World Electr. Veh. J.* **2023**, *14*, 14.
https://doi.org/10.3390/wevj14010014

**AMA Style**

Lin M, Yan C, Zeng X.
State of Health Estimation Method for Lithium-Ion Batteries via Generalized Additivity Model and Transfer Component Analysis. *World Electric Vehicle Journal*. 2023; 14(1):14.
https://doi.org/10.3390/wevj14010014

**Chicago/Turabian Style**

Lin, Mingqiang, Chenhao Yan, and Xianping Zeng.
2023. "State of Health Estimation Method for Lithium-Ion Batteries via Generalized Additivity Model and Transfer Component Analysis" *World Electric Vehicle Journal* 14, no. 1: 14.
https://doi.org/10.3390/wevj14010014