# A Novel Long Short-Term Memory Approach for Online State-of-Health Identification in Lithium-Ion Battery Cells

^{*}

## Abstract

**:**

## 1. Introduction

- We deliberately avoid CC or CCCV charge data, discharge data, or their combination; while a number of previous studies [12,13,14,15,16,17] have demonstrated notable success with such current profiles, we instead prioritize analyzing the voltage response to a given current profile or mapping the available capacity by counting charges. In this way, our algorithm aims to provide a deeper understanding of the battery’s health status.
- We deliberately limit the implementation of algorithms in our approach, relying instead on ANNs, feature scaling, and mean value calculations. In this regard, we acknowledge the noteworthy work of Luciani et al. (2022), which is closely related to the research presented in this study. Luciani et al. employed drive cycles to find the age of the storage system and analyzed the SoH by examining the voltage response to a corresponding current pulse. Luciani et al. utilized predefined pulse tests and extracted features as inputs for their ANN; in contrast, our work focuses on filtering out pulses from drive cycles, and solely relies on the information provided by the BMS. Additionally, our algorithm is specifically tailored for real-time applications, while Luciani et al. developed an offline algorithm in order to optimize mobile computing power consumption [18].
- In this study, we avoid impractical parameters such as cycle count due to our recognition of their limited utility in real-world applications; instead, we focus on inputs generated by a standard BMS.

## 2. Materials and Methods

#### 2.1. Battery Technology

#### 2.2. SoH Estimation Algorithms

#### 2.2.1. Model-Based Methods

#### 2.2.2. Data-Driven Methods

- They often outperform traditional rules-based models, as presented in Section 2.2.1.
- When the model has been trained, it requires minimal computational resources to make estimations, making it highly attractive for mobile and online applications.
- Their minimal parameterization requirements make data-driven models an ideal solution for a wide range of applications while reducing the level of expertise required for implementation and maintenance.

#### 2.2.3. Hybrid Methods

#### 2.3. Data Collection

#### 2.3.1. Battery Cells

#### 2.3.2. Method of Measurement

#### 2.3.3. Data Preparation

#### 2.4. Realization of the SoH Model

#### 2.4.1. Strategy

- As our aim was to demonstrate that an ANN can accurately determine the ${\mathrm{SoH}}_{\mathrm{Cap}}$ without prior knowledge of its SoH, the data were randomly shuffled before training and the states within each LSTM neuron were reset after each time frame was processed.
- Instead of analyzing a past output $[{x}_{\mathrm{i}-{\mathrm{h}}_{\mathrm{win}}},{x}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}]=[{y}_{\mathrm{i}-{\mathrm{h}}_{\mathrm{win}}},{y}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}]$ to predict a future output ${y}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}+1}={x}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}+1}$, we want to look at a past input $[{x}_{\mathrm{i}-{\mathrm{h}}_{\mathrm{win}}},{x}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}]\ne [{y}_{\mathrm{i}-{\mathrm{h}}_{\mathrm{win}}},{y}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}]$ to predict a future output ${y}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}\ne {x}_{\mathrm{i}+{\mathrm{h}}_{\mathrm{win}}}$. Thus, this is a sequence-to-vector or one-step estimation issue.

#### 2.4.2. Hyperparameters

- A larger batch size results in a delayed response time before the ANN produces its initial estimation.
- A lower frequency of data processing by the training algorithm prior to the backpropagation process results in a less generalized model [34].

## 3. Results

#### 3.1. Hyperparameter Optimization

#### 3.2. SoH Model

## 4. Discussion

## 5. Conclusions

- Expanding the model’s scope: moving beyond individual cells to modules and complete battery systems is crucial for performance testing.
- Considering alternative ANN methods: exploring convolutional and transformer-based neural networks could be beneficial, as LSTM approaches are known for their time-intensive training and computational costs.
- Diversifying the training dataset: incorporating a more varied dataset could offer a more comprehensive understanding of the approach’s potential. These strategic adjustments could contribute to a more nuanced exploration and application of the proposed model.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Li-Ion | Lithium-Ion |

SoH | State-of-Health |

SoC | State-of-Charge |

LSTM | Long Short-Term Memory |

BMS | Battery Management System |

NASA | National Aeronautics and Space Administration |

CDM | Cell Difference Model |

CCCV | Constant Current/Constant Voltage |

CNN | Convolutional Neural Network |

ANN | Artificial Neural Network |

BoL | Beginning of Life |

EoL | End of Life |

MSE | Mean Square Error |

RMSE | Root Mean Square Error |

WLTP | Worldwide Harmonized Light Vehicles Test Procedure |

ADAM | Adaptive Moment Estimation |

HP | Hyperparameter |

## References

- Peters, J.F.; Baumann, M.; Zimmermann, B.; Braun, J.; Weil, M. The environmental impact of Li-Ion batteries and the role of key parameters—A review. Renew. Sustain. Energy Rev.
**2017**, 67, 491–506. [Google Scholar] [CrossRef] - Chang, C.; Wang, Q.; Jiang, J.; Wu, T. Lithium-ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm. J. Energy Storage
**2021**, 38, 102570. [Google Scholar] [CrossRef] - Cai, L.; Lin, J.; Liao, X. A data-driven method for state of health prediction of lithium-ion batteries in a unified framework. J. Energy Storage
**2022**, 51, 104371. [Google Scholar] [CrossRef] - Jia, J.; Wang, K.; Shi, Y.; Wen, J.; Pang, X.; Zeng, J. A multi-scale state of health prediction framework of lithium-ion batteries considering the temperature variation during battery discharge. J. Energy Storage
**2021**, 42, 103076. [Google Scholar] [CrossRef] - Lin, J.; Yan, G.; Wang, C. Li-ion battery state of health Prediction based on Long Short-Term Memory Recurrent Neural Network. J. Phys. Conf. Ser.
**2021**, 2010, 012133. [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] - Cheng, G.; Wang, X.; He, Y. Remaining useful life and state of health prediction for lithium batteries based on empirical mode decomposition and a long and short memory neural network. Energy
**2021**, 232, 121022. [Google Scholar] [CrossRef] - Kong, D.; Wang, S.; Ping, P. State-of-health estimation and remaining useful life for lithium-ion battery based on deep learning with Bayesian hyperparameter optimization. Int. J. Energy Res.
**2022**, 46, 6081–6098. [Google Scholar] [CrossRef] - Zhou, D.; Fu, P.; Yin, H.; Xie, W.; Feng, S. A Study of Online State-of-Health Estimation Method for In-Use Electric Vehicles Based on Charge Data. IEICE Trans. Inf. Syst.
**2019**, 102, 1302–1309. [Google Scholar] [CrossRef] - Feng, X.; Weng, C.; He, X.; Han, X.; Lu, L.; Ren, D.; Ouyang, M. Online State-of-Health Estimation for Li-Ion Battery Using Partial Charging Segment Based on Support Vector Machine. IEEE Trans. Veh. Technol.
**2019**, 68, 8583–8592. [Google Scholar] [CrossRef] - Wei, Z.; Ruan, H.; Li, Y.; Li, J.; Zhang, C.; He, H. Multistage State of Health Estimation of Lithium-Ion Battery with High Tolerance to Heavily Partial Charging. IEEE Trans. Power Electron.
**2022**, 37, 7432–7442. [Google Scholar] [CrossRef] - Ruan, H.; Wei, Z.; Shang, W.; Wang, X.; He, H. Artificial Intelligence-based health diagnostic of Lithium-ion battery leveraging transient stage of constant current and constant voltage charging. Appl. Energy
**2023**, 336, 120751. [Google Scholar] [CrossRef] - Manoharan, A.; Begum, K.M.; Aparow, V.R. Parallel Recurrent Artificial Neural Networks for Electric Vehicle Battery State of Health Estimation. In Proceedings of the 2022 17th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore, 11–13 December 2022; pp. 590–595. [Google Scholar] [CrossRef]
- Zheng, W.; Bai, C.; Qiao, J.; Yin, H.; Fu, P. Research on Data-Driven-Based Remaining Useful Life of Lithium-ion Battery. In Proceedings of the 2022 International Conference on Sensing, Measurement and Data Analytics in the era of Artificial Intelligence (ICSMD), Harbin, China, 30 November–2 December 2022; pp. 1–6. [Google Scholar] [CrossRef]
- Hemdani, J.; Degaa, L.; Soltani, M.; Rizoug, N.; Telmoudi, A.J.; Chaari, A. Battery Lifetime Prediction via Neural Networks with Discharge Capacity and State of Health. Energies
**2022**, 15, 8558. [Google Scholar] [CrossRef] - Falai, A.; Giuliacci, T.A.; Misul, D.A.; Anselma, P.G. Reducing the Computational Cost for Artificial Intelligence-Based Battery State-of-Health Estimation in Charging Events. Batteries
**2022**, 8, 209. [Google Scholar] [CrossRef] - Sahoo, S.; Hariharan, K.; Agarwal, S.; Swernath, S.; Bharti, R.; Han, S.; Lee, S. Transfer learning based generalized framework for state of health estimation of Li-ion cells. Sci. Rep.
**2022**, 12, 13173. [Google Scholar] [CrossRef] - Luciani, S.; Anselma, P.G.; Silvagni, M.; Bonfitto, A.; Tonoli, A. Enabling Rapid State of Health Offline Estimation of a 48V Lithium-Ion Battery Pack. In Proceedings of the 2022 IEEE Vehicle Power and Propulsion Conference (VPPC), Merced, CA, USA, 1–4 November 2022; pp. 1–6. [Google Scholar] [CrossRef]
- Wang, Y.; Tian, J.; Sun, Z.; Wang, L.; Xu, R.; Li, M.; Chen, Z. A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems. Renew. Sustain. Energy Rev.
**2020**, 131, 110015. [Google Scholar] [CrossRef] - Waldmann, T.; Wilka, M.; Kasper, M.; Fleischhammer, M.; Wohlfahrt-Mehrens, M. Temperature dependent ageing mechanisms in Lithium-ion batteries—A Post-Mortem study. J. Power Sources
**2014**, 262, 129–135. [Google Scholar] [CrossRef] - Ma, S.; Jiang, M.; Tao, P.; Song, C.; Wu, J.; Wang, J.; Deng, T.; Shang, W. Temperature effect and thermal impact in lithium-ion batteries: A review. Prog. Nat. Sci. Mater. Int.
**2018**, 28, 653–666. [Google Scholar] [CrossRef] - Kopp, M.; Ströbel, M.; Fill, A.; Pross-Brakhage, J.; Birke, K.P. Artificial Feature Extraction for Estimating State-of-Temperature in Lithium-Ion-Cells Using Various Long Short-Term Memory Architectures. Batteries
**2022**, 8, 36. [Google Scholar] [CrossRef] - Kucinskis, G.; Bozorgchenani, M.; Feinauer, M.; Kasper, M.; Wohlfahrt-Mehrens, M.; Waldmann, T. Arrhenius plots for Li-ion battery ageing as a function of temperature, C-rate, and ageing state—An experimental study. J. Power Sources
**2022**, 549, 232129. [Google Scholar] [CrossRef] - Sepasi, S.; Ghorbani, R.; Liaw, B.Y. Inline state of health estimation of lithium-ion batteries using state of charge calculation. J. Power Sources
**2015**, 299, 246–254. [Google Scholar] [CrossRef] - Tian, H.; Qin, P.; Li, K.; Zhao, Z. A review of the state of health for lithium-ion batteries: Research status and suggestions. J. Clean. Prod.
**2020**, 261, 120813. [Google Scholar] [CrossRef] - Li, Y.; Vilathgamuwa, M.; Farrell, T.; Choi, S.S.; Tran, N.T.; Teague, J. A physics-based distributed-parameter equivalent circuit model for lithium-ion batteries. Electrochim. Acta
**2019**, 299, 451–469. [Google Scholar] [CrossRef] - Sankarasubramanian, S.; Krishnamurthy, B. A capacity fade model for lithium-ion batteries including diffusion and kinetics. Electrochim. Acta
**2012**, 70, 248–254. [Google Scholar] [CrossRef] - Yao, L.; Xu, S.; Tang, A.; Zhou, F.; Hou, J.; Xiao, Y.; Fu, Z. A Review of Lithium-Ion Battery State of Health Estimation and Prediction Methods. World Electr. Veh. J.
**2021**, 12, 113. [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] - Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; MIT Press: Cambridge, MA, USA, 2016; Available online: http://www.deeplearningbook.org (accessed on 15 May 2023).
- Graves, A. Long Short-Term Memory. In Supervised Sequence Labelling with Recurrent Neural Networks; Springer: Berlin/Heidelberg, Germany, 2012; pp. 37–45. [Google Scholar] [CrossRef]
- Meng, H.; Geng, M.; Xing, J.; Zio, E. A hybrid method for prognostics of lithium-ion batteries capacity considering regeneration phenomena. Energy
**2022**, 261, 125278. [Google Scholar] [CrossRef] - Kingma, D.; Ba, J. Adam: A Method for Stochastic Optimization. arXiv
**2014**, arXiv:1412.6980. [Google Scholar] - Smith, S.L.; Kindermans, P.J.; Ying, C.; Le, Q.V. Don’t Decay the Learning Rate, Increase the Batch Size. arXiv
**2018**, arXiv:1711.00489. [Google Scholar] - Nogueira, F. Bayesian Optimization: Open Source Constrained Global Optimization Tool for Python. 2014. Available online: https://github.com/fmfn/BayesianOptimization (accessed on 15 May 2023).

**Figure 1.**Four diagrams featuring two examples of a single cell’s load performance. The first illustration, labeled (

**a**), depicts a capacity check-up procedure and the second illustration, labeled (

**b**), showcases ten drive cycles along with the corresponding charging cycles. The voltage U, current I, and all temperatures (${T}_{\mathrm{pos}}$, ${T}_{\mathrm{neg}}$, ${T}_{\mathrm{cell}}$, ${T}_{\mathrm{mean}}$, and ${T}_{\mathrm{amb}}$) are displayed.

**Figure 2.**${\mathrm{SoH}}_{\mathrm{Cap}}$ for each of the nine cells plotted over the course of its lifespan.

**Figure 3.**Example showing an extract of a current profile of cell 1 in (

**a**) and the corresponding absolute value of $\Delta I$ as calculated with Equation (7) in (

**b**).

**Figure 6.**The diagrams display the results of the ${\mathrm{SoH}}_{\mathrm{Cap}}$ algorithm applied to data points across all nine cells. These diagrams illustrate the comparison between the actual values ${y}_{\mathrm{GT}}$, the predicted values ${y}_{\mathrm{pred}}$, and the middle values ${y}_{\mathrm{mid}}$.

**Figure 7.**Diagram displaying the MSE values of the middle estimation ${y}_{\mathrm{mid}}$ in relation to the corresponding middle value ${n}_{\mathrm{mid}}$ for each individual cell. The minimum MSE values are highlighted with a red dot, while a green line indicates the average minimum MSE across all cells.

Format | Prismatic |

Cathode | NMC |

Nominal Capacity | ${C}_{\mathrm{N}}=51.0\phantom{\rule{0.277778em}{0ex}}\mathrm{Ah}\phantom{\rule{0.277778em}{0ex}}(1/3\phantom{\rule{0.277778em}{0ex}}\mathrm{C}),50.0\phantom{\rule{0.277778em}{0ex}}\mathrm{Ah}\phantom{\rule{0.277778em}{0ex}}\left(1\phantom{\rule{0.277778em}{0ex}}\mathrm{C}\right)$ |

Nominal Voltage | ${U}_{\mathrm{N}}=3.65\phantom{\rule{0.277778em}{0ex}}\mathrm{V}$ |

Charge limitations | $1.5\phantom{\rule{0.277778em}{0ex}}\mathrm{C}$ (Continuous)@ 25 °C; $3\phantom{\rule{0.277778em}{0ex}}\mathrm{C}$ (30 s, 50% SoC)@ 25 °C |

Discharge limitations | $2\phantom{\rule{0.277778em}{0ex}}\mathrm{C}$ (Continuous)@ 25 °C; $4.2\phantom{\rule{0.277778em}{0ex}}\mathrm{C}$ (30 s, 50% SoC)@ 25 °C |

**Table 2.**Progression of the initial ${C}_{\mathrm{BoL}}$ and current ${C}_{\mathrm{cur}}$ capacity of each cell along with the ${\mathrm{SoH}}_{\mathrm{Cap}}$ calculated with the method outlined in Equation (2).

Cell | ${\mathit{C}}_{\mathbf{BoL}}$ [Ah] | ${\mathit{C}}_{\mathbf{cur}}$ [Ah] | ${\mathrm{SoH}}_{\mathbf{Cap}}$ [%] | ${\mathit{T}}_{\mathbf{amb}}$ [°C] |
---|---|---|---|---|

1 | 52.504 | 47.360 | 90.203 | 25 |

2 | 52.456 | 47.128 | 89.843 | 25 |

3 | 52.417 | 47.520 | 90.658 | 25 |

4 | 52.340 | 41.706 | 79.683 | 45 |

5 | 52.542 | 43.719 | 83.206 | 45 |

6 | 52.500 | 44.341 | 84.459 | 45 |

7 | 52.607 | 48.693 | 92.559 | 5 |

8 | 52.554 | 48.381 | 92.060 | 5 |

9 | 52.497 | 48.834 | 93.023 | 5 |

**Table 3.**The minima (low) and maxima (high) of each input and output parameter across all nine cells under ${x}_{\mathrm{act}}$. The actual values used to scale the data are under ${x}_{\mathrm{use}}$.

${\mathit{x}}_{\mathbf{act}}$ | ${\mathit{x}}_{\mathbf{use}}$ | |||
---|---|---|---|---|

Low | High | Low | High | |

U | 2.793 V | 4.371 V | 2.600 V | 4.500 V |

T | −22.88 °C | 61.62 °C | −25.00 °C | 70.00 °C |

I | −116.0 A | 80.02 A | −120.0 A | 81.00 A |

$dt$ | 0.000 s | $5117\times {10}^{2}$ s | 0.000 s | $10\times {10}^{2}$ s |

C | 41.71 Ah | 52.61 Ah | 40.00 Ah | 54.00 Ah |

HP | ${\mathit{h}}_{\mathbf{win}}$ | ${\mathit{h}}_{\mathbf{lay}}$ | ${\mathit{h}}_{\mathbf{neu}}$ | ${\mathit{h}}_{\mathbf{LR}}$ | ${\mathit{h}}_{\mathbf{I},\mathbf{thr}}$ |
---|---|---|---|---|---|

min | 1 | 1 | 1 | ${10}^{-6}$ | 35 A |

max | 10 | 30 | 120 | ${10}^{-1}$ | 55 A |

Results | 4 | 3 | 66 | $1.75\times {10}^{-4}$ | 44.3 A |

**Table 5.**Table presenting the MSE results of the final trained model. The MSE column illustrates the MSE of the predicted values ${y}_{\mathrm{pred}}$, the ${\mathrm{MSE}}_{\mathrm{low}}$ column displays the MSE of the middle estimations at their optimal middle value ${n}_{\mathrm{mid}}$, and the ${\mathrm{MSE}}_{114}$ column shows the MSE of the middle estimations when ${n}_{\mathrm{mid}}=114$.

Cell | MSE | ${\mathrm{MSE}}_{\mathbf{low}}$ | ${\mathrm{MSE}}_{114}$ | ${\mathrm{RMSE}}_{114}$ |
---|---|---|---|---|

1 | $6.6272\times {10}^{-4}$ | $8.4645\times {10}^{-5}$ | $8.4670\times {10}^{-5}$ | $9.2016\times {10}^{-3}$ |

2 | $6.0713\times {10}^{-4}$ | $81026\times {10}^{-5}$ | $8.1082\times {10}^{-5}$ | $9.0046\times {10}^{-3}$ |

3 | $2.7322\times {10}^{-3}$ | $6.4431\times {10}^{-4}$ | $6.6272\times {10}^{-4}$ | $2.5743\times {10}^{-2}$ |

4 | $1.1279\times {10}^{-3}$ | $1.7370\times {10}^{-4}$ | $1.7371\times {10}^{-4}$ | $1.3180\times {10}^{-2}$ |

5 | $1.1123\times {10}^{-3}$ | $8.6745\times {10}^{-5}$ | $8.7046\times {10}^{-5}$ | $9.3298\times {10}^{-3}$ |

6 | $1.1396\times {10}^{-2}$ | $3.0567\times {10}^{-3}$ | $3.0567\times {10}^{-3}$ | $5.5287\times {10}^{-2}$ |

7 | $2.6580\times {10}^{-4}$ | $4.5865\times {10}^{-5}$ | $5.3300\times {10}^{-5}$ | $7.3007\times {10}^{-3}$ |

8 | $3.0578\times {10}^{-4}$ | $1.0067\times {10}^{-4}$ | $1.4647\times {10}^{-4}$ | $1.2102\times {10}^{-2}$ |

9 | $2.9550\times {10}^{-3}$ | $6.0781\times {10}^{-4}$ | $6.1529\times {10}^{-4}$ | $2.4805\times {10}^{-2}$ |

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. |

© 2024 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**

Kopp, M.; Fill, A.; Ströbel, M.; Birke, K.P.
A Novel Long Short-Term Memory Approach for Online State-of-Health Identification in Lithium-Ion Battery Cells. *Batteries* **2024**, *10*, 77.
https://doi.org/10.3390/batteries10030077

**AMA Style**

Kopp M, Fill A, Ströbel M, Birke KP.
A Novel Long Short-Term Memory Approach for Online State-of-Health Identification in Lithium-Ion Battery Cells. *Batteries*. 2024; 10(3):77.
https://doi.org/10.3390/batteries10030077

**Chicago/Turabian Style**

Kopp, Mike, Alexander Fill, Marco Ströbel, and Kai Peter Birke.
2024. "A Novel Long Short-Term Memory Approach for Online State-of-Health Identification in Lithium-Ion Battery Cells" *Batteries* 10, no. 3: 77.
https://doi.org/10.3390/batteries10030077