# One-Time Prediction of Battery Capacity Fade Curve under Multiple Fast Charging Strategies

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## Abstract

**:**

## 1. Introduction

## 2. The Battery Data for Multiple Fast Charging Strategies

- https://data.matr.io/1/projects/5c48dd2bc625d700019f3204, accessed on 1 January 2024.
- https://data.matr.io/1/projects/5d80e633f405260001c0b60a, accessed on 1 January 2024.

## 3. One-Time Prediction Method for Capacity Fade Curves

#### 3.1. Feature Structure and Label Structure

#### 3.2. The Structure of TM-Seq2Seq Model

#### 3.2.1. SE-net

#### 3.2.2. GRU

#### 3.2.3. Trend Matching

#### 3.3. Parameter Equation of Capacity Fade Curve

## 4. Results and Discussion

- Seq2Seq: The Seq2Seq model consists of an encoder and a decoder. The encoder transforms the input sequence into a fixed-length vector, which is then used by the decoder to generate the output sequence. This model has demonstrated excellent performance in tasks such as predicting capacity fade curves [15].
- CNN: The CNN model captures local features through convolution operations and reduces the number of parameters and computational complexity through pooling operations. It is also proficient in learning time series data. This model has been widely applied to tasks such as battery EOL prediction [18] and capacity fade curve prediction [22,23].
- CNN-BI-LSTM: BI-LSTM is a type of recurrent neural network model used for natural language processing tasks such as named entity recognition and sentiment analysis. The model comprises both forward and backward LSTM layers, allowing it to utilize contextual information at each time step and better capture long-term dependencies. This model has been applied to tasks of battery SOH prediction [31].
- SE-CNN-LSTM: SE-CNN-LSTM is a model that combines Squeeze-and-Excitation (SE) module, Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM). It leverages the SE module to enhance the feature representation of CNN, which allows the model to capture more informative features.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Chen, M.; Ma, G.; Liu, W.; Zeng, N.; Luo, X. An overview of data-driven battery health estimation technology for battery management system. Neurocomputing
**2023**, 532, 152–169. [Google Scholar] [CrossRef] - Hu, X.; Xu, L.; Lin, X.; Pecht, M. Battery Lifetime Prognostics. Joule
**2020**, 4, 310–346. [Google Scholar] [CrossRef] - Fuller, T.F.; Doyle, M.; Newman, J. Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc.
**1994**, 141, 1. [Google Scholar] [CrossRef] - Doyle, M.; Fuller, T.F.; Newman, J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. J. Electrochem. Soc.
**1993**, 140, 1526–1533. [Google Scholar] [CrossRef] - Santhanagopalan, S.; Guo, Q.; Ramadass, P.; White, R.E. Review of models for predicting the cycling performance of lithium ion batteries. J. Power Sources
**2006**, 156, 620–628. [Google Scholar] [CrossRef] - Kindermann, F.M.; Keil, J.; Frank, A.; Jossen, A. A SEI modeling approach distinguishing between capacity and power fade. J. Electrochem. Soc.
**2017**, 164, E287–E294. [Google Scholar] [CrossRef] - Deshpande, R.; Verbrugge, M.; Cheng, Y.-T.; Wang, J.; Liu, P. Battery cycle life prediction with coupled chemical fade and fatigue mechanics. J. Electrochem. Soc.
**2012**, 159, A1730–A1738. [Google Scholar] [CrossRef] - Reniers, J.M.; Mulder, G.; Howey, D.A. Review and performance comparison of mechanical-chemical fade models for lithium-ion batteries. J. Electrochem. Soc.
**2019**, 166, A3189–A3200. [Google Scholar] [CrossRef] - Saha, B.; Goebel, K.; Poll, S.; Christophersen, J. Prognostics methods for battery health monitoring using a Bayesian framework. IEEE Trans. Instrum. Meas.
**2009**, 58, 291–296. [Google Scholar] [CrossRef] - He, W.; Williard, N.; Osterman, M.; Pecht, M. Prognostics of lithium-ion batteries based on Dempster-Shafer theory and the Bayesian Monte Carlo method. J. Power Sources
**2011**, 196, 10314–10321. [Google Scholar] [CrossRef] - Li, P.; Zhang, Z.; Xiong, Q.; Ding, B.; Hou, J.; Luo, D.; Rong, Y.; Li, S. State-of-health estimation and remaining useful life prediction for the lithium-ion battery based on a variant long short term memory neural network. J. Power Sources
**2020**, 459, 228069. [Google Scholar] [CrossRef] - Li, X.; Zhang, L.; Wang, Z.; Dong, P. Remaining useful life prediction for lithium-ion batteries based on a hybrid model combining the long short-term memory and Elman neural networks. J. Energy Storage
**2019**, 21, 510–518. [Google Scholar] [CrossRef] - Wang, F.; Zhao, Z.; Ren, J.; Zhai, Z.; Wang, S.; Chen, X. A transferable lithium-ion battery remaining useful life prediction method from cycle-consistency of fade trend. J. Power Sources
**2022**, 525, 231027. [Google Scholar] - Zhang, Y.; Xiong, R.; He, H.; Pecht, M.G. Long short-term memory recurrent neural network for remaining useful life prediction of lithium-ion batteries. IEEE Trans. Veh. Technol.
**2018**, 67, 5695–5705. [Google Scholar] [CrossRef] - Li, W.; Sengupta, N.; Dechent, P.; Howe, D.; Annaswamy, A.; Sauer, D.U. One-shot battery fade trajectory prediction with deep learning. J. Power Sources
**2021**, 506, 230024. [Google Scholar] [CrossRef] - Severson, K.A.; Attia, P.M.; Jin, N.; Perkins, N.; Jiang, B.; Yang, Z.; Chen, M.H.; Aykol, M.; Herring, P.K.; Fraggedakis, D.; et al. Data-driven prediction of battery cycle life before capacity fade. Nat. Energy
**2019**, 4, 383–391. [Google Scholar] [CrossRef] - Ma, Y.; Wu, L.; Guan, Y.; Peng, Z. The capacity estimation and cycle life prediction of lithium-ion batteries using a new broad extreme learning machine approach. J. Power Sources
**2020**, 476, 228581. [Google Scholar] [CrossRef] - Shen, S.; Nemani, V.; Liu, J.; Hu, C.; Wang, Z. A hybrid machine learning model for battery cycle life prediction with early cycle data. In Proceedings of the 2020 IEEE Transportation Electrification Conference and Expo (ITEC), Chicago, IL, USA, 23–26 June 2020; pp. 181–184. [Google Scholar]
- Hong, J.; Lee, D.; Jeong, E.R.; Yi, Y. Towards the swift prediction of the remaining useful life of lithium-ion batteries with end-to-end deep learning. Appl. Energy
**2020**, 278, 115646. [Google Scholar] [CrossRef] - Fermín-Cueto, P.; McTurk, E.; Allerhand, M.; Medina-Lopez, E.; Anjos, M.F.; Sylvester, J.; Reis, G.D. Identification and machine learning prediction of knee point and knee-onset in capacity fade curve of lithium-ion cells. Energy AI
**2020**, 1, 100006. [Google Scholar] [CrossRef] - Liu, J.; Thelen, A.; Hu, C.; Yang, X.G. An end-to-end learning framework for early prediction of battery capacity trajectory. In Proceedings of the Annual Conference of the PHM Society, Nashville, TN, USA, 29 November–20 December 2021; Volume 13. [Google Scholar]
- Saxena, S.; Ward, L.; Kubal, J.; Lu, W.; Babinec, S.; Paulson, N. A convolutional neural network model for battery capacity fade curve prediction using early life data. J. Power Sources
**2022**, 542, 231736. [Google Scholar] [CrossRef] - Strange, C.; Reis, G.D. Prediction of future capacity and internal resistance of Li-ion cells from one cycle of input data. Energy AI
**2021**, 5, 100097. [Google Scholar] [CrossRef] - Herring, P.; Gopal, C.B.; Aykol, M.; Montoya, J.H.; Anapolsky, A.; Attia, P.M.; Gent, W.; Hummelshoj, J.S.; Hung, L.; Kwon, H.; et al. A Python library for battery evaluation and early prediction. Software
**2020**, 11, 100506. [Google Scholar] [CrossRef] - Attia, P.M.; Grover, A.; Jin, N.; Severson, K.A.; Markov, T.M.; Liao, Y.; Chen, M.H.; Cheong, B.; Perkins, N.; Yang, Z.; et al. Closed-loop optimization of fast-charging protocols for batteries with machine learning. Nature
**2020**, 578, 397–402. [Google Scholar] [CrossRef] [PubMed] - Sutskever, I.; Vinyals, O.; Le, Q.V. Sequence to Sequence Learning with Neural Networks. In Proceedings of the 2014 Proceedings of the 27th International Conference on Neural Information Processing Systems (NIPS), Montreal, QC, Canada, 8–13 December 2014; pp. 3104–3112. [Google Scholar]
- Hu, J.; Shen, L.; Sun, G. Squeeze-and-Excitation Networks. In Proceedings of the 2018 IEEECVF Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA, 18–23 June 2018. [Google Scholar]
- Song, Y.; Li, L.; Peng, Y.; Liu, D. Lithium-Ion Battery Remaining Useful Life Prediction Based on GRU-RNN. In Proceedings of the 2018 12th International Conference on Reliability, Maintainability, and Safety (ICRMS), Shanghai, China, 17–19 October 2018; pp. 317–322. [Google Scholar]
- Zhou, K.; Liu, Z.; Qiao, Y.; Xiang, T.; Loy, C.C. Generalizing to Unseen Domains: A Survey on Domain Generalization. IEEE Trans. Pattern Anal. Mach. Intell.
**2022**, 35, 4396–4415. [Google Scholar] - Du, Y.; Wang, J.; Feng, W.; Pan, S.; Qin, T.; Xu, R.; Wang, C. AdaRNN: Adaptive Learning and Forecasting for Time Series. In Proceedings of the 2021 Proceedings of the 30th ACM International Conference on Information & Knowledge Management (CIKM), Gold Coast, QD, Australia, 1–5 November 2021; pp. 402–414. [Google Scholar]
- Yan, B.; Zheng, W.J.; Tang, D.Y.; Laili, Y.J.; Xing, Y. A knowledge-constrained CNN-BiLSTM model for lithium-ion batteries state-of-charge estimation. Microelectron. Reliab.
**2023**, 150, 115112. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) Capacity fade curves of 132 experimental batteries. (

**b**) The distribution of the total test cycles of 132 batteries.

**Figure 3.**(

**a**) Capacity curves within the first 100 charge–discharge cycles. (

**b**) The subtraction of the Q(V) curve of the first cycle from the Q(V) curve of the 100th cycle of a battery.

Model | MAE | MAPE | RMSE |

Seq2Seq | 83.326 | 11.768% | 109.921 |

CNN | 99.730 | 15.619% | 126.192 |

CNN-BI-LSTM | 85.099 | 13.749% | 105.192 |

SE-CNN-LSTM | 90.418 | 13.898% | 109.803 |

TM-Seq2Seq | 77.043 | 12.246% | 101.336 |

MAE (EOL) | MAPE (EOL) | RMSE (EOL) | |

Seq2Seq | 99.988 | 11.511% | 127.745 |

CNN | 113.772 | 14.853% | 137.954 |

CNN-BI-LSTM | 103.319 | 12.642% | 131.097 |

SE-CNN-LSTM | 103.478 | 12.207% | 125.899 |

TM-Seq2Seq | 87.838 | 10.409% | 114.501 |

SE-net | x | √ | x | √ |

Trend Matching | x | x | √ | √ |

MAE | 88.502 | 81.440 | 85.089 | 77.043 |

MAPE | 13.171% | 13.088% | 13.330% | 12.246% |

RMSE | 114.178 | 108.281 | 122.588 | 101.336 |

MAE (EOL) | 107.513 | 91.506 | 97.728 | 87.838 |

MAPE (EOL) | 12.757% | 11.384% | 12.084% | 10.409% |

RMSE (EOL) | 135.346 | 112.921 | 137.406 | 114.501 |

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**MDPI and ACS Style**

Han, X.; Dai, Z.; Ren, M.; Cui, J.; Shi, Y.
One-Time Prediction of Battery Capacity Fade Curve under Multiple Fast Charging Strategies. *Batteries* **2024**, *10*, 74.
https://doi.org/10.3390/batteries10030074

**AMA Style**

Han X, Dai Z, Ren M, Cui J, Shi Y.
One-Time Prediction of Battery Capacity Fade Curve under Multiple Fast Charging Strategies. *Batteries*. 2024; 10(3):74.
https://doi.org/10.3390/batteries10030074

**Chicago/Turabian Style**

Han, Xiaoming, Zhentao Dai, Mifeng Ren, Jing Cui, and Yunfeng Shi.
2024. "One-Time Prediction of Battery Capacity Fade Curve under Multiple Fast Charging Strategies" *Batteries* 10, no. 3: 74.
https://doi.org/10.3390/batteries10030074