# Remaining-Useful-Life Prediction for Li-Ion Batteries

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## Abstract

**:**

## 1. Introduction

## 2. Properties of Li-Ion Batteries

#### 2.1. State of Charge

#### 2.2. Methods of Battery Charging

#### 2.2.1. Constant-Current Method (CC)

#### 2.2.2. Constant-Voltage Method (CV)

#### 2.2.3. Constant-Current and Constant-Voltage Method (CC-CV)

## 3. Framework for Predictive Maintenance

#### 3.1. Dataset

#### 3.2. Data Preprocessing

#### 3.2.1. Feature Scaling

#### 3.2.2. Feature Analysis

#### 3.2.3. Correlation Analysis

#### 3.3. Model Building

#### 3.3.1. Model Selection

#### 3.3.2. Model Training

#### 3.3.3. Model Testing

## 4. Prediction of Remain Useful Life

#### 4.1. Health Indicator

#### 4.2. Prediction Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Cut-Off Voltage (V) | Current (A) | Capacity (Ahr) | |||
---|---|---|---|---|---|

Charging | Discharging | Charging | Discharging | Rated | Lower Bound |

4.2 | 2.7 | 1.5 | 2 | 2 | 1.4 |

Features | Description |
---|---|

Voltage_b | The battery voltage in the charging stage |

Current_b | The battery current in the charging stage |

Voltage_c | The charger voltage in the charging stage |

Current_c | The charger current in the charging stage |

Voltage_l | The load voltage in the discharging stage |

Current_l | The load current in the discharging stage |

Temperature | The battery temperature in the charging and discharging stages |

Capacity | The capacity after charging and discharging cycles |

Time | The time stamp including date, hour, minute, second |

Item | Formula |
---|---|

Skewness | ${x}_{sk}=\frac{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{3}}{{\left(\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{2}\right)}^{3/2}}$ |

Kurtosis | ${x}_{ku}=\frac{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{4}}{{\left(\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{2}\right)}^{2}}$ |

Shape factor | ${x}_{sf}=\frac{{x}_{rms}}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left|{x}_{i}\right|}$ |

Crest factor | ${x}_{cf}=\frac{\mathrm{max}\left\{{x}_{i}\right\}}{{x}_{rms}}$ |

Impulse factor | ${x}_{if}=\frac{\mathrm{max}\left\{{x}_{i}\right\}}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left|{x}_{i}\right|}$ |

Margin factor | ${x}_{mf}=\frac{\mathrm{max}\left\{{x}_{i}\right\}}{{\left(\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left|{x}_{i}\right|\right)}^{2}}$ |

Item | Description | Correlation |
---|---|---|

1 | time interval of CC charging | ● |

2 | time interval of CV charging | ● |

3 | battery temperature after charging | |

4 | skewness of temperature in charging | |

5 | kurtosis of temperature in charging | |

6 | waveform factor of temperature in charging | ● |

7 | crest factor of temperature in charging | ● |

8 | impulse factor of temperature in charging | ● |

9 | margin factor of temperature in charging | ● |

10 | skewness of battery voltage in charging | ● |

11 | kurtosis of battery voltage in charging | |

12 | waveform factor of battery voltage in charging | ● |

13 | crest factor of battery voltage in charging | ● |

14 | impulse factor of battery voltage in charging | ● |

15 | margin factor of battery voltage in charging | ● |

16 | skewness of charger voltage in charging | |

17 | kurtosis of charger voltage in charging | |

18 | waveform factor of charger voltage in charging | |

19 | crest factor of charger voltage in charging | |

20 | impulse factor of charger voltage in charging | |

21 | margin factor of charger voltage in charging | |

22 | skewness of battery current in charging | |

23 | kurtosis of battery current in charging | |

24 | waveform factor of battery current in charging | |

25 | crest factor of battery current in charging | |

26 | impulse factor of battery current in charging | |

27 | margin factor of battery current in charging | |

28 | skewness of battery voltage in discharging | ● |

29 | kurtosis of battery voltage in discharging | ● |

30 | waveform factor of battery voltage in discharging | ● |

31 | crest factor of battery voltage in discharging | |

32 | impulse factor of battery voltage in discharging | |

33 | margin factor of battery voltage in discharging | ● |

34 | skewness of load voltage in discharging | ● |

35 | crest factor of load voltage in discharging | ● |

36 | waveform factor of load voltage in discharging | ● |

37 | crest factor of load voltage in discharging | ● |

38 | impulse factor of load voltage in discharging | ● |

39 | margin factor of load voltage in discharging | ● |

40 | time interval of discharging | ● |

41 | battery temperature after discharging | |

42 | skewness of temperature in discharging | ● |

43 | kurtosis of temperature in discharging | ● |

44 | waveform factor of temperature in discharging | ● |

45 | crest factor of temperature in discharging | ● |

46 | impulse factor of temperature in discharging | ● |

47 | margin factor of temperature in discharging | ● |

48 | capacity | ● |

Strength | Positive Correlation | Negative Correlation |
---|---|---|

Strong | 0.5–1 | −1–0.5 |

Moderate | 0.3–0.5 | −0.5–0.3 |

Weak | 0.1–0.3 | −0.3–0.1 |

Negligible | <0.1 | −0.1–0 |

Model | RSME | IAE | ISE |
---|---|---|---|

Tree | 0.138 | 6.082 | 10.919 |

NARX | 0.185 | 8.202 | 13.171 |

RNN | 0.045 | 1.641 | 6.433 |

LSTM | 0.038 | 1.423 | 4.593 |

Model | HI | Status |
---|---|---|

Tree | 93.87% | good |

NARX | 95.45% | good |

RNN | 90.05% | good |

LSTM | 91.34% | good |

Real value | 93.84% | good |

Model | HI < 75% (cycle) | RUL (Cycle) | Error Index | ||
---|---|---|---|---|---|

RMSE | IAE | ISE | |||

Tree | na | na | 0.164 | 20.521 | 44.001 |

NARX | 84 | 34 | 0.276 | 35.113 | 30.918 |

RNN | 146 | 96 | 0.129 | 16.869 | 39.781 |

LSTM | 126 | 76 | 0.063 | 7.130 | 18.249 |

Real value | 136 | 84 |

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## Share and Cite

**MDPI and ACS Style**

Chang, Y.-H.; Hsieh, Y.-C.; Chai, Y.-H.; Lin, H.-W. Remaining-Useful-Life Prediction for Li-Ion Batteries. *Energies* **2023**, *16*, 3096.
https://doi.org/10.3390/en16073096

**AMA Style**

Chang Y-H, Hsieh Y-C, Chai Y-H, Lin H-W. Remaining-Useful-Life Prediction for Li-Ion Batteries. *Energies*. 2023; 16(7):3096.
https://doi.org/10.3390/en16073096

**Chicago/Turabian Style**

Chang, Yeong-Hwa, Yu-Chen Hsieh, Yu-Hsiang Chai, and Hung-Wei Lin. 2023. "Remaining-Useful-Life Prediction for Li-Ion Batteries" *Energies* 16, no. 7: 3096.
https://doi.org/10.3390/en16073096