# State of Health Prediction for Lithium-Ion Batteries through Curve Compression and CatBoost

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## Abstract

**:**

^{−5}. The proposed approach also achieves better prediction results in the validation object dataset, indicating its strong generalization capability. Additionally, the proposed model shows significant robustness by accurately predicting SoH and RUL under noisy environmental conditions. Overall, the proposed model shows significant potential to accurately predict SoH and RUL by efficiently addressing the challenges associated with feature engineering for battery attributes, reducing the impact of background noise on prediction results, and exhibiting strong robustness.

## 1. Introduction

## 2. Algorithm Introduction

#### 2.1. Curve Compression Algorithm

#### 2.1.1. Douglas–Peucker Algorithm

#### 2.1.2. Perpendicular Distance Threshold Algorithm

#### 2.2. CatBoost Algorithm Principle

#### 2.2.1. Gradient Boosting Algorithm (GBDT)

#### 2.2.2. CatBoost Algorithm

## 3. Lithium-Ion Battery SoH Prediction Process

## 4. Data Acquisition

#### 4.1. Experimental Protocol

#### 4.1.1. Experimental Setup

#### 4.1.2. Experimental Steps

- Step 1:
- Charge at a constant current of 1 A until the battery reaches 4.2 V using a battery tester.
- Step 2:
- Charge at a constant current of 4.2 V until the detection current is less than 200 mA, then stop charging.
- Step 3:
- Let the battery stand for 10 min.
- Step 4:
- Discharge at a constant power of 6 W until the battery voltage drops to 2.7 V, then stop discharging.
- Step 5:
- Leave the battery on for 20 min.
- Step 6:
- Repeat steps 1–5 for a total of 148 cycles.

- Step 1:
- Charge at a constant current of 1.3 A until the battery reaches 4.2 V using a battery tester.
- Step 2:
- Charge at a constant voltage of 4.2 V until the detected charging current is less than 50 mA, then stop charging.
- Step 3:
- Let the battery stand for 10 min.
- Step 4:
- Discharge at a constant current of 3.9 A until the battery voltage drops to 2.7 V, then stop discharging.
- Step 5:
- Leave the battery on for 20 min.
- Step 6:
- Repeat steps 1–5 for a total of 148 cycles.

#### 4.2. Introduction to the Dataset

## 5. Instance Validation

#### 5.1. Traditional Threshold Selection Method: Compress Curve

#### 5.2. Improved Threshold Selection Method Compress Curve

#### 5.3. Length Normalization Based on Cubic Spline Interpolation and Outlier Detection

#### 5.3.1. Cubic Spline Interpolation to Add Feature Points

#### 5.3.2. LOF Anomaly Detection to Remove Feature Points

#### 5.3.3. Determination of the Optimal Length L

#### 5.4. SoH Prediction Based on the CatBoost Model

^{−3}. These results indicate that the proposed feature engineering and CatBoost model utilized in this study have significant advantages in the realm of State of Health (SoH) estimation.

#### 5.5. Comparison of the Effects of Different Models

^{−5}) is significantly lower than that of Random Forest and XGBoot. Additionally, the prediction goodness-of-fit of the CatBoost model is better; the average value of ${R}^{2}$ is 0.9922, improved by 0.0228 and 0.0152, respectively. Therefore, the CatBoost method can effectively enhance the accuracy of SoH estimation and operational efficiency and exhibit good performance in SoH estimation.

#### 5.6. Model Generalizability Validation

#### 5.7. Model Robustness Verification

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Curve compression results with different threshold selections using the median threshold. (

**a**) The compression result of the discharge voltage curve in the 5th cycle. (

**b**) The compression result of the discharge voltage curve in the 105th cycle.

**Figure 10.**Curve compression results with different threshold selections using the minimum distance threshold. (

**a**) The compression result of the 5th discharge voltage curve. (

**b**) The compression result of the 105th discharge voltage curve.

**Figure 12.**Curve compression effect after improving the threshold selection method of the B0005 battery. (

**a**) The compression result of the 5th discharge voltage curve. (

**b**) The compression result of the 105th discharge voltage curve.

**Figure 16.**Original signal and dynamically regularized signal. (

**a**) Unregulated signal. (

**b**) Post-regulation signal.

**Figure 18.**Prediction results for the test set of dataset A. (

**a**) B0005 test set prediction results. (

**b**) B0006 test set prediction results. (

**c**) B0007 test set prediction results.

**Figure 19.**SoH prediction error distribution. (

**a**) B0005 test set prediction results. (

**b**) B0006 test set prediction results. (

**c**) B0007 test set prediction results.

**Figure 21.**Data set B curve compression results. (

**a**) the compression results of the discharge voltage curve in the 1st cycle of battery number 2. (

**b**) the compression results of the discharge voltage curve in the 61st cycle of battery number 2.

**Figure 22.**Prediction results of dataset B. (

**a**) Battery number 1 in dataset B. (

**b**) Battery number 2 in dataset B.

**Figure 23.**Predicted results of batteries after adding noise. (

**a**) Prediction of battery B0005 in dataset A. (

**b**) Prediction of Battery number 2 in dataset B.

Projects | Specification | Projects | Specification | |
---|---|---|---|---|

Housing material | Nickel-plated steel | Charging strategy (CC/CV) Operating temperature | Standard | 0.5C_5A × 7.5 h |

Nominal capacity | 1300 mAh | Fast | 1C_5A × 2.5 h | |

Rated capacity | 3.7 V | Charging | 0 °C~45 °C 32 °F~113 °F | |

Charging Voltage (Max) | 4.2 V | |||

Discharge cut-off voltage | 2.7 V | Discharge | −15 °C~60 °C 5 °F~140 °F | |

Charging Current (Max) | 1 C_{5} | |||

Discharge current (Max) | 3 C_{5} | Storage | −20 °C~60 °C −4 °F~113 °F | |

Internal resistance (Max at 1000 Hz) | ≤25 mΩ |

Battery Number | MSE | RMSE | MAE | AE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|

5 | 3.7248 × 10^{−5} | 0.0061 | 0.0052 | 0 | 0.9967 |

6 | 2.1665 × 10^{−5} | 0.0047 | 0.0040 | 1 | 0.9915 |

7 | 9.2121 × 10^{−5} | 0.0030 | 0.0026 | 0 | 0.9883 |

Predictive Models | Battery Number | MSE | RMSE | MAE | AE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|

Random Forest | 5 | 0.0030 | 0.0546 | 0.0442 | 4 | 0.9602 |

6 | 8.9984 × 10^{−4} | 0.0300 | 0.0238 | 3 | 0.9769 | |

7 | 0.0072 | 0.0850 | 0.0755 | 2 | 0.9713 | |

XGBoost | 5 | 1.3301 × 10^{−4} | 0.0115 | 0.0084 | 2 | 0.9808 |

6 | 6.2771 × 10^{−4} | 0.0251 | 0.0195 | 1 | 0.9813 | |

7 | 1.3129 × 10^{−4} | 0.0115 | 0.0086 | 2 | 0.9689 | |

CatBoost | 5 | 3.7248 × 10^{−5} | 0.0061 | 0.0052 | 0 | 0.9967 |

6 | 2.1665 × 10^{−5} | 0.0047 | 0.0040 | 1 | 0.9915 | |

7 | 9.2121 × 10^{−5} | 0.0030 | 0.0026 | 0 | 0.9883 |

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## Share and Cite

**MDPI and ACS Style**

Yin, J.; Zhang, M.; Feng, T.
State of Health Prediction for Lithium-Ion Batteries through Curve Compression and CatBoost. *World Electr. Veh. J.* **2023**, *14*, 180.
https://doi.org/10.3390/wevj14070180

**AMA Style**

Yin J, Zhang M, Feng T.
State of Health Prediction for Lithium-Ion Batteries through Curve Compression and CatBoost. *World Electric Vehicle Journal*. 2023; 14(7):180.
https://doi.org/10.3390/wevj14070180

**Chicago/Turabian Style**

Yin, Jun, Mei Zhang, and Tao Feng.
2023. "State of Health Prediction for Lithium-Ion Batteries through Curve Compression and CatBoost" *World Electric Vehicle Journal* 14, no. 7: 180.
https://doi.org/10.3390/wevj14070180