# Online Capacity Estimation for Lithium-Ion Batteries Based on Semi-Supervised Convolutional Neural Network

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Input and Output Structures

_{i}, y

_{i}} of the SS-CNN. The output vector is the discharge capacity (i.e., y

_{i}= Q

_{i}). The input vector is obtained from the battery monitoring signal.

_{1}= V

_{initial}) is selected according to the depth of discharge. Then, the charging data from t

_{1}(time corresponding to V

_{1}) to a fixed length of time interval (t

_{L}) are used to build the input vector, which is defined as:

_{1}to t

_{l}, which is calculated using the coulomb counting method ${C}_{l}={{\displaystyle \int}}_{{t}_{1}}^{{t}_{l}}I\mathrm{d}t$.

#### 2.2. Design of the SS-CNN

_{0}is the bias while ${x}_{i}^{\left(0\right)}=1$.

#### 2.3. Design of the Training Strategy

#### 2.3.1. Unsupervised Reconstruction

#### 2.3.2. Supervised Regression

#### 2.3.3. Supervised Fine-Tuning

## 3. Results and Discussion

#### 3.1. Battery Dataset

#### 3.2. Capacity Estimation Results

#### 3.3. Effect of the Starting Charge Voltage

#### 3.4. Effect of the Training Sample Size

#### 3.4.1. Different Sizes of Unlabeled Samples

#### 3.4.2. Different Sizes of Labeled Samples

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Capacity estimation results for battery #7: (

**a**) NN model; (

**b**) CNN model; (

**c**) SS-CNN-S2 model; (

**d**) SS-CNN-S3 model.

**Figure 5.**Evolution of the voltage curves with the battery cycles with different starting voltages: (

**a**) Starting voltage = 3.7 V; (

**b**) Starting voltage = 3.8 V; (

**c**) Starting voltage = 3.9 V.

Method | Index | Battery #5 (%) | Battery #6 (%) | Battery #7 (%) | Battery #18 (%) | Average (%) |
---|---|---|---|---|---|---|

RMSE | 1.2983 | 1.3293 | 1.1586 | 1.4239 | 1.3025 | |

NN | MAE | 1.0498 | 1.0893 | 0.9782 | 1.2843 | 1.1004 |

MaxRE | 3.7945 | 3.8098 | 3.6555 | 4.0128 | 4.0128 | |

RMSE | 1.1349 | 1.2302 | 1.0204 | 1.2983 | 1.1709 | |

CNN | MAE | 0.9825 | 1.0472 | 0.7938 | 1.0529 | 0.9691 |

MaxRE | 3.6416 | 3.1983 | 3.0781 | 3.7231 | 3.7231 | |

RMSE | 0.8248 | 0.8339 | 0.7702 | 0.9149 | 0.8359 | |

SS-CNN-S2 | MAE | 0.7849 | 0.7639 | 0.6329 | 0.8539 | 0.7589 |

MaxRE | 2.6839 | 2.8493 | 2.5479 | 3.0329 | 3.0329 | |

RMSE | 0.7382 | 0.8137 | 0.6839 | 0.9087 | 0.7861 | |

SS-CNN-S3 | MAE | 0.6782 | 0.7483 | 0.5225 | 0.8389 | 0.6970 |

MaxRE | 2.5392 | 2.7839 | 2.4440 | 2.8403 | 2.8403 |

Starting Voltage (V) | 3.7 | 3.75 | 3.8 | 3.85 | 3.9 |
---|---|---|---|---|---|

RMSE (%) | 0.6544 | 0.8969 | 0.6839 | 1.0550 | 1.0765 |

MAE (%) | 0.4966 | 0.7125 | 0.5225 | 0.7619 | 0.7568 |

MaxRE (%) | 2.7178 | 2.9214 | 2.4440 | 3.5384 | 3.5370 |

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**MDPI and ACS Style**

Wu, Y.; Li, W.
Online Capacity Estimation for Lithium-Ion Batteries Based on Semi-Supervised Convolutional Neural Network. *World Electr. Veh. J.* **2021**, *12*, 256.
https://doi.org/10.3390/wevj12040256

**AMA Style**

Wu Y, Li W.
Online Capacity Estimation for Lithium-Ion Batteries Based on Semi-Supervised Convolutional Neural Network. *World Electric Vehicle Journal*. 2021; 12(4):256.
https://doi.org/10.3390/wevj12040256

**Chicago/Turabian Style**

Wu, Yi, and Wei Li.
2021. "Online Capacity Estimation for Lithium-Ion Batteries Based on Semi-Supervised Convolutional Neural Network" *World Electric Vehicle Journal* 12, no. 4: 256.
https://doi.org/10.3390/wevj12040256