# Data Augmentation and Feature Selection for the Prediction of the State of Charge of Lithium-Ion Batteries Using Artificial Neural Networks

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Origin and Data Augmentation

#### 2.2. Machine Learning Models

#### 2.2.1. Linear Regression

#### 2.2.2. Artificial Neural Networks

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

BEV | Battery electric vehicle |

BMS | Battery management system |

CNN | Convolutional neural network |

LIB | Lithium-ion battery |

MAE | Mean absolute error |

ML | Machine learning |

MLP | Multilayer perceptron |

PCA | Principal component analysis |

RMSE | Root mean square error |

RNN | Recurrent neural network |

SoC | State-of-Charge |

SVD | Singular value decomposition |

SVM | Support vector machine |

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**Figure 1.**Discharge cycle of the analyzed battery cell with voltage plotted over the SoC. The cell is discharged in 10% intervals and rested after each interval.

**Figure 2.**Results of the data augmentation method. On the left, the accuracy of the voltage estimation model for real data is presented. Real measurements are compared to the results of the voltage estimation model. On the right, results of the estimation model with slightly modified input values resulting in two artificially created discharge curves are shown.

**Figure 3.**Structure of a CNN with a feature map followed by a convolution, a pooling layer, and a fully connected layer. The filter is moved across the features.

**Figure 4.**Convergence of the different models. MAE is shown over the epochs for the MLP (

**a**) and the CNN (

**b**) with and without augmented data.

**Figure 5.**Error bars and standard deviation of the five times retrained models without data augmentation, with ten times the initial data and 20 times the initial data. The MAE is shown for the MLP and the CNN.

**Figure 6.**Test results of the SoC estimation model in comparison with the real values for the MLP (

**a**) and for the CNN (

**b**). The results for the SoC are shown over the last voltage value for the estimation.

**Table 1.**Results of the linear regression with the three different sizes of training datasets. The mean of five times retraining the model and the corresponding standard deviations are shown.

Linear | Training | Test | ||
---|---|---|---|---|

Regression | MAE | RMSE | MAE | RMSE |

Without augmented data | 3.874 (±0.021)% | 4.941 (±0.012)% | 4.089 (±0.205)% | 4.999 (±0.095)% |

With augmented data (10×) | 3.914 (±0.029)% | 4.970 (±0.018)% | 4.041 (±0.220)% | 4.980 (±0.100)% |

With augmented data (20×) | 4.004 (±0.027)% | 5.066 (±0.036)% | 3.977 (±0.050)% | 5.044 (±0.052)% |

**Table 2.**Results of the MLP with the three different sizes of training datasets. The mean of five times of retraining the model and the corresponding standard deviations are shown.

MLP | Training | Test | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

Without augmented data | 0.828 (±0.292)% | 1.072 (±0.329)% | 0.553 (±0.051)% | 0.805 (±0.072)% |

With augmented data (10×) | 0.626 (±0.184)% | 0.848 (±0.190)% | 0.539 (±0.087)% | 0.758 (±0.109)% |

With augmented data (20×) | 0.722 (±0.222)% | 0.977 (±0.242)% | 0.727 (±0.217)% | 0.978 (±0.246)% |

**Table 3.**Results of the CNN with the three different sizes of training datasets. The mean of five times of retraining the model and the corresponding standard deviations are shown.

CNN | Training | Test | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

Without augmented data | 0.975 (±0.459)% | 1.173 (±0.531)% | 0.505 (±0.201)% | 0.723 (±0.249)% |

With augmented data (10×) | 0.371 (±0.269)% | 0.494 (±0.315)% | 0.315 (±0.140)% | 0.478 (±0.124)% |

With augmented data (20×) | 0.261 (±0.071)% | 0.392 (±0.102)% | 0.270 (±0.068)% | 0.437 (±0.101)% |

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**MDPI and ACS Style**

Pohlmann, S.; Mashayekh, A.; Kuder, M.; Neve, A.; Weyh, T.
Data Augmentation and Feature Selection for the Prediction of the State of Charge of Lithium-Ion Batteries Using Artificial Neural Networks. *Energies* **2023**, *16*, 6750.
https://doi.org/10.3390/en16186750

**AMA Style**

Pohlmann S, Mashayekh A, Kuder M, Neve A, Weyh T.
Data Augmentation and Feature Selection for the Prediction of the State of Charge of Lithium-Ion Batteries Using Artificial Neural Networks. *Energies*. 2023; 16(18):6750.
https://doi.org/10.3390/en16186750

**Chicago/Turabian Style**

Pohlmann, Sebastian, Ali Mashayekh, Manuel Kuder, Antje Neve, and Thomas Weyh.
2023. "Data Augmentation and Feature Selection for the Prediction of the State of Charge of Lithium-Ion Batteries Using Artificial Neural Networks" *Energies* 16, no. 18: 6750.
https://doi.org/10.3390/en16186750