# State of Health Estimation Based on the Long Short-Term Memory Network Using Incremental Capacity and Transfer Learning

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Data Preprocessing

#### 2.1. Data Acquisition

#### 2.2. Increment Capacity Curve Analysis

^{2}(R) with zero bases, the DWT can be defined as:

## 3. Methodologies

#### 3.1. Grey Relation Analysis

_{i}(k) between x

_{i}(k) and y

_{i}(k):

_{i}between reference sequence Y and comparison sequence x

_{i}is calculated:

_{i}∈ [0, 1], the closer the correlation degree r

_{i}is to 1, the greater the correlation between X

_{i}and Y.

#### 3.2. Long Short-Term Memory Modeling

_{t}is the input data comprised of increment capacity curve peak and corresponding voltage, subscript t indicates the time step, among them, i, f, and o are three gates, representing input gate, forgetting gate, and output gate, respectively. Long short-term memory can voluntarily add or forget information through the input gate and forget gate, W, b are the weights and biases. The activation function is represented as σ, The sigmoid function is often used to adjust its output value and limit it to values between 0 and 1. When generating candidate memory, the activation function selects tanh to accelerate the convergence of the model. The battery SOH estimation model based on LSTM in this article is based on TensorFlow in Python, which is a commonly used deep learning framework.

## 4. Results and Discussion

#### 4.1. Model Training Structure

#### 4.2. Estimation Results of the Model

#### 4.3. Estimation Results of the Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Battery aging process and discharge voltage variation: (

**a**) capacity attenuation curve; (

**b**) voltage variation of the aging cycle schemes follow another format.

**Figure 3.**ICA curves after different wavelet filtering. (

**a**) Layers:5, wave:sym6. (

**b**) Layers:5, wave:db4. (

**c**) Layers:6, wave:sym6. (

**d**) Layers:6, wave:db4. (

**e**) Layers:7, wave:sym6. (

**f**) Layers:7, wave:db4.

**Figure 5.**LSTM for 5# and 6# batteries (

**a**–

**c**). The predicted results of different features for 5#. (

**d**) The loss of battery 5# (

**e**–

**g**). The predicted results of different features for 6# (

**h**). The loss of battery 6#.

**Figure 6.**LSTM for 7# and 18# batteries (

**a**–

**c**). The predicted results of different features for 7# (

**d**). The loss of battery 7# (

**e**–

**g**). The predicted results of different features for 18# (

**h**). The loss of battery 18#.

**Figure 7.**Transform learning for 6# battery (

**a**–

**c**). The predicted results of different features for 6# (

**d**). The loss of battery 6#.

**Figure 8.**Transfer learning on the Mendeley dataset. (

**a**) 80% of the training data. (

**b**) 70% of the training data. (

**c**) 60% of the training data. (

**d**) 50% of the training data.

Battery Number | Discharge Current | Voltage Upper | Voltage Lower |
---|---|---|---|

B0005 | 2 A | 4.2 V | 2.7 V |

B0006 | 2 A | 4.2 V | 2.5 V |

B0007 | 2 A | 4.2 V | 2.2 V |

B0018 | 2 A | 4.2 V | 2.2 V |

Battery Number | Grey Relation Coefficient | |||||
---|---|---|---|---|---|---|

F1 | F2 | F3 | F4 | F5 | F6 | |

5# | 0.7815 | 0.8009 | 0.5735 | 0.7184 | 0.8036 | 0.7674 |

6# | 0.7842 | 0.8074 | 0.5109 | 0.8081 | 0.7506 | 0.6611 |

7# | 0.8161 | 0.8151 | 0.5519 | 0.6642 | 0.8308 | 0.8235 |

18# | 0.8361 | 0.8459 | 0.6090 | 0.7801 | 0.8506 | 0.7799 |

Parameters | Value |
---|---|

Number of units in the LSTM 1 | 75 |

Number of units in the LSTM 2 | 80 |

Dense | 25 |

Dropout | 0.5 |

Dense | 1 |

B0005 | B0006 | |||||
---|---|---|---|---|---|---|

LSTM 4F | LSTM ICA | LSTM 2F | LSTM 4F | LSTM ICA | LSTM 2F | |

RMSE | 0.0212 | 0.0183 | 0.0162 | 0.0399 | 0.0496 | 0.0435 |

MAE | 0.0173 | 0.0149 | 0.0124 | 0.0352 | 0.0390 | 0.0328 |

B0007 | B00018 | |||||
---|---|---|---|---|---|---|

LSTM 4F | LSTM ICA | LSTM 2F | LSTM 4F | LSTM ICA | LSTM 2F | |

RMSE | 0.0198 | 0.0185 | 0.0148 | 0.0229 | 0.0168 | 0.0206 |

MAE | 0.0167 | 0.0124 | 0.0111 | 0.0194 | 0.0137 | 0.0174 |

Train Scale (%) | RMSE | MAE |
---|---|---|

80 | 0.0174 | 0.0146 |

70 | 0.0269 | 0.0236 |

60 | 0.0319 | 0.0208 |

50 | 0.0381 | 0.0248 |

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**MDPI and ACS Style**

Yao, L.; Wen, J.; Xu, S.; Zheng, J.; Hou, J.; Fang, Z.; Xiao, Y.
State of Health Estimation Based on the Long Short-Term Memory Network Using Incremental Capacity and Transfer Learning. *Sensors* **2022**, *22*, 7835.
https://doi.org/10.3390/s22207835

**AMA Style**

Yao L, Wen J, Xu S, Zheng J, Hou J, Fang Z, Xiao Y.
State of Health Estimation Based on the Long Short-Term Memory Network Using Incremental Capacity and Transfer Learning. *Sensors*. 2022; 22(20):7835.
https://doi.org/10.3390/s22207835

**Chicago/Turabian Style**

Yao, Lei, Jishu Wen, Shiming Xu, Jie Zheng, Junjian Hou, Zhanpeng Fang, and Yanqiu Xiao.
2022. "State of Health Estimation Based on the Long Short-Term Memory Network Using Incremental Capacity and Transfer Learning" *Sensors* 22, no. 20: 7835.
https://doi.org/10.3390/s22207835