# State of Health Assessment for Lithium-Ion Batteries Using Incremental Energy Analysis and Bidirectional Long Short-Term Memory

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Battery Health Status Definition

## 3. Incremental Energy Analysis

_{0}and t

_{1}represent the start and end times of CC charging phase, respectively, V denotes the voltage of the CC charging phase, and f indicates the functional relation of E and V.

## 4. BiLSTM

_{t}and ${\tilde{c}}_{t}$ are the respective outputs of the input gate and input node at time t, f

_{t}, o

_{t}, and h

_{t}denote the output of forget gate, output gate, and hidden layer at time t, respectively, C

_{t}is an intermediate storage variable that multiplies the state information of the input gate into the state space, w

_{i}, w

_{f}, w

_{c}, and w

_{o}represent the weight parameters of the input gate, forget gate, input state, and output gate, respectively, b

_{i}, b

_{f}, b

_{c}, and b

_{o}indicate the bias term of the input gate, forget gate, input state, and output gate, respectively, and tanh represents the sigmoid and hyperbolic tangent activation function.

## 5. Experimental Results and Analysis

#### 5.1. Battery Dataset

#### 5.2. The SOH Estimation Process

#### 5.3. Evaluation Metrics

^{2}are used to measure estimation performance in this work; they are respectively defined as follows:

#### 5.4. Experimental Results and Analysis

^{2}is to 1, the more accurately the model estimates the real SOH decline. In summary, the proposed method can closely estimate the battery SOH deterioration trend.

**R**.

^{2}## 6. Conclusions

^{2}values. The RMSE of the proposed method for charging rates of 0.2C and 0.1C were 0.2745% and 0.3358%, respectively; the BiLSTM model reduced the RMSE by 9.31–47.88% at 0.2C and by 14.74–36.41% at 0.1C, and the determination coefficients at 0.2C and 0.1C were 98.72% and 98.31%, respectively. In addition, the proposed BiLSTM model increased the R

^{2}value by 0.29–5.26% at 0.2C and by 0.16–4.21% at 0.1C.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The IE aging curves under two different charging rates: (

**a**) IE aging curves at 0.2C and (

**b**) IE aging curves at 0.1C.

**Figure 9.**Comparative results of SOH estimation under two different charging rates: (

**a**) 0.2C and (

**b**) 0.1C.

Charging Rate | I Peak | II Peak | III Peak | IV Peak |
---|---|---|---|---|

0.2C | 0.9723 | 0.9895 | 0.9115 | 0.9873 |

0.1C | 0.9715 | 0.9872 | 0.9566 | 0.9896 |

Specification | Value |
---|---|

Rated capacity | 2.4 Ah |

Normal voltage | 3.6 V |

Allowed voltage range | 3 V~4.2 V |

End-of-charge current | 48 mA |

Max charging/discharging current | 2400 mA/1200 mA |

Charging Rate | MAE (%) | RMSE (%) | R^{2} |
---|---|---|---|

0.2C | 0.2437 | 0.2745 | 0.9872 |

0.1C | 0.2585 | 0.3358 | 0.9831 |

Charging Rate | Estimation Method | MAE (%) | RMSE (%) | R^{2} |
---|---|---|---|---|

0.2C | BiLSTM | 0.2437 | 0.2745 | 0.9872 |

LSTM | 0.3341 | 0.4096 | 0.9764 | |

SVM | 0.3604 | 0.4724 | 0.9406 | |

ELM | 0.4183 | 0.5267 | 0.9379 | |

0.1C | BiLSTM | 0.2585 | 0.3358 | 0.9831 |

LSTM | 0.3014 | 0.3499 | 0.9421 | |

SVM | 0.2688 | 0.3348 | 0.9471 | |

ELM | 0.4415 | 0.5277 | 0.9435 |

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**MDPI and ACS Style**

Li, Y.; Luo, L.; Zhang, C.; Liu, H.
State of Health Assessment for Lithium-Ion Batteries Using Incremental Energy Analysis and Bidirectional Long Short-Term Memory. *World Electr. Veh. J.* **2023**, *14*, 188.
https://doi.org/10.3390/wevj14070188

**AMA Style**

Li Y, Luo L, Zhang C, Liu H.
State of Health Assessment for Lithium-Ion Batteries Using Incremental Energy Analysis and Bidirectional Long Short-Term Memory. *World Electric Vehicle Journal*. 2023; 14(7):188.
https://doi.org/10.3390/wevj14070188

**Chicago/Turabian Style**

Li, Yanmei, Laijin Luo, Chaolong Zhang, and Huihan Liu.
2023. "State of Health Assessment for Lithium-Ion Batteries Using Incremental Energy Analysis and Bidirectional Long Short-Term Memory" *World Electric Vehicle Journal* 14, no. 7: 188.
https://doi.org/10.3390/wevj14070188