# A Data-Driven Comprehensive Battery SOH Evaluation and Prediction Method Based on Improved CRITIC-GRA and Att-BiGRU

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## Abstract

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## 1. Introduction

- (1)
- Based on the characteristics of real-world EV data, basic health indicators including capacity, ohmic resistance, and maximum output power are extracted using specific methods suitable for EV application scenarios.
- (2)
- An improved criteria importance through the inter-criteria correlation (CRITIC) weighting method is introduced in order to obtain objective weights for three typical battery health indicators. These weights are then combined with the grey relational analysis (GRA) method to construct a comprehensive evaluation indicator for battery health.
- (3)
- Leveraging the advantages of bidirectional gated recurrent unit (BiGRU) and attention mechanism, an Att-BiGRU deep learning model is developed to predict the comprehensive health state of batteries.

## 2. Data Introduction and Health Indicators Extraction

#### 2.1. Data Introduction

#### 2.2. Extraction of Health Representation Indicators

#### 2.2.1. Capacity

#### 2.2.2. Ohmic Resistance

#### 2.2.3. Maximum Output Power

## 3. Methods

#### 3.1. Comprehensive Battery Health Indicator Based on Improved CRITIC and GRA

#### 3.1.1. Improved CRITIC Weighting Method

- Data normalization

- 2.
- Calculate the comparative strength of indicators based on information entropy

- 3.
- Calculate the conflict between indicators

- 4.
- Calculate the weights for each indicator

#### 3.1.2. GRA Comprehensive Evaluation Method

- Construct the evaluation matrix

- 2.
- Determine the reference sequence

- 3.
- Calculate the grey relational coefficient

- 4.
- Calculate the grey relational grade

#### 3.1.3. The Improved CRITIC-GRA Method

#### 3.2. Battery Comprehensive Health Prediction Model Based on Att-BiGRU

#### 3.2.1. Feature Extraction for Model Input

#### 3.2.2. Att-BiGRU

## 4. Results and Discussion

#### 4.1. Results of Comprehensive Battery Health Evaluation

#### 4.2. Prediction of Comprehensive Health Indicator

^{2}. With the largest RMSE and MAE, XGBoost consistently demonstrates the least accuracy among the models. Deep learning methods such as GRU, BiGRU, and especially Att-BiGRU exhibit a marked improvement in predictive accuracy compared to XGBoost. While BiGRU offers a slight advantage over GRU, the enhancement is moderate. Incorporating the attention mechanism into BiGRU significantly enhances predictive accuracy and reduces prediction errors. For Vehicle A, Att-BiGRU yields an RMSE of 0.056, representing a 32% reduction compared to BiGRU. Furthermore, Att-BiGRU’s MAE of 0.048 is 29% lower than BiGRU. For Vehicle B, the RMSE of Att-BiGRU is 0.071, which is 28% lower than BiGRU. In addition, Att-BiGRU’s MAE of 0.063 is 26% lower than BiGRU. For Vehicle C, the RMSE of Att-BiGRU is 0.070, which is 27% lower than BiGRU. In addition, Att-BiGRU’s MAE of 0.045 is 35% lower than BiGRU. Similarly, for Vehicle D, Att-BiGRU achieves an RMSE of 0.032, 29% lower than BiGRU and an MAE of 0.025, indicating a 32% improvement over BiGRU. In addition, Att-BiGRU achieves the largest R

^{2}values among all models in all four vehicles, reaching more than 0.956, which means that the prediction results fit the real curve well. Especially compared with XGBoost, the R

^{2}value has been improved by 6% on average. Hence, the employed Att-BiGRU model for comprehensive battery health indicator prediction proves to be highly effective.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Comprehensive indicator of battery health: (

**a**) Vehicle A; (

**b**) Vehicle B; (

**c**) Vehicle C; (

**d**) Vehicle D.

**Figure 9.**Prediction results of Att-BiGRU model: (

**a**) Vehicle A; (

**b**) Vehicle B; (

**c**) Vehicle C; (

**d**) Vehicle D.

Parameter | Value |
---|---|

Cathode material | LiFePO_{4} |

Battery capacity | 240 Ah |

Driving range | 300 km |

Motor power | 100 kW |

Curb weight | 8500 kg |

Number | Feature | Number | Feature |
---|---|---|---|

F1 | Accumulated mileage | F6 | Charging start voltage |

F2 | Temperature | F7 | Charging end voltage |

F3 | Charging start SOC | F8 | Charging voltage difference |

F4 | Charging end SOC | F9 | Maximum charging current |

F5 | Charging SOC difference | F10 | Average charging current |

Vehicle | Capacity | Resistance | Power |
---|---|---|---|

A | 0.38 | 0.41 | 0.21 |

B | 0.34 | 0.48 | 0.18 |

C | 0.53 | 0.21 | 0.26 |

D | 0.54 | 0.24 | 0.22 |

Model | A | B | C | D | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | |

XGB | 0.132 | 0.097 | 0.924 | 0.205 | 0.150 | 0.910 | 0.214 | 0.128 | 0.908 | 0.116 | 0.081 | 0.927 |

GRU | 0.094 | 0.072 | 0.942 | 0.107 | 0.088 | 0.928 | 0.106 | 0.081 | 0.933 | 0.087 | 0.067 | 0.945 |

BiGRU | 0.082 | 0.068 | 0.951 | 0.098 | 0.085 | 0.937 | 0.096 | 0.069 | 0.949 | 0.045 | 0.037 | 0.972 |

Att-BiGRU | 0.056 | 0.048 | 0.973 | 0.071 | 0.063 | 0.956 | 0.070 | 0.045 | 0.971 | 0.032 | 0.025 | 0.985 |

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**MDPI and ACS Style**

Liu, P.; Liu, C.; Wang, Z.; Wang, Q.; Han, J.; Zhou, Y.
A Data-Driven Comprehensive Battery SOH Evaluation and Prediction Method Based on Improved CRITIC-GRA and Att-BiGRU. *Sustainability* **2023**, *15*, 15084.
https://doi.org/10.3390/su152015084

**AMA Style**

Liu P, Liu C, Wang Z, Wang Q, Han J, Zhou Y.
A Data-Driven Comprehensive Battery SOH Evaluation and Prediction Method Based on Improved CRITIC-GRA and Att-BiGRU. *Sustainability*. 2023; 15(20):15084.
https://doi.org/10.3390/su152015084

**Chicago/Turabian Style**

Liu, Peng, Cheng Liu, Zhenpo Wang, Qiushi Wang, Jinlei Han, and Yapeng Zhou.
2023. "A Data-Driven Comprehensive Battery SOH Evaluation and Prediction Method Based on Improved CRITIC-GRA and Att-BiGRU" *Sustainability* 15, no. 20: 15084.
https://doi.org/10.3390/su152015084