# State-of-Health Estimate for the Lithium-Ion Battery Using Chi-Square and ELM-LSTM

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## Abstract

**:**

## 1. Introduction

## 2. SOH Definition

## 3. Chi-Squared Statistic

## 4. ELM-LSTM Algorithm

#### 4.1. LSTM Neural Network

#### 4.2. ELM Neural Network

#### 4.3. Integrated Approach for the ELM and LSTM Neural Network

- (1)
- Divide the acquired lithium-ion battery aging data into preliminary modelling training set, integrated modelling training set and testing set.
- (2)
- Initialize the ELM and LSTM neural network parameters, randomly.
- (3)
- Based on the preliminary modelling training set, the initial lithium-ion battery SOH estimation models are constructed using ELM and LSTM, respectively.
- (4)
- Calculate the output error series of the preliminary lithium-ion battery SOH estimation model based on the integrated modelling training set, and then obtain the standard deviation of the error series.
- (5)
- Establish the integrated estimation model of lithium-ion battery SOH, and the output weights of LSTM and ELM are calculated by Equations (14) and (15), respectively.

## 5. Experiment Process, Results and Discussions

#### 5.1. Experiment Data

#### 5.2. Experiment Procedure

- (1)
- Calculate the chi-squared statistic of voltage and mean temperature in each charging stage to reflect the capacity loss, and then the SOH data of the batteries are obtained after each discharge stage.
- (2)
- Divide the processed data into preliminary modelling training set, integrated modelling training data and testing set. In this work, the preliminary modelling training set, integrated modelling training data and testing set are divided according to 1:1:2 of the measured data
- (3)
- Based on the preliminary modelling training data, ELM and LSTM neural network, respectively, used for the preliminary modelling.
- (4)
- Establish the integrated SOH estimation model for the lithium-ion battery based on the standard deviation of the error series, which is produced by the preliminary model with the integrated modelling training set as input.
- (5)
- Generate the estimated battery SOH based on the testing data.

#### 5.3. Experiment Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 7.**Estimation results of the comparative experiment, (

**a**) Battery 5, (

**b**) Battery 6, (

**c**) Battery pack.

**Figure 8.**Estimation errors of the comparative experiment, (

**a**) Battery 5, (

**b**) Battery 6, (

**c**) Battery pack.

Case | Proposed Method | ELM Neural Network | LSTM Neural Network | BP Neural Network | ||||
---|---|---|---|---|---|---|---|---|

AE (%) | ME (%) | AE (%) | AE (%) | ME (%) | ME (%) | AE (%) | ME (%) | |

Battery 5 | 0.95 | 1.17 | 1.85 | 1.22 | 1.41 | 2.45 | 2.40 | 3.29 |

Battery 6 | 0.97 | 1.19 | 1.80 | 1.37 | 1.77 | 2.3 | 2.34 | 3.26 |

Battery pack | 0.97 | 1.86 | 2.04 | 2.41 | 1.06 | 1.73 | 2.43 | 3.37 |

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**MDPI and ACS Style**

Jiang, J.; Zhao, S.; Zhang, C.
State-of-Health Estimate for the Lithium-Ion Battery Using Chi-Square and ELM-LSTM. *World Electr. Veh. J.* **2021**, *12*, 228.
https://doi.org/10.3390/wevj12040228

**AMA Style**

Jiang J, Zhao S, Zhang C.
State-of-Health Estimate for the Lithium-Ion Battery Using Chi-Square and ELM-LSTM. *World Electric Vehicle Journal*. 2021; 12(4):228.
https://doi.org/10.3390/wevj12040228

**Chicago/Turabian Style**

Jiang, Jianfeng, Shaishai Zhao, and Chaolong Zhang.
2021. "State-of-Health Estimate for the Lithium-Ion Battery Using Chi-Square and ELM-LSTM" *World Electric Vehicle Journal* 12, no. 4: 228.
https://doi.org/10.3390/wevj12040228