# An Optimized Random Forest Regression Model for Li-Ion Battery Prognostics and Health Management

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## Abstract

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## 1. Introduction

#### 1.1. Review of the Methods for SOH

#### 1.1.1. Direct Measurement

#### 1.1.2. Model-Based Methods

#### 1.1.3. Data-Driven Methods

#### 1.2. Review of the Methods for RUL

#### 1.2.1. Model-Based Methods

#### 1.2.2. Data-Driven Methods

#### 1.3. Contribution of the Paper

## 2. Aging Features for SOH and RUL

#### 2.1. Battery Aging Datasets and Aging Features

#### 2.2. The Extrapolation of the Aging Features

## 3. Methodologies

#### 3.1. Random Forest Regression Optimization Model

#### 3.2. Bayesian Optimization

Algorithm 1: Bayesian optimization |

for n=1, 2, …, doselect new x _{n+1} by optimizing acquisition function α${x}_{n+1}=\mathrm{arg}\underset{x}{{\displaystyle}}\mathrm{max}\alpha (x;{D}_{n})$ query objective function to obtain y _{n+1}$\mathrm{augment}\text{}\mathrm{data}\text{}{D}_{n+1}=\left\{{D}_{n},({x}_{n+1},{y}_{n+1})\right\}$ update statistical model end for |

#### 3.3. The Flowchart for SOH and RUL

## 4. Results and Discussion

#### 4.1. SOH Estimation

#### 4.2. RUL Prediction

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

EV | Electric vehicle |

PHM | Prognostics and health management |

SOH | State of health |

RUL | Remaining useful life |

EM | Electrochemical model |

ECM | Equivalent circuit model |

PF | Particle filter |

SOC | State of charge |

EKF | Extended Kalman filter |

AF | Aging feature |

BO | Bayesian optimization |

BMS | Battery management system |

RF | Random forest |

SVR | Support vector regression |

EIS | Electrochemical impedance spectroscopy |

RVM | Relevance vector machine |

ELM | Extreme learning machine |

ICC | Incremental capacity curve |

ICA | Incremental capacity analysis |

PSO | Particle swarm optimization |

LOWESS | Locally weighted scatterplot smoothing |

PICC | Peak of the incremental capacity curve |

CCEV | Charged capacity of equal voltage |

BPNN | Back propagation neural networks |

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Index | MAE (%) | RMSE |
---|---|---|

CS 35 | 1.0379 | 0.4185 |

CS 37 | 2.5925 | 1.0976 |

Mean | 1.8152 | 0.7581 |

Index | MAE (Cycle) | RMSE |
---|---|---|

CS 35 | 32 | 20.3961 |

CS 37 | 32 | 29.3198 |

Mean | 32 | 24.8580 |

Batteries | Index | Mean MAE | Mean RMSE |
---|---|---|---|

BPNN | SOH estimation | 2.6138 | 1.0838 |

RUL prediction | 33.5 | 28.2835 | |

SVM | SOH estimation | 3.1786 | 1.3333 |

RUL prediction | 33.5 | 33.5 | |

RF | SOH estimation | 2.7293 | 1.1627 |

RUL prediction | 33.5 | 30.6125 |

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## Share and Cite

**MDPI and ACS Style**

Wang, G.; Lyu, Z.; Li, X.
An Optimized Random Forest Regression Model for Li-Ion Battery Prognostics and Health Management. *Batteries* **2023**, *9*, 332.
https://doi.org/10.3390/batteries9060332

**AMA Style**

Wang G, Lyu Z, Li X.
An Optimized Random Forest Regression Model for Li-Ion Battery Prognostics and Health Management. *Batteries*. 2023; 9(6):332.
https://doi.org/10.3390/batteries9060332

**Chicago/Turabian Style**

Wang, Geng, Zhiqiang Lyu, and Xiaoyu Li.
2023. "An Optimized Random Forest Regression Model for Li-Ion Battery Prognostics and Health Management" *Batteries* 9, no. 6: 332.
https://doi.org/10.3390/batteries9060332