# Design of an Improved Remaining Useful Life Prediction Model Based on Vibration Signals of Wind Turbine Rotating Components

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## Abstract

**:**

## 1. Introduction

## 2. Building a Health Index

#### 2.1. Data Description

#### 2.2. Health Index of Bearing

#### 2.2.1. Feature Extraction

- Feature Extraction in Time Domain

- b.
- Feature Extraction in Frequency Domain

#### 2.2.2. Choosing the Right Features

#### 2.2.3. PCA-Based HI Construction

#### 2.2.4. Outlier Region Correction

- ${h}_{{t}_{c}}^{i}$ is new HI when removing the outliers region
- ${h}_{{t}_{s}}^{c}$ is HI at the time ${t}_{s}$ when the outlier region begins to appear.
- ${h}_{{t}_{e}}^{c}$ is HI at the time ${t}_{e}$ at the end of the exception region

## 3. Designing a RUL Prediction Model Based on the HI

#### 3.1. Similarity Models

#### 3.2. Degradation Models

^{2}.

#### 3.3. RUL Prediction Results

- Similarity Models

- b.
- Degradation Models

- c.
- Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

COE | Cost of Energy |

IMS | Intelligent Maintenance Systems |

IAE | International Energy Agency |

IEA | International Energy Agency |

RUL | Remaining Useful Life |

HI | Health Index |

PCA | Principal Component Analysis |

LSTM | Long Short-term Memory |

RMS | Root Mean Square |

SVM | Support Vector Machine |

RNN | Recurrent Neural Networks |

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**Figure 2.**Indices performance metrics: (

**a**) Monotonicity; (

**b**) robustness; (

**c**) correlation; (

**d**) 0.5 Mon + 0.25 Corr + 0.25 Rob.

Case | Recording Duration | No. of Files | Description |
---|---|---|---|

Set No. 1 | 22 October 2003 12:06:24 to 25 November 2003 23:39:56 | 2156 (8 channels) | At the end of the test-to-failure experiment, inner race defect occurred in bearing 3 and roller element defect in bearing 4. |

Set No. 2 | 12 February 2004 10:32:39 to 19 February 2004 06:22:39 | 984 (4 channels) | At the end of the test-to-failure experiment, outer race failure occurred in bearing 1 |

Set No. 3 | 4 March 2004 09:27:46 to 4 April 2004 19:01:57 | 4448 (4 channels) | At the end of the test-to-failure experiment, outer race failure occurred in bearing 3 |

Feature | Formula |
---|---|

Mean | $\overline{y}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{y}_{i}$ |

Standard deviation | $\sigma ={\left(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left({y}_{i}-\overline{y}\right)\right)}^{\frac{1}{2}}$ |

Skewness | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\frac{{\left({y}_{i}-\overline{y}\right)}^{3}}{{\rho}^{3}}$ |

Kurtosis | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\frac{{\left({y}_{i}-\overline{y}\right)}^{4}}{{\rho}^{4}}$ |

Peak to Peak | ${y}_{max}-{y}_{min}$ |

Root mean square (RMS) | $RMS{=\left(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{{y}_{i}}^{2}\right)}^{\frac{1}{2}}$ |

Crest factor | $\frac{{y}_{max}}{RMS}$ |

Shape factor | $\frac{RMS}{\frac{1}{N}\sum _{i=1}^{N}\left|{y}_{i}\right|}$ |

Impulse factor | $\frac{{y}_{max}}{\frac{1}{N}\sum _{i=1}^{N}\left|{y}_{i}\right|}$ |

Margin factor | $\frac{{y}_{max}}{{\left(\frac{1}{N}\sum _{i=1}^{N}\left|{y}_{i}\right|\right)}^{2}}$ |

Energy | $\sum _{i=1}^{N}}{{y}_{i}}^{2$ |

AI Model | Parameters |
---|---|

AI model node | 1024 LSTM |

Activation function | Sigmoid |

Epoch | 100 |

Batch size | 120 |

Optimizer | Adam |

Drop output | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Le, T.-T.; Lee, S.-J.; Dinh, M.-C.; Park, M.
Design of an Improved Remaining Useful Life Prediction Model Based on Vibration Signals of Wind Turbine Rotating Components. *Energies* **2024**, *17*, 19.
https://doi.org/10.3390/en17010019

**AMA Style**

Le T-T, Lee S-J, Dinh M-C, Park M.
Design of an Improved Remaining Useful Life Prediction Model Based on Vibration Signals of Wind Turbine Rotating Components. *Energies*. 2024; 17(1):19.
https://doi.org/10.3390/en17010019

**Chicago/Turabian Style**

Le, Thi-Tinh, Seok-Ju Lee, Minh-Chau Dinh, and Minwon Park.
2024. "Design of an Improved Remaining Useful Life Prediction Model Based on Vibration Signals of Wind Turbine Rotating Components" *Energies* 17, no. 1: 19.
https://doi.org/10.3390/en17010019