# A Novel Method for Multistage Degradation Predicting the Remaining Useful Life of Wind Turbine Generator Bearings Based on Domain Adaptation

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- RUL prediction methods for WT generator bearings under composite working conditions are proposed, which utilizes TCN with local enhanced residual module to extract temporal features and unsupervised K-means to partition the degradation status of generator bearings.
- (2)
- Aiming at the problem that the prediction accuracy of the full life data of WT generator bearings is affected by the cross-fusion working conditions, the MDSDM module is proposed, which can reduce the influence of composite working conditions on the model and help the model learn the degradation features independent of working conditions.
- (3)
- In view of the different degradation trends of WT generator bearings caused by working conditions, fault types, and other reasons, the DA module is added to the model to improve the prediction accuracy of the model in the target domain bearings.

## 2. Description of the Datasets and Data Preprocessing

#### 2.1. Description of the Datasets

#### 2.2. Data Preprocessing

#### 2.3. HI Construction

**Y**is the fitting vector,

**A**is the coefficient matrix,

**X**is the independent variable matrix, and

**E**is the residual. The above equation can usually be solved by using the least square method.

## 3. The Proposed New Method MDA-LETCN

#### 3.1. Temporal Feature Extraction Module

- Causal dilated convolutions

_{t}

_{+1}. The formula is:

#### 3.2. Multistage Degradation State Division

#### 3.3. Multistage Degradation Stage Distribution Matching (MDSDM)

_{i}and D

_{j}of different degradation stages, the loss of MDSDM is:

#### 3.4. Domain Adaptation

#### 3.5. RUL Prediction

_{s}is the number of source domain. The target domain is ${D}^{T}=\left({\mathit{x}}_{1}^{t},{\mathit{x}}_{2}^{t},\cdots ,{\mathit{x}}_{{n}_{t}^{\prime}}^{t}\right)$, ${n}_{t}^{\prime}$ is the number of health-state data that the target domain participates in training, and ${\mathit{x}}_{n}^{s}$ and ${\mathit{x}}_{n}^{t}$ both contain 11 features. D

^{S}and D

^{T}together form the training set, with the remaining samples from the target domain used as the test set.

## 4. Case Studies

#### 4.1. Parameter Settings

#### 4.2. Results of Degradation State Divided and Prediction RUL

#### 4.3. Ablation Experiment

#### 4.4. Comparison with Other Methods

## 5. Conclusions

- (1)
- MDA-LETCN can effectively extract the degradation features of WT generator bearings from the run-to-failure data under composite working conditions and introduce DA to effectively improve the model’s prediction performance of target bearing RUL based on the differences in the degradation processes of each bearing. Through comparative experiments on the generator bearing data of WTs, the methods proposed in this paper, RMS, and MAE have the smallest and the highest scores, which are superior to the comparative methods.
- (2)
- In MDA-LETCN, unsupervised clustering is carried out on the extracted temporal features to adaptively classify the degradation state of generator bearings under composite working conditions, which can effectively improve the prediction effect of the model.
- (3)
- The MDSDM module measures and minimizes the distribution differences in different degradation stages, which can help the model learn the domain-invariant time-dependent features in different degradation stages. Ablation experiments have proved that the MDSDM module can effectively improve the prediction accuracy of the model under composite working conditions.

- (1)
- MDA-LETCN is a data-driven black-box model and, in our future work, we plan to introduce the mechanism model into the network to enhance the interpretability of the model.
- (2)
- Due to data reasons, this paper only studies the transfer learning prediction between NU1030M bearings. In future work, transfer learning tasks between different types of bearings will be studied to improve the robustness of the model.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**SRMS curves are obtained from different parameters in SG: (

**a**) m = 5, k = 2; (

**b**) m = 15, k = 2; (

**c**) m = 25, k = 2; (

**d**) m = 30, k = 2; (

**e**) m = 35, k = 2; (

**f**) m = 45, k = 2; (

**g**) m = 25, k = 3; (

**h**) m = 30, k = 3; (

**i**) m = 30, k = 4.

Features | Equations | Features | Equations |
---|---|---|---|

Peak | $T{F}_{1}=\mathrm{max}\left|{x}_{t}\right|$ | Kurtosis | $T{F}_{7}=\frac{1}{T\cdot T{F}_{5}^{4}}{\displaystyle \sum _{t=1}^{T}{\left({x}_{t}-T{F}_{2}\right)}^{4}}$ |

Mean absolute value | $T{F}_{2}=\frac{1}{T}{\displaystyle \sum _{t=1}^{T}\left|{x}_{t}\right|}$ | Square root amplitude | $T{F}_{8}={\left(\frac{1}{T}{\displaystyle \sum _{t=1}^{T}\sqrt{\left|{x}_{t}\right|}}\right)}^{2}$ |

Peak to peak | $T{F}_{3}=\mathrm{max}\left({x}_{t}\right)-\mathrm{min}\left({x}_{t}\right)$ | Crest factor | $T{F}_{9}=\frac{T{F}_{1}}{T{F}_{4}}$ |

Root mean square(RMS) | $T{F}_{4}=\sqrt{\frac{1}{T}{\displaystyle \sum _{t=1}^{T}{x}_{t}^{2}}}$ | Clearance factor | $T{F}_{10}=\frac{T{F}_{1}}{T{F}_{8}}$ |

Standard deviation | $T{F}_{5}=\sqrt{\frac{1}{T-1}{\displaystyle \sum _{t=1}^{T}{\left({x}_{t}-T{F}_{2}\right)}^{2}}}$ | Impulse factor | $T{F}_{11}=\frac{T{F}_{1}}{T{F}_{2}}$ |

Skewness | $T{F}_{6}=\frac{1}{T\cdot T{F}_{5}^{3}}{\displaystyle \sum _{t=1}^{T}{\left({x}_{t}-T{F}_{2}\right)}^{3}}$ | Shape factor | $T{F}_{12}=\frac{T{F}_{4}}{T{F}_{2}}$ |

Task | Source | Target |
---|---|---|

Task1 | 10# | 19# |

Task2 | 10# | 21# |

Task3 | 19# | 10# |

Task4 | 19# | 21# |

Task5 | 21# | 10# |

Task6 | 21# | 19# |

LETCN + MDSDM | LETCN + DA | TCN + MDSDM + DA | MDA-LETCN | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | Score | RMSE | MAE | Score | RMSE | MAE | Score | RMSE | MAE | Score | |

Task1 | 0.154 | 0.145 | 0.307 | 0.148 | 0.127 | 0.238 | 0.122 | 0.108 | 0.304 | 0.063 | 0.048 | 0.494 |

Task2 | 0.127 | 0.118 | 0.275 | 0.176 | 0.143 | 0.201 | 0.127 | 0.114 | 0.353 | 0.077 | 0.066 | 0.399 |

Task3 | 0.177 | 0.159 | 0.278 | 0.139 | 0.124 | 0.256 | 0.119 | 0.095 | 0.411 | 0.056 | 0.044 | 0.554 |

Task4 | 0.167 | 0.144 | 0.233 | 0.181 | 0.169 | 0.198 | 0.164 | 0.137 | 0.301 | 0.084 | 0.068 | 0.403 |

Task5 | 0.159 | 0.136 | 0.254 | 0.172 | 0.158 | 0.224 | 0.157 | 0.135 | 0.396 | 0.069 | 0.056 | 0.545 |

Task6 | 0.154 | 0.139 | 0.273 | 0.153 | 0.136 | 0.191 | 0.124 | 0.123 | 0.388 | 0.064 | 0.052 | 0.475 |

Average | 0.154 | 0.145 | 0.307 | 0.162 | 0.143 | 0.218 | 0.136 | 0.119 | 0.359 | 0.069 | 0.056 | 0.478 |

CLSTM | VLSTM-LWSAN | TLHAM | MTSTAN | MDA-LETCN | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | Score | RMSE | MAE | Score | RMSE | MAE | Score | RMSE | MAE | Score | RMSE | MAE | Score | |

Task1 | 0.247 | 0.229 | 0.105 | 0.202 | 0.184 | 0.208 | 0.181 | 0.165 | 0.234 | 0.231 | 0.217 | 0.138 | 0.063 | 0.048 | 0.494 |

Task2 | 0.243 | 0.212 | 0.112 | 0.165 | 0.143 | 0.243 | 0.169 | 0.147 | 0.282 | 0.194 | 0.177 | 0.194 | 0.077 | 0.066 | 0.399 |

Task3 | 0.233 | 0.209 | 0.147 | 0.191 | 0.177 | 0.258 | 0.172 | 0.153 | 0.279 | 0.205 | 0.195 | 0.151 | 0.056 | 0.044 | 0.554 |

Task4 | 0.227 | 0.201 | 0.162 | 0.142 | 0.136 | 0.267 | 0.155 | 0.140 | 0.301 | 0.166 | 0.152 | 0.216 | 0.084 | 0.068 | 0.403 |

Task5 | 0.235 | 0.214 | 0.131 | 0.189 | 0.168 | 0.242 | 0.176 | 0.144 | 0.265 | 0.186 | 0.163 | 0.180 | 0.069 | 0.056 | 0.545 |

Task6 | 0.215 | 0.199 | 0.188 | 0.137 | 0.119 | 0.261 | 0.164 | 0.151 | 0.299 | 0.178 | 0.154 | 0.234 | 0.064 | 0.052 | 0.475 |

Average | 0.233 | 0.211 | 0.141 | 0.171 | 0.155 | 0.247 | 0.170 | 0.150 | 0.277 | 0.193 | 0.176 | 0.186 | 0.069 | 0.056 | 0.478 |

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## Share and Cite

**MDPI and ACS Style**

Tian, M.; Su, X.; Chen, C.; An, W.
A Novel Method for Multistage Degradation Predicting the Remaining Useful Life of Wind Turbine Generator Bearings Based on Domain Adaptation. *Appl. Sci.* **2023**, *13*, 12332.
https://doi.org/10.3390/app132212332

**AMA Style**

Tian M, Su X, Chen C, An W.
A Novel Method for Multistage Degradation Predicting the Remaining Useful Life of Wind Turbine Generator Bearings Based on Domain Adaptation. *Applied Sciences*. 2023; 13(22):12332.
https://doi.org/10.3390/app132212332

**Chicago/Turabian Style**

Tian, Miao, Xiaoming Su, Changzheng Chen, and Wenjie An.
2023. "A Novel Method for Multistage Degradation Predicting the Remaining Useful Life of Wind Turbine Generator Bearings Based on Domain Adaptation" *Applied Sciences* 13, no. 22: 12332.
https://doi.org/10.3390/app132212332