# Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss

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## Abstract

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## 1. Introduction

## 2. LSTM Neural Network for Fault Diagnosis

#### 2.1. Structure of LSTM

- The input gate i(t), which decides whether the information can get in the memory element;
- The forget gate f(t), which decides whether the internal information needs to be forgotten;
- The output gate o(t), which decides what information can pass through the gate and get into the rest of the neural network.

_{jx}, W

_{jh}and b

_{j}, $j=g,j,f,o$ denote the input weight matrixes, hidden weight matrixes and bias vectors separately; ∗, σ and Φ are element-wise multiplications of two vectors, the sigmoid function and tanh function, respectively.

#### 2.2. Architecture of LSTM for Fault Diagnosis

## 3. Cos-LSTM

#### 3.1. Cosine Loss

#### 3.2. The Process of Cos-LSTM for Fault Diagnosis

_{2,i}for ${s}_{v1}\left(t\right)\mathrm{and}\text{}{s}_{v2}\left(t\right)$, which denote the vibration signals of the gearbox in the horizontal and vertical directions respectively.

## 4. Experimental Validation

#### 4.1. Experiment Description

#### 4.2. Experimental Results

#### 4.3. Comparison Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Item | Parameter |
---|---|

Sensor | PCB ICP 353C03 accelerometer |

Data acquisition box Software | NI cDAQ-9234 LabVIEW |

Sampling rate | 50 kHz |

Pattern Number | Faulty Component | Faulty Name | Input Speed (rpm) | Load (V) | View of the Failure |
---|---|---|---|---|---|

1 | N/A | N/A | 480, 720, 900 | 0, 10, 30 | N/A |

2 | Gear Z_{1} | Worn tooth | 480, 720, 900 | 0, 10, 30 | |

3 | Gear Z_{2} | Chafing tooth | 480, 720, 900 | 0, 10, 30 | |

4 | Gear Z_{3} | Pitting tooth | 480, 720, 900 | 0, 10, 30 | |

5 | Gear Z_{3} | Worn tooth | 480, 720, 900 | 0, 10 30 | |

6 | Gear Z_{4} | Root crack tooth | 480, 720, 900 | 0, 10, 30 | |

7 | Gear Z_{4} | Chafing tooth | 480, 720, 900 | 0, 10, 30 | |

8 | Bearing 1 | Inner race fault | 480, 720, 900 | 0, 10, 30 | |

9 | Bearing 1 | Outer race fault | 480, 720, 900 | 0, 10, 30 | |

10 | Bearing 1 | Ball fault | 480, 720, 900 | 0, 10, 30 | |

11 | House 1 | Eccentric | 480, 720, 900 | 0, 10, 30 |

Feature | Fault Diagnosis Methods | Accuracy Rate |
---|---|---|

The energy sequence | Cos-LSTM | 98.55% |

LSTM | 96.72% | |

SVM | 65.48% | |

KNN | 83.93% | |

BP neural network | 69.64% | |

Wavelet Energy entropy | Cos-LSTM | 98.08% |

Item | Parameter | Accuracy Rate |
---|---|---|

Wavelet basis function | Daubechies 3 | 98.55% |

Daubechies 2 | 96.36% | |

Haar | 93.82% | |

Symlet | 97.09% | |

Segment size | 2 | 96.63% |

3 | 97.12% | |

4 | 98.55% |

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## Share and Cite

**MDPI and ACS Style**

Yin, A.; Yan, Y.; Zhang, Z.; Li, C.; Sánchez, R.-V.
Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss. *Sensors* **2020**, *20*, 2339.
https://doi.org/10.3390/s20082339

**AMA Style**

Yin A, Yan Y, Zhang Z, Li C, Sánchez R-V.
Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss. *Sensors*. 2020; 20(8):2339.
https://doi.org/10.3390/s20082339

**Chicago/Turabian Style**

Yin, Aijun, Yinghua Yan, Zhiyu Zhang, Chuan Li, and René-Vinicio Sánchez.
2020. "Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss" *Sensors* 20, no. 8: 2339.
https://doi.org/10.3390/s20082339