# A Bearing Fault Diagnosis Method Based on Wavelet Packet Transform and Convolutional Neural Network Optimized by Simulated Annealing Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Data Set Description

## 3. The Proposed Bearing Fault Diagnosis Method

#### 3.1. Feature Extraction Based on Wavelet Packet Transform

#### 3.2. Fault Classification Based on a Convolutional Neural Network

#### 3.2.1. Convolutional Layer

#### 3.2.2. Activation Function

#### 3.2.3. Pooling Layer

#### 3.2.4. Fully Connected Layer

#### 3.2.5. Fault Classification

#### 3.3. Optimization Based on Simulated Annealing Algorithm

## 4. Analysis of Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Schematic diagram of the method presented in this paper. First, input the original signal with a length of 400, perform wavelet packet transformation, and obtain a spectrogram. The obtained spectrogram is then used as a training data set and sent to the convolutional neural network. Finally, the simulated annealing algorithm is used to adjust the parameters of the convolutional neural network.

**Figure 5.**WPT decomposition tree structure [34].

**Figure 12.**Convolutional neural network structure used in the experiment (partial) [25].

Class | Name | Samples | Distribution | Description |
---|---|---|---|---|

1 | normal_FE_1 | 846 | 22.2% | normal, 1 hp load |

2 | normal_DE_2 | 846 | 22.2% | normal, 2 hp load |

3 | Inner_FE_1_007 | 212 | 5.56% | 0.007’’, 1 hp load |

4 | Inner_DE_1_007 | 212 | 5.56% | 0.007’’, 1 hp load |

5 | Ball_FE_1_007 | 211 | 5.53% | 0.007’’, 1 hp load |

6 | Ball_DE_1_007 | 211 | 5.53% | 0.007’’, 1 hp load |

7 | Outer_FE_1_007 | 212 | 5.56% | 0.007’’, 1 hp load |

8 | Outer_DE_1_007 | 212 | 5.56% | 0.007’’, 1 hp load |

9 | Inner_FE_1_014 | 212 | 5.56% | 0.014’’, 1 hp load |

10 | Inner_FE_2_014 | 212 | 5.56% | 0.014’’, 2 hp load |

11 | Inner_DE_2_028 | 212 | 5.56% | 0.028’’, 2 hp load |

12 | Inner_DE_3_028 | 212 | 5.56% | 0.028’’, 3 hp load |

**Table 2.**Experimental omparison. The experimental results come from the implementation of the existing methods. On the machine equipped with GTX 1660TI, the matlab neural network toolbox is used to conduct multiple experiments, and the average value is obtained to obtain the result.

Class | Method | Sample Number | Accuracy(%) |
---|---|---|---|

1 | SVM | 1000 | 16.67 |

2 | BP | 1000 | 81.31 |

3 | EMD+CNN | 1000 | 66.76 |

4 | EMD+SVM | 1000 | 51.32 |

5 | EMD+BP | 1000 | 87.53 |

6 | WPT+CNN | 1000 | 92.13 |

7 | WPT+CNN+SA | 1000 | 97.12 |

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**MDPI and ACS Style**

He, F.; Ye, Q.
A Bearing Fault Diagnosis Method Based on Wavelet Packet Transform and Convolutional Neural Network Optimized by Simulated Annealing Algorithm. *Sensors* **2022**, *22*, 1410.
https://doi.org/10.3390/s22041410

**AMA Style**

He F, Ye Q.
A Bearing Fault Diagnosis Method Based on Wavelet Packet Transform and Convolutional Neural Network Optimized by Simulated Annealing Algorithm. *Sensors*. 2022; 22(4):1410.
https://doi.org/10.3390/s22041410

**Chicago/Turabian Style**

He, Feng, and Qing Ye.
2022. "A Bearing Fault Diagnosis Method Based on Wavelet Packet Transform and Convolutional Neural Network Optimized by Simulated Annealing Algorithm" *Sensors* 22, no. 4: 1410.
https://doi.org/10.3390/s22041410