# Rolling Bearing Incipient Fault Diagnosis Method Based on Improved Transfer Learning with Hybrid Feature Extraction

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries and Methods

#### 2.1. Domain Adaptation Algorithm CORAL

Algorithm 1 CORAL for Unsupervised Domain Adaptation |

Input: Data of Source Domain ${D}_{S}$, Data of Target Domain ${D}_{T}$ |

Output: Data of Adjusted Source ${D}_{s}^{\ast}$ |

${C}_{S}$ = $cov\left({D}_{S}\right)+eye\left(size({D}_{S},2)\right)$ |

${C}_{T}$ = $cov\left({D}_{T}\right)+eye\left(size({D}_{T},2)\right)$ |

${D}_{S}$ = ${D}_{S}\ast {C}_{S}^{\frac{-1}{2}}$ |

${D}_{S}^{\ast}$ = ${D}_{S}\ast {C}_{T}^{\frac{1}{2}}$ |

#### 2.2. Feature Extraction

#### 2.2.1. Time and Frequency Domain Analysis

#### 2.2.2. Wavelet Scattering Network

#### 2.2.3. Stacked Auto-Encoder Network

_{2}regularization term, and the sparsity regularization term, as shown below:

#### 2.3. Geodesic Flow Kernel

#### 2.4. K Nearest Neighbor Classification

## 3. Experiments and Results

#### 3.1. Data Description

#### 3.2. Experiment Results and Analysis

- (a)
- Effect of Domain Adaptation

- (b)
- Effect of Feature Extraction

- (c)
- Effect of Sigmoid Entropy

- (d)
- Effect of Neighbor Number

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The process of CORAL algorithm: (

**a**) the original data distributions of source domain and target domain; (

**b**) the data distribution of source domain after decorrelation; (

**c**) the data distribution of source domain after re-correlation using covariance of target domain.

**Figure 6.**The structure of SAE: (

**a**) the structure of the first SAE (the encoder output is the input of second SAE in (

**b**)); (

**b**) the structure of the second SAE.

**Figure 8.**Vibration signals of two faults and non-fault in time-domain: (

**a**) vibration signal of inner race wearing in time-domain; (

**b**) vibration signal of outer race wearing in time-domain; (

**c**) vibration signal of normal bearing in time-domain.

Source Domain | Target Domain | |
---|---|---|

Working Conditions | 1797 | 2250 |

Sample Numbers | 600 | 900 |

Vibration Signals in Each Sample | 500 | 500 |

Fault Type | inner race and outer race wearing | Unknown |

Label | 1 and 2 | None |

Approach | Source Samples | Target Samples | Accuracy |
---|---|---|---|

Without sigmoid entropy | 600 | 900 | 75.44% |

Without GFK | 600 | 900 | 79.90% |

KNN with K = 1 | 600 | 900 | 86.00% |

Statistical Feature only | 600 | 900 | 92.00% |

GFK approach | 600 | 900 | 60.17% |

Proposed Approach | 600 | 900 | 95.56% |

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## Share and Cite

**MDPI and ACS Style**

Yang, Z.; Yang, R.; Huang, M.
Rolling Bearing Incipient Fault Diagnosis Method Based on Improved Transfer Learning with Hybrid Feature Extraction. *Sensors* **2021**, *21*, 7894.
https://doi.org/10.3390/s21237894

**AMA Style**

Yang Z, Yang R, Huang M.
Rolling Bearing Incipient Fault Diagnosis Method Based on Improved Transfer Learning with Hybrid Feature Extraction. *Sensors*. 2021; 21(23):7894.
https://doi.org/10.3390/s21237894

**Chicago/Turabian Style**

Yang, Zhengni, Rui Yang, and Mengjie Huang.
2021. "Rolling Bearing Incipient Fault Diagnosis Method Based on Improved Transfer Learning with Hybrid Feature Extraction" *Sensors* 21, no. 23: 7894.
https://doi.org/10.3390/s21237894