# Rolling Bearing Fault Diagnosis across Operating Conditions Based on Unsupervised Domain Adaptation

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Foundation

#### 2.1. Fast Fourier Transform (FFT)

#### 2.2. Autoencoder (AE)

#### 2.3. Convolutional Neural Network (CNN)

#### 2.4. Balanced Distribution Adaptation (BDA)

## 3. Proposed Architecture

## 4. Experiments and Analysis

#### 4.1. Variable Load Dataset from the CWRU

#### 4.1.1. Data Description

#### 4.1.2. Signal Pre-Processing

#### 4.1.3. Signal Reconstruction and Feature Extraction

#### 4.1.4. Feature Migration and Analysis

#### 4.1.5. Fault Classification and Analysis

- (1)
- TCA-KNN
- (2)
- TCA-GBDT
- (3)
- CORAL-KNN
- (4)
- JDA-KNN
- (5)
- BDA-KNN
- (6)
- BDA-SVM
- (7)
- BDA-GBDT
- (8)
- DFCNN
- (9)
- DEEP FEATURE-KNN
- (10)
- CAE-DTLN
- (11)
- 1DRCAE

#### 4.2. Southeastern University Gearbox Dataset

#### 4.2.1. Data Description

#### 4.2.2. Signal Pre-Processing

#### 4.2.3. Signal Reconstruction and Feature Extraction

#### 4.2.4. Feature Migration

#### 4.2.5. Fault Classification and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AE | autoencoder |

BDA | balanced distribution adaption |

CNN | convolutional neural network |

DFT | discrete Fourier transform |

FFT | fast Fourier transform |

GAN | generative adversarial network |

KNN | K-nearest neighbor |

MMD | maximum mean discrepancy |

T-SNE | T-distributed stochastic neighbor embedding |

${D}_{S}$ | source domain space |

${D}_{t}$ | target domain space |

$X(k)$ | spectral function |

$\widehat{X}$ | output of decoder |

${l}_{AE}$ | reconstruction error |

$p(x)$ | marginal distribution |

$p(y|x)$ | conditional distribution |

$\mu $ | balance factor |

$\kappa $ | regenerative kernel Hilbert space |

H | central matrix |

I | unit matrix |

A | transformation matrix |

$\varphi $ | Lagrangian operator |

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**Figure 11.**Histograms of the comparative results in Table 3.

**Figure 19.**Histograms of the comparative results in Table 5.

Layer | Type | Kernel Size/Stride | Output |
---|---|---|---|

Input | Data | / | 1 × 1024 |

Conv1 | Convolution1d | 32/16 | 128 × 16 |

Pool | MaxPool | 2/2 | 64 × 16 |

Conv2 | Convolution1d | 3/1 | 64 × 32 |

Pool | MaxPool | 2/2 | 32 × 32 |

Conv3 | Convolution1d | 3/1 | 32 × 64 |

Pool | MaxPool | 2/2 | 16 × 64 |

Conv4 | Convolution1d | 3/1 | 16 × 64 |

Pool | MaxPool | 2/2 | 8 × 64 |

Conv5 | Convolution1d | 3/1 | 6 × 64 |

Pool | MaxPool | 2/2 | 3 × 64 |

Upsample | MaxUnpool | 2/2 | 6 × 64 |

Deconv1 | ConvTranspose1d | 3/1 | 8 × 64 |

Upsample | MaxUnpool | 2/2 | 16 × 64 |

Deconv2 | ConvTranspose1d | 3/1 | 16 × 64 |

Upsample | MaxUnpool | 2/2 | 32 × 64 |

Deconv3 | ConvTranspose1d | 3/1 | 32 × 32 |

Upsample | MaxUnpool | 2/2 | 64 × 32 |

Deconv4 | ConvTranspose1d | 3/1 | 64 × 16 |

Deconv5 | ConvTranspose1d | 3/1 | 1 × 1024 |

Class | Fault | Damage Diameter (inch) | Load (HP) |
---|---|---|---|

Source1 | Normal | 0.007 | 1 |

Source2 | Ball | 0.007 | 1 |

Source3 | Inner | 0.007 | 1 |

Source4 | Outer | 0.007 | 1 |

Target1 | Normal | 0.014 | 3 |

Target2 | Ball | 0.014 | 3 |

Target3 | Inner | 0.014 | 3 |

Target4 | Outer | 0.014 | 3 |

Evaluating Indicator | TCA_KNN | TCA_GBDT | CORAL_KNN | JDA_KNN | BDA_KNN | BDA_SVM | BDA_GBDT | DFCNN | DEEP FEATURE-KNN | CAE-DTLN | 1DRCAE |
---|---|---|---|---|---|---|---|---|---|---|---|

Mean accuracy | 0.776 | 0.431 | 0.256 | 0.820 | 0.985 | 0.974 | 0.536 | 0.674 | 0.704 | 0.963 | 0.954 |

std | 0.017 | 0.116 | 0.013 | 0.058 | 0.014 | 0.018 | 0.088 | 0.036 | 0.043 | 0.021 | 0.024 |

Class | Fault | Condition |
---|---|---|

Source1 | Normal | 20 HZ-0 V |

Source2 | Ball | 20 HZ-0 V |

Source3 | Inner | 20 HZ-0 V |

Source4 | Outer | 20 HZ-0 V |

Source5 | Combination | 20 HZ-0 V |

Target1 | Normal | 30 HZ-2 V |

Target2 | Ball | 30 HZ-2 V |

Target3 | Inner | 30 HZ-2 V |

Target4 | Outer | 30 HZ-2 V |

Target5 | Combination | 30 HZ-2 V |

**Table 5.**Accuracy and standard deviation of different methods on the Southeastern University dataset.

Evaluating Indicator | TCA_KNN | TCA_GBDT | CORAL_KNN | JDA_KNN | BDA_KNN | BDA_SVM | BDA_GBDT | DFCNN | DEEP FEATURE-KNN | CAE-DTLN | 1DRCAE |
---|---|---|---|---|---|---|---|---|---|---|---|

Mean accuracy | 0.617 | 0.639 | 0.252 | 0.599 | 0.982 | 0.961 | 0.971 | 0.605 | 0.604 | 0.957 | 0.947 |

std | 0.020 | 0.105 | 0.019 | 0.072 | 0.019 | 0.024 | 0.021 | 0.033 | 0.053 | 0.026 | 0.029 |

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## Share and Cite

**MDPI and ACS Style**

Zhong, Z.; Liu, H.; Mao, W.; Xie, X.; Cui, Y.
Rolling Bearing Fault Diagnosis across Operating Conditions Based on Unsupervised Domain Adaptation. *Lubricants* **2023**, *11*, 383.
https://doi.org/10.3390/lubricants11090383

**AMA Style**

Zhong Z, Liu H, Mao W, Xie X, Cui Y.
Rolling Bearing Fault Diagnosis across Operating Conditions Based on Unsupervised Domain Adaptation. *Lubricants*. 2023; 11(9):383.
https://doi.org/10.3390/lubricants11090383

**Chicago/Turabian Style**

Zhong, Zhidan, Hao Liu, Wentao Mao, Xinghui Xie, and Yunhao Cui.
2023. "Rolling Bearing Fault Diagnosis across Operating Conditions Based on Unsupervised Domain Adaptation" *Lubricants* 11, no. 9: 383.
https://doi.org/10.3390/lubricants11090383