# Improvement of Generative Adversarial Network and Its Application in Bearing Fault Diagnosis: A Review

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## Abstract

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## 1. Introduction

## 2. Research Methodology and Initial Analysis

#### 2.1. Research Methodology

#### 2.2. Initial Literature Analysis

## 3. Data Augmentation Methods for Bearing Fault Diagnosis

#### 3.1. Data Augmentation Using Oversampling Techniques

#### 3.2. Data Augmentation Using Data Transformations

#### 3.3. Data Augmentation Using GANs

## 4. Improvements and Applications of GANs in Bearing Fault Diagnosis

#### 4.1. Improvements in the Network Structure

#### 4.1.1. Information-Based Improvements

#### 4.1.2. Input-Based Improvements

#### 4.1.3. Layer-Based Improvements

#### 4.2. Improvements in the Loss Function

#### 4.2.1. Metric-Based Improvements

#### 4.2.2. Regularization-Based Improvements

#### 4.2.3. Summary

#### 4.3. Evaluation of Generated Samples

#### 4.4. Applications of GAN in Bearing Fault Diagnosis

## 5. Conclusions

#### 5.1. Summary

#### 5.2. Outlook

- •
- Explainability from physicsDue to the black-box properties of DL models, the generated samples lack physical interpretability. Based on our literature research, most studies do not take physical knowledge into account in their models. Although there is a large body of literature on physics-guided neural networks [88,89], there is still a lack of research on introducing physical knowledge into GANs. From our point of view, physics-guided GAN can be studied from two perspectives in the field of bearing fault diagnosis. Based on the taxonomy of improvements of GAN in this paper, the first idea belongs to the improvement of the network structure. For example, the bearing fault mechanism model can be integrated into GAN. The second idea aims to improve the loss function by adding physically interpretable regularization terms to the original loss function.
- •
- Advanced evaluation metricsTo date, the evaluation of the generated samples is not comprehensive. Almost all of the literature we researched only considered the similarity of the generated samples to the real samples. Apart from similarity, the creativity and diversity of the generated samples should be taken into account to achieve a more comprehensive evaluation. More appropriate evaluation metrics deserve further investigation.
- •
- Application for RUL predictionBased on our collation of the literature, there are still a number of promising variants or improvements in GAN that have not yet been applied to bearing fault diagnosis, which deserve further research. For the application in bearing fault diagnosis, the majority of reported GAN variants possess the potential to achieve satisfying results, even under imbalanced or small datasets through sample generation. However, concerning RUL prediction, it is quite another matter. In contrast to fault samples, which have obvious features such as different fault characteristic frequencies for different fault types, samples in the aging period do not have such distinct one-to-one features. Therefore, generating aging samples for bearing during the degradation process with GAN remains an open question. Improving the GAN to generate aging samples for RUL prediction under a dataset with limited run-to-failure trajectories is a challenging but rewarding research topic.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ACGAN | Auxiliary classifier GAN |

ACGAN-SN | Auxiliary classifier GAN with spectral normalization |

AE | Stacked autoencoder |

ANN | Artificial neural network |

BEGAN | Boundary equilibrium GAN |

CNN | Convolutional neural networks |

CS | Cosine similarity |

CGAN | Conditional GAN |

C-DCGAN | DCGAN integrated with CGAN |

DBN | Deep belief network |

DCGAN | Deep convolutional GAN |

DL | Deep learning |

EM | Expectation maximization |

EBGAN | Energy-based GAN |

FCFs | Fault characteristic frequencies |

GAN | Generative adversarial network |

KLD | K-L divergence |

LSTM | Long short-term memory |

LSGAN | Least squares GAN |

ML | Machine learning |

MMD | Maximum mean discrepancy |

MS-PGAN | Multi-scale progress GAN |

PCC | Pearson correlation coefficient |

PCWAN-GP | Parallel classification WGAN with gradient penalty |

PHM | Prognostics and health management |

PSNR | Peak signal-to-noise ratio |

RGAN | Relativistic GAN |

RNN | Recurrent neural network |

RUL | Remaining useful life |

SSIM | Structural similarity index measure |

STFT | Short-time Fourier transform |

SCOTE | Sample-characteristic oversampling technique |

SI-SMOTE | Sample information-based SMOTE |

SM | Self-modulation |

SMOTE | Synthetic minority over-sampling technique |

SNGAN | Spectral normalization GAN |

SVM | Support vector machine |

TL | Transfer learning |

VAE | Variational autoencoder |

VAEGAN | GAN combined with VAE |

WGAN | Wasserstein GAN |

WGAN-GP | WGAN with the gradient penalty |

kNN | k-nearest neighbor |

t-SNE | t-distributed stochastic neighbor embedding |

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**Figure 2.**Publications related to data augmentation and GANs (from 2013 to 2022). (

**a**) Publications related to bearing data augmentation. (

**b**) Publications related to bearing fault diagnosis and GANs.

**Figure 5.**Structure of the original DCGAN generator [53].

Number | Loss | Formulation | Source |
---|---|---|---|

1 | PCWGAN-GP |
$$PC\left(\right)open="("\; close=")">{\tilde{x}}_{j}^{k},{\overline{x}}^{k}\sqrt{{\sum}_{m=1}^{M}{\left(\right)}^{{\tilde{x}}_{j,m}^{k}}2\sqrt{{\sum}_{m=1}^{M}{\left(\right)}^{{\overline{x}}_{m}^{k}}2}}$$
| [71] |

2 | MS-PGAN |
$$MM{D}^{2}\left(\right)open="["\; close="]">{D}_{X},{D}_{Y}$$
| [56] |

3 | FCFE |
$${L}_{\mathrm{frequency}\phantom{\rule{4.pt}{0ex}}}=\sum _{i=1}^{N}\left(\right)open="("\; close=")">\left(\right)open="|"\; close="|">{M}_{\mathrm{real}\phantom{\rule{4.pt}{0ex}}}^{i}-{M}_{\mathrm{fake}\phantom{\rule{4.pt}{0ex}}}^{i}$$
| [72] |

4 | WCGAN-HFM |
$$HFM=\sum _{l}{\omega}_{l}\xb7\left(\right)open="|"\; close="|">{D}_{l}(x\mid y)-{D}_{l}\left(G(z\mid y)\right)$$
| [73] |

5 | Entropy |
$$H\left(G\left(z\right)\right)={E}_{z\sim {P}_{z}}\left(\right)open="["\; close="]">{\left(\right)}^{z}2$$
| [74] |

Number | Metric | Formulation | Source |
---|---|---|---|

1 | CS |
$$cos\theta =\frac{\overrightarrow{m}\xb7\overrightarrow{n}}{|\overrightarrow{m}|\xb7|\overrightarrow{n}|}$$
| [72] |

2 | MMD |
$$MMD[F,p,q]=\underset{f\in F}{sup}\left(\right)open="("\; close=")">{E}_{x\sim p}\left[f\left(x\right)\right]-{E}_{x\sim q}\left[f\left(x\right)\right]$$
| [56] |

3 | PCC |
$$PC{C}_{X,Y}=\frac{cov(X,Y)}{{\sigma}_{X}{\sigma}_{Y}}$$
| [57,60,71] |

4 | KLD |
$${D}_{\mathrm{KL}}(P\parallel Q)=\sum _{x\in \mathcal{X}}P\left(x\right)log\left(\right)open="("\; close=")">\frac{P\left(x\right)}{Q\left(x\right)}$$
| [51] |

5 | WD |
$$\mathrm{WD}\left(\right)open="("\; close=")">{\mathrm{P}}_{1},{\mathrm{P}}_{2}{\mathbb{E}}_{(\mathrm{x},\mathrm{y})\sim \gamma}[\parallel \mathrm{x}-\mathrm{y}\parallel ]$$
| [57] |

6 | PSNR |
$$PSNR=10{log}_{10}\left(\right)open="("\; close=")">\frac{{\mathrm{MAX}}_{I}^{2}}{{\mathrm{MSE}}^{2}}$$
| [51] |

7 | SSIM |
$$SSIM(x,y)=\frac{\left(\right)open="("\; close=")">2{\mu}_{x}{\mu}_{y}+{C}_{1}}{\left(\right)}$$
| [51] |

Number | Type | Advantages | Disadvantages |
---|---|---|---|

1 | CGAN | To generate samples with specific attributes such as specific categories. | A large amount of training data with labels are required. |

2 | ACGAN | With auxiliary classifier, different classes of samples can be generated. | (1) Complex training; (2) Limited quality of generated samples. |

3 | VAEGAN | The generated samples can be controlled by the autoencoder. | The training is relatively more difficult. |

4 | DCGAN | The powerful feature extraction capability of CNN is exploited. | More computational resources are required for the training. |

5 | SNGAN | Exploding and vanishing gradient can be solved effectively. | (1) Slow training speed; (2) Limited diversity of generated samples. |

6 | WGAN | Wasserstein distance provides a better measure of the difference between distributions. | The training is not stable enough. |

7 | WGAN-GP | With gradient penalty integrated into WGAN, the stability is improved. | More training time and computational resources. |

8 | LSGAN | Effectively solves the problems of exploding gradient and vanishing gradient. | Excessive penalization of outliers may lead to a reduction in the diversity of samples being generated. |

9 | EBGAN | (1) Energy-based loss function allows better interpretability; (2) Improved stability and diversity of sample generation. | (1) Quite complex to implement and train; (2) Prone to mode collapse. |

10 | BEGAN | Mode collapse can be effectively alleviated. | (1) A relatively complex architecture; (2) Sensitive to hyperparameters. |

11 | RGAN | With relativistic loss, the quality of sample generation is improved and mode collapse is reduced. | (1) A relatively complex architecture; (2) The relativistic loss is difficult to interpret. |

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## Share and Cite

**MDPI and ACS Style**

Ruan, D.; Chen, X.; Gühmann, C.; Yan, J.
Improvement of Generative Adversarial Network and Its Application in Bearing Fault Diagnosis: A Review. *Lubricants* **2023**, *11*, 74.
https://doi.org/10.3390/lubricants11020074

**AMA Style**

Ruan D, Chen X, Gühmann C, Yan J.
Improvement of Generative Adversarial Network and Its Application in Bearing Fault Diagnosis: A Review. *Lubricants*. 2023; 11(2):74.
https://doi.org/10.3390/lubricants11020074

**Chicago/Turabian Style**

Ruan, Diwang, Xuran Chen, Clemens Gühmann, and Jianping Yan.
2023. "Improvement of Generative Adversarial Network and Its Application in Bearing Fault Diagnosis: A Review" *Lubricants* 11, no. 2: 74.
https://doi.org/10.3390/lubricants11020074