# Collaborative Optimization of CNN and GAN for Bearing Fault Diagnosis under Unbalanced Datasets

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Theory of the GAN

#### 2.2. Fault Data Generation Based on GAN and CNN

#### 2.3. Improvement of Loss Function with Envelope Spectrum

#### 2.4. Collaborative Training Mechanism of the GAN and CNN

## 3. Experimental dataset

#### 3.1. Introduction of Bearing Test Bench and Dataset

#### 3.2. Data Preprocessing

## 4. Results and Analysis

#### 4.1. Fault Data Generation Based on Optimized GAN

#### 4.2. Fault Diagnosis Based on CNN_GAN

## 5. Conclusions

- A collaborative network GAN_CNN is developed. The GAN generates an almost balanced dataset with data augmentation for the inner ring and the cage fault samples. Once the generated samples are added, the CNN evaluates the extended dataset quality and outputs the fault classification result to modify the loss function of the GAN’s generator.
- Besides the overall similarity, the similarity on the envelope spectrum is considered when building the GAN. The envelope spectrum error from the 1st-5th order $FCF$ between the experimental data and the generated data is taken as a correction term to the general cross-entropy based loss function of the GAN’s generator.

- When constructing the loss function for a GAN, the GAN performance can be improved by considering the envelope spectrum error. The generated samples have higher fidelity and contain more accurate fault information, which, in turn, contribute to the CNN’s accuracy improvement.
- The collaborative network CNN_GAN performs better than the GAN or the CNN. The GAN generates more accurate data if the CNN’s classification results are considered into the GAN’s loss function. The CNN’s fault classification accuracy can be significantly enhanced after the GAN generates more data for the unbalanced training dataset.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CNN | Convolutional Neural Networks |

GAN | Generative Adversarial Networks |

FCF | Fault characteristic frequency |

LSTM | Long Short Term Memory |

BPFO | Ball Passing Frequency on Outer race |

BPFI | Ball Passing Frequency on Inner race |

FTF | Fundamental Train Frequency |

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**Figure 3.**XJTU-SY experimental setup [19].

**Figure 6.**Comparison between original sample and generated sample in time domain; (

**a**), (

**b**) and (

**c**) represent bearing 2_1, bearing 2_3 and bearing 3_3 respectively, while (

**1**), (

**2**) and (

**3**) represent the original sample, general GAN and optimized GAN respectively.

Hyperparameters | Values |
---|---|

Initial learning rate of generator | 0.0001 |

Initial learning rate of discriminator | 0.0001 |

Kernel size of discriminator’s 1st layer | $8\times 8$ |

Kernel size of discriminator’s other layers | $4\times 4$ |

Number of filters in discriminator’s n-th layer | $16\times {2}^{n-1}$ |

Kernel size of generator’s last layer | $8\times 8$ |

Kernel size of discriminator’s other layers | $4\times 4$ |

Number of filters in generator’s n-th layer | $512/{2}^{n-1}$ |

Max epochs | 2000 |

Hyperparameters | Values |
---|---|

Initial learning rate | 0.0002 |

Max epochs | 1000 |

Batch size | 20 |

Kernel size of 1st layer | $7\times 7$ |

Kernel size of other layers | $3\times 3$ |

Number of filters in n-th layer | $16\times {2}^{n-1}$ |

Parameters | Values | Parameters | Values |
---|---|---|---|

Inner raceway diameter | $29.30$ $\mathrm{m}$$\mathrm{m}$ | Ball diameter | $7.92$ $\mathrm{m}$$\mathrm{m}$ |

Outer raceway diameter | $39.80$ $\mathrm{m}$$\mathrm{m}$ | Number of balls | 8 |

Pitch diameter | $34.55$ $\mathrm{m}$$\mathrm{m}$ | Initial contact angle | 0${}^{\circ}$ |

Condition | Test Bearing | Measurement Sample Size | Fault Location |
---|---|---|---|

(1) ${f}_{s}$ = 35 $\mathrm{Hz}$ ${F}_{r}$ = 12 $\mathrm{k}$$\mathrm{N}$ | bearing 1_1 | 123 | outer ring |

bearing 1_2 | 161 | outer ring | |

bearing 1_3 | 158 | outer ring | |

bearing 1_4 | 122 | cage | |

bearing 1_5 | 52 | outer ring & inner ring | |

(2) ${f}_{s}$ = $37.5$ $\mathrm{Hz}$ ${F}_{r}$ = 11 $\mathrm{k}$$\mathrm{N}$ | bearing 2_1 | 491 | inner ring |

bearing 2_2 | 161 | outer ring | |

bearing 2_3 | 533 | cage | |

bearing 2_4 | 42 | outer ring | |

bearing 2_5 | 339 | outer ring | |

(3) ${f}_{s}$ = 40 $\mathrm{Hz}$ ${F}_{r}$ = 10 $\mathrm{k}$$\mathrm{N}$ | bearing 3_1 | 2538 | outer ring |

bearing 3_2 | 2496 | inner ring & element & cage & outer ring | |

bearing 3_3 | 371 | inner ring | |

bearing 3_4 | 1515 | inner ring | |

bearing 3_5 | 114 | outer ring |

Fault Location | Test Bearing | Measurement Sample Size | Training Sets | Test Sets |
---|---|---|---|---|

Outer race | bearing 1_1 | 58 | 518 | 130 |

bearing 1_2 | 108 | |||

bearing 1_3 | 69 | |||

bearing 2_2 | 77 | |||

bearing 2_4 | 12 | |||

bearing 2_5 | 173 | |||

bearing 3_1 | 55 | |||

bearing 3_5 | 106 | |||

Inner race | bearing 2_1 | 26 | 110 | 28 |

bearing 3_3 | 28 | |||

bearing 3_4 | 84 | |||

Cage | bearing 1_4 | 1 | 167 | 42 |

bearing 2_3 | 208 |

Generated Sample | Cosine Similarity | |
---|---|---|

GAN | Optimized GAN | |

bearing 2_1 | 0.3214 | 0.3739 |

bearing 3_3 | 0.3374 | 0.3408 |

bearing 2_3 | 0.2009 | 0.2675 |

Sample Source | Parameter | 1st—$\mathit{BPFI}$ | 2nd—$\mathit{BPFI}$ | 3rd—$\mathit{BPFI}$ | 4th—$\mathit{BPFI}$ | 5th—$\mathit{BPFI}$ |
---|---|---|---|---|---|---|

Original sample | Frequency (Hz) | 178.944 | 357.889 | 536.833 | 715.788 | 931.449 |

Amplitude | 0.176 | 0.062 | 0.124 | 0.072 | 0.020 | |

Sample from general GAN | Frequency (Hz) | 178.944 | 357.889 | 536.833 | 715.788 | 928.323 |

Error (%) | 0 | 0 | 0 | 0 | 0.34 | |

Amplitude | 0.117 | 0.023 | 0.086 | 0.053 | 0.011 | |

Error (%) | 33.3 | 62.0 | 30.1 | 26.1 | 44.1 | |

Sample from optimized GAN | Frequency | 178.944 | 357.889 | 536.833 | 715.788 | 931.449 |

Error (%) | 0 | 0 | 0 | 0 | 0 | |

Amplitude | 0.149 | 0.047 | 0.106 | 0.060 | 0.018 | |

Error (%) | 15.3 | 23.8 | 14.2 | 16.5 | 9.4 |

Sample Source | Parameter | 1st—$\mathit{BPFI}$ | 2nd—$\mathit{BPFI}$ | 3rd—$\mathit{BPFI}$ | 4th—$\mathit{BPFI}$ | 5th—$\mathit{BPFI}$ |
---|---|---|---|---|---|---|

Original sample | Frequency (Hz) | 192.229 | 384.457 | 576.686 | 808.767 | 994.744 |

Amplitude | 0.127 | 0.168 | 0.104 | 0.015 | 0.013 | |

Sample from general GAN | Frequency (Hz) | 192.229 | 384.457 | 576.686 | 808.767 | 990.055 |

Error (%) | 0 | 0 | 0 | 0 | 0.5 | |

Amplitude | 0.104 | 0.131 | 0.088 | 0.019 | 0.006 | |

Error (%) | 18.0 | 22.1 | 15.9 | 26.0 | 49.5 | |

Sample from optimized GAN | Frequency (Hz) | 192.229 | 384.457 | 576.686 | 808.767 | 961.143 |

Error (%) | 0 | 0 | 0 | 0 | 0 | |

Amplitude | 0.124 | 0.143 | 0.096 | 0.020 | 0.011 | |

Error (%) | 2.2 | 14.7 | 7.9 | 26.7 | 14.4 |

Sample Source | Parameter | 1st—$\mathit{FTF}$ | 2nd—$\mathit{FTF}$ | 3rd—$\mathit{FTF}$ | 4th—$\mathit{FTF}$ | 5th—$\mathit{FTF}$ |
---|---|---|---|---|---|---|

Original sample | Frequency (Hz) | 14.847 | 28.912 | 42.978 | 57.825 | 71.890 |

Amplitude | 0.069 | 0.043 | 0.064 | 0.022 | 0.031 | |

Sample from general GAN | Frequency | 14.066 | 28.131 | 42.978 | 57.043 | 71.890 |

Error (%) | 5.3 | 2.7 | 0 | 1.4 | 0 | |

Amplitude | 0.018 | 0.019 | 0.019 | 0.020 | 0.014 | |

Error | 73.3 | 55.4 | 70.6 | 10.7 | 54.1 | |

Sample from optimized GAN | Frequency (Hz) | 14.066 | 28.912 | 42.978 | 58.606 | 71.890 |

Error (%) | 5.3 | 0 | 0 | 1.4 | 0 | |

Amplitude | 0.082 | 0.028 | 0.057 | 0.021 | 0.033 | |

Error (%) | 17.5 | 35.3 | 10.9 | 4.6 | 6.4 |

Imbalance Ratio | CNN | CNN_GAN | ||
---|---|---|---|---|

Accuracy | Cross-Entropy Error | Accuracy | Cross-Entropy Error | |

Training set 1 (5:1:1.5) | 98% | 0.6071 | 100% | 0.5645 |

Training set 2 (10:1:2) | 88% | 0.7013 | 90% | 0.6642 |

Training set 3 (20:1:2) | 68% | 0.8478 | 88% | 0.7012 |

Diagnosis Network | Confusion Matrix on Testing Set | ||
---|---|---|---|

Training with Set 1 Unbalance Ratio (5:1:1.5) | Training with Set 2 Unbalance Ratio (10:1:2) | Training with Set 3 Unbalance Ratio (20:1:2) | |

CNN | |||

CNN_GAN |

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**MDPI and ACS Style**

Ruan, D.; Song, X.; Gühmann, C.; Yan, J.
Collaborative Optimization of CNN and GAN for Bearing Fault Diagnosis under Unbalanced Datasets. *Lubricants* **2021**, *9*, 105.
https://doi.org/10.3390/lubricants9100105

**AMA Style**

Ruan D, Song X, Gühmann C, Yan J.
Collaborative Optimization of CNN and GAN for Bearing Fault Diagnosis under Unbalanced Datasets. *Lubricants*. 2021; 9(10):105.
https://doi.org/10.3390/lubricants9100105

**Chicago/Turabian Style**

Ruan, Diwang, Xinzhou Song, Clemens Gühmann, and Jianping Yan.
2021. "Collaborative Optimization of CNN and GAN for Bearing Fault Diagnosis under Unbalanced Datasets" *Lubricants* 9, no. 10: 105.
https://doi.org/10.3390/lubricants9100105