# Fault Diagnosis Method for Rolling Bearings Based on Two-Channel CNN under Unbalanced Datasets

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feature Extraction Method

#### 2.1. FFT

#### 2.2. GST

## 3. TC-CNN Model Framework

#### 3.1. CNN

#### 3.1.1. Convolutional Layer

#### 3.1.2. Activation Function

#### 3.1.3. Pooling Layer

#### 3.1.4. Fully Connected Layer

#### 3.2. The Proposed TC-CNN Model

#### 3.3. Evaluation Criterion

Predicted | |||

Actual | Positive | Negative | |

Positive | True Positive (TP) | False Positive (FP) | |

Negative | False Negative (FN) | True Negative (TN) |

#### 3.3.1. Accuracy

#### 3.3.2. Precision

#### 3.3.3. Recall

#### 3.3.4. F1 Score

## 4. Experimental Analysis

#### 4.1. Experimental Data

#### 4.2. Model Parameters

#### 4.3. Fault Diagnosis Results under a Balanced Dataset

#### 4.4. Fault Diagnosis Results under the Unbalanced Dataset

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Location | Fault Diameter (inch) | Fault Orientation | Label |
---|---|---|---|

${f}_{1}$ | Ball | 0.007 | - |

${f}_{2}$ | Ball | 0.014 | - |

${f}_{3}$ | Ball | 0.021 | - |

${f}_{4}$ | Inner race | 0.007 | - |

${f}_{5}$ | Inner race | 0.014 | - |

${f}_{6}$ | Inner race | 0.021 | - |

${f}_{7}$ | Outer race | 0.007 | Center @6:00 |

${f}_{8}$ | Outer race | 0.014 | Center @6:00 |

${f}_{9}$ | Outer race | 0.021 | Center @6:00 |

${f}_{0}$ | Normal | - | - |

Layer Name | Parameter | Layer Size |
---|---|---|

${I}_{1,1}$ | - | $1\times 513\times 1$ |

${I}_{2,1}$ | - | $64\times 64\times 3$ |

${C}_{1,1}$ | Conv($1\times 6$), kernel size = 6 | $1\times 508\times 6$ |

${C}_{2,1}$ | Conv($3\times 6$), kernel size = 5 | $60\times 60\times 6$ |

${P}_{1,1}$ | kernel size = 4 | $1\times 127\times 6$ |

${P}_{2,1}$ | kernel size = 2 | $30\times 30\times 6$ |

${C}_{1,2}$ | Conv($6\times 16$), kernel size = 5 | $1\times 123\times 16$ |

${C}_{2,2}$ | Conv($6\times 16$), kernel size = 5 | $26\times 26\times 16$ |

${P}_{1,2}$ | kernel size = 3 | $1\times 41\times 16$ |

${P}_{2,2}$ | kernel size = 2 | $13\times 13\times 16$ |

$F{C}_{1}$ | - | 656 |

$F{C}_{2}$ | - | 2704 |

${C}^{*}$ | - | 3360 |

D | - | 3360 |

$F{C}_{1}^{*}$ | $3360\times 84$ | 84 |

$F{C}_{2}^{*}$ | SVM | 10 |

O | - | $1\times 10$ |

Method | Accuracy (%) | ||
---|---|---|---|

Training Set | Validation Set | Test Set | |

TC-CNN | 100.00 | 99.50 | 99.50 |

1D-CNN | 100.00 | 81.25 | 82.50 |

2D-CNN | 100.00 | 95.00 | 94.00 |

CWT+2DCNN | 97.71 | 96.25 | 96.50 |

DBN | 100.00 | 74.00 | 72.50 |

1D-CNN+2D-CNN | 100.00 | 91.00 | 88.00 |

Label | Method | |||||
---|---|---|---|---|---|---|

TC-CNN | 1D-CNN | 2D-CNN | CWT+2DCNN | DBN | 1D-CNN+2D-CNN | |

${f}_{1}$ | 1.00 | 0.74 | 0.86 | 0.94 | 0.58 | 0.73 |

${f}_{2}$ | 1.00 | 0.70 | 0.77 | 0.96 | 0.71 | 0.75 |

${f}_{3}$ | 1.00 | 0.87 | 1.00 | 0.90 | 1.00 | 1.00 |

${f}_{4}$ | 1.00 | 0.81 | 1.00 | 1.00 | 0.58 | 0.87 |

${f}_{5}$ | 0.98 | 0.71 | 0.92 | 0.98 | 0.51 | 0.88 |

${f}_{6}$ | 1.00 | 0.81 | 1.00 | 1.00 | 0.72 | 0.89 |

${f}_{7}$ | 1.00 | 0.96 | 1.00 | 1.00 | 0.74 | 0.97 |

${f}_{8}$ | 1.00 | 1.00 | 1.00 | 0.90 | 1.00 | 1.00 |

${f}_{9}$ | 1.00 | 0.81 | 0.95 | 1.00 | 0.52 | 0.83 |

${f}_{0}$ | 1.00 | 0.98 | 0.97 | 1.00 | 0.96 | 1.00 |

F1 score (macro) | 1.00 | 0.83 | 0.94 | 0.97 | 0.73 | 0.89 |

Unbalanced Cases | Size of Normal Condition | Size of Each Kind of Fault Conditions | |||
---|---|---|---|---|---|

Training Dataset | Testing Dataset | Training Dataset | Testing Dataset | ||

Case 1 | 2:1 | 300 | 100 | 150 | 100 |

Case 2 | 5:1 | 300 | 100 | 60 | 100 |

Case 3 | 10:1 | 300 | 100 | 30 | 100 |

Case 4 | 20:1 | 300 | 100 | 15 | 100 |

Case 5 | 30:1 | 300 | 100 | 10 | 100 |

Case 6 | 50:1 | 300 | 100 | 6 | 100 |

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**MDPI and ACS Style**

Qin, Y.; Shi, X.
Fault Diagnosis Method for Rolling Bearings Based on Two-Channel CNN under Unbalanced Datasets. *Appl. Sci.* **2022**, *12*, 8474.
https://doi.org/10.3390/app12178474

**AMA Style**

Qin Y, Shi X.
Fault Diagnosis Method for Rolling Bearings Based on Two-Channel CNN under Unbalanced Datasets. *Applied Sciences*. 2022; 12(17):8474.
https://doi.org/10.3390/app12178474

**Chicago/Turabian Style**

Qin, Yufeng, and Xianjun Shi.
2022. "Fault Diagnosis Method for Rolling Bearings Based on Two-Channel CNN under Unbalanced Datasets" *Applied Sciences* 12, no. 17: 8474.
https://doi.org/10.3390/app12178474