# A Fuzzy Fusion Rotating Machinery Fault Diagnosis Framework Based on the Enhancement Deep Convolutional Neural Networks

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Work

#### 2.1. Signal Processing Techniques

#### 2.2. General Introduction of Conventional CNN

#### 2.3. Conventional Fusion Strategies

## 3. Framework of the Proposed Method

#### 3.1. Enhancement CNN Models

#### 3.2. Decision-Level Fuzzy Fusion Strategy

## 4. Experiments

#### 4.1. Datasets

#### 4.2. Implementation

#### 4.3. Training Process Analysis

#### 4.4. Comparison of Fuzzy Fusion with Empirical Fusion

#### 4.5. Classifier Ranking and Interactive

#### 4.6. Comparison with State-of-the-Art

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**CNN structures used in the proposed method. (

**a**) the structure based on the raw vibration signal, (

**b**) the structure based on the frequency-domain signal, (

**c**) the structure based on the 2-dimensional data, including the raw vibration signal directly reshaped into 2-D signal and transformed by STFT.

**Figure 7.**Training time of the modified CNN and conventional CNN. (

**a**) MFPT bearing dataset. (

**b**) PU bearing dataset.

**Figure 8.**Training process of the modified CNN and conventional CNN. (

**a**) MFPT training loss. (

**b**) MFPT validation accuracy. (

**c**) PU training loss. (

**d**) PU validation accuracy.

**Figure 9.**The explainable features of fuzzy fusion with MFPT bearing fault dataset. (

**a**) The contributions of each signal in fuzzy fusion. (

**b**) The interaction index among signals.

**Figure 10.**The explainable features of fuzzy fusion with PU bearing fault dataset. (

**a**) The contributions of each signal in fuzzy fusion. (

**b**) The interaction index among signals.

Feature Used | MFPT | PU | ||||||
---|---|---|---|---|---|---|---|---|

ReLU MaxPool | Mish MaxPool | ReLU SoftPool | Mish SoftPool | ReLU MaxPool | Mish MaxPool | ReLU SoftPool | Mish SoftPool | |

Raw vibration | 84.17% | 86.11% | 84.44% | 88.33% | 90.92% | 90.98% | 92.18% | 93.32% |

FFT | 94.44% | 95.56% | 96.11% | 97.50% | 96.09% | 96.70% | 96.69% | 98.62% |

Slice | 71.19% | 72.22% | 73.22% | 74.44% | 92.97% | 93.31% | 92.34% | 93.49% |

STFT | 86.16% | 89.72% | 88.56% | 90.00% | 95.24% | 95.27% | 95.49% | 96.69% |

Model | Signal | SNR | Average | |||||
---|---|---|---|---|---|---|---|---|

0 | 2 | 4 | 6 | 8 | 10 | |||

ReLU + MaxPool | Raw | 68.05% | 71.94% | 73.33% | 80.55% | 81.67% | 84.72% | 76.71% |

FFT | 82.50% | 85.83% | 89.44% | 89.44% | 90.28% | 91.94% | 88.23% | |

Slice | 41.11% | 48.61% | 52.50% | 55.83% | 61.39% | 65.00% | 54.07% | |

STFT | 64.44% | 68.33% | 69.17% | 80.55% | 81.11% | 82.22% | 74.30% | |

Mish + SoftPool | Raw | 74.17% | 78.89% | 80.27% | 84.72% | 85.55% | 87.78% | 81.89% |

FFT | 85.83% | 87.78% | 91.11% | 92.22% | 93.33% | 94.17% | 90.74% | |

Slice | 50.28% | 52.22% | 59.44% | 63.33% | 64.17% | 66.11% | 59.26% | |

STFT | 65.56% | 76.94% | 78.11% | 81.94% | 82.78% | 84.44% | 78.26% |

Model | Signal | SNR | Average | |||||
---|---|---|---|---|---|---|---|---|

0 | 2 | 4 | 6 | 8 | 10 | |||

ReLU + MaxPool | Raw | 79.49% | 81.95% | 85.66% | 87.02% | 88.08% | 88.91% | 85.19% |

FFT | 81.92% | 87.38% | 88.91% | 92.60% | 92.86% | 93.12% | 89.47% | |

Slice | 78.54% | 83.41% | 84.66% | 89.03% | 89.37% | 90.82% | 85.97% | |

STFT | 81.33% | 86.66% | 87.34% | 90.26% | 91.03% | 91.16% | 87.96% | |

Mish + SoftPool | Raw | 83.01% | 84.63% | 86.42% | 89.22% | 90.43% | 91.79% | 87.58% |

FFT | 82.48% | 89.08% | 92.01% | 92.58% | 94.34% | 95.21% | 90.95% | |

Slice | 81.23% | 86.18% | 88.98% | 91.54% | 91.34% | 92.21% | 88.58% | |

STFT | 85.43% | 87.31% | 89.52% | 90.08% | 94.18% | 95.79% | 90.39% |

Fusion Strategy | Datasets | |
---|---|---|

MFPT | PU | |

Average | 95.55% | 96.04% |

Majority Vote | 96.67% | 96.31% |

Proposed Fusion | 98.06% | 96.62% |

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**MDPI and ACS Style**

Yang, D.; Karimi, H.R.; Gelman, L.
A Fuzzy Fusion Rotating Machinery Fault Diagnosis Framework Based on the Enhancement Deep Convolutional Neural Networks. *Sensors* **2022**, *22*, 671.
https://doi.org/10.3390/s22020671

**AMA Style**

Yang D, Karimi HR, Gelman L.
A Fuzzy Fusion Rotating Machinery Fault Diagnosis Framework Based on the Enhancement Deep Convolutional Neural Networks. *Sensors*. 2022; 22(2):671.
https://doi.org/10.3390/s22020671

**Chicago/Turabian Style**

Yang, Daoguang, Hamid Reza Karimi, and Len Gelman.
2022. "A Fuzzy Fusion Rotating Machinery Fault Diagnosis Framework Based on the Enhancement Deep Convolutional Neural Networks" *Sensors* 22, no. 2: 671.
https://doi.org/10.3390/s22020671