# Automatic Transmission Bearing Fault Diagnosis Based on Comprehensive Index Method and Convolutional Neural Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. CEEMDANICA Method Introduction

_{1}, IMF

_{2}, … IMF

_{n}obtained from CEEMDAN processing, some components still contained noise. In the practical applied environment of bearing faults, there are multiple noise sources from gears and other bearings in the vehicle transmission. At the same time, the compound bearing faults are included, so it is necessary to further extract the features of multiple signal components. The original signal is masked by the medium and low-frequency high-energy noise, so that the independent source signal cannot be obtained. In view of this situation, the signal preprocessing method of CEEMDANICA is proposed. The process is as follows:

_{j}(·), it is used to solve the jth IMF of a signal through EMD decomposition.

^{i}, and the range of ω

^{i}is 0 to 1. Noise with an amplitude coefficient of ε

_{k}is added during the EMD decomposition.

_{(t)}represents the original signal to be decomposed by CEEMDAN. The basic steps are as follows:

_{(t)}+ ε

_{0}ω

^{i}(t), the average value of the first IMF component can be obtained by EMD decomposition, and it is recorded as IMF

_{1}, and described as:

_{1}, IMF

_{2}, … IMF

_{n}obtained by the above formula, some components are still mixed with residual noise. ICA is used to process these components again and treat each IMF as a mixed signal. Let h

_{1}, h

_{2}, … h

_{k}= IMF

_{1}, IMF

_{2},… IMF

_{k}, and the matrix can be expressed as:

_{1}(t), I

_{2}(t), …, I

_{n}(t)]

^{T}, I(t) is assumed to be a matrix composed of a group of mutually independent signal sources, and W(t) = [W

_{1}(t), W

_{2}(t), …, W

_{n}(t)]

^{T}, W(t) is composed of independent signal sources in I(t), which can be shown as follows:

_{1}(t),y

_{2}(t), …, y

_{n}(t)]

^{T}is the estimation of the source signal I(t). Repeat the above steps until all independent source signals, called ICA

_{1}, ICA

_{2}… ICA

_{n}, which constitute IMF components are decomposed.

#### 2.2. Comprehensive Index Method

#### 2.2.1. Multiscale Permutation Entropy (MPE)

_{j}

^{(s)}is obtained after the coarse graining operation. The expression is:

_{j}

^{(s)}.

#### 2.2.2. Box Dimension

_{i}⊂y, y is a closed set on R

^{n}. Use as thin as possible ε Grid division, N(ε) is the minimum number of meshes covered by the set y.

_{1}and k

_{2}are the starting point and the end point, respectively, and have a good linear relationship.

_{B}is:

#### 2.2.3. Correlation Coefficient

#### 2.2.4. Kurtosis

#### 2.3. Two-Dimensional Convolutional Neural Network

## 3. Bench Vibration Test of Rolling Bearing of Automatic Transmission

#### 3.1. Two-Speed Automatic Mechanical Transmission

#### 3.2. Test Platform

#### 3.3. Signal Acquisition

## 4. Fault Diagnosis of Rolling-Element Bearing of Automatic Transmission

#### 4.1. Signal Processing Based on CEEMDANICA

_{1}, ICA

_{2}, ICA

_{5}, ICA

_{7}, ICA

_{8}and ICA

_{9}were selected as the TDCNN model sample set in order of decreasing size from large to small.

#### 4.2. Fault Diagnosis of Rolling-Element Bearing Based on TDCNN

#### 4.3. Comparison of Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The two-speed automatic mechanical transmission: (

**a**) Structural diagram; (

**b**) Transmission prototype.

Number of Layers | Layer Name | Parameters |
---|---|---|

1 | input layer | input matrix 40 × 40 |

2 | convolution layer_1 | core size 17, number 20, step size 1 |

3 | batch integration | number of channels: 20 |

4 | activation function | ReLU |

5 | pooling layer_1 | 2 × 2 |

6 | convolution layer_2 | Core size 9, number 40, step size 1 |

7 | batch integration | number of channels: 40 |

8 | activation function | ReLU |

9 | pooling layer_2 | 2 × 2 |

10 | full connection layer | 100 |

11 | Output layer (softmax) | 10 |

Fault Type | Fault Size/mm | Signal Length | Speed (r/min) | Torque (Nm) |
---|---|---|---|---|

Normal_1 | - | 40,000 | 1965–2366 | 32 |

Inner ring_2 | 0.53 | 40,000 | 1965–2366 | 32 |

Ball_3 | 0.53 | 40,000 | 1965–2366 | 32 |

Outer ring_4 | 0.53 | 40,000 | 1965–2366 | 32 |

Outer & inner ring_5 | 0.18 | 40,000 | 1965–2366 | 32 |

Inner ring & ball_6 | 0.18 | 40,000 | 1965–2366 | 32 |

Outer ring & ball_7 | 0.18 | 40,000 | 1965–2366 | 32 |

ICA Components | MPE_{1} | MPE_{2} | MPE_{3} | MPE_{4} | MPE_{5} | Box Dimension | Kurtosis | Correlation Coefficient |
---|---|---|---|---|---|---|---|---|

ICA_{1} | 0.9702 | 0.9463 | 0.9834 | 0.9702 | 0.9655 | 1.6102 | 6.2456 | 0.0460 |

ICA_{2} | 0.9805 | 0.9832 | 0.9769 | 0.9716 | 0.9640 | 1.6569 | 8.4172 | 0.1186 |

ICA_{3} | 0.7454 | 0.5638 | 0.4908 | 0.4339 | 0.4115 | 1.2235 | 8.3421 | 0.0105 |

ICA_{4} | 0.6027 | 0.5334 | 0.5211 | 0.5373 | 0.5616 | 1.3262 | 4.7376 | 0.0061 |

ICA_{5} | 0.9862 | 0.9831 | 0.9794 | 0.9713 | 0.9683 | 1.6448 | 5.3347 | 0.6510 |

ICA_{6} | 0.4897 | 0.6912 | 0.8233 | 0.9021 | 0.9405 | 1.4517 | 4.1905 | 0.0053 |

ICA_{7} | 0.9745 | 0.9878 | 0.9819 | 0.9723 | 0.9647 | 1.7026 | 5.3354 | 0.2754 |

ICA_{8} | 0.8014 | 0.9237 | 0.9208 | 0.9416 | 0.8569 | 1.5732 | 3.8780 | 0.1003 |

ICA_{9} | 0.9838 | 0.9659 | 0.9783 | 0.9700 | 0.9699 | 1.6555 | 4.0085 | 0.1583 |

ICA_{10} | 0.7497 | 0.9718 | 0.9531 | 0.9690 | 0.9565 | 1.5524 | 4.2529 | 0.0166 |

Model | Recognition Accuracy (%) | Iteration Time (s) | |
---|---|---|---|

Training Accuracy | Testing Accuracy | ||

CEEMDANICA-TDCNN | 100 | 100 | 131 |

CEEMDANICA-BPNN | 96.76 | 99.52 | 170 |

CEEMDANICA-SAE | 95.1 | 95.67 | 97 |

CEEMDANICA-MLP | 100 | 71.43 | 84 |

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**MDPI and ACS Style**

Li, G.; Chen, Y.; Wang, W.; Wu, Y.; Liu, R.
Automatic Transmission Bearing Fault Diagnosis Based on Comprehensive Index Method and Convolutional Neural Network. *World Electr. Veh. J.* **2022**, *13*, 184.
https://doi.org/10.3390/wevj13100184

**AMA Style**

Li G, Chen Y, Wang W, Wu Y, Liu R.
Automatic Transmission Bearing Fault Diagnosis Based on Comprehensive Index Method and Convolutional Neural Network. *World Electric Vehicle Journal*. 2022; 13(10):184.
https://doi.org/10.3390/wevj13100184

**Chicago/Turabian Style**

Li, Guangxin, Yong Chen, Wenqing Wang, Yimin Wu, and Rui Liu.
2022. "Automatic Transmission Bearing Fault Diagnosis Based on Comprehensive Index Method and Convolutional Neural Network" *World Electric Vehicle Journal* 13, no. 10: 184.
https://doi.org/10.3390/wevj13100184