# Fault Diagnosis Method of Roadheader Bearing Based on VMD and Domain Adaptive Transfer Learning

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Introduction

#### 2.1. Variational Mode Decomposition

^{2}norm of the analytic signal was given, and the variational mode was obtained as follows:

^{−6}is taken in this paper.

#### 2.2. Transfer Learning

_{s}and n

_{t}denote the number of data in SD and TD, respectively. The purpose of TL is to utilize the knowledge of the SD to solve the problem of the TD. The data distribution between TD $P\left({x}^{t}\right)$ and SD $P\left({x}^{s}\right)$ is different.

#### 2.2.1. Maximum Mean Difference

_{1}and n

_{2}represent the number of samples in X and Y. $\varphi (\cdot )$ represents the nonlinear mapping relationship between samples and RKHS. In application, to improve the measurement ability of MMDS for complex domains $\varphi (\cdot )$ is often replaced by the kernel function.

#### 2.2.2. Domain Adaptive

- (1)
- Adaptive boundary distribution domain

- (2)
- The adaptive domain of conditional distribution

- (3)
- Jointly distributed domain adaptive

#### 2.2.3. Convolutional Neural Network

#### 2.3. VMD-DACNN Method

#### 2.3.1. VMD-DACNN Networks

#### 2.3.2. Fault Diagnosis

#### 2.3.3. Flowchart of the VMD-DACNN Algorithm

- (1)
- The vibration data of the roadheader machine collected under VWC were processed with the maximum (minimum) normalization. According to the working conditions, the data were divided into SD data with labeled information and TD data without labeled information. SD data and part of the TD data were combined to form a model training set, and the remaining TD samples were utilized as test sets to verify the model’s performance;
- (2)
- We initialized the network parameters of the VMD-DACNN model and trained the model with the training set until the maximum number of iterations was reached, leading to the fault diagnosis model of the roadheader machine under VWC;
- (3)
- The test set was input into the trained VMD-DACNN model for fault diagnosis, and the fault diagnosis results of the roadheader machine were obtained.

## 3. Experiment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ji, X.; Yang, Y.; Qu, Y.; Jiang, H.; Wu, M. Health Diagnosis of Roadheader Based on Reference Manifold Learning and Improved K-Means. Shock Vib.
**2021**, 2021, 6311795. [Google Scholar] [CrossRef] - Huang, Z.; Zhang, Z.; Li, Y.; Song, G.; He, Y. Nonlinear dynamic analysis of cutting head-rotor-bearing system of the roadheader. J. Mech. Sci. Technol.
**2019**, 33, 1033–1043. [Google Scholar] [CrossRef] - Liu, Y.; Gao, Y.; Zhang, Y.; Fu, J.; Huang, C. Working Vibration Analysis of the Bearing Plate on Roadheader Test Bed. In MATEC Web of Conferences; EDP Sciences: Les Ulis, France, 2015; p. 03019. [Google Scholar]
- Liu, Q.; Liu, S.; Dai, Q.; Cui, Y.; Xie, Q. A novel exponential degradation approach for predicting the remaining useful life of roadheader bearings. Meas. Sci. Technol.
**2023**, 34, 035114. [Google Scholar] [CrossRef] - Liu, Q.; Liu, S.; Dai, Q.; Yu, X.; Teng, D.; Wei, M. Data-Driven Approaches for Diagnosis of Incipient Faults in Cutting Arms of the Roadheader. Shock Vib.
**2021**, 2021, 8865068. [Google Scholar] [CrossRef] - Liang, X.; Yao, J.; Zhang, W.; Wang, Y. A Novel Fault Diagnosis of a Rolling Bearing Method Based on Variational Mode Decomposition and an Artificial Neural Network. Appl. Sci.
**2023**, 13, 3413. [Google Scholar] [CrossRef] - Zhu, H.; He, Z.; Xiao, Y.; Wang, J.; Zhou, H. Bearing Fault Diagnosis Method Based on Improved Singular Value Decomposition Package. Sensors
**2023**, 23, 3759. [Google Scholar] [CrossRef] - Bai, H.; Zhan, X.; Yan, H.; Wen, L.; Jia, X. Combination of Optimized Variational Mode Decomposition and Deep Transfer Learning: A Better Fault Diagnosis Approach for Diesel Engines. Electronics
**2022**, 11, 1969. [Google Scholar] [CrossRef] - Gharesi, N.; Arefi, M.M.; Razavi-Far, R.; Zarei, J.; Yin, S. A neuro-wavelet based approach for diagnosing bearing defects. Adv. Eng. Inform.
**2020**, 46, 101172. [Google Scholar] [CrossRef] - Abas, A.R.; Elhenawy, I.; Zidan, M.; Othman, M. BERT-CNN: A Deep Learning Model for Detecting Emotions from Text. Cmc-Comput. Mater. Contin.
**2022**, 71, 2943–2961. [Google Scholar] - Zhang, P.; Zhuo, T.; Huang, W.; Chen, K.; Kankanhalli, M. Online object tracking based on CNN with spatial-temporal saliency guided sampling. Neurocomputing
**2017**, 257, 115–127. [Google Scholar] [CrossRef] - Wan, H.; Gu, X.; Yang, S.; Fu, Y. A Sound and Vibration Fusion Method for Fault Diagnosis of Rolling Bearings under Speed-Varying Conditions. Sensors
**2023**, 23, 3130. [Google Scholar] [CrossRef] [PubMed] - Liu, W.; Zhang, Z.; Zhang, J.; Huang, H.; Zhang, G.; Peng, M. A Novel Fault Diagnosis Method of Rolling Bearings Combining Convolutional Neural Network and Transformer. Electronics
**2023**, 12, 1838. [Google Scholar] [CrossRef] - Ding, X.; Wang, H.; Cao, Z.; Liu, X.; Liu, Y.; Huang, Z. An Edge Intelligent Method for Bearing Fault Diagnosis Based on a Parameter Transplantation Convolutional Neural Network. Electronics
**2023**, 12, 1816. [Google Scholar] [CrossRef] - Shao, X.R.; Kim, C.S. Unsupervised Domain Adaptive 1D-CNN for Fault Diagnosis of Bearing. Sensors
**2022**, 22, 4156. [Google Scholar] [CrossRef] [PubMed] - Wang, Z.; Liu, Q.; Chen, H.; Chu, X. A deformable CNN-DLSTM based transfer learning method for fault diagnosis of rolling bearing under multiple working conditions. Int. J. Prod. Res.
**2021**, 59, 4811–4825. [Google Scholar] [CrossRef] - Shin, J.; Lee, S. Robust and Lightweight Deep Learning Model for Industrial Fault Diagnosis in Low-Quality and Noisy Data. Electronics
**2023**, 12, 409. [Google Scholar] [CrossRef] - Yoo, Y.; Jo, H.; Ban, S.W. Lite and Efficient Deep Learning Model for Bearing Fault Diagnosis Using the CWRU Dataset. Sensors
**2023**, 23, 3157. [Google Scholar] [CrossRef] - Zhou, Y.; Dong, Y.; Zhou, H.; Tang, G. Deep Dynamic Adaptive Transfer Network for Rolling Bearing Fault Diagnosis with Considering Cross-Machine Instance. IEEE Trans. Instrum. Meas.
**2021**, 70, 1–11. [Google Scholar] [CrossRef] - Wu, J.; Zhao, Z.; Sun, C.; Yan, R.; Chen, X. Few-shot transfer learning for intelligent fault diagnosis of machine. Measurement
**2020**, 166, 108202. [Google Scholar] [CrossRef] - Cao, N.; Jiang, Z.N.; Gao, J.J.; Cui, B. Bearing State Recognition Method Based on Transfer Learning Under Different Working Conditions. Sensors
**2020**, 20, 234. [Google Scholar] [CrossRef] - Jiang, L.; Zheng, C.P.; Li, Y.B. Rotating machinery fault diagnosis based on transfer learning and an improved convolutional neural network. Meas. Sci. Technol.
**2022**, 33, 105012. [Google Scholar] [CrossRef]

**Figure 11.**Accuracy and loss curve during training. (

**a**) Accuracy of source and target domains and (

**b**) loss curve.

**Figure 14.**Visualization of the results of each algorithm. (

**a**) SVM (

**b**) CNN (

**c**) MMD-CNN (

**d**) CORAL-CNN (

**e**) DACNN and (

**f**) VMD-DACNN.

Modulus | IMF1 | IMF2 | IMF3 | IMF4 |
---|---|---|---|---|

Kr | 4.15 | 3.11 | 3.913 | 3.22 |

Health Condition | Classify | Label | Date1 (D1) 1482 RPM | Date2 (D2) 736 RPM |
---|---|---|---|---|

Normal | 0 | N | 400 | 400 |

Outer fault | 1 | OR | 400 | 400 |

Inner fault | 2 | IR | 400 | 400 |

Ball fault | 3 | B | 400 | 400 |

Network Structure | Channel | Kernel Size | Fill |
---|---|---|---|

Input layer | / | / | / |

Convolution layer 1 | 16 | 16 × 1 | Yes |

Normalized layer 1 | / | / | / |

Pooling layer 1 | 16 | 2 × 1 | / |

Convolution layer 2 | 32 | 3 × 1 | Yes |

Normalized layer 2 | / | / | / |

Pooling layer 2 | 32 | 2 × 1 | / |

Convolution layer 3 | 32 | 3 × 1 | Yes |

Normalized layer 3 | / | / | / |

Pooling layer 3 | 32 | 2 × 1 | / |

Fully-connected layer | 256 | / | / |

Dropout | / | 0.4 | / |

Output layer | 4 | / | / |

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**MDPI and ACS Style**

Qu, X.; Zhang, Y.
Fault Diagnosis Method of Roadheader Bearing Based on VMD and Domain Adaptive Transfer Learning. *Sensors* **2023**, *23*, 5134.
https://doi.org/10.3390/s23115134

**AMA Style**

Qu X, Zhang Y.
Fault Diagnosis Method of Roadheader Bearing Based on VMD and Domain Adaptive Transfer Learning. *Sensors*. 2023; 23(11):5134.
https://doi.org/10.3390/s23115134

**Chicago/Turabian Style**

Qu, Xiaofei, and Yongkang Zhang.
2023. "Fault Diagnosis Method of Roadheader Bearing Based on VMD and Domain Adaptive Transfer Learning" *Sensors* 23, no. 11: 5134.
https://doi.org/10.3390/s23115134