# Multisensor Feature Fusion Based Rolling Bearing Fault Diagnosis Method

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## Abstract

**:**

## 1. Introduction

- (1)
- A multisensor signals-based feature fusion method is proposed for one-dimensional vibration signals.
- (2)
- The vibration signal of each sensor is preprocessed with VMD, and the time domain, frequency domain and multiscale entropy features of the signal are extracted and fused into one multidomain feature dataset.
- (3)
- To promote further fusion of features, a novel deep autoencoder network is proposed for feature extraction and classification.

## 2. Theoretical Basis

#### Autoencoder

**X**to the hidden layer feature

**H**. The process is as follows:

**H**to obtain the output vector $\widehat{X}$. The process is as follows:

## 3. Proposed Method

#### 3.1. Fusion Model Architecture for Multisensor Signals

#### 3.2. Implementation Process

#### 3.2.1. Multisensor Feature Fusion

- (1)
- The vibration signal ${X}^{1}{}_{l\times 1},{X}^{2}{}_{l\times 1},\cdots ,{X}_{l\times 1}{}^{n}$ is collected from $n$ sensors of different directions, where $l$ is the sample length.
- (2)
- Take the data length $i$ as a sample and divide ${X}^{1}{}_{l\times 1},{X}^{2}{}_{l\times 1},\cdots ,{X}_{l\times 1}{}^{n}$ into ${X}^{1}{}_{m\times i},{X}^{2}{}_{m\times i},\cdots ,{X}^{n}{}_{m\times i}$, where $m$ is the number of samples.
- (3)
- Using the VMD to decompose ${X}^{1}{}_{m\times i},{X}^{2}{}_{m\times i},\cdots ,{X}^{n}{}_{m\times i}$, a number of IMF components of each sensor are obtained, and base on the decomposition results, the first few components already contain the main information of the raw signal [28], so in this paper, we take the modal number $k=3$ and decompose it to obtain ${X}^{1}{}_{m\times 3\times 1024},{X}^{2}{}_{m\times 3\times 1024},\cdots ,{X}^{n}{}_{m\times 3\times 1024}$.
- (4)
- Feature extraction is performed for IMF components, and 12 time-domain features and five frequency-domain features [29] are extracted for each IMF component. To further reflect the degree of self-similarity and complexity of vibration signals under different scale factors of the same time series, five multiscale entropy values are extracted for each IMF component, denoted as ${X}^{1}{}_{m\times 3\times 22},{X}^{2}{}_{m\times 3\times 22},\cdots ,{X}^{n}{}_{m\times 3\times 22}$.
- (5)
- The raw feature multidomain set is formed by fusing the proposed features, denoted as ${X}^{1}{}_{m\times 66},{X}^{2}{}_{m\times 66},\cdots ,{X}^{n}{}_{m\times 66}$, and further fusing the raw feature multidomain set of sensors in each direction to obtain $\tilde{X}=\left[{X}^{1}{}_{m\times 66},{X}^{2}{}_{m\times 66},\cdots ,{X}^{n}{}_{m\times 66}\right],\tilde{X}\in {\mathbb{R}}_{m\times 66\times n}$.

#### 3.2.2. Deep Feature Learning and Classification

- (1)
- The first stage fused feature $\tilde{X}$ is used as the input of the DAEN;
- (2)
- Forward propagation. The hidden layer features of the first AE ${h}_{1}$ is used as the input of the second AE for unsupervised training until all hidden layers are trained;
- (3)
- The backpropagation (BP) algorithm [32] is used for supervised fine-tuning to further optimize all the weights and biases;
- (4)
- The last hidden layer feature, ${h}_{n}^{}$, of the DAEN is fed into the Softmax classifier;
- (5)
- The classification result is obtained.

#### 3.3. Rolling Bearing Fault Diagnosis Process Based on the Proposed Method

- (1)
- Acquisition of rolling bearing vibration data from multiple sensors;
- (2)
- The vibration signal of each sensor is preprocessed with VMD, and the 22 features of the signal are extracted based on the preferred IMF;
- (3)
- The extracted feature is fused into multidomain feature dataset;
- (4)
- The multidomain feature dataset is divided into either a training dataset or a testing dataset, according to the set ratio;
- (5)
- The DAEN model is constructed. The parameters of the DAEN model are initialized, the training dataset is taken as the input to the model and the model loss function is minimized;
- (6)
- The test dataset is fed into the trained DAEN model to obtain the test accuracy.

## 4. Experiment

#### 4.1. Rolling Bearing Test Bench

#### 4.2. Rolling Bearing Multisensor Signals

#### 4.3. Dataset Construction

#### 4.4. Comparative Experiments and Analysis of Results

#### 4.4.1. The Feasibility and Effectiveness of Multisensor Collaborative Diagnosis

#### 4.4.2. Verification of the Superiority of the Proposed Method

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Feature visualization. (

**a**) Feature visualization of raw signal; (

**b**) Feature visualization of Softmax layer.

Fault Type | Fault Depth/mm | Size of Training Dataset | Size of Testing Dataset | Label |
---|---|---|---|---|

Inner race fault 1 | 0.3 | 90 | 10 | 1 |

Inner race fault 2 | 0.4 | 90 | 10 | 2 |

Outer race fault 1 | 0.2 | 90 | 10 | 3 |

Outer race fault 2 | 0.3 | 90 | 10 | 4 |

Rolling ball fault | 0.2 | 90 | 10 | 5 |

Normal | 0 | 90 | 10 | 6 |

Method | Average Test Accuracy (%) | Standard Deviation |
---|---|---|

Multisensor fusion (The proposed method) | 97.55 | 0.485 |

Senor 1 | 93.12 | 0.589 |

Senor 2 | 87.45 | 1.418 |

Senor 3 | 91.28 | 1.803 |

Method | Average Test Accuracy(%) | Standard Deviation |
---|---|---|

The proposed method | 97.55 | 0.485 |

SSAE | 90.67 | 1.792 |

RF | 85.83 | 1.801 |

SVM | 84.16 | 2.255 |

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## Share and Cite

**MDPI and ACS Style**

Tong, J.; Liu, C.; Pan, H.; Zheng, J.
Multisensor Feature Fusion Based Rolling Bearing Fault Diagnosis Method. *Coatings* **2022**, *12*, 866.
https://doi.org/10.3390/coatings12060866

**AMA Style**

Tong J, Liu C, Pan H, Zheng J.
Multisensor Feature Fusion Based Rolling Bearing Fault Diagnosis Method. *Coatings*. 2022; 12(6):866.
https://doi.org/10.3390/coatings12060866

**Chicago/Turabian Style**

Tong, Jinyu, Cang Liu, Haiyang Pan, and Jinde Zheng.
2022. "Multisensor Feature Fusion Based Rolling Bearing Fault Diagnosis Method" *Coatings* 12, no. 6: 866.
https://doi.org/10.3390/coatings12060866