# A Multichannel Data Fusion Method Based on Multiple Deep Belief Networks for Intelligent Fault Diagnosis of Main Reducer

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Deep Learning and Fusion of Deep Representative Features

#### 2.1. Deep Belief Networkwith Gaussian-Bernoulli RBM

_{v}and N

_{h}separately represent the number of visible units and hidden units. Considering the standard deviation of visible units, the joint energy of visible and hidden layer units of GRBM is given as follows:

^{(1)}, h

^{(2)},…, h

^{(L)}) in which input layer and h

^{(1)}form GRBM1, h

^{(1)}and h

^{(2)}form GRBM2, h

^{(L−1)}and h

^{(L)}form GRBM L.

#### 2.2. Deep Learning of Multichannel Data Using MDBNs

^{1}, DBN

^{2},…, DBN

^{M}) wherein DBN

^{i}is used to learn deep representative features of the vibration signals collected from the ith channel of M channels expressed as Channel 1, Channel 2,…, Channel M. By using MDBNs, after multiple non-linear hierarchical transformations of the input data from multichannel, the deep representative features of the raw data are acquired.

^{(1)}, X

^{(2)},…, X

^{(M)}, the output of the ith DBN is expressed as:

^{(i)}is converted into deep representative features expressed as ${p}^{i}$.

#### 2.3. Random Forest Fusion of Deep Representative Features

## 3. Application to Intelligent Fault Diagnosis of Main Reducer

#### 3.1. Multiple Modalities Features of Multichannel Vibration Signal

^{J}energies of the Jth level as condition parameters of time-frequency domain.

^{J}condition parameters of the time-frequency domain expressed as follows:

^{1},…,Z

^{i},…Z

^{M}] in which Z

^{i}= [z

_{1}

^{i},z

_{2}

^{i},z

_{3}

^{i}] represents multiple modalities features of vibration signal collected from the ith sensor.

#### 3.2. The Proposed Diagnostic Model of MDBNF

^{1}(t), X

^{2}(t),…, X

^{M}(t). Define fault patterns for fault diagnosis.

## 4. Experiment and Discussion

#### 4.1. Experiment Setup

#### 4.2. Data Preprocessing

^{6}coefficients are obtained by using WPT and the energy of each coefficient is combined to form a set of condition parameters. In this way, multiple modalities features for the vibration signal collected from each sensor with the dimension of 80 are extracted and stored in a matrix of 1400 rows (number of samples) and 80 columns (number of features).

#### 4.3. Model Design

#### 4.4. Experimental Results and Discussions

#### 4.4.1. Results of the Proposed Model of MDBNF

#### 4.4.2. Principal Component Analysis of the Deep Representative Features

#### 4.4.3. Effectiveness of the Fusion Model

#### 4.4.4. Comparison of Different Diagnostic Models

- (1)
- With the same deep learning architecture of MDBNs, average classification accuracies of diagnostic models that use KNN and SVC to fuse deep representative features of multichannel data have reached 94.63% and 95.79%. However, the performances of these two models are still inferior to the proposed model of MDBNF that uses random forest fusion for multichannel data with the accuracy of 97.72%. It indicates that random forest fusion with majority voting strategy is better than simple classification strategy of KNN and SVC.MDBNF can fuse deep features outputted from DBNs with the input of multichannel data to obtain the final result in higher layer.
- (2)
- Without using multiple sensors to collect vibration signals, the performance of the DBN model with deep learning of single sensory data is 88.58%, which is not ideal and inferior to models with multichannel data fusion. It indicates that sensory data in different channels may contain various failure-sensitive characteristics. Therefore, multichannel data could exhibit more complete characteristic information of the main reducer.
- (3)
- The classification accuracies of models based on SVM with shallow learning of representative features are the worst, namely 73.16% and 74.37%, no matter which kind of data is selected. It indicates that deep learning architecture indeed extracts more fault-sensitive features of main reducer than shallow learning and could effectively establish non-linear relationships between vibration measurements and fault patterns of main reducer.
- (4)
- Compared with all the peer models, the performance of the proposed diagnostic model of MDBNF with multichannel data is superior to other models for main reducer fault diagnosis. This phenomenon indicates that multichannel data and deep learning architecture can improve the reliability and accuracy for fault diagnosis.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The diagnostic model of main reducer based on multiple deep belief networks fusion (MDBNF).

**Figure 7.**Multichannel data of main reducer: (

**a**) vibration signals collected from sensor 1, (

**b**) vibration signals collected from sensor 2.

**Figure 10.**Comparison experiment results: (

**a**) classifier output for ${p}^{1}$ of ${x}_{268}^{1\prime}\left(t\right)$; (

**b**) classifier output for ${p}^{2}$ of ${x}_{268}^{2\prime}\left(t\right)$; (

**c**) output of fusion model for $\left[{p}^{1},{p}^{2}\right]$; (

**d**) comparison result of classification accuracy for testing set.

Fault Pattern | Condition Patterns |
---|---|

C1 | Normal status |

C2 | Gear error |

C3 | Gear burr |

C4 | Gear hard point |

C5 | Misalignment |

C6 | Gear tooth broken |

C7 | Gear crack |

Fault Patterns | Diagnostic Result | Accuracy | ||||||
---|---|---|---|---|---|---|---|---|

C1 | C2 | C3 | C4 | C5 | C6 | C7 | ||

C1 | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 100% |

C2 | 0 | 49 | 0 | 1 | 0 | 0 | 0 | 98% |

C3 | 0 | 0 | 49 | 0 | 0 | 1 | 0 | 98% |

C4 | 0 | 1 | 0 | 48 | 0 | 0 | 1 | 96% |

C5 | 0 | 0 | 1 | 0 | 49 | 0 | 0 | 98% |

C6 | 0 | 0 | 0 | 0 | 1 | 49 | 0 | 98% |

C7 | 0 | 1 | 0 | 0 | 0 | 1 | 48 | 96% |

No. | Data Type | Learning Level | Diagnostic Models | Accuracy |
---|---|---|---|---|

(1) | Multichannel | Deep learning | MDBNF | 97.72% |

(2) | Multichannel | Deep learning | MDBNs with KNN fusion | 94.63% |

(3) | Multichannel | Deep learning | MDBNs with SVC fusion | 95.79% |

(4) | Single-channel | Deep learning | DBN | 88.58% |

(5) | Multichannel | Shallow learning | SVM | 73.16% |

(6) | Single-channel | Shallow learning | SVM | 74.37% |

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**MDPI and ACS Style**

Ye, Q.; Liu, C.
A Multichannel Data Fusion Method Based on Multiple Deep Belief Networks for Intelligent Fault Diagnosis of Main Reducer. *Symmetry* **2020**, *12*, 483.
https://doi.org/10.3390/sym12030483

**AMA Style**

Ye Q, Liu C.
A Multichannel Data Fusion Method Based on Multiple Deep Belief Networks for Intelligent Fault Diagnosis of Main Reducer. *Symmetry*. 2020; 12(3):483.
https://doi.org/10.3390/sym12030483

**Chicago/Turabian Style**

Ye, Qing, and Changhua Liu.
2020. "A Multichannel Data Fusion Method Based on Multiple Deep Belief Networks for Intelligent Fault Diagnosis of Main Reducer" *Symmetry* 12, no. 3: 483.
https://doi.org/10.3390/sym12030483