# Study on a Novel Fault Diagnosis Method Based on VMD and BLM

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Method

#### 2.1. VMD

#### 2.2. Deep Belief Network

#### 2.3. Broad Learning Model

**W**

^{m}are the connecting weights of BLM.

## 3. A New Fault Diagnosis Method Based on VMD, HT and BLM

#### 3.1. The Idea of the VHBLFD Method

#### 3.2. The Fault Diagnosis Model and Steps

#### 3.3. The Steps of the Fault Diagnosis Method

**Step 1:**The acceleration sensors are used to collect vibration acceleration signals of rolling bearings of the AC motor.

**Step 2:**Initialize these parameters of the proposed VHBLFD method using VMD, HT and BLM. These parameters mainly include the number of decompositions of VMD, the number of feature nodes per window, the windows and the enhancement nodes of BLM, and so on.

**Step 3:**The VMD is used to decompose the vibration acceleration signals into a series of IMFs.

**Step 4:**According to the number of decompositions of the VMD method, four IMF components are determined.

**Step 5:**The HT is used to process the four IMF components to obtain the Hilbert envelope spectrum for obtaining fault features.

**Step 6:**The Hilbert envelope spectrums of four IMF components are connected by the beginning and the end to construct the feature matrix.

**Step 7:**The fault features are proportionally divided into the training feature samples and the test feature samples.

**Step 8:**Calculate the feature nodes of the BLM according to Formula (8) and the enhancement nodes of the BLM according to Formula (9).

**Step 9:**Calculate the output of the BLM based on the feature nodes and the enhancement nodes using the pseudo inverse operation.

**Step 10:**Input the training feature samples to train BLM in order to obtain the trained BLM for realizing the fault diagnosis.

**Step 11:**Test feature samples are used to validate the effectiveness of the proposed VHBLFD to obtain diagnosis results. Analyze and verify the effectiveness and the rapidity of the VHBLFD method.

## 4. Validation and Analysis of the VHBLFD Method

#### 4.1. Experiment Data and Environment

#### 4.2. Feature Extraction

#### 4.3. Fault Diagnosis Results

#### 4.4. Comparision and Analysis for Diagnosis Results

#### 4.5. The Influences of Parameters in BLM for Diagnosis Accuracy

#### 4.5.1. The Influences of the Number of Feature Nodes for Diagnosis Accuracy

^{−30}, and the enhance node reduction ratio s is 0.8 in Table 1. N11 is the number of feature nodes. N2 is the number of feature node windows. N33 is the number of enhancement nodes.

#### 4.5.2. The Influences of the Number of Feature Node Windows for Diagnosis Accuracy

^{−30}, and the enhance node reduction ratio s is 0.8 in Table 5.

#### 4.5.3. The Influences of the Number of Enhancement Nodes for Diagnosis Accuracy

^{−30}, and the enhance node reduction ratio s is 0.8 in Table 6.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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No. | Inner Race | Outer Race | Rolling Element |
---|---|---|---|

1 | −0.0830 | 0.0085 | −0.0028 |

2 | −0.1957 | 0.4235 | −0.0963 |

3 | 0.2334 | 0.0130 | 0.1137 |

4 | 0.1040 | −0.2652 | 0.2573 |

5 | −0.1811 | 0.2372 | −0.0583 |

6 | 0.0556 | 0.5909 | −0.1260 |

7 | 0.1738 | −0.0930 | 0.2074 |

8 | −0.0469 | −0.4069 | 0.1727 |

9 | −0.1119 | 0.2794 | −0.2199 |

10 | 0.0596 | 0.4370 | −0.1561 |

11 | 0 | −0.3529 | 0.2240 |

… | … | … | … |

2041 | 0.2305 | 0.0309 | 0.2375 |

2042 | 0.0461 | 0.1186 | −0.0271 |

2043 | −0.5122 | −0.0061 | −0.1327 |

2044 | 0.1481 | −0.0979 | 0.0929 |

2045 | 0.6280 | 0.0914 | 0.1106 |

2046 | −0.2043 | 0.1494 | −0.1499 |

2047 | −0.2640 | −0.2355 | −0.1108 |

2048 | 0.4662 | −0.3224 | 0.1467 |

Fault Diagnosis Method | Diagnostic Accuracy (%) | Test Time (s) |
---|---|---|

VHBLFD1 (100,5,1000) | 95.99 | 6.45 |

VHBLFD2 (100,15,17000) | 97.74 | 22.29 |

Diagnosis Methods | Diagnostic Accuracy (%) | Test Time (s) |
---|---|---|

VHSMFD | 40.46 | 274.71 |

EHDNFD | 95.02 | 664.57 |

EEHDNFD | 96.55 | 630.37 |

VHDNFD | 97.68 | 459.21 |

VHBLFD | 97.74 | 22.29 |

**Table 4.**Test results for different feature nodes. (N11 is the number of feature nodes, N2 is the number of feature node windows, and N33 is the number of enhancement nodes).

(N11, N2, N33) | Test Accuracy (%) | Total Average Time (s) |
---|---|---|

40, 15, 3000 | 96.9902 | 4.8618 |

50, 15, 3000 | 96.9601 | 5.2248 |

60, 15, 3000 | 96.3506 | 5.6163 |

70, 15, 3000 | 96.2904 | 6.0630 |

80, 15, 3000 | 96.2302 | 6.5115 |

90, 15, 3000 | 95.8239 | 7.0634 |

100, 15, 3000 | 95.5982 | 7.5683 |

200, 15, 3000 | 92.0692 | 15.0772 |

300, 15, 3000 | 89.7968 | 21.7082 |

Number of Nodes (N11, N2, N33) | Test Accuracy (%) | Total Average Time (s) |
---|---|---|

100, 5, 1000 | 95.8239 | 3.4090 |

100, 10, 1000 | 95.7787 | 4.9404 |

100, 15, 1000 | 95.9443 | 6.4226 |

100, 20, 1000 | 95.9819 | 7.9057 |

100, 25, 1000 | 95.9142 | 9.4303 |

100, 30, 1000 | 96.0797 | 10.9200 |

100, 35, 1000 | 95.6734 | 12.4819 |

100, 40, 1000 | 95.7035 | 14.1060 |

100, 45, 1000 | 95.7863 | 15.8277 |

100, 50, 1000 | 95.7562 | 17.6226 |

100, 55, 1000 | 95.4778 | 19.6315 |

100, 60, 1000 | 95.7411 | 20.9249 |

100, 65, 1000 | 95.6358 | 22.5161 |

100, 70, 1000 | 95.7712 | 24.0979 |

100, 75, 1000 | 95.6659 | 35.2004 |

100, 80, 1000 | 95.4778 | 26.8084 |

100, 85, 1000 | 95.5304 | 28.5762 |

100, 90, 1000 | 95.6358 | 30.5728 |

Number of Nodes (N11, N2, N33) | Test Accuracy (%) | Total Average Time (s) |
---|---|---|

100, 15, 1000 | 95.9970 | 6.4500 |

100, 15, 2000 | 96.5613 | 7.1869 |

100, 15, 3000 | 95.5982 | 7.5683 |

100, 15, 4000 | 90.0000 | 8.0937 |

100, 15, 5000 | 80.7374 | 8.9812 |

100, 15, 6000 | 93.4989 | 9.2012 |

100, 15, 7000 | 95.6810 | 9.9691 |

100, 15, 8000 | 96.5162 | 10.7368 |

100, 15, 9000 | 97.0880 | 11.6575 |

100, 15, 10000 | 97.1257 | 12.7143 |

100, 15, 11000 | 97.2611 | 13.6536 |

100, 15, 12000 | 97.3589 | 14.8280 |

100, 15, 13000 | 97.4643 | 16.0800 |

100, 15, 14000 | 97.6072 | 17.3710 |

100, 15, 15000 | 97.5320 | 18.6380 |

100, 15, 16000 | 97.7200 | 20.8649 |

100, 15, 17000 | 97.7351 | 22.2932 |

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**MDPI and ACS Style**

Zheng, J.; Yuan, Y.; Zou, L.; Deng, W.; Guo, C.; Zhao, H.
Study on a Novel Fault Diagnosis Method Based on VMD and BLM. *Symmetry* **2019**, *11*, 747.
https://doi.org/10.3390/sym11060747

**AMA Style**

Zheng J, Yuan Y, Zou L, Deng W, Guo C, Zhao H.
Study on a Novel Fault Diagnosis Method Based on VMD and BLM. *Symmetry*. 2019; 11(6):747.
https://doi.org/10.3390/sym11060747

**Chicago/Turabian Style**

Zheng, Jianjie, Yu Yuan, Li Zou, Wu Deng, Chen Guo, and Huimin Zhao.
2019. "Study on a Novel Fault Diagnosis Method Based on VMD and BLM" *Symmetry* 11, no. 6: 747.
https://doi.org/10.3390/sym11060747