# A Diagnosis Method for the Compound Fault of Gearboxes Based on Multi-Feature and BP-AdaBoost

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## Abstract

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## 1. Introduction

- The vibration signal of the gearbox is a non-stationary, nonlinear signal and contains a certain amount of noise [44]. In the process of signal processing, the traditional signal processing methods such as Fourier transform and its improved algorithms, short-time Fourier transform, and wavelet transform have some limitations in processing the vibration signals of the gearbox.
- Traditional fault diagnosis methods rely on expert knowledge and experience to select feature parameters, and mostly extract feature parameters from a single time domain, frequency-domain, or time-frequency-domain analysis. Although some research reveals some fault features, there is still not enough to distinguish different fault modes accurately.
- At present, there is little research on the compound fault diagnosis of gearbox, but, in actual situations, there may be different faults of multiple gears. Although some researchers have made some progress in the diagnosis method of compound faults of gearboxes, the diagnosis accuracy is not high enough, and the algorithm is relatively complex.

- Collect vibration signals of the gearbox under different operating conditions, decompose the original vibration signal of gearbox by EMD, and select the appropriate intrinsic mode functions (IMFs) to reconstruct the new signal;
- First perform time domain analysis on the reconstructed signal, calculate time domain statistical parameters, and select sensitive time domain feature parameters through sensitivity analysis;
- Then, perform wavelet packet analysis on the reconstructed signal, calculate the waveband energy of each frequency band by wavelet packet decomposition, construct band energy feature vectors, and finally form gearbox state feature vectors with the selected time domain feature parameters;
- Establish the BP-AdaBoost model, select training samples and test samples, and use the training samples to train the model;
- Input the test samples into the trained BP-AdaBoost model to obtain the fault diagnosis results.

- By combining BP-AdaBoost with sensitivity analysis and wavelet packet analysis, a novel intelligent fault diagnosis method for the compound fault of gearboxes is proposed, which can effectively diagnose the compound fault of gearboxes.
- In order to improve the accuracy of fault diagnosis, we improve the traditional fault diagnosis method in three aspects. Firstly, EMD decomposition and reconstruction are used to denoise the signal, then sensitivity analysis is used to select the time domain feature parameters with high sensitivity and combine them with wavelet packet energy feature parameters to form the state feature vector. Finally, BP-AdaBoost is used to build the fault diagnosis model.
- The proposed method has certain reference significance and engineering application value for the compound fault of gearboxes as well as other types of faults and machinery.

## 2. Basic Principle of the Proposed Method

#### 2.1. EMD

#### 2.2. Time Domain Analysis

#### 2.3. Wavelet Packet Analysis

#### 2.4. BP-AdaBoost Algorithm

## 3. Experimental Verification and Analysis

#### 3.1. Denoising with EMD

#### 3.2. Time Domain Analysis of a Gearbox Vibration Signal

#### 3.3. Wavelet Packet Analysis of a Gearbox Vibration Signal

#### 3.4. Gearbox Fault Diagnosis Based on BP-AdaBoost

## 4. Comparison Experiment and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The comparison figure of frequency band division between wavelet decomposition and wavelet packet decomposition.

Mode | Preset Fault | Big Gear | Small Gear | Speed | Workload |
---|---|---|---|---|---|

1 | None (Healthy) | Healthy | Healthy | 880 r/min | 0.2 A |

2 | Tooth pitting | Tooth pitting | Healthy | ||

3 | Tooth wear | Healthy | Tooth wear | ||

4 | Broken tooth | Broken tooth | Healthy | ||

5 | Tooth pitting & wear | Tooth pitting | Tooth wear | ||

6 | Broken tooth & wear | Broken tooth | Tooth wear |

Parameters | Mode 1 | Mode 2 | Mode 3 | Mode 4 | Mode 5 | Mode 6 |
---|---|---|---|---|---|---|

P1 | 0.0121 | 0.0267 | −0.2018 | −0.0233 | 0.2207 | 0.0723 |

P2 | 4.2915 | 3.5691 | 20.0055 | 6.3319 | 15.9963 | 19.2551 |

P3 | 2.6146 | 2.0551 | 12.9985 | 4.0900 | 9.3023 | 12.3354 |

P4 | 3.1970 | 2.5351 | 15.5513 | 4.9034 | 11.5979 | 14.8461 |

P5 | 18.4172 | 12.7383 | 400.2220 | 40.0932 | 255.8814 | 370.7581 |

P6 | 21.4670 | 24.6709 | 82.7674 | 24.5781 | 60.6313 | 86.1785 |

P7 | −19.4246 | −29.4615 | −69.0499 | −33.4569 | −91.3556 | −80.3758 |

P8 | 40.8916 | 54.1324 | 151.8173 | 58.0350 | 151.9869 | 166.5542 |

P9 | 1.3424 | 1.4079 | 1.2864 | 1.2913 | 1.3792 | 1.2970 |

P10 | 5.0022 | 6.9124 | 4.1372 | 3.8816 | 3.7903 | 4.4756 |

P11 | 6.7148 | 9.7318 | 5.3222 | 5.0125 | 5.2278 | 5.8048 |

P12 | 8.2103 | 12.0045 | 6.3674 | 6.0093 | 6.5179 | 6.9863 |

P13 | −0.0542 | −0.0886 | 0.0576 | −0.1437 | −0.5402 | −0.1214 |

P14 | 4.5205 | 8.4587 | 3.4973 | 3.7180 | 5.1208 | 3.7584 |

Mode | E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | E10 | E11 |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.0261 | 0.1276 | 0.1610 | 0.1981 | 0.0114 | 0.1179 | 0.1870 | 0.1709 | 0.0574 | 18.8602 | −0.0838 |

··· | |||||||||||

2 | 0.0656 | 0.2726 | 0.1319 | 0.2498 | 0.0133 | 0.0535 | 0.1283 | 0.0851 | −0.0250 | 12.5383 | −0.0711 |

··· | |||||||||||

3 | 0.0247 | 0.0913 | 0.2021 | 0.1237 | 0.0052 | 0.1856 | 0.1230 | 0.2443 | −0.1034 | 369.1129 | −0.0236 |

··· | |||||||||||

4 | 0.0405 | 0.1118 | 0.2245 | 0.1474 | 0.0115 | 0.1833 | 0.1186 | 0.1623 | −0.0190 | 36.2753 | −0.1532 |

··· | |||||||||||

5 | 0.0462 | 0.1319 | 0.2056 | 0.2100 | 0.0041 | 0.0544 | 0.1395 | 0.2082 | 0.1430 | 255.7761 | −0.5698 |

··· | |||||||||||

6 | 0.0406 | 0.2337 | 0.1185 | 0.1365 | 0.0194 | 0.2443 | 0.0696 | 0.1374 | 0.0159 | 352.1008 | −0.0651 |

··· |

Item | Mode 1 | Mode 2 | Mode 3 | Mode 4 | Mode 5 | Mode 6 | Total |
---|---|---|---|---|---|---|---|

Test samples | 60 | 60 | 60 | 60 | 60 | 60 | 360 |

Correct number | 60 | 58 | 57 | 60 | 56 | 58 | 349 |

Accuracy | 100.00% | 96.67% | 95.00% | 100.00% | 93.33% | 96.67% | 96.94% |

Diagnostic Method | Feature Vector | Total Accuracy |
---|---|---|

BPNN | Time domain feature vectors | 80.28% |

BPNN | Frequency domain feature vectors | 45.28% |

BPNN | Energy feature vectors | 81.11% |

BPNN | Multi-feature vectors | 89.17% |

SVM | Time domain feature vectors | 76.11% |

SVM | Frequency domain feature vectors | 50.28% |

SVM | Energy feature vectors | 85.28% |

SVM | Multi-feature vectors | 91.11% |

Proposed method | Multi-feature vectors | 96.94% |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Jia, Y.; Wu, W.; Cheng, Z.; Su, X.; Lin, A.
A Diagnosis Method for the Compound Fault of Gearboxes Based on Multi-Feature and BP-AdaBoost. *Symmetry* **2020**, *12*, 461.
https://doi.org/10.3390/sym12030461

**AMA Style**

Zhang Y, Jia Y, Wu W, Cheng Z, Su X, Lin A.
A Diagnosis Method for the Compound Fault of Gearboxes Based on Multi-Feature and BP-AdaBoost. *Symmetry*. 2020; 12(3):461.
https://doi.org/10.3390/sym12030461

**Chicago/Turabian Style**

Zhang, Yangyang, Yunxian Jia, Weiyi Wu, Zhonghua Cheng, Xiaobo Su, and Aqiang Lin.
2020. "A Diagnosis Method for the Compound Fault of Gearboxes Based on Multi-Feature and BP-AdaBoost" *Symmetry* 12, no. 3: 461.
https://doi.org/10.3390/sym12030461