# A Hybrid Feature Model and Deep-Learning-Based Bearing Fault Diagnosis

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Statistical Features

#### 2.2. Envelope Power Spectrum

#### 2.3. Wavelet Packet Transform (WPT)

#### 2.4. Sparse Stacked Autoencoders (SSAEs)

## 3. Dataset

## 4. Results and Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The proposed hierarchical fault diagnosis model, where SAE stands for stacked autoencoder.

**Figure 2.**Envelope power spectrum: (

**a**) inner raceway fault; (

**b**) outer raceway fault, and (

**c**) roller element fault.

**Figure 3.**An illustration of a three-level wavelet packet tree decomposition, where I/P stands for input.

**Figure 4.**Wavelet energy features, (

**a**) baseline condition; (

**b**) inner fault signals; (

**c**) outer fault signals; and (

**d**) roller fault signals.

**Figure 6.**Case Western Reserve University’s seeded fault bearing testbed [46].

**Figure 7.**Bearing fault classification results for the first layer (i.e., the fault pattern recognition layer), BPNN and RBF-OAASVM stand for back-propagation neural network and radial basis function-one against all support vector machine, respectively.

Features | Equations | Features | Equations | Features | Equations |
---|---|---|---|---|---|

Mean value (MV) | $\overline{x}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}}$ | Standard deviation (SD) | ${\sigma}^{2}=\frac{1}{N-1}{\displaystyle \sum _{i=1}^{N}{({x}_{i}-\overline{x})}^{2}}$ | Root mean square (RMS) | $RMS={(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{2}})}^{{\scriptscriptstyle \frac{1}{2}}}$ |

Peak-to-peak value (PPV) | $PPV=\mathrm{max}({x}_{i})-\mathrm{min}({x}_{i})$ | Skewness value (SV) | $SV=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{(\frac{{x}_{i}-\overline{x}}{\sigma})}^{3}}$ | Margin factor (MF) | $MF=\frac{\mathrm{max}(|{x}_{i}|)}{{(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\sqrt{|{x}_{i}|}})}^{2}}$ |

Crest factor (CF) | $MF=\frac{\mathrm{max}(|{x}_{i}|)}{(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{2}){\scriptscriptstyle \frac{1}{2}}}}$ | Impulse factor (IF) | $IF=\frac{\mathrm{max}(|{x}_{i}|)}{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}|{x}_{i}|}}$ | Square root of the magnitude (SRM) | $SRM=(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\sqrt{|{x}_{i}|}{)}^{2}}$ |

Kurtosis value (KV) | $KV=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{\left(\frac{{x}_{i}-\overline{x}}{\sigma}\right)}^{4}}$ | Kurtosis factor (KF) | $KF=\frac{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{(\frac{{x}_{i}-\overline{x}}{\sigma})}^{4}}}{(\frac{1}{N}{\displaystyle \sum _{1}^{N}{x}_{i}^{2}{)}^{2}}}$ |

Feature | Equation |
---|---|

RMS frequency | $RM{S}_{f}={(\frac{1}{K}{\displaystyle \sum _{i=1}^{K}{{y}_{K}}^{2}})}^{{\scriptscriptstyle \frac{1}{2}}}$ |

Frequency center | $FC=\frac{1}{K}{\displaystyle \sum _{i=1}^{K}{y}_{K}}$ |

Standard deviation | ${\sigma}_{f}^{2}=\frac{1}{K}{\displaystyle \sum _{i=1}^{K}{({y}_{K}-FC)}^{2}}$ |

Root variance frequency | $RVF={(\frac{1}{K}{\displaystyle \sum _{i=1}^{K}{({y}_{K}-FC)}^{2}})}^{{\scriptscriptstyle \frac{1}{2}}}$ |

Spectral kurtosis | ${K}_{f}=\frac{1}{K}\frac{{\displaystyle \sum _{i=1}^{K}{({y}_{K}-FC)}^{4}}}{{({\sigma}_{f}^{2})}^{2}}$ |

Fault Type | Fault Location | Fault Size (Inches) | Training Samples | Test Samples | Sample Length | Accelerometer Position | Shaft Load (hp) |
---|---|---|---|---|---|---|---|

Normal | None | 0 | 40 | 30 | 12,000 | Drive End Bearings | 0, 1, 2, 3 |

Inner raceway | IR | 0.007 | 30 | 30 | |||

IR | 0.014 | 30 | 30 | ||||

IR | 0.021 | 30 | 30 | ||||

Outer raceway | OR | 0.007 | 30 | 30 | |||

OR | 0.014 | 30 | 30 | ||||

OR | 0.021 | 30 | 30 | ||||

Roller | RE | 0.007 | 30 | 30 | |||

RE | 0.014 | 30 | 30 | ||||

RE | 0.021 | 30 | 30 |

Method | Layer 1 Average Accuracy (%) | Layer 2 Average Accuracy (%) | Total (%) | ||
---|---|---|---|---|---|

0.007 Inches | 0.014 Inches | 0.021 Inches | |||

VSI [47] | 60.15 | 55 | 55 | 84.6 | 63.68 |

Proposed | 99.75 | 100 | 100 | 96.66 | 99.10 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sohaib, M.; Kim, C.-H.; Kim, J.-M. A Hybrid Feature Model and Deep-Learning-Based Bearing Fault Diagnosis. *Sensors* **2017**, *17*, 2876.
https://doi.org/10.3390/s17122876

**AMA Style**

Sohaib M, Kim C-H, Kim J-M. A Hybrid Feature Model and Deep-Learning-Based Bearing Fault Diagnosis. *Sensors*. 2017; 17(12):2876.
https://doi.org/10.3390/s17122876

**Chicago/Turabian Style**

Sohaib, Muhammad, Cheol-Hong Kim, and Jong-Myon Kim. 2017. "A Hybrid Feature Model and Deep-Learning-Based Bearing Fault Diagnosis" *Sensors* 17, no. 12: 2876.
https://doi.org/10.3390/s17122876