# Low-Speed Bearing Fault Diagnosis Based on Permutation and Spectral Entropy Measures

^{1}

^{a}. Arizmendiarrieta 2, 20500 Arrasate-Mondragón, Spain

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Permutation Entropy

#### 2.2. Spectral Entropy

## 3. Experimental Set-Up

## 4. Methodology

- The raw vibration signal is used for the PE process. As a result, the PE signal is obtained from the PE process.
- The PE signal is later used by the SE process to calculate the SE value according to the rotation time.

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AE | acoustic emission |

CBM | condition based maintenance |

D1 | damage 1 scenario |

D2 | damage 2 scenario |

EEMD | ensemble empirical mode decomposition |

EMD | empirical mode decomposition |

HS | healthy scenario |

O&M | operation and maintenance |

PE | permutation entropy |

PSD | power spectral density |

RMS | root mean square |

rpm | revolutions per minute |

SE | spectral entropy |

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**Figure 1.**Test-rig for low speed bearings: (

**a**) General view of the test-rig. (

**b**) Position of sensor is highlighted with the red arrow. (

**c**) Damage seeded.

**Figure 2.**Several permutation entropy (PE) signals calculated from a D2 bearing at 10 rpm, with ${O}_{p}=3$ and varying ${W}_{p}$.

**Figure 3.**Several PE signals calculated from a D2 bearing at 10 rpm, with ${W}_{p}=2048$ and varying ${O}_{p}$.

**Figure 5.**Results of the spectral entropy (SE) calculation for the PE signal from the raw vibration signal for all scenarios at 5 rpm. (

**a**) Values for each rotation of the bearing. (

**b**) Box plot for statistical analysis of the calculated values.

**Figure 6.**Results of the SE calculation for the PE signal from the raw vibration signal for all scenarios at 10 rpm. (

**a**) Values for each rotation of the bearing. (

**b**) Box plot for statistical analysis of the calculated values.

Slope | y-intercept | |
---|---|---|

healthy | −4.24 × 10^{−6} | 0.29 |

damage 1 | −4.74 × 10^{−5} | 0.26 |

damage 2 | −3.18 × 10^{−5} | 0.13 |

$\overline{\mathit{x}}$ | Md | s | |
---|---|---|---|

healthy | 0.292 | 0.291 | 0.012 |

damage 1 | 0.254 | 0.256 | 0.014 |

damage 2 | 0.129 | 0.125 | 0.031 |

Slope | y-intercept | |
---|---|---|

healthy | −3.05 × 10^{−5} | 0.25 |

damage 1 | −1.51 × 10^{−5} | 0.23 |

damage 2 | −1.71 × 10^{−5} | 0.18 |

$\overline{\mathit{x}}$ | Md | s | |
---|---|---|---|

healthy | 0.245 | 0.246 | 0.016 |

damage 1 | 0.225 | 0.225 | 0.022 |

damage 2 | 0.173 | 0.175 | 0.018 |

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## Share and Cite

**MDPI and ACS Style**

Sandoval, D.; Leturiondo, U.; Pozo, F.; Vidal, Y. Low-Speed Bearing Fault Diagnosis Based on Permutation and Spectral Entropy Measures. *Appl. Sci.* **2020**, *10*, 4666.
https://doi.org/10.3390/app10134666

**AMA Style**

Sandoval D, Leturiondo U, Pozo F, Vidal Y. Low-Speed Bearing Fault Diagnosis Based on Permutation and Spectral Entropy Measures. *Applied Sciences*. 2020; 10(13):4666.
https://doi.org/10.3390/app10134666

**Chicago/Turabian Style**

Sandoval, Diego, Urko Leturiondo, Francesc Pozo, and Yolanda Vidal. 2020. "Low-Speed Bearing Fault Diagnosis Based on Permutation and Spectral Entropy Measures" *Applied Sciences* 10, no. 13: 4666.
https://doi.org/10.3390/app10134666