# Fault Diagnosis of Rolling Bearing Using Multiscale Amplitude-Aware Permutation Entropy and Random Forest

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## Abstract

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## 1. Introduction

- (1)
- In this paper, a fault diagnosis method of rolling bearings is presented. On the basis of accurately identifying the fault types of rolling bearings, the fault severity of rolling bearings can be analyzed.
- (2)
- Multiscale amplitude-aware permutation entropy is proposed for the first time, and it is successfully applied to fault feature extraction of rolling bearings.
- (3)
- The random forest multi-classifier is used to identify the fault feature of rolling bearings and analyze the fault severity, and the fault identification accuracy is high.

## 2. Methods

#### 2.1. Multiscale Entropy

#### 2.2. Amplitude-Aware Permutation Entropy

#### 2.3. Random Forest

## 3. The Proposed Fault Diagnosis Method for Rolling Bearings

- (1)
- Set the scale factor $\tau =1,2,\cdots ,n$ of rolling bearings, and $n$ coarse-grained vibration signals are obtained for each vibration signal in the set.
- (2)
- For each coarse-grained vibration signal, calculate $n$ amplitude-aware permutation entropy values to construct the fault feature vector.
- (3)
- The fault feature vector set is constructed by the fault feature vectors extracted by Step (3).
- (4)
- The random tree classifier is established by the fault feature vector set.
- (5)
- The testing vibration signal can be analyzed by the proposed method and get the fault type and fault severity of rolling bearings.

## 4. Experiments and Results

#### 4.1. Experimental Setup

#### 4.2. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

MAAPE | Multiscale amplitude-aware permutation entropy |

WT | Wavelet transform |

WPT | Wavelet packet transform |

EMD | Empirical mode decomposition |

EEMD | Ensemble empirical mode decomposition |

CEEMD | Complete ensemble empirical mode decomposition |

LMD | Local mean decomposition |

ApEn | Approximate entropy |

SampEn | Sample entropy |

MSE | Multiscale entropy |

PE | Permutation entropy |

RBF | Radical basis function |

BP | Back-propagation |

SVM | Support vector machine |

SKF | Svenska Kullager-Fabriken |

RF | Random forest |

IMPE | Improved multiscale permutation entropy |

RCMPE | Refined composite multiscale permutation entropy |

IMSE | Improved multiscale entropy |

IMFE | Improved multiscale fuzzy entropy |

RCMSE | Refined composite multiscale entropy |

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**Figure 1.**Coarse-graining procedure diagram of multiscale entropy (MSE). (

**a**) Scale factor $\tau =2$; (

**b**) Scale factor $\tau =3$.

**Figure 3.**The time-domain waveforms of rolling bearing vibration signals with different types and fault severity under 0 load.

**Figure 5.**MAAPE feature values of rolling bearing vibration signal under inner race fault condition with different loads. (

**a**) Inner race fault, 7 mils, with load 0 hp. (

**b**) Inner race fault, 7 mils, with load 1 hp. (

**c**) Inner race fault, 7 mils, with load 2 hp. (

**d**) Inner race fault, 7 mils, with load 3 hp.

**Figure 6.**MAAPE feature values of rolling bearing vibration signal under different fault conditions with the same loads. (

**a**) Inner race fault, 7 mils, with load 1 hp. (

**b**) Outer race fault, 7 mils, with load 1 hp. (

**c**) Ball elements fault, 7 mils, with load 1 hp.

**Figure 7.**Feature clustering graph of MAAPE with different loads. (

**a**) Load 0 hp. (

**b**) Load 1 hp. (

**c**) Load 2 hp. (

**d**) Load 3 hp.

**Figure 8.**MAAPE feature clustering diagram of each fault severity under different loads. (

**a**) Load 0 hp. (

**b**) Load 1 hp. (

**c**) Load 2 hp. (

**d**) Load 3 hp.

Fault Type | Labels | Fault Diameter (mils) | Load (hp) | |||
---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | |||

Normal | NM | - | ✓ | ✓ | ✓ | ✓ |

Inner race fault | IR07 | 7 | ✓ | ✓ | ✓ | ✓ |

IR14 | 14 | ✓ | ✓ | ✓ | ✓ | |

IR21 | 21 | ✓ | ✓ | ✓ | ✓ | |

Outer race fault | OR07 | 7 | ✓ | ✓ | ✓ | ✓ |

OR14 | 14 | ✓ | ✓ | ✓ | ✓ | |

OR21 | 21 | ✓ | ✓ | ✓ | ✓ | |

Ball elements fault | BE07 | 7 | ✓ | ✓ | ✓ | ✓ |

BE14 | 14 | ✓ | ✓ | ✓ | ✓ | |

BE21 | 21 | ✓ | ✓ | ✓ | ✓ |

Feature Extraction Methods | Average Between-Class Distance | Average Within-Class Distance | Average Time-Consuming (S) |
---|---|---|---|

MAAPE | 1.24 | 0.20 | 0.39 |

IMPE | 0.95 | 0.23 | 0.57 |

RCMPE | 0.96 | 0.30 | 1.11 |

IMSE | 2.22 | 0.94 | 0.42 |

IMFE | 3.72 | 0.33 | 17.30 |

RCMSE | 4.02 | 0.38 | 0.40 |

**Table 3.**Fault identification accuracy by combining different fault feature extraction methods with random forest.

Feature Extraction Methods | Fault Identification Accuracy (%) |
---|---|

MAAPE | 96.0% |

IMPE | 96.0% |

RCMPE | 97.50% |

IMSE | 84.25% |

IMFE | 96.25% |

RCMSE | 92.25% |

**Table 4.**Identification rate of the proposed rolling bearing fault diagnosis method for different fault severity.

Type Labels | NM | IR07 | IR14 | IR21 | OR07 | OR14 | OR21 | BE07 | BE14 | BE21 | Identification Accuracy (%) |
---|---|---|---|---|---|---|---|---|---|---|---|

NM | 40 | - | - | - | - | - | - | - | - | - | 100 |

IR07 | - | 40 | - | - | - | - | - | - | - | - | 100 |

IR14 | - | - | 39 | - | - | - | - | - | 1 | - | 97.5 |

IR21 | - | - | - | 40 | - | - | - | - | - | - | 100 |

OR07 | - | - | - | - | 40 | - | - | - | - | - | 100 |

OR14 | - | - | - | - | - | 39 | - | - | 1 | - | 97.5 |

OR21 | - | 1 | - | - | - | - | 39 | - | - | 97.5 | |

BE07 | - | - | - | - | - | - | - | 40 | - | - | 100 |

BE14 | - | - | - | - | - | 2 | - | 2 | 34 | 2 | 85 |

BE21 | - | - | - | - | - | - | - | 4 | 1 | 35 | 87.5 |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Zhang, T.; Zhao, W.; Luo, Z.; Sun, K.
Fault Diagnosis of Rolling Bearing Using Multiscale Amplitude-Aware Permutation Entropy and Random Forest. *Algorithms* **2019**, *12*, 184.
https://doi.org/10.3390/a12090184

**AMA Style**

Chen Y, Zhang T, Zhao W, Luo Z, Sun K.
Fault Diagnosis of Rolling Bearing Using Multiscale Amplitude-Aware Permutation Entropy and Random Forest. *Algorithms*. 2019; 12(9):184.
https://doi.org/10.3390/a12090184

**Chicago/Turabian Style**

Chen, Yinsheng, Tinghao Zhang, Wenjie Zhao, Zhongming Luo, and Kun Sun.
2019. "Fault Diagnosis of Rolling Bearing Using Multiscale Amplitude-Aware Permutation Entropy and Random Forest" *Algorithms* 12, no. 9: 184.
https://doi.org/10.3390/a12090184