# Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis

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## Abstract

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## 1. Introduction

## 2. Improved LMD Method and Phase Space Reconstruction of MPE

## 3. Diagnosis Flow Based on HMM

- (1)
- The characteristic index of bearing failure degree is extracted from the fault signal of the needle roller bearing with different degrees of damage, and the feature index is normalized and quantized [24]. When the HMM is established, the sequence of observations should be a finite discrete value, and the discretized value can be used as the model training eigenvalue after quantization.
- (2)
- Diagnosis Flow Based on HMM [25] in Figure 5. The Baum–Welch algorithm [26,27] is used to train, adjust and optimize the parameters of the observation sequence, so that the observed sequence of probability values in the observed sequence is similar to the observed value sequence. We calculate the maximum, HMM state identification, different fault levels of the state to establish the corresponding HMM, the unknown fault state data and in turn enter the various models, calculate and compare the likelihood. The output probability of the largest model is the unknown signal fault type. It is estimated that the most probable path through the sequence is observed by the Baum–Welch algorithm.

## 4. Experimental Data Analysis

## 5. Conclusions

- (1)
- Improved LMD for bearing non-stationary signal processing has a strong signal frequency domain recognition capability. The experiment shows that the improved LMD has greatly improved the reduction of the border. The improved LMD can effectively remove the excess noise and extract important information.
- (2)
- The MI and the FNN can effectively reconstruct the space, reflecting the multi-scale permutation entropy and the mutation performance under different scales.
- (3)
- HMM model of the various states of the bearings can be trained, and successfully diagnoses the bearing fault features. Improved LMD and HMM has a high recognition rate and it is very suitable for a large amount of information, and non-stationarity of the characteristic repeatability fault signal.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Section | BF | OBF | IBF | Normal |
---|---|---|---|---|

t | 1 | 1 | 1 | 2 |

m | 6 | 4 | 5 | 7 |

Fault Condition | Logarithm Likelihood Probabilities of the Input Sample Model | ||||
---|---|---|---|---|---|

λ1 | λ2 | λ3 | λ4 | Recognition Result | |

BF | −9.75854 | −24.5979 | $-\infty $ | $-\infty $ | λ1 |

OBF | −157.594 | −15.1449 | $-\infty $ | $-\infty $ | λ2 |

IBF | $-\infty $ | −55.9402 | −9.33311 | −792.054 | λ3 |

Normal | $-\infty $ | −24.0932 | −59.6398 | −5.63077 | λ4 |

Recognition Model | BF | OBF | IBF | Normal | Recognition Rate | |
---|---|---|---|---|---|---|

Improved LMD | HMM | 5 | 5 | 4 | 5 | 95.0% |

BP | 5 | 4 | 5 | 4 | 90.0% | |

LMD | HMM | 5 | 4 | 4 | 5 | 90.0% |

BP | 5 | 4 | 4 | 4 | 85.0% |

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**MDPI and ACS Style**

Gao, Y.; Villecco, F.; Li, M.; Song, W.
Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis. *Entropy* **2017**, *19*, 176.
https://doi.org/10.3390/e19040176

**AMA Style**

Gao Y, Villecco F, Li M, Song W.
Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis. *Entropy*. 2017; 19(4):176.
https://doi.org/10.3390/e19040176

**Chicago/Turabian Style**

Gao, Yangde, Francesco Villecco, Ming Li, and Wanqing Song.
2017. "Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis" *Entropy* 19, no. 4: 176.
https://doi.org/10.3390/e19040176