# A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology

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## Abstract

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## 1. Introduction

## 2. Empirical Wavelet Transform

#### 2.1. The Empirical Scaling Function and the EWT

#### 2.2. Segmentation of Fourier Spectrum

#### 2.3. Basic Principle of EWT

## 3. The Maximum-Minimum Length Curve Method

## 4. An Enhanced EWT (MSCEWT) Based on Maximum-Minimum Length Curve

#### 4.1. The Idea of the MSCEWT Method

#### 4.2. The Flow and Steps of the MSCEWT Method

**.**Establish a band-pass filter based on wavelet transform on the spectrum segmentation interval.

#### 4.3. Experimental Environment and Results

#### 4.3.1. Experimental Environment and Data

#### 4.3.2. Experimental Results

## 5. Experimental Comparison and Analysis

#### 5.1. Comparison and Analysis of Improved Scale Space Representation

#### 5.1.1. Result Comparison and Analysis of Inner Race Vibration Signal

#### 5.1.2. Result Comparison and Analysis of Outer Race Vibration Signal

#### 5.1.3. Result Comparison and Analysis of Roller Ball Vibration Signal

#### 5.2. Comparison and Analysis of the MSCEWT Method with EMD and EEMD Methods

#### 5.2.1. Result Comparison and Analysis of Inner Race Fault

#### 5.2.2. Result Comparison and Analysis of Outer Race Fault

#### 5.2.3. Result Comparison and Analysis of Roller Ball Fault

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Inner Race | Outer Race | Ball | Rotation Frequency |
---|---|---|---|

162.19 Hz | 107.29 Hz | 141.08 Hz | 29.93 Hz |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | |
---|---|---|---|---|---|---|---|---|

SSR | 164.06 | 93.75 | 29.30 | 117.19 | 29.30 | 29.30 | 29.30 | 164.06 |

MSSR | 357.42 | 117.19 | 29.30 | 29.30 | 164.06 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | |
---|---|---|---|---|---|---|---|

SSR | 58.59 | 164.06 | 58.59 | 164.06 | 164.06 | 70.31 | 164.06 |

LocalMaxmin | 58.59 | 164.06 | 164.06 | 58.59 | |||

MSSR | 58.59 | 164.06 | 164.06 | 164.06 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | |
---|---|---|---|---|---|---|---|---|

SSR | 11.71 | 152.34 | 29.30 | 52.73 | 105.47 | 58.59 | 117.19 | 105.47 |

LocalMaxmin | 87.89 | 17.58 | 11.72 | 46.88 | ||||

MSSR | 152.34 | 29.30 | 105.47 | 58.59 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | |
---|---|---|---|---|---|---|---|---|---|---|

SSR | 146.48 | 11.72 | 58.59 | 140.63 | 29.30 | 58.59 | 29.30 | 58.59 | 29.30 | 58.59 |

LocalMaxmin | 117.19 | 111.33 | 29.30 | 17.58 | 23.44 | 76.17 | ||||

MSSR | 117.19 | 140.63 | 29.30 | 222.66 | 58.59 | 58.59 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | IMF11 | |
---|---|---|---|---|---|---|---|---|---|---|---|

EMD | 164.06 | 164.06 | 164.06 | 158.20 | 17.58 | 23.44 | 5.86 | 5.86 | 5.86 | ||

EEMD | 164.06 | 164.06 | 164.06 | 58.59 | 41.02 | 41.02 | 23.44 | 23.44 | 11.72 | 11.72 | 5.86 |

MSCEWT | 58.59 | 164.06 | 164.06 | 164.06 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | IMF11 | |
---|---|---|---|---|---|---|---|---|---|---|---|

EMD | 105.47 | 46.88 | 152.34 | 5.86 | 17.58 | 5.86 | 11.72 | 11.72 | 5.86 | ||

EEMD | 105.47 | 105.47 | 105.47 | 58.59 | 58.59 | 17.59 | 17.59 | 5.86 | 5.86 | 5.86 | 5.86 |

MSCEWT | 152.34 | 29.30 | 105.47 | 58.59 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | IMF11 | |
---|---|---|---|---|---|---|---|---|---|---|---|

EMD | 222.66 | 328.13 | 11.72 | 41.02 | 29.30 | 11.72 | 11.72 | 5.86 | 5.86 | 5.86 | |

EEMD | 222.66 | 222.66 | 328.13 | 146.48 | 169.92 | 29.30 | 17.58 | 11.72 | 5.86 | 5.86 | 5.86 |

MSCEWT | 117.19 | 140.63 | 29.30 | 222.66 | 58.59 | 58.59 |

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**MDPI and ACS Style**

Zhao, H.; Zuo, S.; Hou, M.; Liu, W.; Yu, L.; Yang, X.; Deng, W.
A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology. *Sensors* **2018**, *18*, 3323.
https://doi.org/10.3390/s18103323

**AMA Style**

Zhao H, Zuo S, Hou M, Liu W, Yu L, Yang X, Deng W.
A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology. *Sensors*. 2018; 18(10):3323.
https://doi.org/10.3390/s18103323

**Chicago/Turabian Style**

Zhao, Huimin, Shaoyan Zuo, Ming Hou, Wei Liu, Ling Yu, Xinhua Yang, and Wu Deng.
2018. "A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology" *Sensors* 18, no. 10: 3323.
https://doi.org/10.3390/s18103323