# Feature Extraction of Ship-Radiated Noise Based on Permutation Entropy of the Intrinsic Mode Function with the Highest Energy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Permutation Entropy

#### 2.2. Multi-Scale Permutation Entropy

#### 2.3. Empirical Mode Decomposition

## 3. The Analysis of the Permutation Entropy of Each Intrinsic Mode Function

#### 3.1. The Choice of Permutation Entropy Parameters

#### 3.2. The Empirical Mode Decomposition of the Ship-Radiated Noise

#### 3.3. The PE of Each IMF

_{mn}, then its instantaneous intensity is:

_{mn}= b

^{2}

_{mn}

## 4. Feature Extraction of SRN Signal

#### 4.1. Feature Extraction Based on the PE of the IMF with the Highest Energy

#### 4.2. Feature Extraction Based on MPE

#### 4.3. Feature Extraction Based on Energy Difference

#### 4.4. Comparison of Feature Extraction Methods

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The time-domain waveform for three types of SRN signals. (

**a**) The first type of SRN signal; (

**b**) The second type of SRN signal; (

**c**) The third type of SRN signal.

**Figure 2.**The PEs for three types of SRN signals with different embedding dimension and sequence length. (

**a**) The first type of SRN signal; (

**b**) The second type of SRN signal; (

**c**) The third type of SRN signal.

**Figure 4.**The results of EMD for three types of SRN signals. (

**a**) The first type of SRN signal; (

**b**) The second type of SRN signal; (

**c**) The third type of SRN signal.

First Type | Second Type | Third Type | |
---|---|---|---|

EIMF (level) | 6 | 4 | 3 |

PE of EIMF | 0.2528 | 0.3310 | 0.4054 |

First Type | Second Type | Third Type | |
---|---|---|---|

MPE (scale = 1) | 0.8837 | 0.7105 | 0.7852 |

MPE (scale = 17) | 0.8562 | 0.9717 | 0.9123 |

First Type | Second Type | Third Type | |
---|---|---|---|

Energy difference (db) | −12.013 | −2.4347 | −1.5990 |

**Table 4.**The four feature parameters for three types SRN signals (each type includes fifty samples).

First Type | Second Type | Third Type | |
---|---|---|---|

The average value of PE of EIMF | 0.2524 | 0.3458 | 0.4287 |

The range of PE of EIMF | 0.2473~0.2612 | 0.3325~0.3641 | 0.3825~0.4526 |

The average value of PE | 0.8825 | 0.7164 | 0.7482 |

The range of PE | 0.8673~0.8934 | 0.6926~0.7458 | 0.7129~0.7912 |

The average value of MPE (scale = 17) | 0.8452 | 0.9758 | 0.9137 |

The range of MPE (scale = 17) | 0.7912~0.9034 | 0.9553~0.9876 | 0.8457~0.9625 |

The average value of energy difference (db) | −13.9462~−11.6412 | −4.3344~−1.7516 | −1.9847~−0.8835 |

The range of energy difference (db) | −12.6240 | −2.9339 | −1.4713 |

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**MDPI and ACS Style**

Li, Y.-X.; Li, Y.-A.; Chen, Z.; Chen, X.
Feature Extraction of Ship-Radiated Noise Based on Permutation Entropy of the Intrinsic Mode Function with the Highest Energy. *Entropy* **2016**, *18*, 393.
https://doi.org/10.3390/e18110393

**AMA Style**

Li Y-X, Li Y-A, Chen Z, Chen X.
Feature Extraction of Ship-Radiated Noise Based on Permutation Entropy of the Intrinsic Mode Function with the Highest Energy. *Entropy*. 2016; 18(11):393.
https://doi.org/10.3390/e18110393

**Chicago/Turabian Style**

Li, Yu-Xing, Ya-An Li, Zhe Chen, and Xiao Chen.
2016. "Feature Extraction of Ship-Radiated Noise Based on Permutation Entropy of the Intrinsic Mode Function with the Highest Energy" *Entropy* 18, no. 11: 393.
https://doi.org/10.3390/e18110393