# Research on Feature Extraction of Ship-Radiated Noise Based on Multiscale Fuzzy Dispersion Entropy

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## Abstract

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## 1. Introduction

## 2. Theory and Method

#### 2.1. Dispersion Entropy

#### 2.2. Fuzzy Dispersion Entropy

#### 2.3. Multiscale Fuzzy Dispersion Entropy

#### 2.4. The Proposed Ship-Radiated Noise Feature Extraction Method

## 3. Simulation Signal Feature Extraction Analysis

#### 3.1. Gaussian White Noise Simulation Experiment

#### 3.2. Amplitude-Modulated Chirp Signal Simulation Experiment

#### 3.3. Various Noise Simulation Experiments

## 4. Experiments for Ship-Radiated Noise

#### 4.1. Introduction of the Ship-Radiated Noise and Experimental Parameter Setting

#### 4.2. Single Feature Analysis Experiment

#### 4.3. Double-Number Feature Analysis Experiment

#### 4.4. Triple-Number Feature Analysis Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Multiscale results of FDE and DE of Gaussian white noise at different lengths (

**a**) $s$ = 2; (

**b**) $s$ = 5.

**Figure 4.**FDE and DE variation curves of amplitude-modulated chirp signal at multiple scales: (

**a**) $s$ = 2; (

**b**) $s$ = 5.

**Figure 5.**MFDE of three types of noise with different embedding dimensions and scales: (

**a**) $m$ = 2; (

**b**) $m$ = 3; (

**c**) $m$ = 4; (

**d**) $m$ = 5; (

**e**) $m$ = 6.

**Figure 6.**MFDE of three types of noise with different categories and scales: (

**a**) $c$ = 3; (

**b**) $c$ = 4; (

**c**) $c$ = 5; (

**d**) $c$ = 6; (

**e**) $c$ = 7; (

**f**) $c$ = 8.

**Figure 7.**Feature distribution of MFDE at 10 scales. (

**a**) s = 1; (

**b**) $s=2$; (

**c**) $s=3$; (

**d**) $s=4$; (

**e**) $s=5$; (

**f**) $s=6$; (

**g**) $s=7$; (

**h**) $s=8$; (

**i**) $s=9$; (

**j**) $s=10$.

**Figure 8.**Feature distribution of four types of entropy under double-number feature. (

**a**) MDE; (

**b**) MFDE; (

**c**) MSE; (

**d**) MPE.

**Figure 9.**Feature distribution of four types of entropies under triple-number features. (

**a**) MDE; (

**b**) MFDE; (

**c**) MSE; (

**d**) MPE.

Entropy | Scales | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||

Recognition rate (%) | MFDE | 74.67 | 74.00 | 79.17 | 81.00 | 81.00 | 77.50 | 71.83 | 70.33 | 62.00 | 56.83 |

MDE | 55.17 | 55.17 | 70.50 | 71.83 | 65.17 | 60.33 | 60.50 | 53.00 | 46.67 | 46.50 | |

MSE | 73.83 | 47.83 | 35.33 | 22.33 | 20.17 | 20.83 | 20.33 | 20.00 | 20.00 | 20.00 | |

MPE | 54.83 | 61.33 | 75.50 | 76.00 | 72.33 | 68.17 | 64.17 | 62.50 | 62.50 | 54.00 |

Entropy | MFDE | MDE | MSE | MPE |
---|---|---|---|---|

Scale combination | (2, 9) | (1, 10) | (1, 2) | (1, 3) |

Recognition rate (%) | 99.00 | 93.83 | 64.83 | 90.67 |

Entropy | MFDE | MDE | MSE | MPE |
---|---|---|---|---|

Scale combination | (2, 5, 9) | (1, 5, 10) | (1, 2, 3) | (1, 3, 5) |

Recognition rate (%) | 99.50 | 97.67 | 45.17 | 90.67 |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Lou, Y.; Liang, L.; Zhang, S.
Research on Feature Extraction of Ship-Radiated Noise Based on Multiscale Fuzzy Dispersion Entropy. *J. Mar. Sci. Eng.* **2023**, *11*, 997.
https://doi.org/10.3390/jmse11050997

**AMA Style**

Li Y, Lou Y, Liang L, Zhang S.
Research on Feature Extraction of Ship-Radiated Noise Based on Multiscale Fuzzy Dispersion Entropy. *Journal of Marine Science and Engineering*. 2023; 11(5):997.
https://doi.org/10.3390/jmse11050997

**Chicago/Turabian Style**

Li, Yuxing, Yilan Lou, Lili Liang, and Shuai Zhang.
2023. "Research on Feature Extraction of Ship-Radiated Noise Based on Multiscale Fuzzy Dispersion Entropy" *Journal of Marine Science and Engineering* 11, no. 5: 997.
https://doi.org/10.3390/jmse11050997