# A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy

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## Abstract

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## 1. Introduction

## 2. Basic Theory

#### 2.1. ICEEMDAN

#### 2.2. Mutual Information and Normalized Mutual Information

#### 2.3. MIPE

#### 2.4. The Proposed Feature Extraction Method

## 3. Simulation Results

#### 3.1. Analysis of Artificial Signal Based on ICEEMDAN

#### 3.2. Analysis of Artificial Signal Based on MIPE

## 4. Experimental Results

#### 4.1. Feature Extraction Based on ICEEMDAN-norMI-MIPE

#### 4.2. Ship Classification

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The flowchart of the improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm.

**Figure 5.**The decomposition results of the artificial signal: (

**a**) empirical mode decomposition (EMD) result; (

**b**) complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) result; and (

**c**) ICEEMDAN result.

**Figure 6.**The entropy analysis results of the AR processes: (

**a**) multiscale improved permutation entropy (MIPE) result; and (

**b**) multiscale permutation entropy (MPE) result.

**Figure 7.**The waveforms of five types of ship-radiated noise.4.1. Feature extraction based on power spectrum density (PSD).

**Figure 8.**The PSD analysis results of five types of ship-radiated noise: (

**a**) Type A; (

**b**) Type B; (

**c**) Type C; (

**d**) Type D; and (

**e**) Type E.

**Figure 9.**The ICEEMDAN analysis results of five types of ship-radiated noise: (

**a**) Type A; (

**b**) Type B; (

**c**) Type C; (

**d**) Type D; and (

**e**) Type E.

**Figure 12.**The analysis results of other feature extraction schemes: (

**a**) MIPE result; and (

**b**) VMD-SIMF-FDE result.

**Figure 13.**The feature extraction results under 5 dB condition: (

**a**) ICEEMDAN-norMI-MIPE result; (

**b**) MIPE result; and (

**c**) VMD-SIMF-FDE result.

**Table 1.**The predefined correlation coefficients for generating autoregressive (AR) processes with different orders.

${\mathsf{\alpha}}_{1}$ | ${\mathsf{\alpha}}_{2}$ | ${\mathsf{\alpha}}_{3}$ | ${\mathsf{\alpha}}_{4}$ | ${\mathsf{\alpha}}_{5}$ | ${\mathsf{\alpha}}_{6}$ | ${\mathsf{\alpha}}_{7}$ | |

$A{R}_{1}$ | 0.5 | - | - | - | - | - | - |

$A{R}_{2}$ | 0.5 | 0.25 | - | - | - | - | - |

$A{R}_{3}$ | 0.5 | 0.25 | 0.125 | - | - | - | - |

$A{R}_{4}$ | 0.5 | 0.25 | 0.125 | 0.0625 | - | - | - |

$A{R}_{5}$ | 0.5 | 0.25 | 0.125 | 0.0625 | 0.0313 | - | - |

$A{R}_{6}$ | 0.5 | 0.25 | 0.125 | 0.0625 | 0.0313 | 0.0156 | - |

$A{R}_{7}$ | 0.5 | 0.25 | 0.125 | 0.0625 | 0.0313 | 0.0156 | 0.0078 |

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**MDPI and ACS Style**

Chen, Z.; Li, Y.; Cao, R.; Ali, W.; Yu, J.; Liang, H.
A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy. *Entropy* **2019**, *21*, 624.
https://doi.org/10.3390/e21060624

**AMA Style**

Chen Z, Li Y, Cao R, Ali W, Yu J, Liang H.
A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy. *Entropy*. 2019; 21(6):624.
https://doi.org/10.3390/e21060624

**Chicago/Turabian Style**

Chen, Zhe, Yaan Li, Renjie Cao, Wasiq Ali, Jing Yu, and Hongtao Liang.
2019. "A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy" *Entropy* 21, no. 6: 624.
https://doi.org/10.3390/e21060624