# Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory Description

#### 2.1. VMD Algorithm

#### 2.2. PE and NPE

#### 2.3. Analysis of the Simulation Signal Using VMD and NPE

## 3. Denoising and Feature Extraction Algorithms Using VMD and NPE

#### 3.1. Denoising Algorithm

- Step 1
- Decompose signal by EMD.
- Step 2
- Select the decomposition level of VMD according to the decomposition level of EMD.
- Step 3
- Decompose signal by VMD, IMFs can be obtained.
- Step 4
- Calculate the NPE of each IMF.
- Step 5
- Screen out the noise IMFs according to the value of NPE. Normally when NPE of IMF is less than 0.1, it is regarded as the noise IMF.
- Step 6
- Reconstruct the useful IMFs with NPE greater than 0.1. After the reconstruction, the process of denoising is completed.

#### 3.2. Feature Extraction Algorithm

- Step 1
- Decompose the reconstructed signal by EMD.
- Step 2
- Select the decomposition level of VMD according to the decomposition level of EMD.
- Step 3
- Decompose the reconstructed signal by VMD, IMFs can be obtained.
- Step 4
- Calculate the energy intensity of each IMF.
- Step 5
- Select the principal IMF, namely PIMF. Normally PIMF is the IMF with the maximum energy intensity.
- Step 6
- Calculate the NPEs of PIMFs.
- Step 7
- Put the NPEs of PIMFs into SVM, the classification results can reflect the effectiveness of the feature extraction algorithm.

## 4. Denoising of Simulation Signal

#### 4.1. Simulation Experiment 1

#### 4.2. Simulation Experiment 2

## 5. Feature Extraction of SN

#### 5.1. The Denoising of SN

#### 5.2. The VMD of SN

#### 5.3. Feature Extraction of SN

#### 5.4. Classification of SN

## 6. Conclusions

- (1)
- NPE, a new kind of PE, is firstly applied to denoising and feature extraction of SN combined with VMD.
- (2)
- The simulation results show that the proposed denoising algorithm has better denoising performance than the existing algorithms and overcomes the problem of threshold selection.
- (3)
- The proposed denoising algorithm is used to denoise SN signal; it concluded that the features of PE and NPE after denoising are beneficial to classification and recognition for SN signal.
- (4)
- The proposed feature extraction algorithm is used to extract the feature of SN signal, the experimental results show that the feature of NPE has a higher recognition rate than that of PE in [11].

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**The simulation signals and the decomposition result of EMD, EEMD and VMD. (

**a**) Original signals; (

**b**) EMD result; (

**c**) EEMD result; (

**d**) VMD result.

**Figure 5.**The denoising results of different algorithms. (

**a**) Denoising using VMD and CC; (

**b**) Denoising using VMD and PE; (

**c**) Denoising using VMD and NPE; (

**d**) Denoising using WT.

**Figure 6.**The clear signal, noisy signal and denoising result. (

**a**) The clear signal; (

**b**) The noisy signal; (

**c**) The denoising result of the proposed denoising algorithm.

**Figure 7.**The three kinds of SN before and after denoising. (

**a**) Ship 1 before denoising; (

**b**) Ship 1 after denoising; (

**c**) Ship 2 before denoising; (

**d**) Ship 2 after denoising; (

**e**) Ship 3 before denoising; (

**f**) Ship 3 after denoising.

**Figure 9.**The PEs distribution of PIMFs before and after denoising. (

**a**) The PEs before denoising; (

**b**) The PEs after denoising.

**Figure 10.**The NPEs distribution of PIMFs before and after denoising. (

**a**) The NPEs before denoising; (

**b**) The NPEs after denoising.

Data Length | 100 Hz | 200 Hz | 500 Hz | 1000 Hz |
---|---|---|---|---|

1000 | 0.445 | 0.4869 | 0.5937 | 0.7154 |

2000 | 0.4447 | 0.4866 | 0.5929 | 0.7139 |

3000 | 0.449 | 0.496 | 0.5834 | 0.6915 |

Data Length | 100 Hz | 200 Hz | 500 Hz | 1000 Hz |
---|---|---|---|---|

1000 | 0.3137 | 0.2948 | 0.2418 | 0.1678 |

2000 | 0.3137 | 0.2948 | 0.2419 | 0.1681 |

3000 | 0.3136 | 0.2945 | 0.2426 | 0.171 |

Signal | PE | EMD | EEMD | VMD | |||
---|---|---|---|---|---|---|---|

S1 | 0.4213 | IMF3 | 0.4217 | IMF5 | 0.4291 | IMF3 | 0.4195 |

S2 | 0.4483 | IMF2 | 0.449 | IMF4 | 0.4816 | IMF2 | 0.4469 |

S3 | 0.4946 | IMF1 | 0.4962 | IMF3 | 0.4963 | IMF1 | 0.4936 |

Signal | NPE | EMD | EEMD | VMD | |||
---|---|---|---|---|---|---|---|

S1 | 0.3235 | IMF3 | 0.3235 | IMF5 | 0.321 | IMF3 | 0.3235 |

S2 | 0.3137 | IMF2 | 0.3137 | IMF4 | 0.3007 | IMF2 | 0.3137 |

S3 | 0.2947 | IMF1 | 0.2944 | IMF3 | 0.2944 | IMF1 | 0.2946 |

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

CC | 0.1643 | 0.1425 | 0.1567 | 0.1633 | 0.147 | 0.1607 | 0.196 | 0.4075 | 0.6919 |

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

PE | 0.9296 | 0.9909 | 0.999 | 0.9764 | 0.9466 | 0.8782 | 0.7427 | 0.6054 | 0.4463 |

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

NPE | 0.0458 | 0.0088 | 0.0017 | 0.0084 | 0.0383 | 0.0688 | 0.1642 | 0.2416 | 0.3146 |

Parameter | Y | CC | PE | NPE | WT |
---|---|---|---|---|---|

SNR (db) | 2.7178 | 12.0307 | 14.7721 | 15.5929 | 8.3378 |

RMSE | 0.56 | 0.1448 | 0.1453 | 0.1434 | 0.1671 |

Denoising Algorithms | The Variance of Gaussian White Noise | ||
---|---|---|---|

0.4 | 0.5 | 0.6 | |

The Proposed Denoising Algorithm (db) | 12.58 | 11.69 | 11.25 |

The Convex 1-D 2-Order Total Variation Algorithm (db) | 12.13 | 11.31 | 10.28 |

The Convex 1-D 1-Order Total Variation Algorithm (db) | 4.69 | 3.31 | 2.17 |

Wavelet Denoising Algorithm (db) | 10.28 | 9.20 | 8.31 |

The noisy signal (db) | 0.9778 | –0.0494 | –0.8239 |

Level | Ship 1 | Ship 2 | Ship 3 |
---|---|---|---|

The level of PIMF | 8 | 8 | 7 |

Ship | Train | Test | Overall Correctness (%) | ||
---|---|---|---|---|---|

Number | Correctness (%) | Number | Correctness (%) | ||

Ship 1 | 25 | 15 | 25 | 16 | 79.33 |

Ship 2 | 25 | 0 | 25 | 0 | |

Ship 3 | 25 | 0 | 25 | 0 |

Ship | Train | Test | Overall Correctness (%) | ||
---|---|---|---|---|---|

Number | Error | Number | Error | ||

Ship 1 | 25 | 10 | 25 | 12 | 85.33 |

Ship 2 | 25 | 0 | 25 | 0 | |

Ship 3 | 25 | 0 | 25 | 0 |

Ship | Train | Test | Overall Correctness (%) | ||
---|---|---|---|---|---|

Number | Error | Number | Error | ||

Ship 1 | 25 | 11 | 25 | 10 | 86 |

Ship 2 | 25 | 0 | 25 | 0 | |

Ship 3 | 25 | 0 | 25 | 0 |

Ship | Train | Test | Overall Correctness (%) | ||
---|---|---|---|---|---|

Number | Error | Number | Error | ||

Ship 1 | 25 | 6 | 25 | 6 | 92 |

Ship 2 | 25 | 0 | 25 | 0 | |

Ship 3 | 25 | 0 | 25 | 0 |

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**MDPI and ACS Style**

Li, Y.; Li, Y.; Chen, X.; Yu, J.
Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise. *Symmetry* **2017**, *9*, 256.
https://doi.org/10.3390/sym9110256

**AMA Style**

Li Y, Li Y, Chen X, Yu J.
Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise. *Symmetry*. 2017; 9(11):256.
https://doi.org/10.3390/sym9110256

**Chicago/Turabian Style**

Li, Yuxing, Yaan Li, Xiao Chen, and Jing Yu.
2017. "Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise" *Symmetry* 9, no. 11: 256.
https://doi.org/10.3390/sym9110256