#
Noise Reduction of Steel Cord Conveyor Belt Defect Electromagnetic Signal by Combined Use of Improved Wavelet and EMD^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Basic Theory of Signal Noise Reduction Method

#### 2.1. Wavelet Noise Reduction Principle

#### 2.1.1. Wavelet Basis Function Selection

#### 2.1.2. Wavelet Multi-Scale Decomposition

#### 2.1.3. Wavelet Threshold Selection

#### 2.1.4. Signal Reconstruction

#### 2.2. New Improved Threshold Wavelet Method

#### 2.3. EMD Noise Reduction Method by Dominant Eigenvalues

#### 2.3.1. Noise Reduction Principle by EMD

#### 2.3.2. New IMF Component Extraction Method by Dominant Eigenvalue

- Calculate the eigenvalues ${\mathsf{\lambda}}_{1},{\mathsf{\lambda}}_{2},\xb7\xb7\xb7,{\mathsf{\lambda}}_{n}$ of each order IMF component ${s}_{i}(t)$ and the residual component ${r}_{n}(t)$ by the Singular Value Decomposition (SVD) [21].
- Extract the effective IMF component by the Dominant Eigenvalue Method (DEM) [22].

_{i}of adjacent singular eigenvalues is used in this paper to determine the boundary between the dominant and non-dominant eigenvalues to then extract the effective IMF components. The expression of K

_{i}is defined as Equation (7)

_{i}is expressed as Equation (8)

_{i}.

_{m}is smaller than 1.0, the corresponding eigenvalues λ

_{1}, λ

_{2}, …, λ

_{m+1}are dominant. In other words, the components from IMF

_{1}to IMF

_{m+1}are effective.

#### 2.3.3. New Noise Reduction Method Based on the Improved Threshold Wavelet and EMD by Dominant Eigenvalue

## 3. Verification of Noise Reduction Method by Combined Use of Improved Wavelet and EMD

#### 3.1. Test Rig Setup

#### 3.2. Noise Reduction Evaluation Index

#### 3.3. Electromagnetic Signal Collection

#### 3.4. Denoising Analysis of Defect Signal

#### 3.4.1. Noise Reduction of Joint Electromagnetic Signal

_{6}is smaller than 1.0. Thus, the selected IMF components are IMF

_{1}to IMF

_{7}. The reconstruction result of seven IMF components is shown in Figure 8d, and two denoising methods are compared, as shown in Table 2. According to Table 2 and Figure 8c,d, the proposed method obtained by combined use of the improved wavelet and EMD has the better noise reduction effect for the non-stationary strong-noise joint electromagnetic signal and the SNR is bigger.

#### 3.4.2. Noise Reduction of Electromagnetic Signal with Wire Rope Break

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Electromagnetic testing rig of steel cord conveyor belt: (

**a**) Tested belt conveyor prototype; (

**b**) Installed electromagnetic testing device; (

**c**) Electromagnetic testing system setup.

**Figure 7.**Joint and break of steel cord conveyor belt and responding electromagnetic signal: (

**a**) Internal structure of conveyor belt joint; (

**b**) Electromagnetic signal at joint; (

**c**) Steel wire rope break of belt; (

**d**) Electromagnetic signal of wire rope break defect.

**Figure 8.**Comparison of two noise reduction methods for joint electromagnetic signal: (

**a**) Joint electromagnetic signal with noise; (

**b**) Normalized spectrum diagram of joint signal; (

**c**) Denoised result by improved threshold wavelet; (

**d**) Denoised result by combined use of improved threshold wavelet and EMD.

**Figure 9.**Comparison of two noise reduction methods for wire rope break electromagnetic signal: (

**a**) Electromagnetic signal with noise of wire rope break; (

**b**) Normalized spectrum diagram of wire rope break; (

**c**) Denoised result by the improved threshold wavelet; (

**d**) Denoised result by combined use of improved wavelet and EMD.

IMF Component | Eigenvalue ${\mathsf{\lambda}}_{\mathbf{i}}$ | ${\mathbf{K}}_{\mathit{i}}=\raisebox{1ex}{${\mathsf{\lambda}}_{\mathit{i}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\lambda}}_{\mathit{i}+1}$}\right.$ | ${\u2206}_{\mathit{i}}=\raisebox{1ex}{${\mathbf{K}}_{\mathit{i}}$}\!\left/ \!\raisebox{-1ex}{${\mathbf{K}}_{\mathit{i}+1}$}\right.$ |
---|---|---|---|

IMF_{1} | 29.62 | 1.68 | 1.37 |

IMF_{2} | 17.61 | 1.23 | 1.04 |

IMF_{3} | 14.34 | 1.18 | 1.008 |

IMF_{4} | 12.19 | 1.17 | 1.04 |

IMF_{5} | 10.45 | 1.12 | 1.06 |

IMF_{6} | 9.36 | 1.05 | 0.30 |

IMF_{7} | 8.91 | 3.50 | 0.82 |

IMF_{8} | 2.55 | 4.21 | 0.38 |

IMF_{9} | 0.60 | 11.21 | 0.15 |

IMF_{10} | 0.054 | 73.43 | — |

IMF_{11} | 0.00073 | — | — |

Method | SNR (dB) | RSME |
---|---|---|

Before denoising | −2.72 | 0.36 |

Improved threshold wavelet | 5.027 | 0.17 |

Combined use of improved threshold wavelet and EMD | 11.63 | 0.069 |

IMF Component | Eigenvalue ${\mathsf{\lambda}}_{\mathit{i}}$ | ${\mathbf{K}}_{\mathit{i}}=\raisebox{1ex}{${\mathsf{\lambda}}_{\mathit{i}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\lambda}}_{\mathit{i}+1}$}\right.$ | ${\u2206}_{\mathit{i}}=\raisebox{1ex}{${\mathbf{K}}_{\mathit{i}}$}\!\left/ \!\raisebox{-1ex}{${\mathbf{K}}_{\mathit{i}+1}$}\right.$ |
---|---|---|---|

IMF_{1} | 25.28 | 1.25 | 1.045 |

IMF_{2} | 20.20 | 1.20 | 1.034 |

IMF_{3} | 16.87 | 1.16 | 1.035 |

IMF_{4} | 14.57 | 1.12 | 1.034 |

IMF_{5} | 12.99 | 1.083 | 1.025 |

IMF_{6} | 11.99 | 1.056 | 0.21 |

IMF_{7} | 11.36 | 4.98 | 0.28 |

IMF_{8} | 2.28 | 17.54 | 0.32 |

IMF_{9} | 0.13 | 54.24 | 7.27 × 10^{−11} |

IMF_{10} | 0.0025 | 7.46 × 10^{11} | — |

IMF_{11} | 3.35 × 10^{−15} | — | — |

Method | SNR(dB) | RSME |
---|---|---|

Before denoising | −0.76 | 0.34 |

Improved threshold wavelet | 6.42 | 0.14 |

Combined use of improved threshold wavelet and EMD | 7.08 | 0.13 |

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**MDPI and ACS Style**

Ma, H.-W.; Fan, H.-W.; Mao, Q.-H.; Zhang, X.-H.; Xing, W.
Noise Reduction of Steel Cord Conveyor Belt Defect Electromagnetic Signal by Combined Use of Improved Wavelet and EMD. *Algorithms* **2016**, *9*, 62.
https://doi.org/10.3390/a9040062

**AMA Style**

Ma H-W, Fan H-W, Mao Q-H, Zhang X-H, Xing W.
Noise Reduction of Steel Cord Conveyor Belt Defect Electromagnetic Signal by Combined Use of Improved Wavelet and EMD. *Algorithms*. 2016; 9(4):62.
https://doi.org/10.3390/a9040062

**Chicago/Turabian Style**

Ma, Hong-Wei, Hong-Wei Fan, Qing-Hua Mao, Xu-Hui Zhang, and Wang Xing.
2016. "Noise Reduction of Steel Cord Conveyor Belt Defect Electromagnetic Signal by Combined Use of Improved Wavelet and EMD" *Algorithms* 9, no. 4: 62.
https://doi.org/10.3390/a9040062