# Recognition of Broken Wire Rope Based on Remanence using EEMD and Wavelet Methods

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Remanence Information Collection

#### 2.1. Data Collection Platform

#### 2.2. Data Collection

## 3. Data Processing

#### 3.1. EEMD Theory

- (1)
- For an IMF component, the number of its maxima and minima is equivalent to 0 crossings, or they differ by 1 at most.
- (2)
- The average of the maxima and minima, as defined by the envelope, should be 0 at any given moment.

#### 3.2. Wavelet Theory

#### 3.3. Algorithm Description

- EEMD was implemented to the ith channel signal x
_{i}:- (1)
- The signal ${x}_{i}$ was extended to obtain the extended signal $\stackrel{~}{{x}_{i}}$;
- (2)
- The white noise of normal distribution was added to the signal $\stackrel{~}{{x}_{i}}$, resulting in signal ${y}_{i}$;
- (3)
- EMD was used to decompose the signal ${y}_{i}$ to obtain its IMF components;
- (4)
- Steps (1) and (2) were repeated k times, and then k groups of IMFs with different white noise were obtained;
- (5)
- The average of these IMFs was calculated, and each IMF of the signal ${x}_{i}$ was obtained;
- (6)
- It was determined whether the termination condition was met; if satisfied, decomposition was stopped. Otherwise, step (3) was repeated to continue the break down.

- Wavelet soft threshold denoising was used for IMF components which contain a defect signal:
- (1)
- A db5 wavelet was selected to decompose the IMF with 8-level decomposition;
- (2)
- The low-frequency coefficient was cleared, and soft threshold quantization was performed by the universal threshold $\sqrt{2\mathrm{log}()}$ for the high-frequency coefficients at each decomposition scale;
- (3)
- The processing wavelet coefficients t were reconstructed by a one-dimensional wavelet reconstruction function, with which the filtered IMF component was obtained.

- The processed IMF components were superimposed to obtain the clean data.

_{s}/V

_{n}), where V

_{s}is the maximum peak–peak value of the MFL signal, and V

_{n}is the maximum peak-–peak value of the noise. We compared the proposed algorithm with four recent algorithms with the SNR, such as the Variational Mode Decomposition (VMD) algorithm proposed in Ref. [26], the Empirical Wavelet Transform (EWT) algorithm proposed in Ref. [27], the HHT-WFCS algorithm proposed in Ref. [16], and the improved EEMD algorithm proposed in Ref. [28]. The groups of experimental data were included to 15, in order to prove the robustness and effectiveness of the proposed algorithm, as shown in Table 1. It can be seen that the average SNR of the original signal is 17.55 dB, the average SNR of the signal denoised by the VMD algorithm is 44.31 dB, the average SNR of the signal denoised by the EWT algorithm is 42.70 dB, the average SNR of the signal denoised by the HHT-WDCS algorithm is 41.32 dB, and the average SNR of the signal denoised by the improved EEMD algorithm is 42.36 dB. However, implementing the proposed algorithm increases the average SNR to 70.01 dB. The results demonstrate that the proposed algorithm exhibits a good property for the wire rope remanence signal.

## 4. Magnetic Image Enhancement

#### 4.1. Normalization and Defect Segmentation

- (1)
- The maximum and minimum of the LMF data was found and recorded;
- (2)
- Each piece of LMF data was processed by the following equation:$$dat(i,j)=\frac{data(i,j)-\mathrm{min}}{\mathrm{max}-\mathrm{min}}\times 255$$
- (3)
- The processed data was converted into 8-bit unsigned integer data and stored.

- (1)
- The circumferential average, and a 1D mean signal d(j) (1 ≤ j ≤ N), which is the number of sampling points, was calculated.
- (2)
- A threshold was implemented to $d(j)$, where the greater value was retained, and the others were set to 0. Then, $d\prime (j)$ and position the maximum of $d\prime (j)$, which is the axial position of the defect, were obtained;
- (3)
- According to defect width, the axial length was approximately 300 pixels, so a 300 × 300 image was segmented along the axial direction;
- (4)
- Along the axial direction, pixels are added to obtain a 1D a(i) (1 ≤ i ≤ 300), then position the maximum of a(i), which is the defect circumferential location.

#### 4.2. Wavelet Super-Resolution Reconstruction

## 5. Quantitative Identification

#### 5.1. Feature Extraction

#### 5.2. BP Neural Network

#### 5.3. Results Statistics

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Cao, Y.N.; Zhang, D.L.; Dianguo, X.U. The state-of.Art of quantitative nondestructive testing of wire ropes. Nondestr. Test.
**2005**, 27, 91–95. [Google Scholar] - Tian, J.; Zhou, J.; Wang, H.; Meng, G. Literature Review of Research on the Technology of Wire Rope Nondestructive Inspection in China and Abroad. In Proceedings of the International Conference on Engineering Technology and Application, Taipei, Taiwan, 22–24 April 2015. [Google Scholar]
- Sharatchandra Singh, W.; Rao, B.P.C.; Mukhopadhyay, C.K.; Jayakumar, T. Gmr-based magnetic flux leakage technique for condition monitoring of steel track rope. Insight Non-Destr. Test. Cond. Monit.
**2011**, 53, 377–381. [Google Scholar] [CrossRef] - Jomdecha, C.; Prateepasen, A. Design of modified electromagnetic main-flux for steel wire rope inspection. Ndt E Int.
**2009**, 42, 77–83. [Google Scholar] - Fedorko, G.; Molnár, V.; Ferková, Ž.; Peterka, P.; Krešák, J.; Tomašková, M. Possibilities of failure analysis for steel cord conveyor belts using knowledge obtained from non-destructive testing of steel ropes. Eng. Fail. Anal.
**2016**, 67, 33–45. [Google Scholar] - Park, S.; Kim, J.W.; Lee, C.; Lee, J.J. Magnetic flux leakage sensing-based steel cable nde technique. Shock Vib.
**2014**, 2014, 1–8. [Google Scholar] [CrossRef] - Li, R. A new magnetic flux leakage sensor based on open magnetizing method and its on-line automated structural health monitoring methodology. Struct. Health Monit.
**2015**, 14, 1–21. [Google Scholar] - Wang, H.Y.; Tian, J. Method of magnetic collect detection for coal mine wire rope base on finite element analysis. J. China Coal Soc.
**2013**, 38, 256–260. [Google Scholar] - Wang, H.Y.; Zhao, X.U.; Hua, G.; Tian, J.; Zhou, B.B.; Yan-Hong, L.U.; Chen, F.J. Key technique of a detection sensor for coal mine wire ropes. Int. J. Min. Sci. Technol.
**2009**, 19, 170–175. [Google Scholar] - Wanli, L.I.; Feng, W.; Zhenzhen, L.I.; Yan, C. Dimension design of excitation structure for wire rope nondestructive testing. J. Tongji Univ.
**2012**, 40, 1888–1893. [Google Scholar] - Xu, F.; Wang, X.; Wu, H. Inspection method of cable-stayed bridge using magnetic flux leakage detection: Principle, sensor design, and signal processing. J. Mech. Sci. Technol.
**2012**, 26, 661–669. [Google Scholar] - Cao, Y.N.; Zhang, D.L.; Dian-Guo, X.U. Study on algorithms of wire rope localized flaw quantitative analysis based on three-dimensional magnetic flux leakage. Acta Electron. Sin.
**2007**, 35, 1170–1173. [Google Scholar] - Zhao, M.; Zhang, D.L.; Zhou, Z.H. The research on quantitative inspection technology to wire rope defect based on hall sensor array. Nondestr. Test.
**2012**, 34, 57–60. [Google Scholar] - Peterka, P.; KreåÃK, J.; Kropuch, S.; BãReåOvã, A.; MitrãK, D.A. Non-destructive testing of steel wire rope transmission area to rope end by magnetic flux leakage. Appl. Mech. Mater.
**2014**, 683, 39–44. [Google Scholar] [CrossRef] - Zhang, J.; Tan, X. Quantitative inspection of remanence of broken wire rope based on compressed sensing. Sensors
**2016**, 16, 1366. [Google Scholar] [CrossRef] [PubMed] - Zhang, J.; Tan, X.; Zheng, P. Non-destructive detection of wire rope discontinuities from residual magnetic field images using the hilbert-huang transform and compressed sensing. Sensors
**2017**, 17, 608. [Google Scholar] [CrossRef] [PubMed] - Zhang, D.; Zhao, M.; Zhou, Z. Quantitative inspection of wire rope discontinuities using magnetic flux leakage imaging. Mater. Eval.
**2012**, 70, 872–878. [Google Scholar] - Zhang, D.; Zhao, M.; Zhou, Z.; Pan, S. Characterization of wire rope defects with gray level co-occurrence matrix of magnetic flux leakage images. J. Nondestr. Eval.
**2013**, 32, 37–43. [Google Scholar] [CrossRef] - Tian, J.; Wang, H.; Zhou, J.; Meng, G. Study of pre-processing model of coal-mine hoist wire-rope fatigue damage signal. Int. J. Min. Sci. Technol.
**2015**, 25, 1017–1021. [Google Scholar] [CrossRef] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.C.; Chi, C.T.; Liu, H.H. The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Math. Phys. Eng. Sci.
**1998**, 454, 903–995. [Google Scholar] [CrossRef] - Zhaohua, W.U.; Huang, N.E. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv. Adapt. Data Anal.
**2005**, 1. [Google Scholar] [CrossRef] - Wu, Z.; Huang, N.E. A study of the characteristics of white noise using the empirical mode decomposition method. Proc. Math. Phys. Eng. Sci.
**2004**, 460, 1597–1611. [Google Scholar] [CrossRef] - Siracusano, G.; Lamonaca, F.; Tomasello, R.; Garescì, F.; Corte, A.L.; Carnì, D.L.; Carpentieri, M.; Grimaldi, D.; Finocchio, G. A framework for the damage evaluation of acoustic emission signals through hilbert–huang transform. Mech. Syst. Signal Process.
**2016**, 75, 109–122. [Google Scholar] [CrossRef] - Kopsinis, Y.; Mclaughlin, S. Development of emd-based denoising methods inspired by wavelet thresholding. IEEE Trans. Signal Process.
**2009**, 57, 1351–1362. [Google Scholar] [CrossRef] - Li, N.; Li, P. An improved algorithm based on emd-wavelet for ecg signal de-noising. In Proceedings of the International Joint Conference on Computational Sciences and Optimization, Sanya, China, 24–26 April 2009; pp. 825–827. [Google Scholar]
- Liu, W.; Fanglin, L.V.; Mengda, L.I. Magnetic flux leakage detection defect of oil storage tank applying variational mode decomposition. Struct. Health Monit.
**2017**. [Google Scholar] [CrossRef] - Singh, O.; Sunkaria, R.K. Ecg signal denoising via empirical wavelet transform. Aust. Phys. Eng. Sci. Med.
**2017**, 40, 219. [Google Scholar] [CrossRef] [PubMed] - Qiao, T.Z.; Li, Z.X.; Jin, B.Q. Identification of mining steel rope broken wires based on improved eemd. Int. J. Min. Miner. Eng.
**2016**, 7, 224. [Google Scholar] [CrossRef]

**Figure 6.**Schematic of single-channel data before and after denoising: (

**a**) Single-channel raw signal; (

**b**) signal denoised by VMD algorithm; (

**c**) signal denoised by EWT algorithm; (

**d**) signal denoised by HHT-WFCS algorithm; (

**e**) signal denoised by improved EEMD algorithm; (

**f**) signal denoised by proposed algorithm.

**Figure 12.**Different numbers of hidden layer node recognition results: hidden layers have (

**a**) 15 nodes, (

**b**) 17 nodes, (

**c**) 21 nodes, and (

**d**) 25 nodes.

Group | Raw Data | VMD Algorithm | EWT Algorithm | HHT-WFCS Algorithm | Improved EEMD Algorithm | Proposed Algorithm |
---|---|---|---|---|---|---|

1 | 12.67 dB | 49.99 dB | 46.26 dB | 37.10 dB | 35.30 dB | 51.46 dB |

2 | 18.50 dB | 51.45 dB | 48.40 dB | 51.52 dB | 45.00 dB | 63.62 dB |

3 | 14.53 dB | 29.39 dB | 23.63 dB | 34.19 dB | 31.58 dB | 74.61 dB |

4 | 17.15 dB | 59.01 dB | 40.10 dB | 46.82 dB | 47.44 dB | 61.09 dB |

5 | 17.51 dB | 49.63 dB | 47.78 dB | 43.63 dB | 42.82 dB | 60.24 dB |

6 | 19.31 dB | 22.10 dB | 21.05 dB | 35.78 dB | 44.20 dB | 80.67 dB |

7 | 20.45 dB | 39.38 dB | 54.17 dB | 45.31 dB | 53.59 dB | 83.71 dB |

8 | 19.23 dB | 43.13 dB | 52.93 dB | 33.43 dB | 53.59 dB | 78.82 dB |

9 | 14.39 dB | 34.45 dB | 32.43 dB | 49.09 dB | 35.51 dB | 61.70 dB |

10 | 10.29 dB | 42.58 dB | 54.72 dB | 37.01 dB | 52.16 dB | 66.09 dB |

11 | 19.66 dB | 50.97 dB | 53.73 dB | 37.35 dB | 45.99 dB | 58.63 dB |

12 | 22.46 dB | 32.45 dB | 27.20 dB | 40.51 dB | 32.97 dB | 81.20 dB |

13 | 20.90 dB | 62.07 dB | 55.33 dB | 53.17 dB | 42.30 dB | 87.79 dB |

14 | 20.84 dB | 61.12 dB | 55.94 dB | 32.48 dB | 43.99 dB | 80.64 dB |

15 | 15.42 dB | 36.95 dB | 26.76 dB | 42.37 dB | 28.99 dB | 59.85 dB |

Average | 17.55 dB | 44.31 dB | 42.70 dB | 41.32 dB | 42.36 dB | 70.01 dB |

Broken Wires | A | R | E | ${\mathit{\varphi}}_{1}$ | ${\mathit{\varphi}}_{2}$ | ${\mathit{\varphi}}_{3}$ | ${\mathit{\varphi}}_{4}$ | ${\mathit{\varphi}}_{5}$ | ${\mathit{\varphi}}_{6}$ | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 2.37 × 10^{4} | 0.549 | 0.404 | 6.664 | 28.63 | 35.55 | 39.67 | 80.75 | 54.36 | 77.35 |

2 | 3.55 × 10^{4} | 0.702 | 0.222 | 6.664 | 29.53 | 39.09 | 35.19 | 72.91 | 49.96 | 72.54 |

3 | 4.72 × 10^{4} | 0.744 | 0.262 | 6.665 | 26.87 | 33.75 | 35.69 | 71.36 | 49.62 | 74.19 |

4 | 3.08 × 10^{4} | 0.763 | 0.412 | 6.667 | 26.75 | 33.39 | 33.40 | 69.74 | 47.93 | 67.98 |

5 | 5.82 × 10^{4} | 0.609 | 0.568 | 6.668 | 25.43 | 33.08 | 33.34 | 66.60 | 46.42 | 68.99 |

7 | 9.74 × 10^{4} | 0.732 | 0.727 | 6.669 | 26.89 | 33.73 | 31.82 | 66.01 | 47.26 | 64.72 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Zheng, P.; Tan, X.
Recognition of Broken Wire Rope Based on Remanence using EEMD and Wavelet Methods. *Sensors* **2018**, *18*, 1110.
https://doi.org/10.3390/s18041110

**AMA Style**

Zhang J, Zheng P, Tan X.
Recognition of Broken Wire Rope Based on Remanence using EEMD and Wavelet Methods. *Sensors*. 2018; 18(4):1110.
https://doi.org/10.3390/s18041110

**Chicago/Turabian Style**

Zhang, Juwei, Pengbo Zheng, and Xiaojiang Tan.
2018. "Recognition of Broken Wire Rope Based on Remanence using EEMD and Wavelet Methods" *Sensors* 18, no. 4: 1110.
https://doi.org/10.3390/s18041110