# Ultrasonic Flaw Echo Enhancement Based on Empirical Mode Decomposition

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Required Tools

#### 2.1. EMD and EEMD

#### 2.2. Denoising Strategies Based on EMD

#### 2.3. Sample Entropy

#### 2.4. Otsu’s Method for Thresholding

## 3. Analysis of Modes from Ultrasonic Signals

#### 3.1. The Clutter Model

#### 3.2. Signal Decomposition

#### 3.3. SampEn Values of IMFs

## 4. Proposed Methodology

#### 4.1. Relevant Mode Selection

#### 4.2. Mixed Noise Suppression

#### 4.3. Summarization of the Proposed Methodology

## 5. Simulated Signal Processing

#### 5.1. Performance Assessment

#### 5.2. Signal Processing Results

## 6. Experimental Study

^{3}kg/m

^{3}and the sound wave velocity was 6300 m/s. The two cracks, denoted F1 and F2, were machined using wire electrical discharge machining. The buried depths of F1 and F2 were 60 mm and 35 mm, respectively, and the sampling frequency was 100 MHz. The ultrasonic testing system and the specimen are shown in Figure 5.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Shankar, P.M.; Karpur, P.; Newhouse, V.L.; Rose, J.L. Split-spectrum processing: Analysis of polarity threshold algorithm for improvement of signal-to-noise ratio and detectablity in ultrasonic signals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1989**, 36, 101–108. [Google Scholar] [CrossRef] [PubMed] - Gustafsson, M.G.; Stepinski, T. Studies of split spectrum processing, optimal detection, and maximum likelihood amplitude estimation using a simple clutter model. Ultrasonics
**1997**, 35, 31–52. [Google Scholar] [CrossRef] - Rodriguez, A.; Miralles, R.; Bosch, I.; Vergara, L. New analysis and extensions of split-spectrum processing algorithms. NDT E Int.
**2012**, 45, 141–147. [Google Scholar] [CrossRef] - Jafar, S.; Daniel, T.N.; Kevin, D.D. Analysis of order statistic filters applied to ultrasonic flaw detection using split-spectrum processing. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1991**, 38, 133–140. [Google Scholar] [CrossRef] - Lazaro, J.C.; San Emeterio, J.L.; Ramos, A.; Fernandez-Marron, J.L. Influence of thresholding procedures in ultrasonic grain noise reduction using wavelets. Ultrasonics
**2002**, 40, 263–267. [Google Scholar] [CrossRef] - Matz, V.; Smid, R.; Starman, S.; Kreidl, M. Signal-to-noise ratio enhancement based on wavelet filtering in ultrasonic testing. Ultrasonics
**2009**, 49, 752–759. [Google Scholar] [CrossRef] [Green Version] - Peng, C.Y.; Gao, X.R.; Wang, A. Novel wavelet self-optimisation threshold denoising method in axle press-fit ultrasonic defect detection. Insight
**2016**, 58, 145–151. [Google Scholar] [CrossRef] - Liu, Y.; Li, Z.; Zhang, W. Crack detection of fibre reinforced composite beams based on continuous wavelet transform. Nondestruct. Test. Eval.
**2010**, 25, 25–44. [Google Scholar] [CrossRef] - Chen, Y.C.; Zhou, X.J.; Yang, C.L.; Li, Z. The ultrasonic evaluation method for the porosity of variable-thickness curved CFRP workpiece: Using a numerical wavelet transform. Nondestruct. Test. Eval.
**2014**, 29, 195–207. [Google Scholar] [CrossRef] - Praveen, A.; Vijayarekha, K.; Abraham, S.T.; Venkatraman, B. Signal quality enhancement using higher order wavelets for ultrasonic TOFD signals from austenitic stainless steel welds. Ultrasonics
**2013**, 53, 1288–1292. [Google Scholar] [CrossRef] - Stockwell, R.G.; Mansinha, L.; Lowe, R.P. Localization of the complex spectrum: The S transform. IEEE Trans. Signal Process.
**1996**, 44, 998–1001. [Google Scholar] [CrossRef] - Ari, S.; Das, M.K.; Chacko, A. ECG signal enhancement using S-Transform. Comput. Biol. Med.
**2013**, 43, 649–660. [Google Scholar] [CrossRef] [PubMed] - Muhammad, A.M.; Jafar, S. S-transform applied to ultrasonic nondestructive testing. In Proceedings of the IEEE Ultrasonics Symposium, Beijing, China, 2–5 November 2008; IEEE: Piscataway, NJ, USA, 2008; pp. 184–187. [Google Scholar] [CrossRef]
- Benammar, A.; Drai, R.; Guessoum, A. Ultrasonic flaw detection using threshold modified S-transform. Ultrasonics
**2014**, 54, 676–683. [Google Scholar] [CrossRef] [PubMed] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.N.; Yen, N.C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A-Math. Phys. Eng. Sci.
**1998**, 454, 903–995. [Google Scholar] [CrossRef] - Gabriel, R.; Patrick, F. One or Two Frequencies? The empirical mode decomposition answers. IEEE Trans. Signal Process.
**2008**, 56, 85–95. [Google Scholar] [CrossRef] - Kazys, R.; Tumsys, O.; Pagodinas, D. Ultrasonic detection of defects in strongly attenuating structures using the Hilbert–Huang transform. NDT E Int.
**2008**, 41, 457–466. [Google Scholar] [CrossRef] - Abdel, O.B.; Jean, C.C. EMD-based signal filtering. IEEE Trans. Instrum. Meas.
**2007**, 56, 2196–2202. [Google Scholar] [CrossRef] - Zhang, Q.; Que, P.W.; Liang, W. Applying sub-band energy extraction to noise cancellation of ultrasonic NDT signal. J. Zhejiang Univ. Sci. A
**2008**, 9, 1134–1140. [Google Scholar] [CrossRef] - Yannis, K.; Stephen, M. Development of EMD-based denoising methods inspired by wavelet thresholding. IEEE Trans. Signal Process.
**2009**, 57, 1351–1362. [Google Scholar] [CrossRef] - Yang, G.L.; Liu, Y.Y.; Wang, Y.Y.; Zhu, Z.L. EMD interval thresholding denoising based on similarity measure to select relevant modes. Signal Process.
**2015**, 109, 95–109. [Google Scholar] [CrossRef] - Bouden, T.; Djerfi, F.; Nibouche, M. Adaptive split spectrum processing for ultrasonic signal in the pulse echo test. Russ. J. Nondestruct. Test.
**2015**, 51, 245–257. [Google Scholar] [CrossRef] - Sharma, G.K.; Kumar, A.; Jayakumar, T.; Rao, B.P.; Mariyappa, N. Ensemble empirical mode decomposition based methodology for ultrasonic testing of coarse grain austenitic stainless steels. Ultrasonics
**2015**, 57, 167–178. [Google Scholar] [CrossRef] [PubMed] - Richman, J.S.; Moorman, J.R. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol.
**2000**, 278, H2039–H2049. [Google Scholar] [CrossRef] - Hu, X.S.; Jiang, J.C.; Cao, D.P.; Bo, E. Battery Health Prognosis for Electric Vehicles Using Sample Entropy and Sparse Bayesian Predictive Modeling. IEEE Trans. Ind. Electron.
**2016**, 63, 2645–2656. [Google Scholar] [CrossRef] - Otsu, N. A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern.
**1979**, 9, 62–66. [Google Scholar] [CrossRef] - Steven, M.P. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA
**1991**, 88, 2297–2301. [Google Scholar] [CrossRef] - Jung, H.J.; Kim, H.J.; Song, S.J.; Kim, Y.H. Model-based enhancement of the TIFD for flaw signal identification in ultrasonic testing of welded joints. In Proceedings of the 29th Annual Review of Progress in Quantitative Nondestructive Evaluation, Western Washington University, Bellingham, WA, USA, 14–19 July 2002; Amer Inst Physics: College Park, MD, USA, 2002; pp. 628–634. [Google Scholar] [CrossRef]

**Figure 4.**Processing results of the simulated signal. (

**a**) The reconstructed signal given by partial reconstruction; (

**b**) the detection interval in which the flaw echo was located; (

**c**) the denoised signal.

**Figure 5.**The ultrasonic test system and specimen. (

**a**) The ultrasonic testing system. (

**b**) The specimen. (

**c**) Geometry of the specimen. (

**d**) Schematic diagram of flaws location and size, with dimensions in millimeters.

**Figure 7.**Processing results of the backscattered signal from F1. (

**a**) The IMFs extracted; (

**b**) the interval in which the flaw echo was located; (

**c**) the denoised signal.

r/SD_{u} | 0.1 | 0.15 | 0.2 |
---|---|---|---|

s_{1} | 2.0121 | 1.7943 | 1.535 |

s_{2} | 1.8823 | 1.4872 | 1.213 |

s_{3} | 0.7224 | 0.6242 | 0.5682 |

s_{4} | 0.646 | 0.5984 | 0.5616 |

s_{5} | 0.5501 | 0.4921 | 0.4472 |

s_{6} | 0.4717 | 0.3589 | 0.2708 |

s_{7} | 0.1095 | 0.0821 | 0.065 |

s_{8} | 0.0526 | 0.036 | 0.0276 |

SNR/dB | MCC/ × 10^{−2} | |
---|---|---|

observed | −3.47 | 1.05 |

partial reconstruction denoised | 1.81 9.42 | 0.06 0.06 |

s_{1} | s_{2} | s_{3} | s_{4} | s_{5} |
---|---|---|---|---|

1.4902 | 1.1739 | 0.5684 | 0.5508 | 0.4764 |

© 2019 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**

Feng, W.; Zhou, X.; Zeng, X.; Yang, C.
Ultrasonic Flaw Echo Enhancement Based on Empirical Mode Decomposition. *Sensors* **2019**, *19*, 236.
https://doi.org/10.3390/s19020236

**AMA Style**

Feng W, Zhou X, Zeng X, Yang C.
Ultrasonic Flaw Echo Enhancement Based on Empirical Mode Decomposition. *Sensors*. 2019; 19(2):236.
https://doi.org/10.3390/s19020236

**Chicago/Turabian Style**

Feng, Wei, Xiaojun Zhou, Xiang Zeng, and Chenlong Yang.
2019. "Ultrasonic Flaw Echo Enhancement Based on Empirical Mode Decomposition" *Sensors* 19, no. 2: 236.
https://doi.org/10.3390/s19020236