# Defect Detection using Power Spectrum of Torsional Waves in Guided-Wave Inspection of Pipelines

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Initialisation

#### 2.2. Conditions

#### 2.2.1. Condition Zero (C0)

#### 2.2.2. Condition One (C1)

#### 2.2.3. Condition Two (C2)

#### 2.2.4. Condition Three (C3)

#### 2.2.5. Condition Four (C4)

#### 2.2.6. Final Results

#### 2.3. Main Loop

## 3. Results

#### 3.1. FEM Test Case

#### 3.1.1. Condition Zero

#### 3.1.2. Condition One

#### 3.1.3. Condition Two

#### 3.1.4. Condition Three

#### 3.1.5. Condition Four

#### 3.1.6. Results Total

#### 3.2. Experimental Results

## 4. Conclusions

- Centre frequency shift must be small.
- Considering the 10 dB bandwidth of the iteration’s power spectrum, the magnitude of each respective frequency bin must be increased when moving toward the centre frequency.
- The achieved magnitude from the neighbouring bins to the centre frequency must be closely related.
- Frequencies outside the 10 dB bandwidth must have less magnitude than the minimum one achieved from within the 10 dB bandwidth.
- The maximum magnitude achieved must be less than the one from the reference.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Lowe, M.J.S.; Alleyne, D.N.; Cawley, P. Defect detection in pipes using guided waves. Ultrasonics
**1998**, 36, 147–154. [Google Scholar] [CrossRef] - Ostachowicz, W.; Kudela, P.; Krawczuk, M.; Zak, A. Guided Waves in Structures for SHM: The Time-Domain Spectral Element Method; Wiley: Hoboken, NJ, USA, 2012; ISBN 0470979836. [Google Scholar]
- ASTM Standard E2775-16. Standard Practice for Guided Wave Testing of Above Ground Steel Pipeword Using Piezoelectric Effect Transducer; ASTM: West Conshohocken, PA, USA, 2017. [Google Scholar]
- Nakhli Mahal, H.; Mudge, P.; Nandi, A.K. Comparison of coded excitations in the presence of variable transducer transfer functions in ultrasonic guided wave testing of pipelines. In Proceedings of the 9th European Workshop on Structural Health Monitoring, Manchester, UK, 10–13 July 2018. [Google Scholar]
- Nakhli Mahal, H.; Yang, K.; Nandi, A. Detection of Defects Using Spatial Variances of Guided-Wave Modes in Testing of Pipes. Appl. Sci.
**2018**, 8, 2378. [Google Scholar] [CrossRef] - Wilcox, P.D. A rapid signal processing technique to remove the effect of dispersion from guided wave signals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2003**, 50, 419–427. [Google Scholar] [CrossRef] [PubMed] - Zeng, L.; Lin, J.; Lei, Y.; Xie, H. Waveform design for high-resolution damage detection using lamb waves. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2013**, 60, 1025–1029. [Google Scholar] [CrossRef] [PubMed] - Garcia-Rodriguez, M. Lamb Wave generation with an air-coupled piezoelectric array using square chirp excitation. In Proceedings of the International Congress on Acoustics, Madrid, Spain, 2–7 September 2007; pp. 2–7. [Google Scholar]
- Garcia-Rodriguez, M.; Yaez, Y.; Garcia-Hernandez, M.J.; Salazar, J.; Turo, A.; Chavez, J.A. Application of Golay codes to improve the dynamic range in ultrasonic Lamb waves air-coupled systems. NDT E Int.
**2010**, 43, 677–686. [Google Scholar] [CrossRef] - Yücel, M.K.; Fateri, S.; Legg, M.; Wilkinson, A.; Kappatos, V.; Selcuk, C.; Gan, T.H. Pulse-compression based iterative time-of-flight extraction of dispersed Ultrasonic Guided Waves. In Proceedings of the 2015 IEEE 13th International Conference on Industrial Informatics (INDIN), Cambridge, UK, 22–24 July 2015; pp. 809–815. [Google Scholar]
- Yücel, M.K.; Fateri, S.; Legg, M.; Wilkinson, A.; Kappatos, V.; Selcuk, C.; Gan, T.H. Coded Waveform Excitation for High-Resolution Ultrasonic Guided Wave Response. IEEE Trans. Ind. Inform.
**2016**, 12, 257–266. [Google Scholar] [CrossRef] - Malo, S.; Fateri, S.; Livadas, M.; Mares, C.; Gan, T. Wave Mode Discrimination of Coded Ultrasonic Guided Waves using Two-Dimensional Compressed Pulse Analysis. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2017**, 64, 1092–1101. [Google Scholar] [CrossRef] [PubMed] - Pedram, S.K.; Fateri, S.; Gan, L.; Haig, A.; Thornicroft, K. Split-spectrum processing technique for SNR enhancement of ultrasonic guided wave. Ultrasonics
**2018**, 83, 48–59. [Google Scholar] [CrossRef] [PubMed] - Pedram, S.K.; Haig, A.; Lowe, P.S.; Thornicroft, K.; Gan, L.; Mudge, P. Split-spectrum signal processing for reduction of the effect of dispersive wave modes in long-range ultrasonic testing. Phys. Procedia
**2015**, 70, 388–392. [Google Scholar] [CrossRef] - Pedram, S.K.; Mudge, P.; Gan, T.-H. Enhancement of ultrasonic guided wave signals using a split-spectrum processing method. Appl. Sci.
**2018**, 8, 1815. [Google Scholar] [CrossRef] - Duan, W.; Kanfoud, J.; Deere, M.; Mudge, P.; Gan, T.-H. Spectral subtraction and enhancement for torsional waves propagating in coated pipes. NDT E Int.
**2018**, 100, 55–63. [Google Scholar] [CrossRef] - Lowe, M.J.S.; Cawley, P. Long Range Guided Wave Inspection Usage—Current Commercial Capabilities and Research Directions; Imperial College London: London, UK, 2006; Available online: http://www3.imperial.ac.uk/pls/portallive/docs/1/55745699.PDF (accessed on 20 November 2018).
- Catton, P. Long Range Ultrasonic Guided Waves for Pipelines Inspection; Brunel University: Uxbridge, UK, 2009. [Google Scholar]
- Nurmalia. Mode Conversion of Torsional Guided Waves for Pipe Inspection: An Electromagnetic Acoustic Transducer Technique; Osaka University: Osaka, Japan, 2013. [Google Scholar]
- Sanderson, R. A closed form solution method for rapid calculation of guided wave dispersion curves for pipes. Wave Motion
**2015**, 53, 40–50. [Google Scholar] [CrossRef] - Wilcox, P.; Lowe, M.; Cawley, P. The effect of dispersion on long-range inspection using ultrasonic guided waves. NDT E Int.
**2001**, 34, 1–9. [Google Scholar] [CrossRef] - Guan, R.; Lu, Y.; Duan, W.; Wang, X. Guided waves for damage identification in pipeline structures: A review. Struct. Control Health Monit.
**2017**, 1–17. [Google Scholar] [CrossRef] - Nakhli Mahal, H.; Mudge, P.; Nandi, A.K. Noise removal using adaptive filtering for ultrasonic guided wave testing of pipelines. In Proceedings of the 57th Annual British Conference on Non-Destructive Testing, Nottingham, UK, 10–12 September 2018; pp. 1–9. [Google Scholar]
- Proakis, J.G.; Manolakis, D.G. Digital Signal Processing, 4th ed.; Pearson: London, UK, 2007. [Google Scholar]
- Nakhli Mahal, H.; Yang, K.; Nandi, A.K. Improved Defect Detection Using Adaptive Leaky NLMS Filter in Guided-Wave Testing of Pipelines. Appl. Sci.
**2019**, 9, 294. [Google Scholar] [CrossRef] - Fateri, S.; Lowe, P.S.; Engineer, B.; Boulgouris, N.V. Investigation of ultrasonic guided waves interacting with piezoelectric transducers. IEEE Sens. J.
**2015**, 15, 4319–4328. [Google Scholar] [CrossRef] - Gresil, M.; Giurgiutiu, V.; Shen, Y.; Poddar, B. Guidelines for Using the Finite Element Method for Modeling Guided Lamb Wave Propagation in SHM Processes. In Proceedings of the 6th European Workshop on Structural Health Monitoring, Dresden, Germany, 3–6 July 2012; pp. 1–8. [Google Scholar]
- Miao, H.; Huan, Q.; Wang, Q.; Li, F. Excitation and reception of single torsional wave T(0,1) mode in pipes using face-shear d24 piezoelectric ring array. Smart Mater. Struct.
**2017**, 26, 1–9. [Google Scholar] [CrossRef] - Teletestndt. Long Range Guided Wave Testing with Teletest Focus+. 2018. Available online: https://www.teletestndt.com/ (accessed on 14 January 2019).
- Dürager, C.; Boller, C.; Cornish, A. Damage feature extraction from measured Lamb wave signals using a model-based approach. In Proceedings of the 8th European Workshop on SHM (EWSHM), Bilbao, Spain, 5–8 July 2016; Volume 4, pp. 5–8. [Google Scholar]

**Figure 1.**(

**a**) Example dispersion curve of T(0,1) wave mode in an 8″ schedule 40 steel pipe. (

**b**) The effect of dispersion on a simulated flexural wave for two propagation distances [20].

**Figure 6.**Example of an outlier case detected using Condition Zero (C0), where (

**a**) shows the time domain of the iteration window and (

**b**) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (x, solid) show the results from each iteration.

**Figure 7.**Example of an outlier case detected using Condition One (C1), where (

**a**) shows the time domain of the iteration window and (

**b**) is its respective power spectrum. The red lines show (dotted, +) the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.

**Figure 8.**Example of an outlier case detected using Condition Two (C2), where (

**a**) shows the time domain of the iteration window and (

**b**) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.

**Figure 9.**Example of an outlier case detected using Condition Three (C3), where (

**a**) shows the time domain of the iteration window and (

**b**) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.

**Figure 10.**Example of an outlier case detected using Condition Four (C4), where (

**a**) shows the time domain of the iteration window and (

**b**) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.

**Figure 11.**The final result (red line) overlaid on the time-domain signal (black line) from the FEM Case. The defect size is 3% cross-sectional area (CSA) and the excitation frequency is 30 kHz.

**Figure 13.**The generated results from the experimental pipe with a defect of 3% CSA and testing frequency of 38 kHz.

**Figure 14.**The final result (red line) overlaid on the time-domain signal (black line) from experimental test case with the excitation frequency of 38 kHz and defect size of 3% CSA.

**Figure 18.**Results achieved using the algorithm where (

**a**) shows the detection amplitude of defect signal and (

**b**) shows the detection amplitude of the outlier. Each line represents a defect with different CSA size. The red dotted line represents the amplitude threshold for filtering the outliers.

**Figure 19.**(

**a**) The signal received from pipe end using 50 kHz and (

**b**) its corresponding power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.

**Figure 20.**The ratio of detection amplitude of defect to outliers. In cases where the defect is not detected, the ratio is set as zero.

Variable Name | Description | Conditions |
---|---|---|

windowSize | Length of the moving window | - |

signalRef | The power spectrum of the normalised excitation sequence | C2, C3, C4 |

frqList | List of the corresponding frequency for each bin number | C0 |

maxRef | Maximum magnitude achieved from signalRef | C4 |

idFC | Bin number of maxRef | C0 |

teFLID | Bin number of the lowest frequency within 10 dB bandwidth | C0, C1, C3 |

teFHID | Bin number of the highest frequency within 10 dB bandwidth | C0, C1, C3 |

teMax | The greater magnitude between teFLID and teFHID from signalRef | C3 |

CSA (%) | Flaw Depth (mm) | Cord Length (mm) | Arc Length (mm) |
---|---|---|---|

2 | 3.1 | 51.75 | 52.24 |

3 | 4.1 | 59.37 | 60.12 |

4 | 5 | 65.43 | 66.48 |

CSA (%) | Frequency (kHz) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

30 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 48 | 50 | |

4 | 7.13 | 8.84 | 11.12 | 12.15 | 13.13 | 13.76 | 13.23 | 11.73 | 9.50 | 6.84 | 3.50 |

3 | 4.29 | 5.97 | 8.15 | 8.62 | 9.08 | 9.51 | 9.00 | 7.60 | 5.43 | 2.82 | −0.51 |

2 | 1.46 | 2.67 | 3.15 | 2.29 | 2.00 | 2.74 | 3.09 | 2.67 | 0.89 | −1.43 | −4.44 |

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**MDPI and ACS Style**

Nakhli Mahal, H.; Yang, K.; Nandi, A.K. Defect Detection using Power Spectrum of Torsional Waves in Guided-Wave Inspection of Pipelines. *Appl. Sci.* **2019**, *9*, 1449.
https://doi.org/10.3390/app9071449

**AMA Style**

Nakhli Mahal H, Yang K, Nandi AK. Defect Detection using Power Spectrum of Torsional Waves in Guided-Wave Inspection of Pipelines. *Applied Sciences*. 2019; 9(7):1449.
https://doi.org/10.3390/app9071449

**Chicago/Turabian Style**

Nakhli Mahal, Houman, Kai Yang, and Asoke K. Nandi. 2019. "Defect Detection using Power Spectrum of Torsional Waves in Guided-Wave Inspection of Pipelines" *Applied Sciences* 9, no. 7: 1449.
https://doi.org/10.3390/app9071449