### Abstract

Original language | English |
---|---|

Number of pages | 19 |

Journal | Inverse Problems in Science and Engineering |

Early online date | 9 Mar 2017 |

DOIs | |

Publication status | E-pub ahead of print - 9 Mar 2017 |

### Fingerprint

### Keywords

- inverse problems
- spectral analysis
- scattering
- ultrasonics
- engineering

### Cite this

*Inverse Problems in Science and Engineering*. https://doi.org/10.1080/17415977.2017.1297437

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*Inverse Problems in Science and Engineering*. https://doi.org/10.1080/17415977.2017.1297437

**A spectral method for sizing cracks using ultrasonic arrays.** / Cunningham, L. J.; Mulholland, A. J.; Tant, K. M. M.; Gachagan, A.; Harvey, G.; Bird, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A spectral method for sizing cracks using ultrasonic arrays

AU - Cunningham, L. J.

AU - Mulholland, A. J.

AU - Tant, K. M. M.

AU - Gachagan, A.

AU - Harvey, G.

AU - Bird, C.

PY - 2017/3/9

Y1 - 2017/3/9

N2 - Ultrasonic phased array systems are becoming increasingly popular as tools for the inspection of safety-critical structures within the non-destructive testing industry. The datasets captured by these arrays can be used to image the internal structure of individual components, allowing the location and nature of any defects to be deduced. Although there exist strict procedures for measuring defects via these imaging algorithms, sizing flaws which are smaller than two wavelengths in diameter can prove problematic and the choice of threshold at which the defect measurements are made can introduce an aspect of subjectivity. This paper puts forward a completely objective approach specific to cracks based on the Kirchhoff scattering model and the approximation of the resulting scattering matrices by Toeplitz matrices. A mathematical expression relating the crack size to the maximum eigenvalue of the associated scattering matrix is derived. Analysis of this approximation shows that the method will provide a unique crack size for a given maximum eigenvalue whilst providing a quick calculation method which avoids the need to numerically generate model scattering matrices (the computation time is up to 10^3 times faster). A sensitivity analysis demonstrates that the method is most effective for sizing defects that are commensurate with or smaller than the wavelength of the ultrasonic wave. The method is applied to simulated FMC data arising from finite element calculations where the crack length to wavelength ratios range between 0.6 and 1.9. The recovered objective crack size exhibits an error of 12%.

AB - Ultrasonic phased array systems are becoming increasingly popular as tools for the inspection of safety-critical structures within the non-destructive testing industry. The datasets captured by these arrays can be used to image the internal structure of individual components, allowing the location and nature of any defects to be deduced. Although there exist strict procedures for measuring defects via these imaging algorithms, sizing flaws which are smaller than two wavelengths in diameter can prove problematic and the choice of threshold at which the defect measurements are made can introduce an aspect of subjectivity. This paper puts forward a completely objective approach specific to cracks based on the Kirchhoff scattering model and the approximation of the resulting scattering matrices by Toeplitz matrices. A mathematical expression relating the crack size to the maximum eigenvalue of the associated scattering matrix is derived. Analysis of this approximation shows that the method will provide a unique crack size for a given maximum eigenvalue whilst providing a quick calculation method which avoids the need to numerically generate model scattering matrices (the computation time is up to 10^3 times faster). A sensitivity analysis demonstrates that the method is most effective for sizing defects that are commensurate with or smaller than the wavelength of the ultrasonic wave. The method is applied to simulated FMC data arising from finite element calculations where the crack length to wavelength ratios range between 0.6 and 1.9. The recovered objective crack size exhibits an error of 12%.

KW - inverse problems

KW - spectral analysis

KW - scattering

KW - ultrasonics

KW - engineering

UR - http://www.tandfonline.com/toc/gipe20/current

U2 - 10.1080/17415977.2017.1297437

DO - 10.1080/17415977.2017.1297437

M3 - Article

JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

SN - 1741-5977

ER -