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Abstract
Ultrasonic phased array systems are becoming increasingly popular as tools for the inspection of safetycritical structures within the nondestructive 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%.
Original language  English 

Number of pages  19 
Journal  Inverse Problems in Science and Engineering 
Early online date  9 Mar 2017 
DOIs  
Publication status  Epub ahead of print  9 Mar 2017 
Keywords
 inverse problems
 spectral analysis
 scattering
 ultrasonics
 engineering
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Dive into the research topics of 'A spectral method for sizing cracks using ultrasonic arrays'. Together they form a unique fingerprint.Projects
 1 Finished

Doctoral Training Grant 2010
McFarlane, A.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/10 → 30/09/14
Project: Research  Studentship