Abstract
This paper puts forward a methodology for applying the frequency domain Factorisation Method to time domain experimental data arising from ultrasonic phased array inspections in a limited aperture setting. Application to both synthetic and experimental data is undertaken and a multi-frequency approach is explored to address the difficulty encountered in empirically choosing the optimum frequency at which to operate. Additionally, a truncated singular value decomposition (TSVD) approach is implemented in the case where the flaw is embedded in a highly scattering medium, to regularise the scattering matrix and minimise the contribution of microstructural noise to the final image. It is shown that when the Factorisation Method is applied to multi-frequency scattering matrices, it can better characterise crack-like scatterers than in the case where the data arises from a single frequency. Finally, a volumetric defect and a lack-of-fusion crack are both successfully reconstructed from experimental data, where the resulting images exhibit only 3\% and 10\% errors respectively in their measurement.
Highlights
Ultrasonic nondestructive testing uses high frequency mechanical waves to inspect components of safety critical structures, ensuring that they operate reliably without compromising their integrity
When each of the N elements are fired sequentially, the N2 time traces arising from each transmit-receive pair of elements (N being the number of elements, usually between 32 and 256) can be processed and stored in a 3D matrix (N × N × T, where T is the number of sample points in the time domain), usually termed the Full Matrix Capture (FMC) [2]
Application of sampling methods to time domain data has been studied before in [20, 21, 22, 23, 24] the authors believe that this paper presents application of the Factorisation Method to experimentally collected time domain ultrasonic phased array data in a limited aperture setting for the first time
Summary
Ultrasonic nondestructive testing uses high frequency mechanical waves to inspect components of safety critical structures, ensuring that they operate reliably without compromising their integrity. The phased array inspection of a weld with a highly scattering material microstructure (taken from experimental electron backscatter diffraction (EBSD) measurements) is modelled within a finite element package This allows us to study noisy signals which closer resemble the data arising from experiment than those created when the simulation is run with a homogeneous host medium and retrospectively perturbed by random noise. Note that the implementation of the factorisation methodology used in this paper assumes a homogeneous host medium and receives no information on the scattering host microstructure and so any inverse crimes are avoided The reconstructions of both volumetric and crack-like scatterers embedded in this heterogeneous environment are presented. As this approach allows increased exploitation of the available data, improved characterisation is subsequently facilitated
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