Laboratory application of sampling approaches to inverse scattering

TL;DR

This paper experimentally evaluates the generalized linear sampling method (GLSM) for non-destructive damage detection in elastic materials, demonstrating its superior resolution and robustness over classical methods using ultrasonic shear waves and laser Doppler vibrometry.

Contribution

It introduces an experimental validation of GLSM for damage detection, showing improved accuracy and robustness with sparse and partial data compared to traditional linear sampling methods.

Findings

GLSM accurately identifies damage support with high resolution.

GLSM outperforms classical LSM in clarity and robustness.

Method remains effective with limited and partial data.

Abstract

This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a prismatic slab of charcoal granite featuring a discontinuity interface induced by the three-point bending (3PB). The interaction of probing waves with the 3PB-induced damage gives rise to transient velocity responses measured on the sample's boundary by a 3D scanning laser Doppler vibrometer. Thus obtained waveform data are then carefully processed to retrieve the associated spectra of scattered displacement fields. On deploying multifrequency sensory data, the GLSM indicators are computed and their counterparts associated with the classical linear sampling method (LSM) for comparative analysis. Verified with in-situ observations, the GLSM map successfully exposes the support of hidden scatterers in the specimen with a remarkable clarity and resolution compared to its predecessor LSM. It is further shown that the GLSM remains robust for sparse and partial-aperture data inversion, thanks to its rigorous formulation. For completeness, the one-sided reconstruction by both indicators is investigated.