A comparison and extensions of algorithms for quantitative imaging of laminar damage in plates. I. Point spread functions and near field imaging

Real-time structural health monitoring (SHM) and safety prognostics require quantitative and continuously updated information on damage size and severity. A unified theoretical solution is presented for three distinct approaches that have been used for in situ imaging of structural damage in plate-like structures. These approaches are based on (i) linearised inverse scattering (or generalised diffraction tomography), (ii) beamforming, and (iii) reverse time migration. In all three approaches, the damaged region is regarded as a weak scatterer. Such an approach is appropriate for early damage detection that is of great practical interest. The linearised inverse is based on a rigorous mathematical formulation, whereas beamforming and reverse time migration are based on heuristic arguments, but the latter are more convenient for practical implementation. It is shown that, in the far-field approximation, the three imaging algorithms have a very similar mathematical structure. Analytical expressions are derived for the point spread functions (PSFs), which represent the reconstructed image for a point-like scatterer. Although the analytical expressions for the PSFs are different, the corresponding profiles are virtually identical. Based on these observed mathematical similarities, modified versions of the diffraction tomography and time-reversal algorithms are presented that combine the advantages of the various approaches. These modified algorithms are extensively evaluated using analytical solutions of a circular scatterer. The resulting algorithms are shown to provide accurate estimates for damage size and damage severity over a range of size and severity that is consistent with the weak scatterer approximation.