Small defects reconstruction in waveguides from multifrequency one-side scattering data
Résumé
Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inver- sion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a L2-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spa- tial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypoth- esis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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