Linear sampling method applied to non destructive testing of an elastic waveguide: theory, numerics and experiments. (English) Zbl 1431.65205
Summary: This paper presents an application of the linear sampling method to ultrasonic non destructive testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the linear sampling method at multiple frequencies, such modal formulation being justified theoretically in [L. Bourgeois et al., Inverse Probl. 27, No. 5, 055001, 27 p. (2011; Zbl 1217.35209)] for rigid obstacles and in [L. Bourgeois and E. Lunéville, Inverse Probl. 29, No. 2, Article ID 025017, 19 p. (2013; Zbl 1334.74011)] for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74J20 | Wave scattering in solid mechanics |
| 74J25 | Inverse problems for waves in solid mechanics |
Keywords:
elastic waveguide; inverse scattering problem; linear sampling method; Lamb modes; experimental dataReferences:
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