A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data

Abstract : A time-domain topological sensitivity (TS) approach is developed for elastic-wave imaging of media of arbitrary geometry. The TS, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal hole, is expressed in terms of the time convolution of the free field and a supplementary adjoint field as a function of that specified location. Following previous studies performed under (mostly) static or time-harmonic conditions, the TS field is here considered as a natural and computationally efficient approach for defining a defect indicator function. This study emphasizes the implementation and exploitation of TS fields using standard displacement-based FEM approaches, a straightforward task once the correct sensitivity formulation is available. A comprehensive set of numerical experiments on 3-D and 2-D elastodynamic and acoustic configurations is reported, allowing to assess and highlight many features of the proposed TS-based fast qualitative identification such as its ability to identify multiple defects and its robustness against data noise.
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Submitted on : Wednesday, January 13, 2010 - 8:58:21 AM
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Cédric Bellis, Marc Bonnet. A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data. International Journal of Solids and Structures, Elsevier, 2010, 47, pp.1221-1242. ⟨10.1016/j.ijsolstr.2010.01.011⟩. ⟨hal-00446550v2⟩

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