Mathematical model of crack diagnosis: inverse acoustic scattering problem and its high-precision numerical solution
Victor A. Kovtunenko1
1Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrich str. 36, 8010 Graz, Austria
1Lavrent’ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 630090, Novosibirsk, Russia
Vibroengineering PROCEDIA, Vol. 22, 2019, p. 31-35.
Received 10 January 2019; accepted 20 January 2019; published 15 March 2019
The inverse acoustic scattering model for crack diagnosis is described by Helmholtz problem within mathematic framework and investigated for the sake of scientific computing. Minimizing the misfit from given measurements leads to an optimality condition-based imaging function which is used for non-iterative identification of the center of an unknown crack put in a test domain. The numerical tests are presented for the cracks of T-junction shape and are carried out based on the Petrov-Galerkin generalized FEM using wavelets basis and level-sets. This shows high-precision identification result and stability to noisy data of the diagnosis, which is illustrated for sound-soft as well as moderately sound-hard cracks when varying the coefficient of surface impedance.
- The inverse acoustic scattering problem is investigated for scientific computing of crack diagnosis
- Minimizing the misfit from given measurements leads to an optimality condition-based imaging
- Imaging function is used for non-iterative identification of the center of a crack put in test domain
- Numerical tests are based on Petrov-Galerkin GFEM and wavelet basis
- T-junction shaped cracks are sound-soft as well as sound-hard with moderate surface impedance
- High-precision identification result and stability to noisy data of the diagnosis are reported
Keywords: crack, acoustic scattering, inverse Helmholtz problem, optimization, imaging, variational method, level set, Petrov-Galerkin generalized FEM, wavelet basis, noisy data.
The author is supported by the Austrian Science Fund (FWF) Project P26147-N26: ‘Object Identification Problems: Numerical Analysis’ (PION) and the Austrian Academy of Sciences (OeAW), the RFBR and JSPS research Project 19-51-50004.
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