Abstract
The paper considers the problem of damage detection arising in nondestructive testing. Applying currents on the boundary of a body and measuring the corresponding responses a conclusion should be made about the presence of damage inside the body.
The detection problem is formulated using a variational approach as a generalized eigenvalue problem. The maximal eigenvalue defines the accuracy of the measurements, which is necessary to detect this distribution of damage. The damage can be detected if there exists such a current in the set of the currents prescribed by the conditions of the experiment that generates perturbation on the boundary greater than the noise level in measurements.
To consider the worst case of detection, the damaged material should be distributed throughout the body in order to minimize the maximal eigenvalue of the spectral operator. An analytical estimate of the perturbation of the maximal eigenvalue is given, depending on the amount of damaged material.
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Cherkaeva, E. Optimal source control and resolution in nondestructive testing. Structural Optimization 13, 12–16 (1997). https://doi.org/10.1007/BF01198370
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DOI: https://doi.org/10.1007/BF01198370