Optimal source control and resolution in nondestructive testing

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.     

Optimal survey design using focused resistivity arrays

The first problem which needs to be solved when planning any geoelectrical survey is a choice of a particular electrode configuration that can give the maximal response from a target inhomogeneity. The authors formulate a problem of maximizing the response as an optimization problem for an applied current intensity distribution on the surface. The solution of this problem is the optimal intensity distribution of the current, which maximizes the response from the inclusion. This problem is solved numerically with singular value decomposition of an impedance matrix. The optimal current array is modeled as a current of varying optimal intensity injected at different electrodes. The problem does not need any information about the inclusion but its measured impedance matrix. Thus an optimal current array can be designed for every particular resistivity distribution. The optimal current patterns are found for a number of models of a conductive inclusion, and responses due to the optimal current are compared with responses due to conventional arrays. This method can be applied to any background and inclusion resistivity distribution