FULL-TEXT - ABSTRACT

The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's conductivity. Electromagnetic field is generated by a pair of wires, which also serves as a measurement probe. The resulting mathematical model is analyzed by first deriving an integral identity, and second, by linearizing the relation between the conductivity anomaly and the data. We show that the problem of reconstructing a conductivity anomaly from eddy current data is quite unstable, and a method based on leastsquares principle would fail to detect conductivity anomalies in some situation. An alternate method, one that obtains gross properties of the anomaly (in this case an average) is proposed, and is shown to be quite robust. This work is contains several numerical experiments which illustrate our main ideas.

*Research partially supported by Air Force Office of Scientific Research, grant number F49620-95-1-0497.
**Research partially supported by the National Science Foundation under grant DMS-9503114, Department of Energy under grant DE-FG02-94ER25225, the Airforce Office of Scientific Research URI-RIP grant F49620-93-1-0500 and grant F49620-95-1-0305.