Evaluation of Material Integrity Using

This paper explores the feasibility of detecting damage within structures such as air foils by application of eddy current based techniques and reduced order modeling. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. Therefore, the forward algorithm must be solved with extremely fast and accurate solution methods. In constructing these forward methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques. The POD technique is a method which creates an \optimal" ordered basis in the sense that information captured in the rst few basis elements is maximized. One then uses a xed number (based on a quantitative formula for percentage energy captured) of the rst few basis elements, called the reduced POD basis, in the forward algorithm. Since one uses only a small number of basis elements, one is able to create a fast forward algorithm that accurately represents the relevant information. In this paper, for illustrative purposes and proof-of-concept, we consider rectangular \cracks" parameterized by a vector parameter q representing the length, thickness, depth, center, etc. of the damage. We attempt to recapture the parameters of a damage assuming we have access to the magnetic vector potential A (which is not pratical experimentally) or the magnetic ux density B. Our analysis uses simulated data  or B̂ with normally distributed noise to represent corrupted experimental data. When recapturing the length or thickness of a damage using the component of the magnetic ux density orthogonal to the eddy current ow in the sample, the methods are shown to be e cient and robust even with data containing 10% relative noise.