Real Time Computational Algorithms for Eddy Current Based Damage Detection

In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion arid flaws in structures such as airplanes and pipelines. In this paper we explore the feasibility of detecting such damages by application of an eddy current based technique coupled with reduced order modeling. We begin by developing a model for a specific eddy current method in which we make some simplifying assumptions reducing the three-dimensional problem to a two-dimensional problem. (We do this for proof-of-concept.) Theoretical results are then presented which establish tile existence and uniqueness of solutions as well as continuous dependence of the solutions on the parameters which represent the damage. We further discuss theoretical issues concerning the least squares parameter estimation problem used in identifying the geometry of the damage. To solve the identification problem an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting the forward algorithm must be solved with extremely fast arid accurate solution methods. In constructing these computational methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques. This approach permits one to create a set of basis elements spanning a data set consisting of either numerical siumlations or experimental data. We discuss two different algorithms for forming the POD approximations, a POD/Galerkin technique and a POD/Interpolation technique. Finally, results of the inverse problem associated with damage detection are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive (GMR) sensor. Prepared in cooperation with NASA Langley Research Center, Hampton, VA.