Real time computational algorithms for eddy-current-based damage detection

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Abstract
In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as aeroplanes and pipelines. In this paper, we explore the feasibility of detecting such damage by application of an eddy-current-based technique coupled with reduced order modelling. 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 the 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 and 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 simulations 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 sensor. The experimental results are based on successfully using experimental data to form the POD basis elements (instead of numerical simulations), thus illustrating the effectiveness of this method on a wide range of applications. In both instances the methods are found to be efficient and robust. Moreover, the methods were fast; our findings demonstrate a significant reduction in computational time.

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