Evaluation of Material Integrity Using Reduced Order Computational Methodology
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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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 tins. 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 PD techniques. The PD technique is a method which creates all optimal ordered basis in the sense that information captured in the first few basis elements is maximized. ne then uses a fixed number based on a quantitative formula for percentage energy captured of the first few basis elennts, called the reduced PCD basis, in the forward algorithm. Since one uses only a small number of basis elennts, one is able to create a fast forward algorithm that accurately represents the relevant information. In this paper, for illustrative purposes and prooofconcept, we consider rectangular cracks parameterized by a vector parameter q representing the length, thickness, depth, center, etc. of the damage. We attempt to recap- ture the parameters of a damage assuming we have access to the magnetic vector potential A which is not pratical experimentally or the magnetic flux density B. ur analysis uses simuhted data A or B with normally dis- tributed noise to represent corrupted experimental data. When recapturing the length or thickness of a damage using the component of the magnetic flux density orthogonal to the eddy current flow in the sample, the methods are shown to be efficient and robust even with data containing 10 relative noise.