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5 May 2000 Reduced order computational methodology for damage detection in structures
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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 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 first few basis elements is maximized. One then uses a fixed number (based on a quantitative formula for percentage energy captured) of the first 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 flux density B. Our analysis uses simulated data perturbed with normally distributed noise to represent corrupted experimental data. When recapturing the length and 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.
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Michele L. Joyner, H. Thomas Banks, Buzz Wincheski, and William P. Winfree "Reduced order computational methodology for damage detection in structures", Proc. SPIE 3994, Nondestructive Evaluation of Aging Aircraft, Airports, and Aerospace Hardware IV, (5 May 2000);

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