<p>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 airplanes and pipelines. In this dissertation, we explore the feasibility of detecting such damages by application of an eddy current based technique and reduced order modeling. <br><br>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 solution 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. <br><br>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. Therefore in constructing these computational methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques which allows one to create a set of basis elements spanning a data set consisting of either numerical simulations or experimental data. <br><br>We investigate two different approaches in forming the POD approximation, a POD/Galerkin technique and a POD/Interpolation technique. We examine the error in the approximation using one approach versus the other as well as present results of the parameter estimation problem for both techniques. <br><br>Finally, results of the parameter estimation problem are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive (GMR) sensor. The experimental results are based on successfully using actual 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. Furthermore, the methods were fast; our findings suggest a significant reduction in computational time. <P>
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-20010608-103545 |
| Date | 11 June 2001 |
| Creators | Joyner, Michele Lynn |
| Contributors | H.T. Banks, H.T. Tran, Pierre A. Gremaud, Kazufumi Ito |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-20010608-103545 |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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