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Mathematical Problems in Engineering
Volume 2015, Article ID 915497, 8 pages
http://dx.doi.org/10.1155/2015/915497
Research Article

Perturbation Approach to Reconstructing Deformations in a Coaxial Cylindrical Waveguide

Department of Electromagnetic Engineering, School of Electrical Engineering, KTH Royal Institute of Technology, 10044 Stockholm, Sweden

Received 20 January 2015; Accepted 4 June 2015

Academic Editor: Franklin A. Mendivil

Copyright © 2015 M. Dalarsson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a detection method for continuous mechanical deformations of coaxial cylindrical waveguide boundaries, using perturbation theory. The inner boundary of the waveguide is described as a continuous PEC structure with deformations modeled by suitable continuous functions. In the present approach, the computation complexity is significantly reduced compared to discrete conductor models studied in our previous work. If the mechanically deformed metallic structure is irradiated by the microwave fields of appropriate frequencies, then, by means of measurements of the scattered fields at both ends, we can reconstruct the continuous deformation function. We apply the first-order perturbation method to the inverse problem of reconstruction of boundary deformations, using the dominant TEM-mode of the microwave radiation. Different orders of Tikhonov regularization, using the L-curve criterion, are investigated. Using reflection data, we obtain reconstruction results that indicate an agreement between the reconstructed and true continuous deformations of waveguide boundaries.