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Perturbation Approach to Reconstructing Deformations in a Coaxial Cylindrical Waveguide
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-9241-8030
2015 (English)In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, 915497Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. 915497
National Category
Other Mathematics
URN: urn:nbn:se:kth:diva-177434DOI: 10.1155/2015/915497ISI: 000364064300001ScopusID: 2-s2.0-84946924717OAI: diva2:872831
Swedish Energy Agency, 34146-1

QC 20151120

Available from: 2015-11-20 Created: 2015-11-20 Last updated: 2016-01-19Bibliographically approved
In thesis
1. Perturbation approach to reconstructions of boundary deformations in waveguide structures
Open this publication in new window or tab >>Perturbation approach to reconstructions of boundary deformations in waveguide structures
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we develop inverse scattering algorithms towards the ultimate goal of online diagnostic methods. The aim is to detect structural changes inside power transformers and other major power grid components, like generators, shunt reactors etc. Power grid components, such as large power transformers, are not readily available from the manufacturers as standard designs. They are generally optimized for specific functions at a specific position in the power grid. Their replacement is very costly and takes a long time.

Online methods for the diagnostics of adverse changes of the mechanical structure and the integrity of the dielectric insulation in power transformers and other power grid components, are therefore essential for the continuous operation of a power grid. Efficient online diagnostic methods can provide a real-time monitoring of mechanical structures and dielectric insulation in the active parts of power grid components. Microwave scattering is a candidate that may detect these early adverse changes of the mechanical structure or the dielectric insulation. Upon early detection, proper actions to avoid failure or, if necessary, to prepare for the timely replacement of the damaged component can be taken. The existing diagnostic methods lack the ability to provide online reliable information about adverse changes inside the active parts. More details about the existing diagnostic methods, both online and offline, and their limitations can be found in the licentiate thesis preceding the present PhD thesis.

We use microwave scattering together with the inverse scattering algorithms, developed in the present work, to reconstruct the shapes of adverse mechanical structure changes. We model the propagation environment as a waveguide, in which measurement data can be obtained only at two ends (ports). Since we want to detect the onset of some deformation, that only slightly alters the scattering situation (weak scattering), we have linearized the inverse problem with good results. We have calculated the scattering parameters of the waveguide in the first-order perturbation, where they have linear dependencies on the continuous deformation function. A linearized inverse problem with a weak scattering assumption typically results in an ill-conditioned linear equation system. This is handled using Tikhonov regularization, with the L-curve method for tuning regularization parameters.

We show that localized one-dimensional and two-dimensional shape deformations, for rectangular and coaxial waveguide models, are efficiently reconstructed using the inverse scattering algorithms developed from the first principles, i.e. Maxwell’s theory of electromagnetism. An excellent agreement is obtained between the reconstructed and actual deformation shapes for a number of studied cases. These results show that it is possible to use the inverse algorithms, developed in the present thesis, as a theoretical basis for the design of a future diagnostic device. As a part of the future work, it remains to experimentally verify the results obtained so far, as well as to further study the theoretical limitations posed by linearization (first-order perturbation theory) and by the assumption of the continuity of the metallic waveguide boundaries and their deformations.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology: KTH Royal Institute of Technology, 2016. xii, 53 p.
TRITA-EE, ISSN 1653-5146 ; 2015:109
inverse problems, waveguides, microwaves, perturbation theory
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
urn:nbn:se:kth:diva-180429 (URN)978-91-7595-801-9 (ISBN)
Public defence
2016-02-12, F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)

QC 20160119

Available from: 2016-01-19 Created: 2016-01-13 Last updated: 2016-02-24Bibliographically approved

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