Perturbation approach to reconstructions of boundary deformations in waveguide structures

Abstract: 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.