Two-dimensional boundary shape reconstructions in rectangular and coaxial waveguides

•Shape reconstruction method for two-dimensional boundary deformations in waveguides.•First-order perturbation approach is used to calculate the scattering parameters.•Scattering parameters given as linear functions of continuous deformation functions.•Reconstructions of two-dimensional deformations of rectangular waveguide boundaries.•Reconstructions of two-dimensional deformations of coaxial waveguide boundaries.

We present a method for shape reconstruction of deformed metallic boundaries in rectangular and coaxial waveguides using microwave scattering. Our developed reconstruction method is a theoretical basis for a future on-line microwave-based monitoring system for power grid components. The bundle of winding conductors in the active part of a typical power grid component is modeled as a continuous metallic surface. Then, electromagnetic field perturbation theory in conjunction with inverse problem theory is used to reconstruct the shape parameters of this surface. We assume small perturbations of the boundaries, such that the scattering parameters of the waveguide in the first-order perturbation have linear dependencies of the continuous deformation function. Thus, the corresponding inverse problem can be linearized and we can employ direct inversion, without the need for optimization which requires a higher computational effort. Tikhonov regularization is used to regularize the arising ill-conditioned linear system. The reconstructions, performed with noisy synthetic measurement data, show a good agreement with the actual shapes of the studied two-dimensional localized shape deformations for both rectangular and coaxial waveguide boundaries.