Nested Kriging with Variable Domain Thickness for Rapid Surrogate Modeling and Design Optimization of Antennas

Design of modern antennas faces numerous difficulties, partially rooted in stringent specifications imposed on both electrical and field characteristics, demands concerning various functionalities (circular polarization, pattern diversity, band-notch operation), but also constraints imposed upon the physical size of the radiators. Conducting the design process at the level of full-wave electromagnetic (EM) simulations, otherwise dictated by reliability, entails considerable computational expenses, which is another and a serious challenge. It is especially pronounced for the procedures involving repetitive EM analyses, e.g., parametric optimization. Utilization of fast surrogate models as a way of mitigating this issue has been fostered in the recent literature. Unfortunately, construction of reliable surrogates for antenna structures is hindered by their highly nonlinear responses and even more by the utility requirements: design-ready models are to be valid over wide ranges of operating conditions and geometry parameters. Recently proposed performance-driven modeling, especially the nested kriging framework, addresses these difficulties by confining the surrogate model domain to a region that encapsulates the designs being optimum with respect to the relevant figures of interest. The result is a dramatic reduction of the number of training samples needed to render a usable model. This paper introduces a variable-thickness domain, which is an important advancement over the basic nested kriging. The major benefit demonstrated using two antenna examples is a further and significant (up to seventy percent) reduction of the training data acquisition cost. It is achieved while ensuring that the model domain covers the regions containing optimum designs for various sets of performance specifications.