On Inadequacy of Sequential Design of Experiments for Performance-Driven Surrogate Modeling of Antenna Input Characteristics

Design of contemporary antennas necessarily involves electromagnetic (EM) simulation tools. Their employment is imperative to ensure evaluation reliability but also to carry out the design process itself, especially, the adjustment of antenna dimensions. For the latter, traditionally used parameter sweeping is more and more often replaced by rigorous numerical optimization, which entails considerable computational expenses, sometimes prohibitive. A potentially attractive way of expediting the simulation-based design procedures is the replacement of expensive EM analysis by fast surrogate models (or metamodels). Unfortunately, due to the curse of dimensionality and considerable nonlinearity of antenna characteristics, applicability of conventional modeling methods is limited to structures described by small numbers of parameters within narrow ranges thereof. A recently proposed nested kriging technique works around these issues by allocating the surrogate model domain within the regions containing designs that are of high quality with respect to the selected performance figures. This paper investigates whether sequential design of experiments (DoE) is capable of enhancing the modeling accuracy over one-shot space-filling data sampling originally implemented in the nested kriging framework. Numerical verification carried out for two microstrip antennas indicates that no noticeable benefits can be achieved, which contradicts the common-sense expectations. This result can be explained by a particular geometry of the confined domain of the performance-driven surrogate. As this set consists of nearly-optimum designs, the average nonlinearity of the antenna responses therein is almost location independent, therefore optimum training data allocation should be close to uniform. This is indeed corroborated by our experiments.