Cost-Efficient Bi-Layer Modeling of Antenna Input Characteristics Using Gradient Kriging Surrogates

Over the recent years, surrogate modeling has been playing an increasing role in the design of antenna structures. The main incentive is to mitigate the issues related to high cost of electromagnetic (EM)-based procedures. Among the various techniques, approximation surrogates are the most popular ones due to their flexibility and easy access. Notwithstanding, data-driven modeling of antenna characteristics is associated with serious practical issues, the primary one being the curse of dimensionality, particularly troublesome due to typically high nonlinearity of antenna responses. This limits applicability of conventional surrogates to simple structures described by a few parameters within narrow ranges thereof, which is grossly insufficient from the point of view of design utility. Many of these issues can be alleviated by the recently proposed constrained modeling techniques that restrict the surrogate domain to regions containing high-quality designs with respect to the relevant performance figures, which are identified using the pre-optimized reference designs at an extra computational effort. This paper proposes a methodology based on gradient-enhanced kriging (GEK). It enables a considerable reduction of the number of reference points required to construct the inverse surrogate (employed in surrogate model definition) by incorporating the sensitivity data into the nested kriging framework. Using two antenna examples, it is demonstrated to yield significant savings in terms of the surrogate model setup cost as compared to both conventional modeling methods and the original nested kriging.