Antenna Modeling Using Variable-Fidelity EM Simulations and Constrained Co-Kriging

Abstract

Utilization of fast surrogate models has become a viable alternative to direct handling of full-wave electromagnetic (EM) simulations in EM-driven design. Their purpose is to alleviate the difficulties related to high computational cost of multiple simulations required by the common numerical procedures such as parametric optimization or uncertainty quantification. Yet, conventional data-driven (or approximation) modeling techniques are severely affected by the curse of dimensionality. This is a serious limitation when it comes to modeling of highly nonlinear antenna characteristics. In practice, general-purpose surrogates can be rendered for the structures described by a few parameters within limited ranges thereof, which is grossly insufficient from the utility point of view. This paper proposes a novel modeling approach involving variable-fidelity EM simulations incorporated into the recently reported nested kriging modeling framework. Combining the information contained in the densely sampled lowand sparsely sampled high-fidelity models is realized using co-kriging. The resulting surrogate exhibits the predictive power comparable to the model constructed using exclusively high-fidelity data while offering significantly reduced setup cost. The advantages over conventional surrogates are pronounced even further. The presented modeling procedure is demonstrated using two antenna examples and further validated through the application case studies. INDEX TERMS Antenna design, surrogate modeling, kriging interpolation, co-kriging, electromagnetic (EM) simulation.

Recent Advances in High Frequency Modeling by Means of Domain Confinement and Nested Kriging

“…Having presented the basic formulation and performance of the nested kriging framework, this section outlines the recent developments of the technique [72]- [77], [82], [83]. These were supposed to address particular aspects of the nested kriging, including further improvement of its predictive power [77], introduction of more efficient data sampling schemes [72], model setup automation [73], reduction of the computational cost of the model setup [74], [75] as well as incorporation of other algorithmic components, especially variable-fidelity simulations [82], [83] and response feature technology [76]. Sections III.A through III.F contain a brief exposition of these developments illustrated using examples of antenna and microwave components.…”

“…13 [mm] For illustration, consider a triple-band dipole antenna shown in Fig. 21 [83]. The antenna is implemented on RO4350 substrate (r = 3.48, h = 0.762 mm) and fed by a coplanar waveguide.…”

“…In the context of modeling of highfrequency structures, it is more suitable for handling components that exhibit wideband characteristics where the discrepancies between the models of various fidelities are mostly vertical (i.e., concern the response levels rather than frequency shifts). In [83] and [88], the nested kriging was combined with co-kriging, which is rather straightforward: the first-level model is constructed in a traditional manner (cf. Section II), whereas the final surrogate is a co-kriging one, using a limited number of high-fidelity data.…”

“…The surrogate model is supposed to be valid within the objective space defined by the parameters of the substrate the antenna is implemented on: permittivity 2.0  r  5.0 and height 0.5 mm  h  1.5 mm. The details concerning the reference designs can be found in [83]. The nested co-kriging model has been constructed using various numbers of high-and low-fidelity samples Nf and Nc: Nf = 20 and Nc = 400, Nf = 50 and Nc = 400, Nf = 100 and Nc = 400, as well as Nf = 50 and Nc = 800.…”

Expedited Yield Optimization of Narrow- and Multi-Band Antennas Using Performance-Driven Surrogates

“…This paper proposes a novel and low-cost procedure for yield optimization of multi-band antennas. Our methodology employs the overall concept of performance-driven modeling [40]- [43] to construct a fast surrogate in the region corresponding to maximum changes of the antenna responses in the vicinity of the nominal design. By appropriate constraining of the model domain, the surrogate can be rendered at a very low cost of a few dozen of EM antenna analyzes while being valid over a sufficiently large parameter ranges to permit efficient optimization of the antenna yield.…”