Kriging metamodels and design re‐utilization for fast parameter tuning of antenna structures

Abstract

The paper addresses the problem of computationally efficient electromagnetic (EM)-driven design closure of antenna structures. The foundations of the presented approach are fast kriging interpolation metamodels, utilized for two purposes: (a) producing a good starting point for further parameter tuning, and (b) yielding a reasonable Jacobian matrix estimate to jump-start the optimization procedure. The models are rendered using available designs, for example, obtained from the previous design work with the same antenna structure. The low cost of design closure is ensured by employing Broydenbased trust-region gradient search along with the aforementioned Jacobian initialization. Our methodology is demonstrated using two planar antennas, a dual-band uniplanar dipole and a quasi-Yagi with a parabolic reflector, both optimized within wide ranges of operating conditions (center frequencies, the dielectric permittivity of the antenna substrate). The redesign process requires only a handful of EM analyses of the respective structure. The presented framework can be viewed as a convenient algorithmic tool that capitalizes on the existing information on the structure at hand to enable warm-start parameter tuning. K E Y W O R D S antenna design, design closure, EM simulation, kriging metamodels, parameter tuning 1 | INTRODUCTION Widespread utilization of electromagnetic (EM) simulation tools revolutionized the development procedures of modern antennas. As a matter of fact, EM-driven design is a practical necessity in a growing number of cases where analytical models are no longer adequate. It is especially pertinent to structures featuring nonnegligible mutual coupling effects 1 and feed radiation, 2 compact antennas, 3 wearable antennas at the presence of human body, 4 or situations where environmental components (connectors, housing) affect the antenna operation. 5 Perhaps the most common usage of EM tools is parameter tuning, 6,7 which is a computationally expensive endeavor. Its complexity may be aggravated by factors such as the need for global search, operating in highly-dimensional parameter spaces, or the need for handling multiple performance figures and constraints. 8,9 Convenience, CPU cost and availability of the algorithms (eg, implemented in commercial software packages) typically suggest the utilization of local optimization procedures, but these require reasonably good initial designs, which are not always at hand. Facilitating EM-driven design procedures has been the subject of intense research over the last two decades or so. Among the various techniques developed, some notable examples include adjoint sensitivities and their applications

Accelerated parameter tuning of antenna structures using inverse and feature‐based forward kriging surrogates

“…This section formulates the parameter tuning procedure proposed in the work. The overall methodology capitalizes on the concepts presented in Reference 53. Therein, the initial design is generated using an inverse surrogate constructed from a set of database designs, available from the previous design work on the same structure or pre‐optimized to set up the design framework.…”

“…The tuning process itself has been conducted using (local) gradient‐based search, which is jump‐started by means of the forward model of the antenna sensitivities. The forward surrogate is the weakest point of the method of Reference 53, because modeling of complex characteristics (here, Jacobian matrices) is very challenging, especially in higher‐dimensional parameter spaces. The major advancement of this work is to incorporate the response feature technology 37 in two ways: (i) to model antenna sensitivities at the level of properly selected feature points instead of the entire characteristics, and (ii) reformulating the design problem in terms of response features.…”

“…Furthermore, the design problem itself is reformulated in terms of the characteristic points, which makes it easier to solve and reduces the computational overhead of the optimization process. Our methodology is validated using two examples of microstrip antennas and compared to the surrogate‐assisted technique of Reference 53. The results indicate that the proposed framework is competitive to the state‐of‐the‐art approaches and allows for reliable and automated re‐design of antennas for broad ranges of operating conditions as low computational costs.…”

“…More sophisticated frameworks rely on inverse regression surrogates, 51 and can be further accelerated by incorporating variable‐fidelity EM simulations 52 . In Reference 53, a surrogate‐based procedure for fast high‐frequency optimization has been proposed that involves two metamodels: an inverse model for initial design generation and a forward model of antenna sensitivities for jump‐starting the tuning process. This technique has been demonstrated to be efficient, yet modeling of gradients is a challenging task, particularly when using a small number of reference designs, which is typical for the warm‐start optimization frameworks discussed in this paragraph and desirable from the computational expenditures perspective.…”

“…This paper proposes a novel methodology for rapid optimization of antenna structures. Our technique capitalizes on the method of Reference 53 and advances over it through a combination with the response feature technology 54 . More specifically, the forward surrogate model of the antenna sensitivities is constructed at the level of response features which makes is considerably more reliable in comparison to the model rendered for the entire frequency characteristics.…”