Cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging

Abstract

Abstract-Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using GradientEnhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided.

Multivariate Adaptive Sampling of Parameterized Antenna Responses

“…Let F M be an N p ×N matrix whose columns are the CBFPs in (1). A singular value decomposition (SVD) of F M is then carried out, from which the first N R (N R N ) left-singular vectors of F M are retained, constituting a (possibly) reduced set of CBFPs, denoted by U R ∈ C Np×N R .…”

“…In [1], an efficient Kriging model that is enhanced with gradient information, is used to model antenna responses. A Bayesian approach is used in [2] for multivariate S-parameter modeling.…”

“…Another variant of variable fidelity methods is investigated in [5]. The techniques in [1]- [5], among others, aim to reduce the computational cost of antenna design by reducing the number of accurate EM simulations required during the optimization of the antenna under consideration. All the above methods develop models for a single figure of merit and models have to be extracted at each frequency of interest, thus implying repeated EM simulations for a given combination of geometric design variables.…”

“…This method makes use of the characteristic basis function pattern (CBFP) method [7]- [9], where the expansion coefficients are parameterized with respect to the antenna's geometric variables. The techniques in [1]- [6] make use of a pre-allocated grid, typically through a latin hypercube sampling (LHS) algorithm [10], of EM data from which models are extracted. Such a pre-allocation scheme may result in over/under-sampling of the design space, resulting in either inaccurate models or in an unnecessarily lengthy model building process.…”

Novel structure and design of compact UWB slot antenna

“…This is because accurate evaluation of compact antenna can only be obtained by means of computationally expensive full-wave electromagnetic (EM) simulations [4]. Also, small dimensions size make electrical properties of the antenna sensitive to the presence of environmental components such as connectors [4] or housing [14]. Consequently, such components have to be accounted for in computational models, which increases the simulation cost even further.…”