A comparison of techniques for finding coefficients of polynomial chaos models for antenna problems

Abstract

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross-polarization of an inset-fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high-volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem-specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte-Carlo analysis.

Modeling of spatial permittivity variations using Karhunen–Loève expansion for stochastic electromagnetic problems

“…The relative permittivity variations, ϵ r (x,θ) in this problem is modeled using KL expansion using Equation (1), where ξ i Ñ 0, 1 ð Þ and {λ n ,f n } are the eigenpair of the covariance kernel. The mean value of relative permittivity, ⟨ϵ r ⟩ ¼ 4 and the variations in relative permittivity considered is 10% of ϵ r (σ ¼ 0:1⟨ϵ r ⟩).…”

“…Most electromagnetic applications are subjected to uncertainties in material properties and geometry, and the effect of these variations is evident in the performance of radome enclosed antennas, millimeter wave structures or Tera hertz antennas. 1 The scenario is particularly relevant in the context of widespread adaptation of 5G communication systems, as the effects of variations in materials are far more evident and critical at millimeter waves. As a result, development of numerical stochastic electromagnetic solvers for quantifying these uncertainties is of special interest to the scientific community.…”

Data driven surrogate modeling of horn antennas for optimal determination of radiation pattern and size using deep learning

“…Data-driven surrogate modeling has proved its usage in the design procedure of highfrequency devices as a low-cost surrogate of the various electrical and field responses of high-frequency stages such as scattering parameters [S], 14,15 reflection phase characteristics in reflect-arrays, 16 characteristic impedance, 17 and prediction resonant frequency of antenna designs. [18][19][20] In each of the mentioned works, different types of Artificial Intelligence (AI) regression methods such as polynomial, 21,22 kriging, [23][24][25] Support Vector Regression (SVR), [26][27][28][29] Artificial Neural Networks (ANNs), [30][31][32][33][34] and Deep Learning (DL) [35][36][37][38][39] had been used to create an accurate, stable mapping between the given input space of the problem and the targeted characteristic as the output of the model.…”

Performance-Driven Yield Optimization of High-Frequency Structures by Kriging Surrogates

“…Improving the computational efficiency of statistical analysis can be achieved using simplistic yet inaccurate methods (e.g., worst-case analysis [19][20][21]) or surrogate-assisted techniques [22,23], where repetitive EM simulations are replaced by an evaluation of a fast replacement model, usually prepared beforehand. Popular modeling methods include polynomial approximation [24], neural networks (NNs) [25,26], or polynomial chaos expansion (PCE) [27][28][29][30][31][32][33]. Despite their advantages, surrogate-based methods are affected by the curse of dimensionality, resulting in excessive costs of model rendition for more complex systems.…”