Statistical analysis of electromagnetic structures and antennas using the polynomial chaos expansion method

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

“…Four methods are most often used to calculate PCE coefficients. The first of these, Spectral Projection, 4 takes advantage of the orthogonal property of the PCE, while the second method, Ordinary Least Squares (OLS), is a linear regression method which determines the coefficients by minimizing the PCE approximation error. The last two methods are both based on OLS, aiming to provide a sparse PCE solution.…”

“…One of the most standard techniques for calculating the coefficients of series expansions of functions, is that of Spectral Projection, 4 in which the integral Equation ( 5) is used to calculate coefficients in a similar fashion to the calculation of Fourier coefficients.…”

“…In these fields, analysis is typically performed using full‐wave electromagnetic analysis, which is computationally very expensive, and the advantages of obtaining statistical information by using only a small set of analysis points become significant. Examples of published applications of PCE includes the modeling of the uncertainty in the resonance frequency of textile antennas due to bending, 2 the statistical modeling of disturbed antennas, 3 general statistical analysis of electromagnetic structures and antennas 4 and the quantification of the performance of the GeReLEO‐SMART satellite antenna under uncertainty 5 . While these and other examples employ different model coefficient calculation techniques, such as the Linear Regression method for multiport microwave circuits, 6 the Ghalerkin method for transmission lines, 7 and the Spectral Projection method for antennas, 2 in none of the examples is consideration given to more than one coefficient calculation technique, even though the correct choice of such a technique can reduce the required number of analysis samples by a significant factor.…”

Uncertainty Quantification in Molecular Signals Using Polynomial Chaos Expansion

“…Therefore, PCE represents a good avenue of research. It is worth noting that even in the whole area of wireless communication, there is a lack of research in uncertainty propagation [18], [19].…”

Assessing Vircators’ Reliability Through Uncertainty and Sensitivity Analyses Using a Surrogate Model

“…During the last decades, several statistical methods have been applied to electromagnetic [13]- [15], mechanical problems [16], and Vircator studies [17]- [20]. From crude Monte Carlo (MC) [21], [22] (known as a brute force technique) to Polynomial Chaos [23], [24], it has been shown how the confidence level could be assessed when dealing with random variables [25]. At the same framework, the analysis of the dominant random variables has been introduced through well-known techniques such as Morris or Sobol' indices [26].…”