Kriging Methodology for Uncertainty Quantification in Computational Electromagnetics

Abstract

We present the implementation and use of the Kriging methodology, i.e., surrogate models based on Kriging interpolation, in uncertainty quantification (UQ) in computational electromagnetics (CEM). We provide consistent, unified, and comprehensive description, derivation, implementation, use, validation, and comparative study of accuracy and convergence of several advanced Kriging approaches, namely, the universal Kriging, Taylor Kriging, and gradient-enhanced Kriging methods, for reconstruction of probability-density function in UQ CEM problems. We also propose, derive, and demonstrate the gradient-enhanced Taylor Kriging (GETK) methodology, novel to science and engineering in general. Numerical results using higher-order finite-element scattering modeling show that Kriging methods for UQ in CEM are able to accurately output probability-density function prediction for a quantity of interest (e.g., radar cross-section) given the probability density of stochastic input parameters (e.g., material uncertainties), as very efficient alternatives to Monte Carlo simulations. The novel GETK method shows dramatic enhancement over all other tested approaches, Kriging and non-Kriging, in terms of surrogate function accuracy and convergence with increasing the number of sample (training) points in all examples.

Keywords

• Adjoints
• computational electromagnetics
• finite element method
• gradient-enhanced Kriging methods
• Kriging
• material uncertainty