An Adaptive Variable Partitioning Approach to Quantifying High-Dimensional Uncertainties in Frequency Selective Surfaces

Due to the inherent errors during the fabrication process, the frequency selective surface (FSS) technique suffers high-dimensional uncertainties, which is especially severe for conformal scenarios. This necessitates the introduction of an effective uncertainty quantification (UQ) technique. To be specific, the transmission and reflection coefficients change not only vastly but nonsmoothly with respect to random input variables. This fact excessively increases the difficulty of a UQ technique. To tackle this problem, we proposed an adaptive sparse polynomial chaos expansion (ASPCE) method for high-dimensional UQ in FSS. This method handles nonsmooth responses by partitioning the stochastic space into nonoverlapping elements and constructing sparse polynomial chaos expansion (PCE) locally. Compared with the state-of-the-art multielement sparse grid (ME-SG) method, ASPCE maximizes the utilization of all samples and optimizes the partition scheme, thereby enhancing the UQ accuracy. Orthonormal polynomials corresponding to partitioned variables are constructed in a data-driven manner. Numerical experiments showcase that the ASPCE method remarkably outperforms the sparse PCE (SPCE) and ME-SG in extracting statistical features of FSS, even when the latter two fail.