Data-Driven Uncertainty Quantification in Applications of Electromagnetics and Wireless Communication via Arbitrary Polynomial Chao

In the last two decades, polynomial chaos expansion (PCE) methods have received considerable attention due to their efficiency and accuracy in modeling stochastic processes. However, implementing these methods require specifying the input distributions of a model a priori. This might not be feasible in data-driven applications in which the inputs are represented as data samples obtained from real-time measurements. Further, fitting the data with parametric distributions may introduce undesirable errors. The arbitrary polynomial chaos (aPC) method overcomes this limitation by constructing a chaos expansion based on the statistical moments rather than the probability distributions. The first objective of this dissertation is to develop a procedure based on aPC for data-driven uncertainty quantification (UQ) in applications of electromagnetics and wireless communication.;Although the aPC method is considered to be simple and effective, it becomes numerically unstable when high-order expansions are sought. Alternatively, the multi-element arbitrary polynomial chaos (ME-aPC) alleviates this drawback by replacing the aPC expansion with a piecewise reduced order one. The second objective of this dissertation is to develop a procedure based on ME-aPC, and to demonstrate its efficiency in data-driven UQ.;The proposed procedures are implemented with several model problems of electromagnetics such as filters and sensors, and with model problems of wireless communications addressing uncertainties in lunar radio links. The accuracy of the procedures is validated with plots of relative error, and in some examples, with results obtained via the classical Monte Carlo (MC) method.