Polynomial-based surrogate models for uncertainty quantification of passive electronic systems
Shangguan, Xingjian
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https://hdl.handle.net/2142/117839
Description
Title
Polynomial-based surrogate models for uncertainty quantification of passive electronic systems
Author(s)
Shangguan, Xingjian
Issue Date
2022-12-09
Director of Research (if dissertation) or Advisor (if thesis)
Chen, Xu
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Polynomial Chaos
Rational Polynomial Chaos
Uncertainty Quantification
Surrogate Model
Electronics Packaging
Principal Component Analysis.
Language
eng
Abstract
In this thesis, the state of the art of polynomial-based surrogate models for uncertainty quantification is reviewed. Different aspects of the surrogate models, including order selection, choice of polynomial basis, quadrature rules and regression-based coefficient obtain process, compression rate of principle component analysis and its relation to the order truncation, as well as the sampling of the design space, are discussed and compared. A new algorithm for sampling and a common denominator rational polynomial chaos formulation are proposed. Numerical results on an analytical distributed circuit model, a differential via structure, and a fan-out package are provided to demonstrate the applicability of the polynomial-based methods to work with passive electronic systems and structures. The proposed sampling method improved the $L_{\infty}$ norm of the error compared to the simulation. And the common denominator formulation provides speed-up to the rational polynomial chaos. And finally, a conclusion and directions for future work are presented.
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