Bifidelity Methods for Polynomial Chaos Expansions

Graduate Thesis Or Dissertation

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/d504rk734

Abstract

This thesis provides an in-depth evaluation of two multi fidelity uncertainty quantification techniques, highlighting the key characteristics, benefits, and shortcomings therein. Physics based simulations subject to uncertain inputs are used to demonstrate the efficacy of each technique in reducing the computational cost of generating a polynomial chaos (PC) approximation of a simulated quantity of interest(QoI). Considered is a weighted ℓ₁ minimization technique, wherein a priori estimates on the decay of PC coefficients are used to generate sparse PC approximations of the QoI. Also considered is a stochastic basis reduction method, which identifies a subspace that spans the PC basis by principle component analysis of the covariance of the QoI. Numerical tests were conducted upon 2 airfoil simulations subject to 6 uncertain inputs (one at high Mach number, one at low) and a lithium ion battery simulation subject to 17 uncertain inputs to evaluate each method. The examples studied illustrate the main characteristics of each method and provide insight to their applicability to UQ in numerical simulations. Appreciable reductions in computational resources were observed in all cases when compared to direct simulation of a high fidelity model.

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