Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering Sciences

First Advisor

Alireza Doostan

Second Advisor

Kurt Maute

Third Advisor

Carlos Felippa

Fourth Advisor

Se-Hee Lee

Fifth Advisor

Brandon Jones


This thesis includes three main parts that are concerned with the propagation of uncertainty across high-dimensional coupled problems with applications to Lithium-ion batteries (LIBs). In all three parts, spectral methods involving polynomial chaos expansions (PCEs) are employed to quantify the effects of propagating the input uncertainties across the system.

In the first part, a stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned treatment of the uncertainty space in coupled domain problems. Sequential construction of the sub-domain solutions with respect to the stochastic dimensionality of each sub-domain enabled by the classical FETI method drastically reduces the overall computational cost and provides a well suited framework for parallel computing. Two high-dimensional stochastic problems, a 2D elliptic PDE with random diffusion coefficient and a stochastic linear elasticity problem, have been considered to study the performance and accuracy of the proposed stochastic coupling approach.

A sampling-based UQ framework to study the effects of input uncertainties on the performance of LIBs using a full-order physics-based electrochemical model is presented in the second part. Developed based on sparse PCEs, the proposed UQ technique enables one to study the effects of LIB model uncertainties on the cell performance using a fairly small number of battery simulations. An LiC6/LiCoO2 cell with 19 random parameters has been considered to study the performance and accuracy of the proposed UQ approach. It was found that the battery discharge rate is a key factor affecting not only the performance variability of the cell, but also the determination of most important random inputs.

The third part provides a comprehensive review of the sampling techniques for the regression-based PCEs. Traditional sampling methods such Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments, Gaussian quadratures as well as more recent techniques such as coherence-optimal and randomized quadratures are discussed. In addition, hybrid sampling methods referred to by the alphabetic coherence-optimal techniques which are a combination of the alphabetic optimality criteria and the coherence-optimal sampling method are proposed. It was observed that the alphabetic-coherence-optimal techniques outperform other sampling methods, specially when high-order PCEs are employed and/or the oversampling ratio is low.