ADVANCES IN UNCERTAINTY QUANTIFICATION AND INVERSE PROBLEMS IN COMPUTATIONAL MECHANICS

This dissertation is composed of three chapters, each of which addresses a specific topic and has been, or is in the process of being published in a research journal. Though relatively diverse, the topics in each chapter fall broadly un-der the theme of advancing research in uncertainty quantification and inverse problems within the field of computational mechanics. The first chapter is based on the stochastic reduced order model (SROM) concept for propagating uncer-tainty in engineering simulations. Here, the algorithm for constructing SROMs of random vectors is modified and significantly enhanced, yielding more ac-curate models in substantially less computational time. The second chapter focusses on inverse material identification in coupled acoustic-structure inter-action (ASI) systems using either solid displacement or fluid pressure measure-ment data. This work represents the first time the modified error in constitutive equation (MECE) approach for inverse problems has been formulated and ap-plied to elasticity imaging problems in ASI. Finally, the third chapter combines elements of the first two chapters and presents a novel approach to solve in