Analysis, Modeling, and Optimal Experimental Design under Uncertainty: From Carbon Nano-Structures to 3D Printing

Abstract

In this thesis, we develop approaches for carrying out inference and model-based experimental design, under both internal and external sources of uncertainty. Specifically, in Chapter 1, we develop a stochastic growth model for the carbon-based super material, Graphene, and propose approaches for relating controllable experimental factors to the underlying growth mechanism. In Chapter 2 we develop a unified framework for carrying out response surface optimization when the input factors are noisy, and in Chapter 3, we explore the problem of designing optimal experiments, under the extra uncertainty generated by noisy inputs. Internal noise, a term used to describe the phenomenon of noisy inputs, is found to adversely affect optimization and model-based optimal designs. We show that accounting for this internal noise during the design and modeling stages significantly improve inference. In particular, we develop a modified optimality criterion for generating optimal experimental data, and show improvements in subsequent inference based on that data. In Chapter 4, a missing data perspective is used to improve inference on deformations along the profile of 3D printed products. We show that these deformations depend on missing angles, which can be used to infer global and local deformation patterns. We use the inferred deformation model to design compensation plans for minimizing deformations on future printed objects.