UC Santa Barbara

Data analysis in materials science is of increased interest due to the rate at which large datasets can be generated. This thesis covers micrograph analysis, mechanistic modeling, and inference techniques for materials problems.

Segmentation based image analysis techniques are routinely employed for quantitative analysis of complex microstructures containing multiple phases. The downside is that computing reliable segmentations is challenging and, if no special care is taken, segmentation artifacts will make subsequent analysis difficult. Using a two phase nickel-base superalloy microstructure as a model system, we demonstrate a new methodology for analysis of precipitate shapes using a segmentation-free approach based on the histogram of oriented gradients feature descriptor (HOG), a classic tool in image analysis. The benefits of this methodology for analysis of microstructure in two and three dimensions are demonstrated.

Bayesian modeling and Hamiltonian Monte Carlo (HMC) are utilized to formulate a robust algorithm capable of simultaneously estimating anisotropic elastic properties and crystallographic orientation of a specimen from a list of measured resonance frequencies collected via Resonance Ultrasound Spectroscopy (RUS). Unlike typical optimization procedures which yield point estimates of the unknown parameters, computing a Bayesian posterior yields probability distributions for the unknown parameters. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys, a specimen of fine-grained polycrystalling Ti-6Al-4V (Ti-64) with random crystallographic texture and isotropic elastic symmetry and a single crystal Ni-based superalloy CMSX-4 specimen. Our unique contributions are: the application of HMC for sampling the Bayesian posterior of a probabilistic RUS model, and the procedure for simultaneous estimation of elastic constants and lattice-specimen misorientation.

Finally, we present a selection criterion for the Euclidean metric adapted during warmup in an HMC sampler. This makes it possible for a sampler to automatically pick the metric based on the model and the availability of warmup draws. Additionally, we present a new adaptation inspired by the selection criterion that requires significantly fewer warmup draws to be effective. The effectiveness of the selection criterion and adaptation are demonstrated on a number of applied problems.