Data-Driven Characterization of Micro-structural Shape and Topology in Engineering Materials

Abstract

This thesis presents a data-driven framework for the quantitative characterization of microstructural shape and topology in engineering materials, integrating invariant geometric descriptors and statistical dimensionality reduction techniques. Specifically, Hu moments, Principal Eigenvalue Moment (PEM), and Principal Component Analysis (PCA) are applied to a diverse dataset comprising experimental images of Titanium-Aluminum alloys and Inconel 718 superalloy, computationally designed meta-materials including unit cells and spinodoids, and synthetic microstructures generated via deep learning models such as Progressive Generative Adversarial Network (PGAN) and Denoising Diffusion Probabilistic Models (DDPM). Both Hu moments and PEM portray a high degree of invariance to rotation and scaling, showing considerable effectiveness in capturing morphologic features like grain size, ellipticity, and asymmetry. PCA provides a complementary perspective by revealing global variance patterns in pixel intensity distributions, although it is sensitive to rotation and color information. The result reflects that synthetic images generated from DDPM closely mimic real microstructure data in terms of both shape and texture, whereas images from the PGAN model align better with color-based PCA. The framework supports reproducible and scalable quantification of microstructures, which aids materials informatics, classification, and computational materials design.