Autoregressive Modelling and Synthetic Generation of High-Fidelity, Statistically Equivalent 3D Microstructures for As-Manufactured Misalignments in Fiber-Reinforced Composites

Abstract

This study presents an integrated framework for processing, modelling, and generating statistically representative three-dimensional fiber microstructures from experimental X-ray-$\mu$CT observations. First, an analytical slice-segment ellipse-intersection method is introduced to extract per-slice and per-fiber in-plane and out-of-plane misalignment profiles along the fiber depth. These descriptors are then used to construct a stochastic model that captures slice-wise misalignment distributions and their depth-wise evolution through, copula-based in-plane dependence, latent autoregressive continuity, and rare extreme-misalignment motifs. The model hyperparameters are calibrated using Bayesian optimization, achieving close agreement with the original statistical descriptors, with deviations generally below 10\%. The optimized statistical model is coupled with a physical generation strategy that begins with variable-radius fiber seeding layer and proceeds through an iterative slice-by-slice 3D growth scheme, where the statistical layer guides fiber evolution and Delaunay-based neighbourhood construction with ellipse-based contact resolution ensures non-overlapping, radius-augmented synthetic microstructures. The framework successfully generates about 2400 synthetic fibers while preserving strong statistical fidelity to the original X-ray-$\mu$CT data. The proposed pipeline provides a promising and scalable route for generating statistically equivalent, geometrically admissible, and simulation-ready fiber composite microstructures for virtual testing and analysis.