Bayesian inference of elastic properties with resonant ultrasound spectroscopy

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, and HMC is an efficient way to compute this posterior. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys. First, the elastic constants for a specimen of fine-grain polycrystalline Ti-6Al-4 V with random crystallographic texture and isotropic elastic symmetry are estimated. Second, the elastic constants and crystallographic orientation for a single crystal Ni-based superalloy CMSX-4 specimen are accurately determined, using only measurements o...