Bayesian Inference of Elastic Properties with Resonant Ultrasound Spectroscopy (Preprint)

Abstract : In this work, 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 Hamiltonian Monte Carlo is an efficient way to compute this posterior. The algorithms described above are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys relevant to aerospace. First, the elastic constants for a specimen of ne-grain polycrystalline Ti- 6Al-4V (Ti-64) with random crystallographic texture and isotropic elastic symmetry are estimated. Secondly, the elastic constants for a single crystal Ni-based superalloy CMSX-4 specimen are estimated. This time, the crystallographic orientation is important due to elastic anisotropy, but the elastic constants are inverted without measuring this orientation. Using only measurements of the specimen geometry, mass, a resonance frequencies, the crystal-specimen reference frame misorientation and elastic properties are accurately determined.