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 of the specimen geometry, mass, and resonance frequencies. The unique contributions of this paper are as follows: 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. Compared to previous approaches these algorithms demonstrate superior convergence behavior, particularly when the initial parameterization is unknown, and enable substantially simplified experimental procedures.

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist.

We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.

A new elastic characterization method for anisotropic bilayer specimens via Bayesian resonant ultrasound spectroscopy.

A novel nondestructive method for complete elastic characterization of substrate-coating bilayer specimens with distinct anisotropic layers via resonant ultrasound spectroscopy (RUS) and Bayesian inversion is developed here. Bayesian formulations of the RUS inversion problem-of quantifying elastic properties given a measured list of resonance frequencies recorded from a single, typically small, precisely fabricated, macroscopically homogeneous, linear-elastic specimen-are a recent development. Here we report the first Bayesian formulation of the bilayer problem, and through a series of practical examples, demonstrate novel parameter estimation capabilities of our open-source CmdStan-RUS code. Finding specimen geometry and the number of resonance modes used for inversion strongly govern the ability to retrieve individual elastic moduli. The concept of "invertability" is explored for a range of relevant geometries using virtual specimens that resemble experimental bilayers of plasma sprayed ceramic coatings on single crystal metallic substrates. A range of Bayesian posterior evaluation methods are addressed, particularly considering the large computational cost of the bilayer forward model. Laplace approximation methods are thus developed and implemented for bilayer geometry design space modeling and expedient estimates of parameter uncertainties. Ideal specimen design, different noise models, the influence of prior distributions, dual-likelihood fits incorporating measurements of the bare substrate, and how Bayesian RUS methods differ from traditional RUS optimization are discussed.