Calibration and uncertainty quantification for Davis Equation of State models for the High Explosive PBX 9501 products

Abstract

This paper investigates the uncertainty in the parameters used in the calibration of an Davis Equation Of State (EOS) for the detonation products of the High Explosive PBX 9501. The procedure sought to make use of all available information about this HE to inform the best set of calibration parameters as well as the uncertainty in these parameters. The procedure made use of historical experimental data, the results from thermo-chemical modeling as well as data on the best isentrope function fit to cylinder test experimental data. Combining all these heterogeneous data sources together in a Bayesian calibration, yielded a posterior mean and covariance. Sampling from the posterior distribution and evaluating an important Quantity Of Interest (QOI) in the EOS model, the detonation speed of a one-inch rate stick, produced a distribution which showed variations which were in agreement with experiments. The uncertainty in the EOS was reported as eleven sets of model calibrations which spanned the range of this QOI.