With the increasing reliance on simulation codes, understanding their uncertainties is clearly becoming a critical issue to address. The uncertainty quantification process consists in developing an uncertainty model for the simulation code through comparison of the code's output to experimental measurements.
Our approach to understanding simulation codes combines the principles of physics and Bayesian analysis. The focus is on understanding and quantifying the uncertainties in the simulation-code submodels and the numerical errors introduced in solving the dynamical equations. Bayesian analysis provides the underpinning for quantifying the uncertainties in models inferred from experimental results, which possess their own degree of uncertainty. The aim is to construct an uncertainty model that is based on inferences drawn from comparing the code's predictions to relevant experimental results. In the context of the proposed framework, it is possible to design new experiments that can best provide data for reducing prediction uncertainty.
The sources of uncertainty in a simulation-code prediction of the outcome to a hypothesized physical situation include a) uncertainties in the dynamical equations, b) uncertainties in submodels that describe material properties, c) numerical-solution errors, and d) uncertainties in the initial and boundary conditions of the physical situation being simulated.
We demonstrate our proposed approach by analyzing the results of a Taylor impact test, in which a metal cylinder is propelled into a rigid wall. The profile of the deformed cylinder is typically measured. We show how such profile data can be used to refine an uncertainty model for the simulation code, which can then be used to predict how well the code should be able to predict the results of the next Taylor test.
Keywords: physics simulation codes, Bayesian calibration, Bayesian analysis, uncertainty estimation, Taylor impact test, plastic flow, Zerilli-Armstrong model, hierarchy of experiments, validation
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