Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

The use of optimization for the propagation of mixed epistemic/aleatory uncertainties is demonstrated within the context of hypersonic flows. Specifically, this work focuses on strategies applicable for models where input parameters can be divided into a set of variables containing only aleatory uncertainties and a set with epistemic uncertainties. With the input parameters divided in this way, uncertainty due to the epistemic variables is propagated via a constrained optimization approach, while the uncertainty due to aleatory variables is propagated via sampling. A statistics-of-intervals approach is proposed in which the constrained optimization results are treated as a random variable and multiple optimizations are performed to quantify the aleatory uncertainty. In order to reduce the total number of optimizations required, a surrogate is employed to model the variation of the optimization results with respect to the aleatory variables, and exhaustive sampling is performed on this surrogate to determine the desired statistics. The properties of the statistics-of-intervals approach are demonstrated by using the Fay-Riddell stagnation heating correlations and compared with a competing method based on uncertain optimization. Additionally, the statistics-of-intervals approach is demonstrated for mixed epistemic/aleatory uncertainty quantification on a real gas computational fluid dynamic simulation.