Quantification of Margins and Uncertainties (QMU) is the main focus of the PSAAP Center. The QMU process being at the heart of the Program, it involves the interaction between all different groups (physical modeling, Uncertainty Quantification (UQ), computational infrastructure, solution verification). In such a complex system, where the interaction of the different subcomponents is critical, it is important to identify all uncertainties at the component level. However, while some uncertainties might be large at a component level, they might not have a crucial impact on the output of interest. Therefore, the propagation of the component uncertainties through the fullsystem must also be considered. 

Typically, 3 major types of uncertainties or errors are present:
 Irreducible uncertainties (also called aleatoric): uncertainties linked to environmental conditions, geometry, material, ...
 Model uncertainties (also called epistemic): uncertainties that can typically be reduced by using more accurate models (e.g., DNS vs. RANS turbulence model)
 Numerical errors: errors from discretization

The Center's approach is to consider all types of uncertainties in the QMU process. Mesh refinement, increase of number of samples or improvement of models are decided according to a rigorous quantification process to ensure that all uncertainties are of the same magnitude. There is no need to refine excessively a computational mesh to reduce numerical errors if the uncertainties linked to the model used are much larger than the numerical errors. 

In a full system simulation, where uncertainties from different subcomponents can interact, it is critical to develop a rigorous process to propagate those uncertainties throughout the system. The chosen approach is the use of gates between the different components. This requires the identification of output metrics and the quantification of failure probability conditioned on those metrics [pdf]. 


Uncertainty Quantification 
The characterization of uncertainties and their propagation through a forward model is a key aspect of the Center's research. In particular, the complexity of the full system requires the use of reduced order models. However, while the use of lowerfidelity models is computationally less expensive, it brings along additional epistemic uncertainties. The characterization of these epistemic uncertainties is therefore critical to perform accurate QMU analyses. Moreover, the number of uncertain parameters can become prohibitively large. Therefore, new techniques are developed to break this curse of dimensionality.
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Control of numerical errors 
In computing the quantities of interest in a full system simulation, it is important to control the numerical errors if confidence is to be placed on the predictions. The objective of this effort is to provide a framework to estimate and manage the numerical errors such that they remain within a specified tolerance. The chosen approach is based on adjoint techniques.
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Full system QMU 
The objective of this analysis is to characterize the thermal choking conditions in the HyShot II system and to quantify the margin associated with the unstart limit. The scramjet peformance (thrust) increases with the heat addition until it reaches the critical unstart limit. Therefore, it is desirable to operate the engine as close as possible to this unstart limit without crossing it. A highly simplified computational model to study scramjet performance is used within the QMU framework to study the confidence in the predictions.
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