Uncertainty Quantification of Time-Dependent Quantities in a System With Adjustable Level of Smoothness

Abstract

We summarize the results of a computational study involved with uncertainty quantification (UQ) in a benchmark turbulent burner flame simulation. UQ analysis of this simulation enables one to analyze the convergence performance of one of the most widely used uncertainty propagation techniques, polynomial chaos expansion (PCE) at varying levels of system smoothness. This is possible because in the burner flame simulations, the smoothness of the time-dependent temperature, which is the study's quantity of interest (QoI), is found to evolve with the flame development state. This analysis is deemed important as it is known that PCE cannot construct an accurate data-fitted surrogate model for nonsmooth QoIs, and thus, estimate statistically convergent QoIs of a model subject to uncertainties. While this restriction is known and gets accounted for, there is no understanding whether there is a quantifiable scaling relationship between the PCE's convergence metrics and the level of QoI's smoothness. It is found that the level of QoI's smoothness can be quantified by its standard deviation allowing to observe its effect on the PCE's convergence performance. It is found that for our flow scenario, there exists a power–law relationship between a comparative parameter, defined to measure the PCE's convergence performance relative to Monte Carlo sampling, and the QoI's standard deviation, which allows us to make a more weighted decision on the choice of the uncertainty propagation technique.