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

Peter J Thomas,Marks Legkovskis,Michael Auinger

doi:10.1115/1.4053161

Abstract

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.

Highlights

Fluctuating operating conditions are ubiquitous in applied environments and need to be considered when performing computational estimates of the relevant system characteristics [1]
Having developed a metric quantifying the polynomial chaos expansion (PCE)’s convergence performance in relation to Monte Carlo (MC), it can be used to observe the changes in the PCE’s convergence performance with increasing standard deviation of the quantity of interest (QoI) found in a sampling zone
This study has demonstrated that there exists a relationship between the convergence performance of polynomial chaos expansion (PCE) in relation to Monte Carlo (MC) sampling, as quantified by the comparative DMCÀPCE parameter, and the degree of smoothness of a quantity of interest (QoI), which is quantified by its standard deviation

Summary

Introduction

Fluctuating operating conditions are ubiquitous in applied environments and need to be considered when performing computational estimates of the relevant system characteristics [1]. This can be achieved by utilizing a technique termed uncertainty quantification (UQ). This is a methodology aiming to understand how predictions of a numerical model are affected by sources of uncertainty. We consider computational fluid dynamics (CFD) models subject to uncertain inputs in which the input–output relation is governed by the Navier–Stokes equations, which are nonlinear partial differential equations (PDEs). For a review of the available UQ methods with a particular focus on CFD applications, the reader is referred to Refs. [2] and [3]

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Results

Discussion

Conclusion