A practical guide to estimation and uncertainty quantification of aerodynamic flows

TL;DR

This paper reviews recent methods for estimating and quantifying uncertainty in aerodynamic flow measurements, emphasizing Bayesian inference, sequential estimation, neural network approximations, and low-dimensional flow encoding.

Contribution

It provides a comprehensive overview of uncertainty quantification techniques in flow estimation, including practical examples and case studies, highlighting recent advances in neural network applications.

Findings

Bayesian inference effectively models flow uncertainty.

Sequential estimation improves unsteady flow tracking.

Neural network encodings enable low-dimensional flow representations.

Abstract

Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or the non-uniqueness of the underlying mapping. Knowledge of this uncertainty can be as important for decision-making as that of the state itself. Uncertainty tracking is challenged by the often-nonlinear relationship between the measurements and the flow state. For example, a collection of passing vortices leaves a footprint in wall pressure that depends nonlinearly on the vortices' strengths and positions. In this paper, we outline recent approaches to flow estimation and illuminate them with worked examples and selected case studies. We review relevant probability tools, including sampling and estimation, in the powerful setting of Bayesian inference and demonstrate these in static flow estimation examples. We then review unsteady examples and illustrate the application of sequential estimation, and particularly, the ensemble Kalman filter. Finally, we discuss uncertainty quantification in neural network approximations of the mappings between sensor measurements and flow states. Recent aerodynamic applications have shown that the flow state can be encoded into a very low-dimensional latent space. We discuss the uncertainty implications of this encoding.