Comparison of Bayesian Models for Uncertainty Quantification in Aerodynamic Databases of Reusable Launch Vehicles

Abstract

The German Aerospace Center (DLR) is currently involved in the CALLISTO project, aiming to develop a demonstrator for a reusable launch vehicle. For assessing the aerodynamic flying qualities of such a vehicle, an aerodynamic database model is crucial, with a key element being the estimation of uncertainties. Traditionally, experts have been consulted in a time-consuming and tedious process to characterize these uncertainties. In contrast, this thesis further establishes an automated, data-driven approach utilizing Bayesian inference and compares the suitability of different models to do so.

In the course of this study, Spline, Fourier Series, and Gaussian Process models were evaluated in terms of predictive accuracy and data coverage. Accuracy was measured using maximum residual error, root mean squared error, and median absolute deviation, while uncertainty estimation was assessed using a coverage probability metric. Three methods were employed: in-sample validation, stratified k-fold cross-validation, and hold-out validation.

Gaussian Processes proved most accurate in in-sample prediction while providing a high data coverage. Some generalized linear models, which include Spline and Fourier models, tended to overfit, but others showed even slightly better accuracy than Gaussian process models when generalizing on new data. However, this advantage was offset by reduced data coverage, which presumably stems from an increased bias. Increasing the data coverage of the most accurate generalized linear model artificially with white noise made it challenging to identify a clear winner.

This thesis contributes significantly to the establishment of Bayesian methods in aerodynamic database model generation. It implements a framework that eases the integration of additional models and offers a streamlined method for predictions on new data through Bayesian inference. In this way, the limitations of the conventional approach are overcome. Through the out-of-sample evaluation of predictive accuracy, especially generalized linear models have been found to hold potential for future modeling. Simply adding white noise for uncertainty quantification led to inaccuracies, suggesting the need for more precise methods in the future. Having effectively compared models for the relationship between the Angle of Attack and the aerodynamic force coefficient Cz , this methodology can be adapted for other variables, thus broadening its applicability in aerospace research.