Applying Bayesian Inference to Estimate Uncertainties in the Aerodynamic Database of CALLISTO

Abstract

The three national space centers DLR, CNES & JAXA have joined their efforts in the project CALLISTO to develop and mature key technologies for future operational Reusable Launch Vehicles (RLVs). The goal of this project is to develop, manufacture and test a reusable Vertical-Takeoff Vertical-Landing (VTVL) first stage demonstrator, which will be operated at the European Spaceport in French Guiana from late 2024. One important aspect in the development of RLVs, but also of aerospace vehicles in general, is the generation of an Aerodynamic Database (AEDB) which characterizes the aerodynamic flying qualities of the vehicle. These databases are commonly aggregated from Computational Fluid Dynamics (CFD) simulations and Wind Tunnel Tests (WTTs) via simple heuristic models. Whereas this classical approach is suitable for the estimation of nominal aerodynamic coefficients, the quantification of uncertainties in this pre-flight data with respect to the final flight behavior is still a difficult task that involves a lot of human expert knowledge and “gut feeling”. Particularly for launch vehicles, these uncertainties are however essential to ensure robust guidance and control algorithms, as well as sufficient vehicle performance for a selected mission profile. For CALLISTO, in parallel to a classical approach, a new methodology has now been tested to estimate these uncertainties within the AEDB: To apply Bayesian Inference to predict a probability distribution over the aerodynamic coefficients, conditional on the available test and simulation results and on prior knowledge. This methodology has already been well-established in other data science domains, but for aerospace engineering only very few use-cases are known so far. With this new approach an objectively traceable modelling of the aerodynamic uncertainties should be possible. This paper presents the current development state of the Bayesian aerodynamic uncertainties model of CALLISTO. After problem definition and a short introduction to the underlying dataset, the paper mainly focuses on the used modelling techniques and the applicability of Bayesian methods to the aerodynamic characterization problem. Selected results are shown for Bayesian models and compared against the classical modelling approach, while advantages and disadvantages of the Bayesian methodology are discussed. It is shown that the implemented Bayesian Gaussian process model can infer the typical characteristics of the AEDB from the available datasets, while having comparable prediction qualities as the reference model. Observed differences in the variance and bias characteristics are discussed for both models.