Adaptive Bayesian learning for stability characterization of re-entry vehicles

Accurate characterization of aerodynamic stability coefficients is essential for predicting the dynamic behavior of atmospheric re-entry vehicles. Estimating these coefficients from free-flight data is challenging due to nonlinear flow–structure coupling, limited data, and high computational costs. Existing nonlinear parameter estimation methods often provide only discrete results without full uncertainty quantification, emphasizing the need for a continuous and uncertainty-aware framework. This study introduces an adaptive Bayesian surrogate approach that combines differential evolution (DE), Markov chain Monte Carlo (MCMC), and Gaussian process regression with an upper confidence bound adaptive-sampling strategy to infer both static and dynamic stability coefficients from computational fluid dynamics data. The approach first uses DE–MCMC to estimate baseline aerodynamic coefficients at discrete control-points and then iteratively refines smooth, uncertainty-bounded functional curves through adaptive learning. Demonstrations on one-degree-of-freedom free-flight simulations of the Genesis re-entry capsule at Mach 1.10–1.50 show that the refined surrogates capture physically consistent trends across the angle of attack range, reduce epistemic uncertainty by more than 50 percent, and achieve mean reconstruction errors below 0.7$$^\circ$$ for training and within 1.5$$^\circ$$ for validation cases. The framework provides an efficient, data-driven route for constructing continuous aerodynamic-stability response surfaces with quantified confidence, supporting predictive modeling and digital-twin development for re-entry systems.