Epistemic Uncertainty Analysis in GPR-Based Modeling of Pitch Damping Sum for 1 DOF Reentry Vehicle Dynamics

This paper presents a Gaussian process regression (GPR)-based surrogate modeling approach for predicting the pitch-damping sum, a critical parameter for understanding the dynamic stability of reentry vehicles in 1-DoF motion scenarios. Markov chain Monte Carlo (MCMC) sampling is first used to evaluate discrete points of the pitch-damping sum at various values of the angle of attack, providing a robust dataset for model construction. Using these discrete data, GPR predicts the continuous functional relationship of the pitch-damping sum across the entire range of angle of attack, while incorporating the uncertainty derived from the MCMC samples. To refine the model further, the upper confidence bound (UCB) criterion is applied, identifying and prioritizing regions of high epistemic uncertainty for improvement. The UCB criterion identifies high-uncertainty regions at α = 15°, 25°, and 2° for additional MCMC sampling, iteratively reducing epistemic uncertainty until the surrogate achieves convergence across 0° ≤ α ≤ 30°. Validation against held-out trajectories at α₀ = 2° and 20° yields RMSEs of 0.84° and 1.13°, respectively, with propagated ±2σ envelopes reliably capturing dynamic response variability. This integrated approach delivers an accurate and reliable uncertainty-aware surrogate model, enabling better predictions of aerodynamic coefficients and dynamic stability, thereby advancing the modeling capabilities for reentry vehicle dynamics.