Optimizing Markov Chain Initial Conditions for Studying Blunt Body Reentry Dynamics Using Differential Evolution

The dynamics of blunt-body reentry vehicles are crucial, as they must withstand the intense aerodynamic forces and extreme heat generated during atmospheric reentry. Despite thermal protection benefits, the blunt body shape can cause dynamic instabilities, especially at transonic and low-supersonic speeds, which are crucial during parachute deployment and scientific measurements. Ensuring robust stability requires precise optimization of system parameters and initial conditions. Markov chain Monte Carlo (MCMC) framework, widely used for nonlinear parameter estimation for these systems, is highly sensitive to initial conditions. However, traditional gradient-based methods are prone to getting stuck in local minima, whereas neural network-based approaches often face challenges such as overfitting, hyperparameter sensitivity, and the curse of dimensionality in navigating complex loss landscapes. This study employs Differential Evolution (DE), an evolutionary algorithm, to optimize initial conditions for MCMC parameter estimation. We present a case study on 1-DoF planar motion blunt body vehicle dynamics, demonstrating that DE improves computational efficiency and solution quality. Using DE, the pitch-damping sum coefficients (a = 1.49, b =-0.78, c =-0.37, d =-0.31, and e =-1.01) were optimized to capture nonlinear aerodynamic behavior through a cubic spline model. The reconstructed angle-of-attack (a) trajectories closely matched high-fidelity CFD data, with a sum of squared errors of 700, validating the accuracy of approach. Additionally, DE reduced computational time significantly, achieving a 30.0% reduction when using 10 CPU cores and a 43.6% reduction with 15 CPU cores compared to 5 CPU cores computation. This research advances our understanding of blunt body dynamics and underscores the value of evolutionary algorithms in complex aerospace applications.