Uncertainty Propagation in Hypersonic Flight Dynamics and Comparison of Different Methods

Abstract

In this work we present a novel computational framework for analyzing evolution of uncertainty in state trajectories of a hypersonic air vehicle due to uncertainty in initial conditions and other system parameters. The framework is built on the so called generalized Polynomial Chaos expansions. In this framework, stochastic dynamical systems are transformed into equivalent deterministic dynamical systems in higher dimensional space. In the research presented here we study evolution of uncertainty due to initial condition, ballistic coefficient, lift over drag ratio and atmospheric density. We compute the statistics using the continuous linearization (CL) approach. This approach computes the jacobian of the perturbational variables about the nominal trajectory. The covariance is then propagated using the riccati equation and the statistics is compared with the Polynomial Chaos method. The latter gives better accuracy as compared to the CL method. The simulation is carried out assuming uniform distribution on the parameters (initial condition, density, ballistic coefficient and lift over drag ratio). The method is then extended for Gaussian distribution on the parameters and the statistics, mean and variance of the states are matched with the standard Monte Carlo methods. The problem studied here is related to the Mars entry descent landing problem.