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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2008-12-194 |
| Date | 16 January 2010 |
| Creators | Prabhakar, Avinash |
| Contributors | Bhattacharya, Raktim |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis |
| Format | application/pdf |
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