  We consider a reduced order model of an air-breathing hypersonic engine with
a time-dependent stochastic inflow that may cause the failure of the engine.
The probability of failure is analyzed by the Freidlin-Wentzell theory, the
large deviation principle for finite dimensional stochastic differential
equations. We compute the asymptotic failure probability by numerically solving
the constrained optimization related to the large deviation problem. A
large-deviation-based importance sampling suggested by the most probable inflow
perturbation is also implemented to compute the probability of failure of the
engine. The numerical simulations show that the importance sampling method is
much more efficient than the basic Monte Carlo method.
