Probability of Failure in Hypersonic Engines Using Large Deviations

TL;DR

This paper models the failure probability of hypersonic engines with stochastic inflow using large deviations theory, providing efficient numerical methods to estimate rare failure events.

Contribution

It applies large deviation principles to hypersonic engine failure analysis and introduces an importance sampling method based on the most probable inflow perturbation.

Findings

Importance sampling greatly improves efficiency over Monte Carlo.

Failure probability can be accurately estimated using large deviations.

Numerical results validate the effectiveness of the proposed method.

Abstract

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.