Safe Flight Envelope Uncertainty Quantification using Probabilistic Reachability Analysis

Loss of Control is the primary contributor to aviation fatalities. To prevent this type of accident, flight envelope protection is considered to be a necessary development. The calculation of the Safe Flight Envelope provides a bound on the states that can safely be approached by the aircraft. Although theoretically accurate, some states may not be reachable under the influence of disturbances (e.g. turbulence). In this paper a stochastic extension to the reachability analysis is applied to a simplified aircraft model. The probabilistic reachability analysis yields the transition probability from a state to the target set. By comparing the deterministic and probabilistic Safe Flight Envelope, it becomes clear that the Safe Flight Envelope can shrink considerably under the influence of turbulence. It is shown that for a 3σ (99.7 %) confidence interval, the envelope can shrink by as much as 50.8% compared to the deterministic envelope. Furthermore, it is found that for high roll angles, some parts of the deterministic envelope have a 0 % transition probability under the influence of turbulence, further emphasizing the importance of probabilistic envelopes.