Machine-Learning-Based Estimation of an Airliner Upset Behavior’s Region of Attraction

Loss of control in flight remains the leading cause of fatal accidents in both commercial and general aviation. Aircraft upset behaviors can be associated with the equilibria of a mathematical system of ordinary differential equations that models the flight dynamics. Consequently, the size of the region of attraction of an equilibrium of this dynamic system reflects the aircraft’s susceptibility to entering the corresponding upset condition. The sum-of-squares (SOS) method has previously been used to estimate the region of attraction of equilibrium points related to aircraft behavior. However, SOS requires a polynomial representation of the dynamics and additional assumptions to reduce the model order. This paper investigates the use of recent machine-learning techniques to estimate regions of attraction in the context of aircraft poststall behavior analysis. After a brief review of existing estimation methods, the selected machine-learning approaches are benchmarked on the classical low-dimensional Van der Pol system in reversed time. Then, the methods are applied to estimate the region of attraction of a steep spiral predicted by the open-source generic transport model. The study serves as a proof-of-concept that machine-learning methods can effectively estimate regions of attraction in flight-dynamics analyses.