Subset Simulation for Estimating Small Failure Probabilities of an Aerial System Subject to Atmospheric Turbulences

Estimation of small failure probabilities is an important task for model based safety analysis. Classical Monte Carlo simulations are no viable option due to the high number of samples required to achieve an adequately high level of confidence. To overcome this performance limitation, this paper focuses on a method called subset simulation where the probability of an unlikely event is computed using a sequence of events with larger conditional probabilities. Markov Chain Monte Carlo simulations with a modified Metropolis-Hastings algorithm are used for the non-trivial task of generating valid subset samples. In this paper, the subset simulation algorithm is applied to evaluate the dynamic response of a controlled system. Automatic close formation flight of two aircraft subject to atmospheric turbulences is analyzed. The underlying simulation environment comprises high-fidelity simulation models of two large transport category aircraft, a modified Dryden turbulence model that also features spatial correlation of the turbulence excitation, and a model for the wake interaction between the aircraft. Analysis is not only carried out to estimate the probability of an unlikely event but also representative samples are examined to highlight the advantage of the subset simulation algorithm of getting additional information about scenarios that may lead to the improbable event. The presented results show a high increase in computational efficiency compared to classical Monte Carlo simulation as well as the potential to gain more detailed information on failure scenarios. This emphasizes the high potential that subset simulation offers for the dynamic analysis of controlled systems subject to a very high number ( 104) of uncertain parameters.