Robust trajectory optimization under arbitrary uncertainty using ensemble weather forecasting and statistical aircraft performance model

Abstract

Aircraft trajectory optimization can improve delay absorption and fuel efficiency; however, existing methods suffer from problems such as insufficient adaptability to uncertainty. This paper introduces a robust trajectory optimization algorithm for optimizing flight profiles in the presence of arbitrary uncertainties in weather forecasting and aircraft performance models. Ensemble forecast data are used to provide the uncertainty in the weather forecasts, and a statistical aircraft performance model based on flight data is utilized to provide the uncertainty in the aircraft performance model. Arbitrary polynomial chaos expansion is applied to efficiently quantify arbitrary uncertainties in aircraft dynamics, and incorporated into the trajectory optimization algorithm. The $\beta$-hill climbing algorithm, a stochastic local search algorithm developed recently, is employed to determine the optimal flight profiles. By conducting numerical simulations on a popular domestic flight route in Japan during time-based metering operations, this study assesses potential fuel savings by the optimal trajectories with speed control and step descent along the planned route, as opposed to radar vectoring. Actual flight data from past flights are utilized for evaluation, and average fuel savings of approximately 2% are expected. Based on the analysis conducted in this study, the effectiveness of the robust trajectory optimization algorithm and fuel savings for time-based metering operations are evaluated and demonstrated.