Abstract
Current research initiatives, such as the Single European Sky Air Traffic Management Research Program, call for an air traffic system with improved safety and efficiency records and environmental compatibility. The resulting multi-criteria system optimization and individual flight trajectories require, in particular, reliable three-dimensional meteorological information. The Global (Weather) Forecast System only provides data at a resolution of around 100 km. We postulate a reliable interpolation at high resolution to compute these trajectories accurately and in due time to comply with operational requirements. We investigate different interpolation methods for aerodynamic crucial weather variables such as temperature, wind speed, and wind direction. These methods, including Ordinary Kriging, the radial basis function method, neural networks, and decision trees, are compared concerning cross-validation interpolation errors. We show that using the interpolated data in a flight performance model emphasizes the effect of weather data accuracy on trajectory optimization. Considering a trajectory from Prague to Tunis, a Monte Carlo simulation is applied to examine the effect of errors on input (GFS data) and output (i.e., Ordinary Kriging) on the optimized trajectory.
Highlights
With the implementation of Free Route Airspaces in Europe, wherein aircraft are requested to fly along four-dimensionally optimized trajectories, aircraft trajectory optimization gains more and more importance
We introduce interpolation methods: linear interpolation, Kriging (Ordinary Kriging and Universal Kriging), Radial Basis Function (RBF) methods, feedforward neural networks, and decision trees with bagging and gradient boosting machines to interpolate spatial dimensions
Given weather scenarios with GFS data and simulated errors, we can examine how the errors from GFS data and Kriging interpolation can impact the trajectories in SOPHIA
Summary
With the implementation of Free Route Airspaces in Europe, wherein aircraft are requested to fly along four-dimensionally (longitude, latitude, altitude, and time) optimized trajectories, aircraft trajectory optimization gains more and more importance. One of the simplest aircraft motion models still induces six nonlinear first-order differential equations of motion. It follows that acceleration forces should be considered for each discrete time step. The atmospheric state ( wind speed, wind direction, and temperature) has a significant impact on the integration of the equations of motion. The aircraft performance model SOPHIA (Sophisticated Aircraft Performance Model) integrates the equations of motion every second and computes the actual speeds and covered distances. Coefficients that cannot be estimated without aircraft-specific aerodynamic properties (i.e., the drag polar and the maximum available thrust as a function of altitude and speed) are obtained from the open-source flight performance model OpenAP [2].
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