Probabilistic Aircraft Conflict Detection and Resolution under the Effects of Weather Uncertainty

This PhD thesis addresses the problem of aircraft conflict detection and resolution (CD&R) considering weather uncertainty. The general framework of this study is the development of methodologies to integrate weather uncertainty into the Air Traffic Management planning process. The study considers the analysis of both a single pair of aircraft and multi-aircraft conflict scenarios, with two- and three-dimensional trajectories. The weather uncertainty data is retrieved from Probabilistic Weather Forecasts, in particular Ensemble Prediction Systems. Different methodologies to probabilistic CD&R are described, and their applicability is presented and discussed. Firstly, an approach to statistically quantify the severity of aircraft conflicts subject to wind forecast uncertainty is presented. The conflicts are characterized by two indicators: conflict intensity and conflict probability. The conflict intensity is measured by the distance of closest approach between the aircraft. The probability of conflict is obtained in terms of the probability density function of the distance of closest approach, which is obtained from the probability density functions of the wind components using the Probabilistic Transformation Method. The case of two en-route aircraft flying at constant altitude and subject to the same random wind is considered first, and results are presented to analyze the influence the wind uncertainty and the traffic configuration have on the conflict detection problem. Then, this methodology is extended to the problem of three-dimensional multi-segment trajectories and a numerical application is presented. Secondly, a probabilistic method for conflict detection and resolution considering the effects of wind forecast uncertainty is presented. The wind components are modeled as random variables, described by a joint probability density function. The probabilistic conflict detection problem is tackled again using the Probabilistic Transformation Method. The probabilistic conflict resolution consists in modifying the aircraft trajectories so that the probability of conflict between any pair of aircraft be less than a predefined safety threshold. This problem is formulated as a constrained nonlinear programming problem, where the optimality criterion is the minimization of the deviation of the aircraft resolution trajectories from their nominal trajectories and the safety condition, i.e. keeping the conflict probability below a threshold, is enforced as a problem constraint. The case of multiple en-route aircraft flying with constant airspeed and flight level is considered, where they follow approaching multi-segment trajectories and are affected by the same uncertain wind. Numerical results are presented for a particular application and the cost of the resolution process is analyzed. Lastly, a methodology to tackle the problem of strategic aircraft conflict detection and resolution, up to 60 minutes in advance, considering wind and temperature uncertainties is presented. The problem of hundreds of aircraft flying multi-segment 3D trajectories is considered. The conflict detection is based on ensemble trajectory prediction, and it is performed using an efficient grid-based procedure. A metaheuristic approach based on the Simulated Annealing algorithm is developed to solve the conflicts. The proposed CR method generates resolution trajectories by modifying the location of the route waypoints (vectoring), with the objective of lowering the probabilities of the conflicts while also minimising the deviation from the nominal paths. The methodology is then applied to a realistic case study that considers the actual flight plans for hundreds of aircraft in the European airspace; numerical results are presented and analyzed. The work presented in this thesis constitutes a step toward the development of future decision support tools for air traffic controllers that integrate weather uncertainties, expanding the capabilities of conflict detection tools currently in use in Europe and contributing to reduce the negative impact of weather on the safety and efficiency of the air traffic.