Aircraft trajectory optimization using parametric optimization theory
- Autores: Alfonso Valenzuela Romero
- Directores de la Tesis: Miguel Pérez-Saborid Sánchez-Pastor (dir. tes.), Damián Rivas Rivas (dir. tes.)
- Lectura: En la Universidad de Sevilla ( España ) en 2012
- Idioma: inglés
- Número de páginas: 114
- Tribunal Calificador de la Tesis: José Luis Montañés García (presid.), Rafael Vázquez Valenzuela (secret.), Juan Antonio Mesa López-Colmenar (voc.), Miguel Angel Gómez Tierno (voc.), Ernesto Staffetti Giammaria (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: Idus
- Resumen
In this thesis, a study of the optimization of aircraft trajectories using parametric optimization theory is presented. To that end, an approach based on the use of predefined trajectory patterns and parametric optimization is proposed. The trajectory patterns are in fact flight intents, formed flight segments which model procedures commonly flown by airlines, following air-traffic-control rules. The patterns allow to describe the trajectory by a small number of parameters, whose values, continuous or discrete, can be chosen to optimize a given property of the trajectory. A mixed-integer nonlinear programming (MINLP) problem is formulated to obtain the optimum values.
Firstly, the approach is used to solve the general problem of minimum direct-operating-cost cruise (unsteady, with variable mass, and without any constraint on speed or altitude) with given range. The trajectory pattern considered in this application is formed by segments at constant Mach number and constant altitude, restricted to take discrete values: Mach numbers multiple of 0.01, and altitudes defined by flight levels. The unrestricted problem in which the Mach numbers and the altitudes are continuous variables is also considered. The optimized procedures define not only the optimum values of speed and altitude for the different cruise segments, but also the optimum lengths of each segment. The main objective of this application is to analyze how the optimized procedures change when the Mach numbers and the altitudes are restricted to take discrete values. The effects of the cost index, of the initial aircraft weight and of an average horizontal wind in the optimized procedures are also analyzed.
Next, the problem of minimum-fuel cruise at constant altitude with fixed range and fixed arrival time is solved and the optimized procedures obtained using the proposed approach are compared with known optimal laws obtained using singular optimal control theory. The trajectory pattern considered in this application is similar to the previous one, formed by segments at constant Mach number restricted to take discrete values. The comparison shows that the optimized procedures approximate very well the optimal laws and give results that are very close to the optimal values.
Following, the approach is applied to a set of aircraft, taking into account the losses of separation that may arise among them. An algorithm for conflict resolution (CR) is presented, in which conflict-free trajectories are optimized. The optimality criterium is defined so that the deviation from the intended (preferred) trajectories in the lateral profile is minimized. This problem is solved in two phases: one in which a first valid solution is found by means of a random search, and another one in which this first valid solution is optimized. The resolution trajectory patterns take into account changes of the nominal waypoints (vectoring) and changes of the aircraft speeds. The algorithm is applied to the case of multiple conflicts among commercial transport aircraft in converging traffic in the terminal area. Different scenarios are considered, which include locked aircraft, that is, aircraft whose trajectories are known and fixed. The cost of the global resolution process is assessed, in terms of extra distance travelled, extra flight time and extra fuel consumed for each aircraft.
Finally, the previous CR algorithm is extended to solve the problem of optimizing conflictfree trajectories that meet scheduled times of arrival (STA). In this application, the resolution process has three steps: avoidance, which generates conflict-free trajectories that meet the given sequence of arrival (which is a hard constraint of the problem); recovery, in which the resolution trajectories are modified to meet the STA (which is a primary objective); and, optimization, to minimize a combination of costs (secondary objective). Two algorithms are presented: one in which the optimization step is applied globally (to all aircraft) after the other two steps are performed for all aircraft, and another one in which the optimization step is applied locally to each aircraft after the other two steps are performed for the given aircraft; this second algorithm is efficient when the scenario is very demanding (in which the global optimization is not effective). Results are presented for two scenarios, one with a traffic of 30 aircraft in an hour, all of the same wake-turbulence category, and another one with 35 aircraft in an hour and with aircraft of different categories.
In all cases, a kinetic trajectory predictor (nonlinear point-mass model with variable mass) is used, which is accurate, flexible and transparent, and provides the high-fidelity prediction required in all the applications.
