Optimal departure aircraft trajectories minimising population annoyance

This paper presents a strategy for designing noise abatement procedures aimed at reducing the global annoyance perceived for the population living around the airports. By using fuzzy logic techniques it is shown how annoyance can be modelled in function of the maximum perceived noise level at a specific noise sensitive location and the time of the day when the departure takes place. Thus, the annoyance is computed for different kinds of sensibility areas, such as residential zones, industrial zones, schools or hospitals and an annoyance figure is obtained for each possible trajectory. Then, a non-linear multiobjective optimal control problem is presented in order to obtain the minimum annoyance trajectory for all sensitive locations. Lexicographic optimisation is used to cope with the difficulties that arise when several criteria appear in the optimisation process. Finally, a practical example is given for an hypothetical scenario where different optimal trajectories are obtained at different day periods.