Expected drag minimization for aerodynamic design optimization based on aircraft operational data

Aerodynamic shape optimization must consider multiple flight conditions to obtain designs that perform well in a range of situations. However, multipoint studies have relied on heuristic choices for the flight conditions and associated weights. To eliminate the heuristics, we propose a new approach where the conditions and weights are based on actual flight data. The proposed approach minimizes the expected drag value given by a probability density function in the space of the flight conditions, which can be estimated based on data from aircraft operations. To demonstrate our approach, we perform drag minimizations of the Aerodynamic Design Optimization Discussion Group Common Research Model wing, for both single-point and multipoint cases. The multipoint cases include five- and nine-point formulations, some of which approximate the expected drag value over the specified flight-condition probability distribution. We conclude that if we focus on the resulting design, a five-point optimization with points based on the flight-condition distribution and equal weights is sufficient to obtain an optimal shape with respect to the expected drag value. However, if it is important to retain the accuracy of the expected drag integration at each optimization iteration, we recommend the proposed approach.