Convex approximation of the design space in the aircraft wing optimization problem

Abstract

A convex approximation of the design space of the submodel of the aircraft wing, which describes the set the wing airfoils in chosen cross-sections, is constructed. In the available model, constraints specifying a nonconvex space are imposed on the cross-section parameters. In the course of the wing modeling procedure, dimensionality reduction methods, which enable wing description with some error by a lesser number of parameters, are used. In this paper, we propose an approach allowing one to replace with the same error constraints specifying a nonconvex set by a system of inequalities describing a convex polyhedron. In the obtained model, the system of constraints for each cross-section can be replaced by one constraint in the form of an extremal ellipsoid constructed based on a set of available reference airfoils.