Design space dimensionality reduction through physics-based geometry re-parameterization

The effective control of the extent of the design space is the sine qua non of successful geometry-based optimization. Generous bounds run the risk of including physically and/or geometrically nonsensical regions, where much search time may be wasted, while excessively strict bounds will often exclude potentially promising regions. A related ogre is the pernicious increase in the number of design variables, driven by a desire for geometry flexibility—this can, once again, make design search a prohibitively time-consuming exercise. Here we discuss an instance-based alternative, where the design space is defined in terms of a set of representative bases (design instances), which are then transformed, via a concise, parametric mapping into a new, generic geometry. We demonstrate this approach via the specific example of the design of supercritical wing sections. We construct the mapping on the generic template of the Kulfan class-shape function transformation and we show how patterns in the coefficients of this transformation can be exploited to capture, within the parametric mapping, some of the physics of the design problem.