The Role of Hierarchy in Response Surface Modeling of Wind Tunnel Data

This paper is intended as a tutorial introduction to certain aspects of response surface modeling, for the experimentalist who has started to explore these methods as a means of improving productivity and quality in wind tunnel testing and other aerospace applications. A brief review of the productivity advantages of response surface modeling in aerospace research is followed by a description of the advantages of a common coding scheme that scales and centers independent variables. The benefits of model term reduction are reviewed. A constraint on model term reduction with coded factors is described in some detail, which requires such models to be well-formulated, or hierarchical. Examples illustrate the consequences of ignoring this constraint. The implication for automated regression model reduction procedures is discussed, and some opinions formed from the author s experience are offered on coding, model reduction, and hierarchy.