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.