ON THE USE OF STATISTICS IN DESIGN AND THE IMPLICATIONS FOR DETERMINISTIC COMPUTER EXPERIMENTS

摘要

Perhaps the most prevalent use of statistics in engineeringdesign is through Taguchi's parameter and robust design -using orthogonal arrays to compute signal-to-noise ratios in aprocess of design improvement. In our view, however, there isan equally exciting use of statistics in design that could becomejust as prevalent: it is the concept of metamodeling wherebystatistical models are built to approximate detailed computeranalysis codes. Although computers continue to get faster,analysis codes always seem to keep pace so that their computationaltime remains non-trivial. Through metamodeling,approximations of these codes are built that are orders of magnitudecheaper to run. These metamodels can then be linked tooptimization routines for fast analysis, or they can serve as abridge for integrating analysis codes across different domains.In this paper we first review metamodeling techniques thatencompass design of experiments, response surface methodology,Taguchi methods, neural networks, inductive learning,and kriging. We discuss their existing applications in engineeringdesign and then address the dangers of applying traditionalstatistical techniques to approximate deterministic computeranalysis codes. We conclude with recommendations for theappropriate use of metamodeling techniques in given situationsand how common pitfalls can be avoided.