文档介绍：CHAPTER 3 Response surface
methodology
Introduction
Response surface methodology (RSM) is a collection of mathematical and statistical
techniques for empirical model building. By careful design of experiments, the
objective is to optimize a response (output variable) which is influenced by several
independent variables (input variables). An experiment is a series of tests, called
runs, in which changes are made in the input variables in order to identify the
reasons for changes in the output response.
Originally, RSM was developed to model experimental responses (Box and
Draper, 1987), and then migrated into the modelling of numerical experiments. The
difference is in the type of error generated by the response. In physical experiments,
uracy can be due, for example, to measurement errors while, puter
experiments, numerical noise is a result of plete convergence of iterative
processes, round-off errors or the discrete representation of continuous physical
phenomena (Giunta et al., 1996; van Campen et al., 1990, Toropov et al., 1996). In
RSM, the errors are assumed to be random.
Response surface methodology 16
The application of RSM to design optimization is aimed at reducing the cost of
expensive analysis methods (. finite element method or CFD analysis) and their
associated numerical noise. The problem can be approximated as described in
Chapter 2 with smooth functions that improve the convergence of the optimization
process because they reduce the effects of noise and they allow for the use of
derivative-based algorithms. Venter et al. (1996) have discussed the advantages of
using RSM for design optimization applications.
For example, in the case of the optimization of the calcination of Roman
cement described in Section , the engineer wants to find the levels of temperature
(x1) and time (x2) that maximize the early age strength (y) of the cement. The early
age strength is a function of the levels of temperature and time,