About the Term Selection Methods

Sequential Replacement

This method of polynomial term selection starts with the constant and adds polynomial terms one at a time so that the fitting errors of the Response Surface Model are minimized at every step. After adding a new polynomial term, Isight will try to find a replacement for each of the selected terms that can reduce the fitting errors further. The fitting errors are checked using the Residual Sum of Squares (sum of squared errors at all design points):

R S S = \sum_{i = 1}^{n} {(Y_{i} - {\bar{Y}}_{i})}^{2}

Here $Y_{i}$ are exact output values, ${\bar{Y}}_{i}$ are approximate output values, and $n$ is the number of design points used for the Response Surface Model.

Stepwise (Efroymson)

This method of polynomial term selection starts with the constant and adds polynomial terms one at a time so that the fitting errors of the RSM are minimized at every step. A new term is added if the following condition is satisfied:

\frac{R S S_{p} - R S S_{p + 1}}{R S S_{p + 1} / (n - p - 2)} > F_{e n t e r}

After adding a new term, Isight examines all selected terms and deletes one or more terms for which the following condition is satisfied:

\frac{R S S_{p - 1} - R S S_{p}}{R S S_{p} / (n - p - 1)} < F_{d e l e t e}

In these formulae, $p$ is the number of polynomial terms, $n$ is the number of designs used for the Response Surface Model, $F_{e n t e r}$ is the F-ratio to add a term, and $F_{d e l e t e}$ is the F-ratio to drop a term. You can specify the maximum value of the F-ratio to drop a polynomial term from the RSM or the minimum value of the F-ratio to add a new polynomial term to the RSM.

Two-At-A-Time Replacement

This method of polynomial term selection starts with the constant and adds polynomial terms one at a time so that the fitting errors of the RSM are minimized at every step. After adding a new polynomial term, Isight considers possible replacements for 1 or 2 of the selected terms that can reduce the fitting errors further. The best replacement combination is found, the terms are replaced, and the next best term is selected and added. The process is repeated at every step until the maximum number of terms is selected. This method has a better chance of finding the best model than the two previous methods, but it is more expensive computationally.

Exhaustive Search

This method generates all possible combinations of polynomial terms and finds the best combination that produces the minimum fitting errors. This method is the most expensive computationally and can take a long time for a large number of design points and large numbers of inputs and outputs. This method is recommended for approximations that have only a few inputs and coefficients.