Configuring Response Surface Model Technique Options

Double-click the Approximation component icon .
The Approximation Component Editor appears.
From the Approximation Component Editor, click the Technique Options tab.

Set the Polynomial Order option.

This option controls the order of the polynomials used by the Response Surface Model. If you selected an array, the number of input parameters shown next to the list includes all the members of the array. The following options are available:

Option	Description
Linear	This option makes all outputs linear functions with respect to inputs. This option is recommended if you want to study first-order (linear) effects of the inputs on the outputs.
Quadratic	If this option is selected, the polynomials for all outputs will contain linear terms, as well as all quadratic terms and all two-way interactions of the inputs. This option is the recommended choice unless you know that the outputs are either linear or highly nonlinear with respect to the inputs. Quadratic polynomials also behave well in optimization.
Cubic	If this option is selected, the polynomials for all outputs will contain, in addition to all linear and quadratic terms, all pure cubic terms. No three-way interactions are included. Cubic polynomials require more design points in the data file. They are recommended only for highly nonlinear output functions, when it is known that quadratic polynomials do not provide an accurate approximation of the outputs.
Quartic	If this option is selected, the polynomials for all outputs will contain, in addition to all linear and quadratic terms, pure cubic terms and pure 4^th order terms. No three-way or four-way interactions are included. The same recommendations that apply to cubic polynomials also apply to quartic ones. It is rarely necessary to use quartic polynomials. Cubic and quartic polynomials may inhibit the optimization process by creating numerous false local minima.

If desired, click Use term selection to select the most significant terms from the polynomial.

You can use term selection to remove some polynomial terms with low significance, which can improve reliability for your approximation and reduce the number of required design points.
1. Select one of the following options from the Term selection method list:
  - Sequential Replacement. This method of polynomial term selection starts with the constant and then 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 tries 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 Yi are exact output values, ${\bar{Y}}_{i}$ are approximate output values, and n is the number of design points used for RSM.
  - Stepwise (Efroymson). This method of polynomial term selection starts with the constant and then 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:
    $\frac{R S S_{p - 1} - R S S_{p}}{R S S_{p} / (n - p - 1)} < F_{d e l e t e}$
    
    Here, p is the number of polynomial terms, n is the number of designs used for RSM, F_enter is the F-ratio to add a term, and Fdelete is the F-ratio to drop a term.
    If you selected Stepwise (Efroymson), enter the following:
    - F-ratio to drop term. The maximum value of the F-ratio to drop a polynomial term from the RSM.
    - F-ratio to add term. 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 all possible replacements for 1 or 2 of the selected terms that can further reduce the fitting errors. The best replacement combination is found and 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 approximation 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.
2. Perform one of the following actions, based on your term selection method:
  - Click Specify number of selected terms, and type the number you want selected in the corresponding text box.
  - (Stepwise (Efroymson) only) Click Specify maximum number of selected terms, and type the maximum number that you want selected in the corresponding text box.
Click OK to save your changes and to close the Approximation Component Editor.