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 Response Surface Optimization
This module helps to find optimum values of technological or other (independent) variables, using observations of some output (dependent or response) variable obtained experimentally. Assumptions are that a) the optimum independent variables settings (e.g. temperature, pressure, drying time) correspond to minimum or maximum of the dependent variable mean, b) dependent variable values were observed for various settings of independent variables, c) minimum or maximum of the dependent variable mean exists and is not very far from experimental settings tried. The Response surface module fits a model through the experimental data – complete Taylor polynomial of second order and tries to find its extremum by looking for a stationary point (a point with zero first partial derivatives). When extremum (minimum or maximum) exists, its estimate and confidence interval are given in the protocol. When the optimized model has no extremum, stationary point corresponds to a saddle point and no optimum setting for independent variables can be found. Optimum independent variables setting can be located outside of experimental region, the estimate is less reliable in such case however.

Response Surface Optimization - Pdf manual

Example

Data:
 Temperature Pressure Power Cons. 50 110 89.15 50 130 88.75 50 150 89.25 55 110 86.14 ... ... ...

Protocol Text Output:
 Optimization of Quadratic Response Surface Task name : Optim1 Independent variable: Temperature Pressure Dependent variable: Power Input No. of variables : 2 No of data : 15 Degrees of freedom : 8 Type of the stationary point : Minimum Stationary point X0 CI Lower bound CI Upper bound Column 1 60.06733711 57.2344181 62.90025611 Column 2 128.3637814 115.4868087 141.240754 Value estimate in X0 : 84.7934742 Confidence interval : 85.09194377 84.49500464 Mean error : 0.118050794 Residual sum of squares (RSS) : 0.311794286 Residual variance : 0.02227102 Condition number kappa : 19.03088768 Correlation coefficient : 0.995943235 Determinant : 1.024524982

Graphical Output:

Reconstruction of the response "curve" for 1 parameter.

Examples of 3D-quadratic surfaces for 2-parameter (factor) optimization