RSMToolkit^TM (Version 1.1)

a toolkit for response surface models

What is RSMToolkit?

ADOPTECH's RSMToolkit is a Java based software tool designed for creating high quality Response Surface Models (RSMs). A Response Surface Model is a computationally efficient mathematical model that approximates a single response quantity (the dependent variable) as function of one or more independent variables. The response quantity is usually generated from experimental data or using a high fidelity computer simulation. Users of RSMToolkit version 1.0 may choose from several different types of polynomial models to generate the response surface. Future versions of RSMToolkit will provide additional types of mathematical approximations such as Kriging, Radial Basis Functions, and Neural Networks.

Why use response surfaces?

The purpose behind utilizing a response surface is to construct one or more computationally efficient lower fidelity models to act as a surrogate for a computationally intensive higher fidelity model. These lower fidelity models can be used to rapidly conduct design and optimization studies. For example, an engineer might have a numerical model that accurately determines the critical displacement of a structural component as a function of several geometry parameters. The engineer wants to connect the numerical model to an optimization code to determine the combination of geometry parameters that will result in the lowest structural weight while limiting the critical deflection to a specified value. However, because each execution of the numerical model takes a significant amount of time to run, and the optimization procedure requires a large number of executions to converge, the engineer determines that the entire optimization process will be very time consuming. To improve the efficiency of the optimization process, the engineer first uses the numerical model to construct a data set consisting of the critical deflection as a function of several different combinations of the geometry variables. This data set is then used to construct a response surface model that approximates the critical deflection as a function of the geometry variables. The response surface can then be used to in conjunction with optimizer for rapidly performing a design study.

The DataViewer provides controls for creating a response surface model. These controls allow the user to construct a response surface and view the response surface properties.

Various polynomial models are available to create a response surface using RSMToolkit. The first two choices, Stepwise Regression (quadratic) and Stepwise Regression (cubic) perform stepwise regression on a full quadratic model and a full cubic model, respectively. Stepwise regression is an automated iterative procedure that will attempt to find the "optimum subset" of polynomial terms for fitting the data.

Custom polynomial models (up to full cubic) can also be created by selecting the Custom button. This feature allows the user to select terms that will be used in creating the response surface.

The RSMViewer provides the user with information about the characteristics and quality of the response surface fit. The information includes:

• A Details report describing statistics of the response surface fit.
• Two-dimensional plot analysis comparing response values vs. response surface output.
• Two-dimensional plot analysis comparing the residual vs each design variable.
• Surface plot analysis for visualizing portions of the response surface in three-dimensional space.

The details report provides a standard Analysis of Variance (ANOVA) table and information about high leverage and outlier points.