Response Surface Modeling

RSM

Response Surface Modeling

RSM stands for Response Surface Model(ing). It is a simple mathematical model of an Simcenter Amesim system or subsystem. This model gives the relationship which can be used to compute an approximation of responses from factors.

When you select Optimization as the study type, you see the RSM Tools field in the Study settings pane:

Figure 70: RSM tools

Working with Response Surface Modeling

The RSM Tools are applicable for both NLPQL and Genetic algorithms.

Optimization can take a long time. You can use the Response Surface Model to perform calculations if you only need a rough idea of the results. This is much faster. An optimization run using RSM is often finished in a few seconds.

Note

Depending on the contents of the RSM file, certain responses or factors cannot be used.

In Simcenter Amesim, an automated process finds the polynomial RSM for you. This facility is available for DOE and Monte Carlo studies and is accessible by right clicking a study and selecting Response Surface, or by clicking the Response Surface button:

When you select this option, the following dialog box appears:

Figure 71: Response Surfaces dialog box

You can select the Response Surface Order which is the order of the polynomial model. Depending on the order chosen for the RSM, the results are displayed in two ways:

• Order > 2:

the coefficients of the polynomial (Q) are given.

V=[1,v1,v2,…,vp,v1²,v1*v2,…]

• Order <= 2:

V=[1,v1,v2,…,vp]

You can select the response you are interested in. The coefficients displayed are the ones used to compute the selected response.

For an order greater than two, you must enter the order you require:

Figure 72: Compute Response Surface dialog box

Note

There is no limitation to the order. But the number of samples must be great enough to allow the computation. If it is not the case, you will be told that the order you selected is too high for the available number of runs:

You can save the RSM into a file. When the button is pressed you are asked for a file name. This file contains the RSM coefficients for all responses for the order currently selected.

This file can be used to define an RSM for an optimization process.

Plotting RSMs

Simcenter Amesim also makes it possible to display RSMs. This feature is available with DOE Central Composite and Monte Carlo studies.

To access it, right click on a study, select Add plot, and select Response Surface as the Plot type:

Figure 73: Response Surface Plot type

A list of all factors and responses is displayed:

Figure 74: List of factors and responses

The plot you will obtain is a 3D plot. This plot displays a quantity on the Z axis against two other quantities on the X and Y axis. Z is a response and the other quantities are variables.

Constructing the plot

The first step is to select the quantities you want to display. Double-click in the data type column on each line.

Figure 75: Select the quantities

For each line you must select one of the following:

• variable: This will be displayed on the X or Y axis.

• response: This will be displayed on the Z axis.

• parameter: This is used to compute the RSM. The value used for the current display is the one specified in the value column.

• unused: The value will not be ignored during the RSM computation, but its contribution will not appear on the plot.

Both factors and responses of the study can be set as variables, responses, or parameters of the graph.

You can also choose the Response Surface Order:

Figure 76: Set the Response Surface Order

Once everything is correctly set, click OK to display the plot:

Figure 77: RSM Plot

You can change the RSM order or the current response or variables. In this case, you will have to click the Update button.

To visualize the effect of a parameter, select the corresponding lines and move the slider available at the bottom of the windows. You can define the range of each parameter or variable by editing the corresponding cells.

You can save the RSM currently displayed into a file by clicking the Save to file button.

The Centered Response Surface check box specifies whether all runs have the same weight or not. If it is checked, the nearer the variables and parameters of the runs are to the "center" values, the more influence they get. Values described as "center" values are those of variables and parameters when the cursor is precisely in the middle.