1. Chapter 3
Response Charts

2. Chapter 3 - Contents Response Charts Defined Response Charts Set up
Design of Experiments - charts overview
Parameter Correlation - charts overview
Response Surface - charts overview
Goal Driven Optimization - charts overview
Response Chart control - charts overview
Response Charts Quality - charts overview

3. Response Charts Defined
Response charts offer several methods to view the results of your optimization information.
Broadly speaking there are 2 types of response charts:
3D response surfaces.
2D response curves.
Keep in mind the following points:
The automatic samples discussed earlier represent actual calculated results points.
The response charts allow one to explore the regions of the design where NO actual solution is calculated.
Based on the response charts, candidate designs are selected.
Candidate designs should be re-solved to verify the actual solutions are valid.

4. Response Chart Setup
The charts are controlled from the Response Surface Outline.
Input Parameters
Response and Derived Parameters
Chart Type

5. 1 input versus 1 response = 2d Response Curve
Response Chart Setup . . .
Properties of Response determines what is displayed in the response charts.
1 input versus 1 response = 2d Response Curve

6. 2 inputs versus 1 response = 3d Response Surface
Response Chart Setup . . .
2 inputs versus 1 response = 3d Response Surface

7. Design of Experiments – charts overview
Parallel chart - graphical display of the DOE matrix using parallel Y axes to represent all of the inputs and outputs.
Chart is interactive –you can get design point number by clicking on the chart.
In Properties of Parameters Parallel check parameters that you would like to plot.

8. Design of Experiments – charts overview
Design Points vs Parameter Chart - a graphical display for plotting design points vs. any input or output parameter.
Chart is interactive –you can get the parameter value for every point by clicking on the chart.
In Properties of Design Points vs. Parameter specify parameters that you would like to plot.

9. Parameters Correlation – charts overview
Correlation scatter chart - to graphically view the sample values of one parameter vs. another. A trend line is drawn showing the correlation of the sample values.
In Properties of Correlation Scatter define parameters on X and Y axis.

10. Parameters Correlation – charts overview
Correlation Matrix – to visualize how closely the various input and output parameters are coupled. The strength of correlation is indicated by color in the matrix.
In Properties of Correlation Matrix check parameters that you would like to plot.

11. Parameters Correlation – charts overview
Sensitivities chart - to graphically view the global sensitivities of each output parameter with respect to the input parameters. The global, statistical sensitivities are based on a correlation analysis using the generated sample points, which are located throughout the entire space of input parameters.
In Properties of Sensitivities you can specify parameters and also chose bar of pie chart.

12. Response Surface – charts overview
Response chart - allow you to graphically view the impact that parameters have on one another.
Information can be displayed in 2d or 3d formats.
Displays are fully interactive.
You can change the parameter values to explore other designs by moving the slider bars, or entering specific values in the accessible value boxes.

13. Response Surface – charts overview
Single parameter sensitivities allow users to assess the relative impact each input parameter has on a single response parameter.
Single Parameter Sensitivities – DesignXplorer calculates the change of the output based on the change of each input independently at the current value of each input parameter. Single parameter sensitivities are local sensitivities.

14. Response Surface – charts overview
Spider charts provide a visual indication of the impact on all responses when inputs are varied.

15. Goal Driven Optimization – chart overview
Trade off chart - to view the Pareto fronts created from the samples generated in the GDO.
Since DesignXplorer allows multi-objective optimization, it is often the case that desired goals conflict with one another.
For example, two reasonable goals in structural analysis might be to reduce the overall mass and increase the stiffness. In such a case, one goal may be realized at the expense of the other.
The trade off plot allows DX users to visualize this give and take among response parameters with stated goals
Note, desired values must be specified before trade off studies are available within a GDO.

16. Goal Driven Optimization – chart overview
In this example the goals were to minimize both mass and deformation. The trade off plot shows the line along which no improvement in one parameter’s goal can be achieved without sacrificing the other (Pareto optimal).
The slider in Properties of the Tradeoff allows control over the number of Pareto points to be displayed. As the number of points is increased, Pareto points of lesser optimality are added (see next slide).
For more detail on the algorithms and techniques used see the “Theory” section of the DesignXplorer documentation for “Goal Driven Optimization”.

17. Goal Driven Optimization – chart overview
Notice that additional Pareto points of less optimality are displayed in different colors from blue to red.
Pareto or non-dominated set, are a group of solutions such that selecting any one of them in place of another will always sacrifice quality for at least one objective, while improving at least one other.

18. Goal Driven Optimization – chart overview
Samples chart - to visually explore a sample set given defined objectives.
The aim of this chart is to provide a multidimensional graphical representation of the parameter space you are studying. The chart uses the parallel Y axes to represent all of the inputs and outputs. Each sample is displayed as a group of line curves where each point is the value of one input or output parameter. The color of the curve identifies the Pareto front that the sample belongs to, or the chart can be set so that the curves display the best candidates and all other samples.

19. Goal Driven Optimization – chart overview
The Samples chart is a powerful exploration tool because of its interactivity. It allows you to first pick a Y axis with the mouse then slide the yellow arrows that appear on the bottom and the top of each axis up or down in order to increase or decrease the axis bounds. Samples are dynamically hidden if they fall outside of the bounds. Repeating the same operation with each axis allows you to manually explore and find trade-offs.

20. Goal Driven Optimization – chart overview
Sensitivities chart (GDO) - to graphically view the global sensitivities of each output parameter with respect to the input parameters.
The sensitivities available under the Goal Driven Optimization and Six Sigma Analysis are statistical sensitivities. Statistical sensitivities are global sensitivities, whereas the single parameter sensitivities available under the Responses view are local sensitivities. The global, statistical sensitivities are based on a correlation analysis using the generated sample points, which are located throughout the entire space of input parameters.

21. Response Chart Controls . . .
By RMB on response surface you can toggle from 2D/3D Chart. Also you can insert response point and design point. Also you can save Image as and edit properties.

22. Response Chart Controls . . .
You can change the parameter values to explore other designs by moving the slider bars, or entering specific values in the accessible value boxes.

23. Response Chart Controls . . .
The triad control at the bottom left in the 3D Response chart window allows you to rotate the chart in freehand mode or quickly view the chart from a particular plane. To zoom any part of the chart, use the normal zooming controls (Shift-middle mouse button, or scroll wheel).

24. Response Chart Controls . . .
You can have as many charts as you like under a response point. You can change the name of a chart cell by clicking on it twice and entering the new name.

25. Response Chart Quality
In the Outline of Response Surface you can select output parameter and Properties of Output reports qualitative information about the “Goodness-of-Fit” of the results.
Look at different measures of goodness of fit since all subsequent optimization/probabilistic analyses are based on the response surface!

26. Response Chart Quality . . .
Coefficient of Determination (R2 measure):
Measures how well the response surface represents output parameter variability.
Should be as close to 1.0 as possible.
Adjusted Coefficient of Determination:
Takes the sample size into consideration when computing the Coefficient of Determination.
Usually this is more reliable than the usual coefficient of determination when the number of samples is small ( < 30).
Maximum Relative Residual:
Similar measure for response surface using alternate mathematical representation.
Should be as close to 0.0 as possible.

27. Response Chart Quality . . .
Root mean square error:
Square root of the average square of the residuals at the DOE points for regression methods.
Relative Root Mean Square Error:
Square root of the average square of the residuals scaled by the actual output values at the DOE points for regression methods.
Relative Maximum Absolute Error:
Absolute maximum residual value relative to the standard deviation of the actual outputs.
Relative Average Absolute Error:
Absolute maximum residual value relative to the standard deviation of the actual output data, modified by the number of samples.
Useful when the number of samples is low ( < 30).

28. Response Chart Quality . . .
Refinement Option – if goodness-of-fit measures are low.
Kriging option to provide a comprehensive goodness of fit report of a standard response surface.