# HS-2000: DOE Method Comparison: Arm Model Study

Learn how to set up DOEs using different methods and then compare methods for accuracy and efficiency.

Before you begin, copy the model files used in this tutorial from <hst.zip>/HS-2000/ to your working directory.
An arm model is used for this tutorial; the arm is clamped at one end and under an axial loading on the other end. It has been meshed and modeled in HyperMesh and analyzed using OptiStruct.
The design can change shape in nine different regions and three output responses of interest are as follows:
Shape input variables
Length1: Lower Bound = -0.5, Initial Bound = 0.0, Upper Bound = 2.0
Length2: Lower Bound = 0.0, Initial Bound = 0.0, Upper Bound = 2.0
Length3: Lower Bound = -1.0, Initial Bound = 0.0, Upper Bound = 1.0
Length4: Lower Bound = -1.0, Initial Bound = 0.0, Upper Bound = 1.0
Length5: Lower Bound = -1.0, Initial Bound = 0.0, Upper Bound = 1.0
Radius1: Lower Bound = -2.0, Initial Bound = 0.0, Upper Bound = 2.0
Radius2: Lower Bound = -0.5, Initial Bound = 0.0, Upper Bound = 1.0
Radius3: Lower Bound = -0.5, Initial Bound = 0.0, Upper Bound = 1.0
Height: Lower Bound = -1.0, Initial Bound = 0.0, Upper Bound = 1.0
Output responses
Volume (Nominal design volume 1.7667e6 mm3)
Max Von Mises Stress (Current design value = 195.29 MPa)
Nodal displacement of the node where the force is applied (mm) (1.411 mm)

You will study the results from different parameter screening DOEs. For each screening, only the results obtained on the Max_stress output response will be reviewed using Pareto plot, Interactions, and Ordination displays.

As you proceed, keep the following points in mind:
• A Full Factorial provides excellent resolution but typically requires an exceedingly large number or runs.
• A Fractional Factorial with a Resolution III confounds main effects with interactions; results could be inaccurate if interactions are significant.
• A Fractional Factorial with a Resolution IV main effects are not confounded, but interactions are confounded with each other.
• A Fractional Factorial with a Resolution V main effects and interactions are not confounded.

## Perform the Study Setup

In this step you will start from an already morphed model. The shape variables are already exported for HyperStudy and a template is created.

Shape variables are created using HyperMesh’s morphing technology HyperMorph.
1. Start HyperStudy.
2. Start a new study in the following ways:
• From the menu bar, click File > New.
• On the ribbon, click .
3. In the Add Study dialog, enter a study name, select a location for the study, and click OK.
4. Go to the Define Models step.
5. Add a Parameterized File model.
1. From the Directory, drag-and-drop the arm_model.tpl file into the work area.
2. In the Solver input file column, enter crank.fem.
This is the name of the solver input file HyperStudy creates during any evaluation.
3. In the Solver execution script column, select OptiStruct (os).
6. Click Import Variables.
HyperStudy imports nine input variables from the arm_model.tpl resource file.
7. Go to the Define Input Variables step.
8. Review the input variable's lower and upper bound ranges.

## Perform Nominal Run

1. Go to the Test Models step.
2. Click Run Definition.
An approaches/setup_1-def/ directory is created inside the study Directory. The approaches/setup_1-def/run__00001/m_1 directory contains the input file, which is the result of the nominal run.

## Create and Evaluate Output Responses

In this step you will create three output responses: Max_Disp, Max_Stress, and Volume.

1. Go to the Define Output Responses step.
2. Create the Max_Disp output response.
1. From the Directory, drag-and-drop the crank.h3d file, located in approaches/setup_1-def/run__00001/m_1, into the work area.
2. In the File Assistant dialog, set the Reading technology to Altair® HyperWorks® (Hyper3D Reader) and click Next.
3. Select Multiple Items at Multiple Time Steps, then click Next.
4. Define the following options, then click Next.
• Set Subcase to Subcase 1 (SUBCASE1).
• Set Type to Displacement (Grids).
• For Request (Start - End), enter N27099 - N40946.
• For Components, select MAG.
5. Set Data Set Dimensions to Single Data Source (1).
6. Enable the Create individual Responses (1) checkbox and set it to Maximum.
7. Click Finish.
The Max_Disp output response is added to the work area.
8. In the work area, Label the second output response Max_Disp.
3. Create the Max_Stress output response.
1. From the Directory, drag-and-drop the crank.h3d file, located in approaches/setup_1-def/run__00001/m_1, into the work area.
2. In the File Assistant dialog, set the Reading technology to Altair® HyperWorks® (Hyper3D Reader) and click Next.
3. Select Multiple Items at Multiple Time Steps, then click Next.
4. Define the following options, then click Next.
• Set Subcase to Subcase 1 (SUBCASE1).
• Set Type to Element Stresses (3D).
• For Request (Start-End), enter E38257 - E94809.
• For Components, select vonMises (2D & 3D).
5. Set Data Set Dimensions to Single Data Source (1).
6. Enable the Create individual Responses (1) checkbox and set it to Maximum.
7. Click Finish.
The Max_Stress output response is added to the work area.
8. In the work area, label the second output response Max_Stress.
4. Create the Volume output response.
1. From the Directory, drag-and-drop the crank.out file, located in approaches/setup_1-def/run__00001/m_1, into the work area.
2. In the File Assistant dialog, set the Reading technology to Altair® HyperWorks® (osmass.tpl) and click Next.
3. Select Single Item in a Time Series, then click Next.
4. Define the following options, then click Next.
• Set Type to OptiStruct Analysis.
• Set Request to Out File.
• Set Component to Volume.
5. Enable the Use Data Source in a new Response checkbox.
6. Label the output response Volume.
7. Set Expression to First Element.
8. Click Finish.
The Volume output response is added to the work area.
5. Minimize the size of the result files in the study directory.
1. Click the Data Sources tab.
2. Clear the Retain checkbox for Displacement (Grids) MAG and Element Stresses (3D) vonMises (2D & 3D) data sources.
6. Click Evaluate to extract the response values.

## Run Full Factorial DOE

In this step you will create a Full Factorial DOE, and set the shape variables to two levels.

Since Full Factorial runs all combinations of input variable values, you will have no loss of information; however you will have an expensive DOE. You will use this study as a reference to compare the loss of accuracy in the conclusions to other DOEs that are less expensive.
1. In the Explorer, right-click and select Add from the context menu.
2. In the Add dialog, select DOE and click OK.
2. Define specifications.
1. Go to the DOE 1 > Specifications step.
2. In the work area, set the Mode to Full Factorial.
3. Click the Levels tab, and verify that the number of levels for each input variable is 2.
Using nine shape variables with two levels gives a full factorial plan made of 512 runs (2^9).
4. Click Apply.
1. Go to the DOE 1 > Evaluate step.
2. Above the Channel Selector, click Multi-Execution and change the number of jobs to 4.
4. Go to the DOE 1 > Post-Processing step.
5. Click the Pareto Plot tab to view Pareto plots obtained from the Full Factorial DOE (512 runs).

A Pareto Plot shows the ranked influence (highest to lowest) of the design variables on the response.

The 5 lengths have the largest influence, and the 3 radii have the least influence on Max_stress. The slope of the hashed lines (positive or negative) indicates a positive or a negative effect of a variable on the response. length_4, length_2, length_5, and length_3 have negative slopes, which indicates that if these variables increase, Max_stress will decrease. On the other hand, length_1 has a positive slope, which indicates that increasing length_1 increases Max_stress.
6. Click the Interactions tab to plot the interactions between input variables.
An interaction is the failure of one variable to produce the same effect on a response at different levels of another variable. An interaction can be either positive or negative. The Interaction plot displays parallel lines if there is no interaction. The bigger the interaction is, the less parallel the lines will be.
Looking at the Max_stress output response, you can see that several of the interactions are very small. You can still find instances with a true interaction, such as the interaction of length_5 and length_4. The effect of the variable length_4 on the output response Max_Stress is in the same direction regardless of the value of length_5, but the effect (magnitude) is much more important when length_5 is larger.
7. Click the Ordination tab to see the Principal Component Analysis results.
Tip: If the 3D Scatter tab is not enabled, click (Show or Hide Tabs), and select 3D Scatter from the Standard Tabs.
Each input variable and output response in the biplot is represented by a line. Lines that point in the same direction have strong correlations (positive or negative depending on whether the lines point in the same or opposite directions). You can see that lengths 2, 3, 4, and 5 contribute the most to the volume value, and improve the structural performance the most along with height and length_1.

## Run Fractional Factorial DOE with Resolution III

In this step you will set up a Fractional Factorial DOE, with resolution III and the same levels as the previous Full Factorial DOE.

Use the nine input variables with two levels, without turning on any interaction, leads to a 12 run Fractional Factorial plan.

1. In the Explorer, right-click and select Add from the context menu.
2. In the Add dialog, select DOE and click OK.
2. Define specifications.
1. Go to the DOE 2 > Specifications step.
2. In the work area, set the Mode to Fractional Factorial.
3. In the Settings tab, set Resolution to III.
4. Click Apply.
1. Go to the DOE 2 > Evaluate step.
4. Go to the DOE 2 > Post-Processing step.
5. Click the Pareto Plot tab to view Pareto plots on Max_stress obtained from the Fractional Factorial III DOE (12 runs).

Compared to the Pareto plot from the Full Factorial, several differences can be observed.

The rank of variables is not the same; for instance, length_4 is the most influential input variable in the Full Factorial, whereas length_2 is the most influential input variable in the Fractional Factorial III.

The effect of length_5 has decreased, while the effects of the three radii has significantly increased, especially the effects of radius_3 and radius_1.
6. Click the Interactions tab to plot the interactions between input variables.
Compare the interaction between length_1 and length_3 on Max_stress. The results provided from the Full Factorial and Fractional Factorial III are quite different. The Full Factorial establishes the real interactions, while the Fractional factorial III detects confounded interactions inaccurately.
7. Click the Ordination tab to see the Principal Component Analysis results obtained with the Fractional factorial III.
In the Full Factorial, you can see that length_2, length_3, and length_5 are correlated to the Volume output response. In the Fractional Factorial III, the relationship is not as clear. In the Fractional Factorial III, the lines representing length_2, length_3, length_5, and Volume are not as collinear as they are in the Full Factorial.

## Run Fractional Factorial DOE with Resolution IV

In this step you will set up a Fractional Factorial DOE with Resolution IV. Using the nine input variables with two levels, without turning on any interaction, leads to a 24 run Fractional Factorial plan.

1. In the Explorer, right-click and select Add from the context menu.
2. In the Add dialog, select DOE and click OK.
2. Define specifications.
1. Go to the DOE 3 > Specifications step.
2. In the work area, set the Mode to Fractional Factorial.
3. In the Settings tab, set Resolution to IV.
4. Click Apply.
1. Go to the DOE 3 > Evaluate step.
4. Go to the DOE 3 > Post-Processing step.
5. Click the Pareto Plot tab to view Pareto plots on Max_stress obtained from the Fractional Factorial IV DOE (24 runs).
Compared to the results obtained from the Full Factorial, you can see that the places of length_2 and length_4 have been inversed in the ranking, but the rest of the information is quite similar.

## Run Fractional Factorial DOE with Resolution V

In this step you will set up a Fractional Factorial DOE with Resolution V. Using the nine input variables with two levels, without turning on any interaction, leads to a 128 run Fractional Factorial plan.

1. In the Explorer, right-click and select Add from the context menu.
2. In the Add dialog, select DOE and click OK.
2. Define specifications.
1. Go to the DOE 4 > Specifications step.
2. In the work area, set the Mode to Fractional Factorial.
3. In the Settings tab, set Resolution to V.
4. Click Apply.
1. Go to the DOE 4 > Evaluate step.
4. Go to the DOE 4 > Post-Processing step.
5. Click the Pareto Plot tab to view Pareto plots on Max_stress obtained from the Fractional Factorial V DOE (128 runs).
The results obtained from both DOE methods are the same, but the number of runs for the Fractional Factorial V is only 1/4th of the runs for the Full Factorial.
6. Click the Ordination tab to see the Principal Component Analysis results obtained from the Fractional factorial V.
There are no differences between the results obtained from the Full Factorial and the Fractional Factorial V.

## Comparison

Conclusions on the screened output responses are summarized for the four DOE methods.

In this tutorial, you focused on the Max_Stress output response, but the same steps should be applied for all output responses.

Results for the Full Factorial and Fractional Factorial V are the same; however, the Fractional Factorial V required only 1/4th the number of runs as the Full Factorial. You can also observe that as the resolution decreased, the accuracy of the information gathered also decreased. For example, the conclusions from the Fractional Factorial III are the least accurate.
Table 1. Comparison of DOE Methods
Full Factorial Fractional Factorial V Fractional Factorial IV Fractional Factorial III
Number of runs 512 128 24 12