tutr_dx_PC

DesignXplorer 14.0: Performing a Parameters Correlation Study

This tutorial gives step-by-step instructions for performing a Parameters Correlation study to calculate

the deformation of a simple cantilever beam under applied force. The workshop uses a design exploration

system linked to Mechanical APDL, demonstrates parameter parsing and selection, and shows the cor-

relation system used.

This tutorial covers the following Parameters Correlation topics:

1.What is Parameters Correlation?

2. Getting Started

3. Defining Parameters

4. Generating Design Points

5. Performing the Parameters Correlation Study

6. Reviewing Correlation Charts and Matrices

1. What is Parameters Correlation?

Overview

As you add more input parameters to your Design of Experiments (DOE), the number of design points

increases dramatically, decreasing the efficiency of the analysis process. (Remember, DX works best

with fewer than 20 parameters.)

In this case, you may wish to exclude any inputs that are not actively contributing toward your intended

design. Removing these less important parameters from the DOE reduces the generation of unnecessary

sampling points.

1Release 14.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

Benefits

A Parameters Correlation study allows you to:

Determine which input parameters have the most (and the least) impact on your design.

Identify the degree to which the relationship is linear/quadratic.

It also provides the following visual tools to assist in your assessment of parametric impacts:

Correlation Matrix and Chart

Determination Matrix and Chart

Correlation Scatter Plot

Sensitivity Chart

Correlation Sampling

A Parameters Correlation study performs simulations on a random sampling of the design space to

identify correlations between all the parameters.

Samples are generated via the Latin Hypercube sampling method (LHS). This means that the points

are randomly generated, but no two points share input parameters of the same value. The image below

illustrate how samples generated via the Latin Hypercube sampling method vary in placement from

those generated by the Monte Carlo sampling method.

Correlation Methods

There are two different correlation methods that you can use for a DesignXplorer Parameters Correlation

study: Pearsons Linear Correlation and Spearmans Rank Correlation.

Pearsons Linear Correlation

Uses actual data for correlation evaluation.

Correlation coefficients are based on the sample values.

Release 14.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.2


Used to correlate linear relationships.

Spearmans Rank Correlation

Uses ranks of data.

Correlation coefficients are based on the rank of samples.

Recognizes non-linear montonic relationships (which are less restrictive than linear ones). In a

monotonic relationship, one of the following two things happens:

As the value of one variable increases, the value of the other variable increases as well.

As the value of one variable increases, the value of the other variable decreases.

Deemed the more accurate method.

2. Getting Started

Model Description

The model is an book example of simple cantilever beam model to calculate deformation under applied

force. In this workshop, the model will be added to the design exploration project by importing a

Mechanical APDL input file. The text of the input file is shown below.

Creating the Project

1. Open ANSYS Workbench 14.0. Under Component Systems, double-click Mechanical APDL.



Getting Started

2. On the Project Schematic, right-click on the Analysis cell of the Mechanical APDL system and select

the Add Input File > Browse menu option from the context menu.

3. In the file browser that opens, locate and open the file BeamEquations.inp.

4. Save the project as PCBeam.wbpj.5. Update the project by clicking the Update Project toolbar button.



3. Defining Parameters

1. On the Project Schematic, double-click on the Analysis cell of the Mechanical APDL system.

2. In the Analysis workspace, select either of the cells in the Outline of Schematic view. If properties are

not displayed in the Properties view below, select the View > Properties option from the main menu

to display them.

3. Select the Process BeamEquations.inp cell.

4. In the Properties view, identify input and output parameters as shown below.

5. Return to the Project Schematic by clicking the Return to Project toolbar button.



Defining Parameters

4. Generating Design Points

1. On the Project Schematic, double-click on the Parameter Set bar.

2. In the Parameters workspace, update the project by clicking the Update Project toolbar button.

3. Note that the Table of Design Points has been updated.

4. Return to the Project Schematic by clicking the Return to Project toolbar button.



5. Performing the Parameters Correlation Study

1. In the Toolbox, expand Design Exploration and double-click on Parameter Correlation.

Alternatively, you can drag Parameter Correlation and drop it on the Project Schematic to create

a standalone system.

2. On the new Parameters Correlation system, double-click on the Parameters Correlation cell.



Performing the Parameters Correlation Study

3. In the Outline view of Parameters Correlation workspace, select the Parameters Correlation cell.

4. In the Properties view, edit properties as follows:

Set Number of Samples to 30.

Set Auto Stop Type to Execute All Simulations.

5. In the Outline view, now select the input parameter P1WIDTH.

6. In the Properties view, under Values, edit the parameter bounds as follows:

Set Lower Bound to 1.75.

Set Upper Bound to 2.25.



7. Following the process outlined in steps 4 and 5, define the bounds for the other input parameters, as

follows:

For P2 HEIGHT, set Lower Bound to 4.5 and Upper Bound to 5.5.

For P3 LENGTH, set Lower Bound to 80 and Upper Bound to 120.

For P4 FORCE, set Lower Bound to 800 and Upper Bound to 1200.

For P5 YOUNG, set Lower Bound to 1.8E+05 and Upper Bound to 2E+05.

8. Update the Parameter Correlation by clicking the Update toolbar button.



Performing the Parameters Correlation Study

6. Reviewing Correlation Charts and Matrices

In this workshop, well only address the Parameters Correlation Matrix and chart, the Sensitivities chart,

the Correlation Scatter plot, and the Determination Histogram chart.

In the Outline view of the Parameters Correlation workspace, expand Charts. The charts that are created

by default with a Parameters Correlation study display below. Click on the various charts to display

them in the Charts view.

To add a new chart, double-click on it in the Toolbox. An instance of the chart will be added to the

Charts list in the Outline view.

Correlation Matrix Chart

Select Correlation Matrix to view the Correlation Matrix table and chart.

The Correlation Matrix chart is a visual rendering of information in the Correlation Matrix table. The

Correlation Coefficient indicates if there is a relationship between two variables and indicates whether

the relationship is a positive or negative number.

In the Correlation Matrix below, we can see that input parameter P3LENGTH is a major input because

it drives all the outputs, particularly P6Volume and P8Displacement.



On the other hand, we can see that input parameter P5YOUNG is not important to the study because

it has little impact on the outputs. In this case, you might want to disable P5YOUNG by deselecting

its check box in the Properties view. When you do this, the chart changes accordingly, as shown below.



Reviewing Correlation Charts and Matrices

Sensitivities Chart

1. Select Sensitivities to view the Sensitivities chart.

2. In the Properties view, set chart Mode to either Bar or Pie.



The Sensitivities chart shows global sensitivities of the output parameters with respect to the input

parameters. Positive sensitivity occurs when increasing the input increases the output. Negative sensit-

ivity occurs when increasing the input decreases the output. The chart below is displayed in Bar mode.

Generally, the impact of an input parameter on an output parameter is driven by the following two

things:

The amount by which the output parameter varies across the variation range of an input parameter.

The variation range of an input parameter. Typically, the wider the variation range is, the larger

the impact of the input parameter will be.

The statistical sensitivities are based on the Spearman-Rank Order Correlation coefficients that simultan-

eously take both aspects into account.

Correlation Scatter Plot

1. Select Correlation Scatter to view the Correlation Scatter plot.

2. In the Properties view, under Axes:

Set the X Axis to P3 LENGTH.

Set the YAxis to P9 BUCKLING.




The Correlation Scatter chart allows you to plot linear and quadratic trend lines for the samples and

extract the linear and quadratic Coefficient of Determination (R2). In this example, you can seen that

in the Properties view under Trend Lines, you can see the both the Linear and Quadratic values for

(R2). Also, since both options are enabled, the linear and quadratic trend lines are each represented by

a separate line on the chart. The closer the samples lie to the curve, the closer the Coefficient of Determ-

ination will be to the optimum value of 1.

Determination Histrogram

1. In the Parameters Correlation workspace Toolbox, double-click Determination Histogram to add an

instance of the Determination Histogram chart.

2. In the Outline view, select Determination Histogram to view the Determination Histogram chart.

3. In the Properties view, set Y Axis to P8DISPLACEMENT.



The Determination Histogram chart allows you to see what inputs drive a selected output parameter.

In the image below, you can see that input parameters P3LENGTH, P2HEIGHT, and P4FORCE all

affect output P8DISPLACEMENT. You can also see that of the three inputs, P3LENGTH has by far

the greatest impact.

When you view a Determination Histogram chart, you should also check the Full Model R2 (%) value

to see how well output variations are explained by input variations. The closer this value is to 100%,

the more certain it is that output variations result from the inputs. The lower the value, the more likely

that other factors such as noise, mesh error, or an insufficient number of points may be causing the

output variations.

In the example below, you can see that the value for a linear determination is 96.2%.

To view the chart for a quadratic determination, in the Properties view, set Determination Type to

Quadratic. In the example below, we can see that with a quadratic determination type, input P5YOUNG

is shown to also have a slight impact on P8DISPLACEMENT. (You can filter your inputs to keep only

the most important parameters, enabling or disabling them with the check boxes in the Outline view.)




In this example, we can also see that the Full Model R2 (%) value is improved slightly, now raised to

97.436%.

Note

In some cases, the relationship between parameters may be more complex and cannot be

explained completely with a linear or quadratic correlation. If you pursue the study with a

Response Surface or Goal Driven Optimization study, it will be difficult to build a standard

(Full 2nd Order Polynomial) response surface. In this case, try using another response surface

type, such as Kriging or Non-Parametric Regression.



DesignXplorer 14.0: Performing a Parameters Correlation Study1. What is Parameters Correlation?2. Getting Started3. Defining Parameters4. Generating Design Points5. Performing the Parameters Correlation Study6. Reviewing Correlation Charts and Matrices

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