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Robust Parameter Design

        

Solution with LS-OPTui

Document Actions

Solution with LS-OPTui

Task

Task

Open the file com.2bar.rbdo.start.

RBDO Task

  1. From the main menu bar select Task → Metamodel-based → RBDO.
rbdo1.png

 

Distribution

Distribution

Normal Distribution

  1. For Type select Normal.
  2. Enter 2 for Mean.
  3. Enter 0.1 for Standard Deviation.
  4. Type in a Distribution Name, e.g. area.
  5. Push the Add button to create the distribution.
normal_dist_area1.png

Variable

Variable

Noise Variable

  1. Select the Variables panel.
  2. Switch the Type from the variable Area to Noise Variable.
  3. Choose area as the Distribution of the noise variable Area.
rpd_variable1.png

Sampling

Sampling

Sampling Panel

  1. Select the Sampling Panel.
  2. Switch the Order from Linear to Linear with Interaction.
  3. Choose Full Factorial.
  4. Select 3 Points Per Variable.
rpd_sampling1.png

Responses

Responses

Response Panel

  1. Select the Responses panel.
  2. Select Standard Deviation.
  3. Choose Stress from the list.
  4. Push the Add button to create the new response.

 

rpd_response1.png

Objective

Objective

Objective Panel

  1. Select the Objective Panel.
  2. Select the previously created response StandardDeviation3 as objective (make sure only this response is selected).
rpd_objective1.png

Constraints

Constraints

Constraints Panel

  1. Select the Constraints Panel.
  2. Deselect the response Stress (make sure that no response is selected).
rpd_constraint1.png

Run

Run

Run Panel

  1. Select the Run panel.
  2. Push the Run button to start the optimization.
run_rbdo1.png

Com-file

Com-file

The created command file may look like this:

"Two-bar Truss"
$ Created on Wed Mar 21 17:39:10 2007
solvers 1
responses 2
$
$ NO HISTORIES ARE DEFINED
$
$
$ PROBABILISTIC DISTRIBUTIONS
$
distribution 1
 distribution 'area' NORMAL  2  0.1  
$
$ DESIGN VARIABLES
$
variables 2
 Noise variable 'Area' distribution 'area'
 Variable 'Base' 0.8
  Lower bound variable 'Base' 0.1
  Upper bound variable 'Base' 1.6
  Range 'Base' 1.6

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      SOLVER "SOLVER_1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
$ DEFINITION OF SOLVER "SOLVER_1"
$
 solver own 'SOLVER_1'
  solver command "echo N o r m a l"
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver order interaction
  solver experiment design 3toK
$ ------ Job information ------
  solver concurrent jobs 1
$
$ WARNING - NO RESPONSES DEFINED FOR SOLVER "SOLVER_1"
$
$
$ RESPONSE EXPRESSIONS FOR SOLVER "SOLVER_1"
$
 response 'Weight' expression { Area * sqrt(1+Base*Base) }
 response 'Stress' expression { 0.124 * sqrt(1+Base*Base) * (8/Area + 1./Area/Base) }

composites 1
$
$ STD DEV COMPOSITES 
$
 composite 'StandardDeviation3' noise 'Stress'
$
$ OBJECTIVE FUNCTIONS
$
 objectives 1
 objective 'StandardDeviation3'
$
$ THERE ARE NO CONSTRAINTS!!!
$
 constraints 0
$
$ JOB INFO
$
 concurrent jobs 1
 iterate param design 0.01
 iterate param objective 0.01
 iterate param stoppingtype and
 iterate 10
STOP

Results

Document Actions

Results

Optimization Histories

Optimization Histories

Variable History

  1. For Type of Plot select Opt History.
  2. Choose the variable Area.

 

→ The Area noise variable remains unchanged during the optimization process.

 

rpd_history-area1.png

Variable History

  1. Stay in the Opt History.
  2. Choose the variable Base.

 

→ The deployment of the variable value (red) and the bounds of the region of interest (blue) during the optimization process. The optimum value of the variable Base is computed as 0.5.

 

rpd_history-base1.png

Composite History

  1. Choose the StandardDeviation3 composite.
  2. Click on the graph to get point information.

 

→ The standard deviation has converged during the optimization process.

rpd_history-stddeviation1.png

Metamodel

Metamodel

Metamodel

  1. For Type of Plot select Metamodel.
  2. Choose StandardDeviation3 as Response to plot.

 

→ Using the metamodel facility you can investigate that a higher value of the variable Base goes together with a lower value of the stress standard deviation.

metamodel1.png

Download

Download

The complete data set (input and command files) is available for download as tar.gz robust_parameter_design.tar.gz or zip-file robust_parameter_design.zip.