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Robust Parameter Design

        

Solution with LS-OPTui

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.
rpd_task1.png

 

Solvers

Solvers

Define the solver (Linux version) rpd_solvers_linux1.png

  1. Select the Solvers panel.
  2. For Command type in echo N o r m a l. This signals LS-OPT a normal termination of the solver.
  3. For Name of Analysis Case enter SOLVER_1.
  4. Push the Add button.

 

 

 

 

 

 

 

 

 

Define the solver (Windows version) rpd_solvers_win1.png

  1. A direct call of the command echo N o r m a l doesn't work for the Windows version. We have to save the command line type N o r m a l in a .bat file and take it as the solver. NOTE: It's necessary to give the complete path of the solver command.

 

 

 

 

 

 

 

 

 

Distribution

Distribution

Normal Distribution

  1. Select the Dist panel.
  2. For Type select Normal.
  3. Enter 2 for Mean.
  4. Enter 0.1 for Standard Deviation.
  5. Type in a Distribution Name, e.g. area.
  6. 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. Deselect the response Weight.
  3. Select the previously created response StandardDeviation3 as objective.
  4. Set  the weight of objective 1.0.
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.
rpd_run1.png

Com-file

Com-file

The created command file may look like this:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.2bar.robust.correct"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Two-bar Truss"
$
$ Created on Fri Feb 25 12:41:39 2011
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' .8
  Lower bound variable 'Base' .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
$ ------ Post-processor --------
$   NO POSTPROCESSOR 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' 1
$
$ THERE ARE NO CONSTRAINTS!!!
$
 constraints 0
$
$ PARAMETERS FOR METAMODEL OPTIMIZATION
$
 Metamodel Optimization Strategy DOMAINREDUCTION
$
  iterate param design 0.01
  iterate param objective 0.01
  iterate param stoppingtype and
$
$ OPTIMIZATION ALGORITHM
$
 Optimization Algorithm hybrid simulated annealing
$
$ JOB INFO
$
 iterate 10
STOP

Results

Results

Optimization Histories

Optimization Histories

Variable History

  1. Go to the Viewer panel and for Type of Plot select Optimization History.
  2. Choose the variable Area.

 

 

 

 

 

 

 

 

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

 

new_plot1.png

rpd_history-area1.png

Variable History

  1. Choose the variable Base.
  2. Click on the graph to get the exact value of 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 0.50489.

 

rpd_history-base1.png

rpd_history-points1.png

Composite History

  1. Choose the StandardDeviation3 composite.
  2. Click on the graph to get the exact value of StandardDeviation3 (see above).

 

→ The standard deviation has converged during the optimization process.

rpd_history-stddeviation1.png

 

Metamodel

Metamodel

Metamodel

  1. Click on "New plot" icon on the menu bar to open another LS-OPT Viewer.
  2. For Type of Plot select Metamodel Surface.

 

 

 

 

 

 

 

 

 

 

 

Set up the panels

  1. Select the Setup panel.
  2. Choose StandardDeviation3 as z-coordinate.
  3. Set the variables Area and Base as x- and y-coordinate, respectively.
  4. Go to the Points panel.
  5. Turn Iterations to Current.
  6. Show all the feasible, infeasible points, the predicted and computed optimum at the meantime.

 

 

 

 

 

 

 

 

 

→ 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.

menubar1.png

new_plot2.png

rpd_surface-panel.png

rpd_surface-plot1.png

Download

Download

The complete data set (input and command files) is available for download:

For Linux

For Windows