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Reliability Based Design Optimization

          

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.
rbdo1.png

 

Solvers

Solvers

Define the solver (Linux version)

  1. Select the Solvers panel. solvers_linux1.png
  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) 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

Statistical Distribution

  1. Select the Distribution panel.
  2. Choose Normal Type.
  3. For Mean enter 0.
  4. For Standard Dev enter 0.1.
  5. Type in a Distribution Name, e.g. area_dist.
  6. Push the Add button.
dist_area1.png
  1. Choose Uniform Type.
  2. For Lower enter 0.
  3. For Upper enter 0.2.
  4. Type in a Distribution Name, e.g. base_dist.
  5. Push the Add button.
dist_base1.png

 

Variables

Variables

Change Variable

  1. Select the Variables panel.
  2. Choose area_dist as the Distribution of the variable Area.
  3. Choose base_dist as the Distribution of the variable Base.
variables_rbdo1.png

Sampling

Sampling

Sampling Panel

  1. Select the Sampling Panel.
  2. Switch the Order from Linear to Quadratic.
sampling_rbdo1.png

Objective

Objective

Objective Function

  1. Select the Objective panel.
  2. Choose the Response Weight as objective.
objective_rbdo1.png

Constraint

Constraint

Constraints Panel

  1. Select the Constraints panel.
  2. Choose the Response Stress as constraint.
  3. For the probability of exceeding the upper bound of the constraint enter 0.05.
constraint_rbdo1.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:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.2bar.robust.start"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Two-bar Truss"
$
$ Created on Wed Dec 15 10:20:36 2010
solvers 1
responses 2
$
$ NO HISTORIES ARE DEFINED
$
$
$ PROBABILISTIC DISTRIBUTIONS
$
distribution 2
 distribution 'area_dist' NORMAL  0  0.1  
 distribution 'base_dist' UNIFORM  0  0.2  
$
$ DESIGN VARIABLES
$
variables 2
 Variable 'Area' 2.
  Lower bound variable 'Area' .2
  Upper bound variable 'Area' 4.
  Range 'Area' 4.
  variable 'Area' distribution 'area_dist'
 Variable 'Base' .8
  Lower bound variable 'Base' .1
  Upper bound variable 'Base' 1.6
  Range 'Base' 1.6
  variable 'Base' distribution 'base_dist'

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      SOLVER "SOLVER_1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
$ 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 quadratic
  solver experiment design dopt
$ ------ 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) }

$
$ OBJECTIVE FUNCTIONS
$
 objectives 1
 objective 'Weight' 1
$
$ CONSTRAINT DEFINITIONS
$
 constraints 1
 constraint 'Stress'
  upper bound constraint 'Stress' 1
  probability upper bound constraint 'Stress' 0.05
$
$ 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

History

History

History of the Variables

  1. Choose the tab "Viewer". In the new window select History under the category Optimization.
  2. Select the variable Area.

 

 

 

 

 

 

 

 

 

→ 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 Area is computed as 1.6.

new_plot1.png

history_area1.png

  1. Select the variable Base.
  2. Click on the graph to get the value of the variable. If you do this, you will see a table, which states all the available data at each iteration (see the next figure).

 

→ 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 0.38.

history_base1.png

history_base2.png

  1. Select the constraint Stress.
  2. As Value to Plot choose RBDO Upper Bound Probability.

 

→ The probability of exceeding the the upper bound has converged to 0.05.

history_probability1.png

 

Stochastic Contribution

Stochastic Contribution

Stochastic Contribution

  1. Click on the first icon "New plot" on the menu bar of the plot window to restart the viewer again.
  2. Choose Stochastic Contribution for this time.
  3. Select the response Stress.

 

 

 

 

 

 

 

 

 

 

 

→ The standard deviation of the Stress response due to all variables is 0.06. Almost all of the variation of the Stress response is caused by the variable Area.

 

 

menubar1.png

 

new_plot2.png

stoch_contrib_stress1.png

Download

Download

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

For Linux

For Windows