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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

 

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 0.1.
  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:

"Two-bar Truss"
$ Created on Thu Mar 22 14:51:18 2007
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' 0.2
  Upper bound variable 'Area' 4
  Range 'Area' 4
  variable 'Area' distribution 'area_dist'
 Variable 'Base' 0.8
  Lower bound variable 'Base' 0.1
  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
$ ------ 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
$
$ JOB INFO
$
 concurrent jobs 1
 iterate param design 0.01
 iterate param objective 0.01
 iterate param stoppingtype and
 iterate 10
STOP

Results

Results

History

History

History of the Variables

  1. For Type of Plot select Opt History.
  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.

history_area1.png
  1. Select the variable Base.
  2. Click on the graph to get the value of the variable.

 

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

 

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

history_probability1.png

Stochastic Contribution

Stochastic Contribution

Stochastic Contribution

  1. For Type of Plot select Stoch Contr.
  2. 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.

 

stoch_contrib_stress1.png

Download

Download

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