Reliability Based Design Optimization
Solution with LS-OPTui
Solution with LS-OPTui
Task
Task
Open the file com.2bar.rbdo.start.
RBDO Task
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Solvers
Solvers
Define the solver (Linux version)
- Select the Solvers panel.

- For Command type in echo N o r m a l. This signals LS-OPT a normal termination of the solver.
- For Name of Analysis Case enter SOLVER_1.
- Push the Add button.
Define the solver (Windows version) 
- 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
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Variables
Variables
Change Variable
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Sampling
Sampling
Sampling Panel
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Objective
Objective
Objective Function
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Constraint
Constraint
Constraints Panel
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Run
Run
Run Panel
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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
→ 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. | |
→ 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. |
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→ The probability of exceeding the the upper bound has converged to 0.05. |
Stochastic Contribution
Stochastic Contribution
Stochastic Contribution
→ 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.
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Download
Download
The complete data set (input and command files) is available for download:
For Linux
For Windows











