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Metamodel-based MC

        

Solution with LS-OPTui

Solution with LS-OPTui

File

File

Open the File

  1. From the main menu bar select File → Open and the command file com.metamodel.start.
open_com-monte-carlo1.png

Task

Task

Monte Carlo Analysis Task

  1. From the main menu bar select Task → Metamodel-based → Monte Carlo Analysis.
task_monte-carlo2.png

Distribution

Distribution

Add the Distributions

  1. Select the Dist panel.
  2. For the distribution Type choose Normal from the category chooser.
  3. For Mean enter 1.
  4. For Standard Deviation enter 0.05.
  5. Enter a Distribution Name, e.g. t1.
  6. Push the Add button to create the distribution.

 

dist_t11.png
  1. For the distribution Type choose Normal from the category chooser.
  2. For Mean enter 1.
  3. For Standard Deviation enter 0.05.
  4. Enter a Distribution Name, e.g. s1.
  5. Push the Add button to create the distribution.
dist_s11.png

Variables

Variables

Change the Variables

  1. Select the Variables panel.
  2. Switch the Type of the variable T1 from Constant to Noise Var.
  3. Choose t1 as the Distribution for this variable.
  4. Switch the Type of the variable SIGY from Constant to Noise Var.
  5. Choose s1 as the Distribution for this variable.

 

noise_varianble1.png

Sampling

Sampling

Quadratic Metamodel

  1. Select the Sampling panel.
  2. For METAMODEL select Polynomial.
  3. Choose a Quadratic Order for the polynomial metamodel and leave the default entries for POINT SELECTION.
sampling_meta_monte1.png

Constraint

Constraint

Set the Constraint

  1. Select the Constraints panel.
  2. Choose the Response TOP_DISP as the constraint.
  3. Enter -230 as the Lower Bound.
constraint_top-disp1.png

Run

Run

Run the Monte Carlo Analysis

  1. Select the Run panel.
  2. Push the Run button to start the metamodel-based Monte Carlo Analysis.
run_meta_monte1.png

Com-file

Com-file

The created command file may look like this:

"Tube Crush Monte Carlo "
$ Created on Tue Jan 22 12:03:19 2008
solvers 1
responses 1
histories 1
$
$ PROBABILISTIC DISTRIBUTIONS
$
distribution 2
 distribution 't1' NORMAL  1  0.05  
 distribution 's1' NORMAL  1  0.05  
$
$ DESIGN VARIABLES
$
variables 2
 Noise variable 'T1' distribution 't1'
 Noise variable 'SIGY' distribution 's1'

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      SOLVER "SOLVER_1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
$ DEFINITION OF SOLVER "SOLVER_1"
$
 solver dyna960 'SOLVER_1'
  solver command "/home/prak1/LS-DYNA/ls971_s_7600_1224_ia32_redhat90"
  solver input file "/home/prak1/LS-OPT/beispiele/reliability_analysis/metamode_monte_carlo/tube.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver order quadratic
  solver experiment design 3toK
$ ------ Job information ------
$
$ RESPONSES FOR SOLVER "SOLVER_1"
$
 response 'TOP_DISP' 1 0 "BinoutResponse -res_type nodout -cmp z_displacement -id 486  -select MIN "
$
$ HISTORIES FOR SOLVER "SOLVER_1"
$
 history 'TOP_DISP_HIST' "BinoutHistory -res_type nodout  -cmp z_displacement -id 486 "

$
$ NO OBJECTIVES DEFINED
$
 objectives 0
$
$ CONSTRAINT DEFINITIONS
$
 constraints 1
 constraint 'TOP_DISP'
  lower bound constraint 'TOP_DISP' -230
$
$ JOB INFO
$
 set noise variable range 2.000000
 analyze metamodel monte carlo
STOP

Results

Results

Statistic

Statistic

Statistics

  1. Select Statistics for Type of Plot.
  2. Choose the Response TOP_DISP.
  3. Verify that it is selected to use the metamodel to compute the statistics.
  4. The mean of the response is -228 and the standard deviation is 7.27.
statistic_top_disp1.png

Probability

To find out the probability of the response being larger than -220 use the following steps:

  1. Select the Bounds tab.
  2. Type in -220 as Upper Bound and confirm with enter.
  3. The probability of the response being larger than -220 is 0.147.

 

→ Use the same steps described above to verify:

  • The probability of the response being less than -230 is 0.39.
  • The probability of the response being less than -235 is 0.15.
probability_2201.png

Stochastic Contribution

Stochastic Contribution

Stochastic Contribution

  1. Select Stoch Contrib for Type of Plot.
  2. Choose the response TOP_DISP from the list.

 

→ The variable T1 contributes the most to the variation of the crush distance.

stochastic_contribution.png

DYNA Stats

DYNA Stats

Fringe Plot

Fringe Plot

Display the Statistics in LS-PrePost (D3Plot)

  1. Select the DYNA Stats panel.
  2. Make sure Quadratic Metamodel is selected.
  3. Choose D3Plot as data.
  4. Select z_displacement from the list.
  5. Choose Mean as statistic.

  +   Push Display in LS-PrePost.

View as fringe plot the mean of the z_displacement.

  1. Choose Std Dev as statistic.

  +   Push Display in LS-PrePost.

View as fringe plot the standard deviation of the z_displacement.

d3plot_mean1.png

Mean of the z_displacement

Metamodels can be used to predict the statistics of the responses. These metamodels (approximations) are computed for all the results for all nodes for all time steps.

→ The minimum occurs at node 259 (min=-64.1077) and the maximum at node 429 (max=0.0170051).

lspp_mean1.png

Standard deviation of the z_displacement.

 

→ The maximum occurs at node 694 (max = 1.32686) where the deformation is large.

lspp_std_dev3.png

History Plot

History Plot

Display the Statistics in LS-PrePost (History)

  1. Choose History as data.
  2. Select TOP_DISP_HISTORY from the list.
  3. Push Display in LS-PrePost.
history_top_disp1.png

Statistics of the LS-OPT History

→ The figure shows the statistics of the TOP_DISP_HIST history (z-displacement at node 486).

lspp_history1.png

Display the Statistics in LS-PrePost (History)

  1. Choose History as data.
  2. Check the Plot All Actual Histories check box.
  3. Push Display in LS-PrePost.
stats_history_individual2.png

Statistics of the LS-OPT History

→ LS-OPT history TOP_DISP_HIST (z-displacement at node 486) of all the LS-DYNA runs can be viewed simultaneously.

lspp_history_all1.png

Single Variable Mode

Single Variable Mode

Single variable Mode (Contribution Analysis)

  1. Choose D3Plot as data.
  2. Select z_displacement from the list.
  3. Select Single Variable as Source.
  4. Choose the variable SIGY.
  5. Push Display in LS-PrePost.
d3plot_variable_sigy1.png

Stochastic Contribution

Metamodels can be used to predict the statistics of the responses. In this case the statistics are computed due to one variable (SIGY).

 

→ The minimum occurs at node 1 (min=0) and the maximum at node 694 (max=1.10725).

z_displacement_single-variable1.png

Single Variable Mode (History)

  1. Choose History as data.
  2. Select TOP_DISP_HIST from the list.
  3. Select Single Variable as Source.
history_single_variable1.png

Stochastic Contribution

The most important variable, or rather the variable responsible for the most variation of the response, can be plotted on the model.

→ In this case the variable T1 produces most of the variation.

top_disp_dueto_variables1.png

Download

Download

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