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Monte Carlo

        

Solution with LS-OPTui

Document Actions

Solution with LS-OPTui

File

File

Open the File

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

Task

Task

Monte Carlo Analysis Task

  1. From the main menu bar select Task → Direct Simulation → Monte Carlo Analysis.
task_monte-carlo3.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

Latin Hypercube Sample

  1. Select the Sampling panel.
  2. For POINT SELECTION choose Latin Hypercube.
  3. Use 10 as Total Number of Simulation Points (to allow the simulation to finish in reasonable time).
sampling_latin-hypercube1.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 Monte Carlo analysis.
run1.png

Com-file

Com-file

The created command file may look like this:

"Tube Crush Monte Carlo "
$ Created on Thu Jan 17 15:21:08 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/monte_carlo/tube.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver experiment design lhd_generalized
  solver number experiments 10
$ ------ 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
$
analyze monte carlo
STOP

Results

Document Actions

Results

Tradeoff

Tradeoff

Tradeoff: View the location of the simulation points

  1. Choose Tradeoff as Type of Plot.
  2. For the X-axis select the Variable T1.
  3. For the Y-axis select the Constraint TOP_DISP.
tradeoff_t11.png
  1. Choose Tradeoff as Type of Plot.
  2. For the X-axis select the Variable SIGY.
  3. For the Y-axis select the Constraint TOP_DISP.
tradeoff_sigy1.png

Statistic

Statistic

Statistic and Probability

  1. Select Statistics for Type of Plot.
  2. Choose the Response TOP_DISP.
  3. Enter 20 for Histogram Bars.
  4. The mean is -227 and the standard deviation is 7.8.
  5. The probability of the response being larger than -220 is 0.2 (two out of ten samples: 2/10 are larger than -220).

 

 

statistic_>-2201.png

Statistic and Probability

  1. The probability of the response being less than -230 is 0.4 (four out of ten samples: 4/10 are less than -230).
  2. The probability of the response being less than -235 is 0.3 (three out of ten samples: 3/10 are less than -235).
statistic-2302.png

Correlation

Correlation

Correlation and Confidence Interval

  1. Select Correlation for Type of Plot.
  2. Choose the response TOP_DISP.

 

→ As shown in the figure the variable T1 contributes the most to the variation of the response TOP_DISP and also has a smaller confidence interval.

correlation1.png

DYNA Stats

Document Actions

DYNA Stats

Fringe Plot

Fringe Plot

Display the Statistics in LS-PrePost (D3Plot)

  1. Select the DYNA Stats panel.
  2. Choose D3Plot as data.
  3. Select z_displacement from the list.
  4. 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.

stats_d3plot_mean1.png

Mean of the z_displacement

The figure shows the mean of the z-displacement.

→ The minimum occurs at node 259 (min=-64.0745) and the maximum at node 429 (max=0.0167404).

lspp_mean_zdisp1.png

Standard deviation of the z_displacement.

The figure shows the standard deviation of the z-displacement.

→ The maximum occurs at node 473 (max = 2.10029) where the deformation is large.

lspp_stddev_zdisp1.png

Display the Statistics in LS-PrePost (D3Plot) - Correlation

  1. Choose D3Plot as data.
  2. Select z_displacement from the list.
  3. Check the Correlation check box.
  4. Push Display in LS-PrePost.

 

 		stats_d3plot_correl1.png

Correlation z_displacement - TOP_DISP

The  figure shows the correlation of the z-displacement withe the response TOP_DISP.

→ The red areas distinguish positive correlation (positive changes in the response are associated with positive changes in the displacement), the dark blue areas distinguish negative correlation (positive changes in the response are associated withe negative changes in the displacement or vice versa). Furthermore green areas mark no correlation.

lspp_correlation_zdisp1.png

History

History

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.
stats_history1.png

Statistics of the LS-OPT History

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

history_top_disp1.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_individual1.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.

history_top_disp_all-runs1.png

Download

Download

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