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Monte Carlo

        

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.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

Solvers

Solvers

Define the solverssolvers1.png

  1. Select the Solvers panel.
  2. For Command specify the LS-DYNA executable ls971_R4_2 (This name can be different on your computer).
  3. For Input File browse the file tube.k.
  4. Enter a name for Name of Analysis Case, e.g. SOLVER_1
  5. Push the Add button.

 

 

 

 

 

 

 

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:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.monte_carlo.start"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Tube Crush Monte Carlo "
$
$ Created on Fri Mar  4 14:24:21 2011
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 "ls971_R4_2"
  solver input file "tube.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Post-processor --------
$   NO POSTPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver experiment design lhd_generalized
  solver number experiments 10
$ ------ Job information ------
  solver concurrent jobs 1
$
$ 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

Results

Scatter Plots

Scatter Plots

Scatter plots: View the location of the simulation points

  1. Choose Scatter Plots as Type of Plot.

 

 

 

 

 

 

 

 

 

 

T1 vs. TOP_DISP

  1. For the Z-axis select No entity to switch to the 2d mode.
  2. For the X-axis select the Variable T1.
  3. For the Y-axis select the Constraint TOP_DISP.

newplot1.png

tradeoff_t11.png

SIGY vs. TOP_DISP

  1. For the X-axis select the Variable SIGY to view the SIGY vs. TOP_DISP plot.
tradeoff_sigy1.png

Statistic

Statistic

Statistic and Probability

  1. Click on the "New plot" icon on the menu bar.
  2. Select Statistical Tools for Type of Plot.

 

 

 

 

 

 

 

 

 

 

 

  1. Choose Histogram for Plot type.
  2. Enter 20 for Histogram Bars.
  3. Select Response⇒TOP_DISP. From the plot title we see that the mean is -227 and the standard deviation is 7.86.
  4. The probability of the response being larger than -220 is 0.2 (two out of ten samples: 2/10 are larger than -220).
  5. The probability of the response being less than -230 is almost 0.4 (four out of ten samples: 4/10 are less than -230).
  6. The probability of the response being less than -235 is 0.3 (three out of ten samples: 3/10 are less than -235).

menubar1.png

newplot2.png

statistic1.png

Correlation

Correlation

Correlation and Confidence Interval

  1. Open a new plot and select Correlation Bars for Type of Plot.

 

 

 

 

 

 

 

 

 

 

 

  1. 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.

newplot3.png

correlation1.png

DYNA Stats

DYNA Stats

Fringe Plot

Fringe Plot

Display the Statistics in LS-PrePost (D3Plot)

  1. Select the DYNA Stats panel.
  2. Click on Create button.

 

 

 

 

 

 

 

 

 

 

  1. Select Fringe plot for the type of plot.

dyna_stats1.png

dyna_stats2_fringe.png

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

  1. Select z_displacement from the list.
  2. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

 

  1. For what to plot select Statistic of D3Plot data.
  2. Choose Mean as statistic.
  3. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

  1. Give a name to this plot, e.g. z_disp-mean.
  2. Push the Finish button.

dyna_stats_panel1.png

dyna_stats_mean_panel2.png

dyna_stats_mean_panel3.png

lspp_mean_zdisp1.png

The figure shows the mean of the z-displacement at time 0.99963s.

→ The minimum occurs at node 259 (min=-64.0775) and the maximum at node 429 (max=0.0167412).

Display the Statistics in LS-PrePost (D3Plot) - Standard deviation

  • It follows the way above, except:
  1. By the second step, choose Std Dev (Standard deviation) as statistic.

 

 

 

 

 

 

 

 

 

 

 

  1. By the last step, give a name to this plot, e.g. z_disp-std_dev.

 

 

dyna_stats_std_dev_panel2.png

dyna_stats_std_dev_panel3.png

lspp_stddev_zdisp1.png

The figure shows the standard deviation of the z-displacement at time 0.99963s.

→ The maximum occurs at node 473 (max = 2.09546) where the deformation is large.

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

  1. Select z_displacement from the list.
  2. Check the Correlation with response check box.
  3. Choose the response TOP_DISP.
  4. Go to the next panel.

 

 

 

 

 

 

 

 

 

  1. For what to plot select Statistic of D3Plot data.
  2. For analysis methed, choose Use actual FEA results.
  3. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

  1. Give a name to this plot, e.g. z_disp-corr.
  2. Push the Finish button.
 

dyna_stats_corr_panel1.png

dyna_stats_corr_panel2.png

dyna_stats_corr_panel3.png

lspp_correlation_zdisp1.png

The  figure shows the correlation of the z-displacement with the response TOP_DISP at time 0.99963s.

→ 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.

 

History

History

Display the Statistics in LS-PrePost (History)

  1. Select the DYNA Stats panel.
  2. Click on Create button.

 

 

 

 

 

 

 

 

 

 

  1. Select History plot for the type of plot.

dyna_stats1.png

dyna_stats2_history.png

  1. Select TOP_DISP_HIST from the list.
  2. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. For what to plot select Statistic of histories.
  2. For analysis methed, choose Use actual FEA results.
  3. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

  1. Give a name to this plot, e.g. state_history.
  2. Push the Finish button.

stats_history1.png

stats_history2.png

stats_history3.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)

  • It follows the way above, except:
  1. By the second step, choose The given history for all runs for what to plot.

 

 

 

 

 

 

 

 

 

 

 

  1. By the last step, give a name to this plot, e.g. stats_hisory_all-runs.

stats_history_all-runs1.png

stats_history_all-runs2.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:

For Linux

For Windows