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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

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

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:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.metamodel.start"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Tube Crush Monte Carlo "
$
$ Created on Fri Mar 11 14:32:17 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 order quadratic
  solver experiment design 3toK
$ ------ 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
$
 set noise variable range 2.000000
 analyze metamodel monte carlo
STOP

Results

Results

Statistic

Statistic

Statistics

  1. Select Statistical Tools for Type of Plot.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Choose the Response TOP_DISP.
  2. Verify that it is selected to use the metamodel to compute the statistics.
  3. The mean of the response is -228 and the standard deviation is 7.22.

newplot4.png

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 radio button.
  2. Type in -220 as Upper Bound and confirm with enter.
  3. The probability of the response being larger than -220 is 0.149.

 

→ Use the same steps described above to verify:

  • The probability of the response being less than -230 is 0.387.
  • The probability of the response being less than -235 is 0.155.
probability_2201.png

 

Stochastic Contribution

Stochastic Contribution

Stochastic Contribution

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Choose the response TOP_DISP from the list.

 

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

menubar1.png

newplot5.png

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. 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. Build Quadratic Metamodel instead of using actual FEA results.
  4. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

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

dyna_stats_panel1.png

metamodel_mean_panel2.png

metamodel_mean_panel3.png

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.

lspp_mean1.png

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

→ The minimum occurs at node 259 (min=-64.1072) and the maximum at node 429 (max=0.0169754).

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-quad.

metamodel_std_dev_panel2.png

metamodel_std_dev_panel3.png

lspp_std_dev3.png

The figure shows the standard deviation of the z-displacement at time 0.99978s.

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

 

History Plot

History Plot

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  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 Build quadratic metamodel from FEA results.
  3. Go to the next panel.

 

 

 

 

 

 

 

 

 

 

 

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

dyna_stats1.png

dyna_stats2_history.png

stats_history1.png

metamodel_history2.png

metamodel_history3.png

Statistics of the LS-OPT History

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

metamodel_top_disp1.png

 

Single Variable Mode

Single Variable Mode

Single variable Mode (Contribution Analysis)

  • It follows the way of drawing a fringle plot, but:
  1. By the second step, select A single variable's contribution to the D3Plot data instead of Statistic of D3plot data.
  2. Select the variable SIGY.
  3. Build quadratic metamodel from FEA result.

 

 

 

 

 

 

 

  1. By the last step, give a name to this plot, e.g. single_variable.

single_fringle_panel2.png

single_fringle_panel3.png

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

z_displacement_single-variable1.png

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

Single Variable Mode (History)

  • It follows the way of drawing a history plot, but:
  1. By the second step, select How much each variable contributes to the history.
  2. Build quadratic metamodel from FEA result.

 

 

 

 

 

 

 

 

 

  1. By the last step, give a name to this plot, e.g. single_history.

single_history_panel2.png

single_history_panel3.png

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:

For Linux

For Windows