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Point MSE

A composite MSE (Mean Square Error) function is used in order to apply parameter identification with simple target values.

Solution with LS-OPTui

Solution with LS-OPTui

Strategy

Strategy

Choose a Strategy

  1. strategy1.pngSelect the Strategy panel.
  2. Switch the radio button of the section “Strategy for Metamodel-based Optimization” to "Sequential with Domain Reduction (SRSM)".

 

 

 

 

 

 

 

 

 

 

 

Solvers

Solvers

Solvers Panel

  1. Select the Solvers panel.
  2. For Command select the LS-DYNA executable ls971_R4_2 (This name can be different on your computer).
  3. For Input File browse the file foam1.k in your directory.
  4. Enter the Name of Analysis Case, e.g. Case1.
  5. Push the Add button to create a new analysis case.
solver1.png

 

Variables

Variables

Define the Variables

  1. Select the Variables panel.
  2. Switch the YMod Type from Constant to Variable.
  3. Enter 500000 for the Minimum.
  4. Enter 2000000 for the Maximum.

 

 var_ymod1.png
  1. Switch the Yield Type from Constant to Variable.
  2. Enter 500 for the Minimum.
  3. Enter 2000 for the Maximum.

 

 var_yield1.png

Histories

Histories

Extract History

 

Define z-slave-force on interface 1

  1. Select the Histories panel.
  2. Select RCFORC from the available LS-DYNA output interfaces.
  3. Enter 1 for the Interface ID.
  4. Select Z slave force.
  5. Enter the label Force as History Name.
  6. Push the Add button to create the new history.

This will extract the Z-slave history Force from the binary LS-DYNA output database RCFORC.

 history1.png

Responses

Responses

Define the Responses

 

Define force response at 2 ms

  1. Select the Responses panel.
  2. From the possible response types select: Response-Expression.
  3. Enter an algebraic expression: Force(0.002). This evaluates the history Force you defined before at t=0.002.
  4. Type in the label F1_1 for Response Name.
  5. Push the Add button to create a new response.
 resp_f11.png

Define force response at 4 ms

  1. From the possible response types select: Response-Expression.
  2. Enter an algebraic expression: Force(0.004).
  3. Type in the label F2_1 for Response Name.
  4. Push the Add button to create a new response.
 resp_f22.png
Define force response at 6 ms
  1. From the possible response types select: Response-Expression.
  2. Enter an algebraic expression: Force(0.006).
  3. Type in the label F3_1 for Response Name.
  4. Push the Add button to create a new response.
 resp_f33.png
Define force response at 8 ms
  1. From the possible response types select: Response-Expression.
  2. Enter an algebraic expression: Force(0.008).
  3. Type in the label F4_1 for Response Name.
  4. Push the Add button to create a new response.
 resp_f44.png
Define composite function
  1. From the possible response types select: Composite.
  2. For Composite Function Type select: MSE
  3. Select the Response F1_1.
  4. For Target type in: 10000.
  5. Select the Response F2_1.
  6. For Target type in: 13000.
  7. Select the Response F3_1.
  8. For Target type in: 15000.
  9. Select the Response F4_1.
  10. For Target type in: 17000.
  11. For Response Name enter: MSE.
  12. Push the Add button to create a new response.
 resp_mse2.png

Objective

Objective

Objective

  1. Select the Objective panel.
  2. Select MSE from the Responses as the objective function.
  3. Leave the default 1.0 for Weight. If you have several objective functions, you may assign weight to each one according to their importance.
objective1.png

Run

Run

Run the Optimization

  1. Select the Run panel.
  2. For Number of iterations enter 5.
  3. Push the Run button to start the optimization. (Save the project as com.mse_point)
run1.png

Com-file

Com-file

The created command file may look like this:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.mse_point"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Optimization Problem"
$
$ Created on Fri Jan  7 16:21:49 2011
solvers 1
responses 4
histories 1
$
$ DESIGN VARIABLES
$
variables 2
 Variable 'YMod' 7.e5
  Lower bound variable 'YMod' 5.e5
  Upper bound variable 'YMod' 2.e6
 Variable 'Yield' 1500.
  Lower bound variable 'Yield' 500.
  Upper bound variable 'Yield' 2.e3

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      OPTIMIZATION METHOD   
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
Optimization Method SRSM

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      SOLVER "Case1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
$ DEFINITION OF SOLVER "Case1"
$
 solver dyna960 'Case1'
  solver command "ls971_R4_2"
  solver input file "foam1.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Post-processor --------
$   NO POSTPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver order linear
  solver experiment design dopt
$ ------ Job information ------
$
$ WARNING - NO RESPONSES DEFINED FOR SOLVER "Case1"
$
$
$ HISTORIES FOR SOLVER "Case1"
$
 history 'Force' "BinoutHistory -res_type RCForc -cmp z_force  -id 1  -side SLAVE"
$
$ RESPONSE EXPRESSIONS FOR SOLVER "Case1"
$
 response 'F1_1' expression {Force(0.002)}
 response 'F2_1' expression {Force(0.004)}
 response 'F3_1' expression {Force(0.006)}
 response 'F4_1' expression {Force(0.008)}

composites 1
$
$ COMPOSITE RESPONSES
$
 composite 'MSE' type standardMSE
  composite 'MSE' response 'F1_1' 10000
  composite 'MSE' response 'F2_1' 13000
  composite 'MSE' response 'F3_1' 15000
  composite 'MSE' response 'F4_1' 17000
$
$ OBJECTIVE FUNCTIONS
$
 objectives 1
 objective 'MSE' 1
$
$ THERE ARE NO CONSTRAINTS!!!
$
 constraints 0
$
$ 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
  Use GSA
$
$ JOB INFO
$
 iterate 5
STOP

Results

Results

Accuracy

Accuracy

Start the LS-OPT Viewer by selecting the View tab and

 

  1. Select Accuracy under Metamodel.
 new_plot1.png
  1. Choose the Response F1_1.

 

→ Good approximation: low distance between predicted (black line) and computed (green points) values. The RMS Err, Sqrt PRESS and R-sq coincide with the plot.

 accuarcy_f11.png
  1. Choose the Response F4_4.

 

→The predicted (black line) values deviate from the computed (green points) values slightly, but they can still be considered as good approximation.

 accuracy_f44.png

Computed vs Predicted in Opt History plot:

 

  1. Restart the LS-OPT Viewer.
  2. Select History under Optimization.

menubar1.png

new_plot2.png
  1. Choose the Response F1.

 

→ Good approximation of optima: The computed values (red points) coincide with the predicted values (black line).

opthistory_f11.png
  1. Choose the Response F4_4.

→  Asymptotical approximation of optima: It shows only a little difference between computed values (red points) and predicted values (black line) at the last two iterations.

opthistory_f44.png

Convergence

Convergence

  1. Restart the LS-OPT Viewer.
  2. Select under Optimization the item History.

menubar1.png

new_plot2.png

Convergence of the Variable YMod

  1. Select the Variable YMod.

 

→ Since we have applied the strategy Sequential with Domain Reduction, the optimal values of the variable (red line) at each iteration varies within the reduced ranges of the domain (blue lines).

→ The variable is rather insignificant (see ANOVA) and therefore isn't converged.

convergence_ymod1.png

Convergence of the Variable Yield

  1. Select the Variable Yield.

 

→ The variable is important for the optimization (see ANOVA) and appears to be converged.

 

convergence_yield1.png

Confidence Intervals

Confidence Intervals

The Confidence Intervals can be found in the lsopt_report file.

  1. From the main menu bar select View → Summary Report.

 

The Confidence Intervals are located at the end of the file.

 

view_summary1.png

Alternatively, we can directly open the lsopt_report file from the main directory with an editor and scroll to the end to find the Confidence Intervals of YMod and Yield.

lsopt_report-file1.png

 

Sensitivities

Sensitivities

Which variable appears to be the most important? The significance of a variable for a response can be illustrated with ANOVA (analysis of variance) or GSA/Sobol (global sensitivity ananlysis).

ANOVA

 

The ANOVA (analysis of variance) result can be displayed as follows in the LS-OPT Viewer:

  1. Restart the LS-OPT Viewer and select under Metamodel the item Sensitivity

 

new_plot3.png

  1. Select Linear ANOVA for Type of Plot.

  2. Choose the response F1_1.

 

→ For response F1_1 the variable YMod is rather insignificant and the variable Yield is important.

anova_f11.png
  1. Stay in the Linear ANOVA Type of Plot.
  2. Choose the response F2_2.

 

→ For response F2_2 the variable YMod is rather insignificant and the variable Yield is more important.

 anova_f22.png

GSA/Sobol

 

  1. Select GSA/Sobol for Type of Plot.

  2. Choose the response F1_1.

 

→ We get the same result by using GSA/Sobol. The variable YMod has hardly influence on F1_1 and the variable Yield affects F1_1 exclusively.

 gsa_f11.png
  1. Stay in the GSA/Sobol Type of Plot.
  2. Choose the response F2_2.

 

→ The variable YMod has only a little influence on F1_1 and the variable Yield affects F1_1 in a great measure.

 gsa_f22.png

 

Download

Download

The complete data set (input and command files) is available for download:

For Linux

For Windows