Personal tools
 
Document Actions

Quadratic RS

This example deals with a quadratic approximation and conducts a trade-off study using the Repair feature.

Solution with LS-OPTui

Document Actions

Solution with LS-OPTui

   

Metamodel

Metamodel

Load the com.linear file you created in the first part or download the input file above.

 

Change Metamodel Order

  1. Select the Sampling panel.
  2. Change the Order of the Polynomial Metamodel from Linear to Quadratic.
  3. Use the default number of simulations required for quadratic. For 2 variables (tbumper and thood) there should be 10 simulations in total.
sampling_quadratic1.png

Repair Task

Repair Task

Repair Task

  1. From the main menu bar select Task → Repair.

task_repair2.png

Run

Run

Run Panel

  1. Select the Run panel.
  2. From the REPAIR category chooser select Add Metamodel points.

  +   Push the Run button.

  1. From the REPAIR category chooser select Run jobs.

  +   Push the Run button.

  1. From the REPAIR category chooser select Extract results.

  +   Push the Run button.

  1. From the REPAIR category chooser select Build Metamodels.

  +   Push the Run button.

  1. From the REPAIR category chooser select Optimize.

  +   Push the Run button.

run_repair_feature1.png

Metamodel Task

Metamodel Task

Metamodel-based Optimization Task

  1. From the main menu bar select Task → Metamodel-based Optimization.
task_repair2.png

Verification

Verification

Verification Run

  1. Select the Run panel.
  2. Check the Clean Start from iteration check box.
  3. Enter 2 in the text box as iteration to begin with.
  4. Push the Run button

This step performs the optimization and the verification run of the predicted optimum point (known as Iteration 2).

clean_start_it_22.png

Com-file

Com-file

The created command file may look like this:

"Optimization Problem"
$ Created on Fri Jan  4 15:46:29 2008
solvers 1
responses 5
$
$ NO HISTORIES ARE DEFINED
$
$
$ DESIGN VARIABLES
$
variables 2
 Variable 'tbumper' 3
  Lower bound variable 'tbumper' 1
  Upper bound variable 'tbumper' 5
 Variable 'thood' 1
  Lower bound variable 'thood' 1
  Upper bound variable 'thood' 5

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

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$      SOLVER "1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
$ DEFINITION OF SOLVER "1"
$
 solver dyna960 '1'
  solver command "/home/prak1/LS-DYNA/ls971_s_7600_1224_ia32_redhat90"
  solver input file "/home/prak1/LS-OPT/beispiele/crash_optimization/files/quadratic2/main.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver order quadratic
  solver experiment design dopt
$ ------ Job information ------
  solver concurrent jobs 1
$
$ RESPONSES FOR SOLVER "1"
$
 response 'Disp2' 1 0 "BinoutResponse -res_type Nodout  -cmp x_displacement -id 432 -select TIME "
 response 'Disp1' 1 0 "BinoutResponse -res_type Nodout  -cmp x_displacement -id 167 -select TIME "
 response 'MaxAccel' 1 0 "BinoutResponse -res_type Nodout  -cmp x_acceleration -id 167 -select MAX -start_time 0.0000 -filter SAE  -filter_freq 60.0"
 response 'MASS' 1 0 "DynaMass 2 3 4 5 MASS"
 response 'HIC' 1 0 "BinoutResponse -res_type Nodout  -cmp HIC15 -gravity 9810.0  -units S -id 432"

composites 1
$
$ COMPOSITE RESPONSES
$
 composite 'Intrusion' type weighted
  composite 'Intrusion' response 'Disp2' -1 scale 1
  composite 'Intrusion' response 'Disp1' 1 scale 1
$
$ OBJECTIVE FUNCTIONS
$
 objectives 1
 objective 'HIC' 1
$
$ CONSTRAINT DEFINITIONS
$
 constraints 1
 constraint 'Intrusion'
  upper bound constraint 'Intrusion' 550
$
$ JOB INFO
$
 concurrent jobs 1
 iterate param design 0.01
 iterate param objective 0.01
 iterate param stoppingtype or
 iterate 1
STOP

Results

Document Actions

Results

Simulation Points

Simulation Points

View the simulation points in the design space

Open the LS-OPT Viewer.

  1. For Type of Plot select Tradeoff from the category chooser.
  2. From X-Axis Entity select Variables → thood.
  3. From Y-Axis Entity select Variables -> tbumper.

 

entity1.png

This can also be done in 3 dimensions.

  1. For Type of Plot select Metamodel from the category chooser.
  2. Select the Points tab.
  3. Choose the Iterations you want to display.
metamodel_points1.png

Accuracy

Accuracy

The accuracy of the response surface.

 

 RMS ErrorR2 Indicator
HIC28.56410.9810
Disp23.8060.9934

The results can either be found in the LS-OPT Viewer or the lsopt_output file.

Start LS-OPT Viewer

  1. Select Opt History for Type of Plot.
  2. Select the response Disp2.
  3. Choose RMS Error for Value to Plot.

 

→ A small RMS error together with a R2 value ~1 indicates low noise and good fit for the response.

accuracy_view1.png

Open the lsopt_output.x file

where x is the 'Extract Results' run from the Repair Task, e.g. x=5

Search for 'Approximation' to find the appropriate values for the root mean square error (RMS error) or the R2 indicator.

accuracy_file1.png

 

Linear vs. Quadratic

Linear vs. Quadratic

The improvement of the optimal design (comparison between linear and quadratic approximation).

 

 

 

LINEAR

(final result)

QUADRATIC

(final result)

 PredictedComputedPredictedComputed
thood 1.546 1.666
tbumper 5 3.697
HIC38126.2113.3169.8
Mass0.65650.65640.60430.6043
Intrusion550550.5550548.9

→ As expected the quadratic approximation gives already after one iteration a better prediction for the ojective function (HIC) than the linear approximation.

Max. Constr. Violation

Max. Constr. Violation

Study the maximum constraint violation history.

 

Maximum Constraint Violation

  1. Select Opt History for Type of Plot.
  2. Choose Max Constr. Violation.

 

→ The constraint is not violated after the first iteration.

max_constr_violation1.png

Download

Download

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