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Linear RS: one iteration

A first assessment of the design: one iteration with a linear response surface.

Solution with LS-OPT

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Solution with LS-OPT

Solver

Solver

Define Solver and Input File

  1. Select the Solvers tab.
  2. For Command specify the dyna executable ls971_single.
  3. For Input File browse the file main.k.
  4. For Name of Analysis Case enter 1.
  5. Push the Add button.
 solver_specify1.png 

 

Variables

Variables

Define the Variables

  1. Select the Variables tab.
  2. For Type of tbumper switch the chooser to Variable.
  3. Enter 1 for the Minimum of the variable.
  4. Enter 5 for the Maximum of the variable.
  5. For Type of thood switch the chooser to Variable.
  6. Enter 1 for the Minimum of the variable.
  7. Enter 5 for the Maximum of the variable.

var_neu.png

 

Responses

Responses

Define the Responses

  1. Select the Responses tab.
  2. From the possible response types select: NODOUT.
  3. For Node ID enter 432.
  4. For Component select from the list Displacement.
  5. For Direction select X Component.
  6. For Response Name enter Disp2.
  7. Push the Add button.
  8. Stay in the Responses tab.
  9. From the possible response types select: NODOUT.
  10. For Node ID enter 167.
  11. For Component select Displacement from the list.
  12. For direction select X Component.
  13. For Response Name enter Disp1.
  14. Push the Add button.
  15. From the possible response types select: NODOUT.
  16. For Node ID enter 167.
  17. For Component select Acceleration from the list.
  18. Select the X Direction.
  19. From Select choose Maximum Value.
  20. Enter 0.0 in the From time field (this will choose the max. value of acceleration in x-direction during the crash).
  21. For Filtering choose SAE Filter.
  22. Enter 60.0 for Frequency.
  23. For Response Name enter MaxAccel.
  24. Push the Add button.
  25. From the possible response types select: NODOUT.
  26. For Node ID enter 432.
  27. For Component select from the list Injury Coefficient.
  28. Select the Head Injury Coefficient (15ms).
  29. For Gravitational Acceleration select Seconds.
  30. Enter 9810.0 for Gravitational Acceleration.
  31. For Response Name enter HIC.
  32. Push the Add button.
  33. From the possible response types select: MASS.
  34. In the List of Parts enter 2.
  35. Push the (Add) > button.
  36. Repeat the previous steps and create this list of parts:
    List of Parts:
    2
    3
    4
    5

    Note The part ID numbers can be found in Fig. 1(b): bumper (2), hood (3), front (4) and underside (5).
  37. For Response Name enter MASS.
  38. Push the Add button.
  39. From the possible response types select: Composite.
  40. For Composite Components select Responses.
  41. From Response select Disp2.
  42. For Weight enter -1.0.
  43. From Response select Disp1.
  44. For Weight enter 1.0.
  45. For Composite Function Type select Weighted.
  46. For Response Name enter Intrusion.
  47. Push the Add button.

resp_disp21.pngresp_disp11.pngresp_maxaccel1.pngresp_HIC2.pngresp_mass1.pngresp_comp_intru1.png

 

Objective

Objective

Objective

  1. Select the Objective tab.
  2. From Response select HIC as the objective.
  3. For Weight leave the default 1.

resp_objective1.png

 

Constraints

Constraints

Constraints

  1. Select the Constraints tab.
  2. From Response select Intrusion as the constraint..
  3. For Lower Bound accept the default -inf.
  4. For Upper Bound enter 550.

resp_constraint1.png

 

Run

Run

Run LS-OPT

  1. Select the Run tab.
  2. For Number of Iterations enter 1.
  3. Push the Run button. (Save the project as com.linear)
 run1.png

 

Com-file

Com-file

The created command file may look like this:

"Optimization Problem"
$ Created on Wed Jan  2 14:00:30 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/lin_1iteration/main.k"
  solver check output on 
  solver compress d3plot off 
$ ------ Pre-processor --------
$   NO PREPROCESSOR SPECIFIED
$ ------ Metamodeling ---------
  solver order linear
  solver experiment design dopt
$ ------ Job information ------
$
$ 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
$
 iterate param design 0.01
 iterate param objective 0.01
 iterate param stoppingtype or
 iterate 1
STOP

Results

Document Actions

Results

Accuracy

Accuracy

What is the approximation error of the result?

The approximation error indicators (predict the meta model accuracy of the results) can be either found in the lsopt_output fie or visualized in the LS-OPT Viewer, e.g. for the response HIC you may find:

 

lsopt_output file

  1. Start the lsopt_output file.
  2. Search in the file for "Approximating".
  3. Find the appropriate values for root mean square error (RMS Error) and R2.
acc_responses_file1.png

LS-OPT Viewer

Start the LS-OPT Viewer (Select the View tab) and

  1. Select Opt. History.
  2. From Entity to Monitor select Responses → HIC.
  3. Select the R2 Error chooser.

→ The coefficient of determination (R2) is high, but the RMS may need further improvement, e.g. more iterations or selection of a more suitable metamodel (Neural Network). Nevertheless for a raw estimate the result may be considered as acceptable.

acc_responses_view1.png

 

With the same procedure you may find the RMS Error and R2 of the other responses:

 

Baseline Value

RMS Error

R2

MASS

0.7742

0

1

Disp1

159.3388

1.9987 (12.5%)

0.4880

Disp2

-694.2894

5.8495 (0.84%)

0.9884

HIC

275.31

76.0208 (27.61%)

0.9229

 

 

ANOVA

ANOVA

Which variable appears to be the most important?

The significance of a variable for a response can be illustrated with ANOVA (analysis of variance), e.g for the response HIC you may find:

 

lsopt_output file

  1. Start the lsopt_output file.
  2. Search in the file for "Ranking".
  3. Find out the importance of each of the variables for the response.

 

anova_file1.png

LS-OPT Viewer

  1. Start the LS-OPT Viewer.
  2. Select  ANOVA from the Type of Plot chooser.
  3. From Response select HIC.

 

 

 

→ For the response HIC the variable thood is important, while the variable tbumper is rather insignificant.		anova_view1.png

 

Computed vs. Predicted

Computed vs. Predicted

Study the change in each of the variables/responses and the accuracy of the predicted compared to the computed result.

The accuracy of the starting point and the approximate optimum points after the first iteration can be illustrated, e.g. for the response HIC you may find:

 

lsopt_output file

The change in each of the variables and responses can be found in the lsopt_output file.

comp.vs.pred_file.png

LS-OPT Viewer

  1. Start the LS-OPT Viewer.
  2. Select the Opt. History chooser.
  3. From Entity to Monitor select Responses → HIC.
  4. For Value to Plot select Value.

 

→ You can find out the appropriate values for the predicted (black) and the computed (red points) results. More iterations may lead to a better predictive capability.

 

comp.vs.pred_view2.png

(Note the range of the values when assessing the accuracy)

 

With the same procedure you may find the other values of the variables and the responses:

 StartFirst Iteration
 PredictedComputedPredictedComputed
thood 1 1.546
tbumper 3 5
MASS0.41030.41030.65650.6564
Intrusion576.9575.7550550.5
HIC74.7267.9438126.2
Max. Constr. Violation26.8625.672.2e-70.5287

 

Download

Download

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