Linear Response Surface with Strategy Single Stage

A first assessment of the design: Strategy "Single Stage" (one iteration) with linear response surface.

Solution with LS-OPT

Strategy

Select a Strategy for Metamodel-based Optimization

Select the Strategy tab.
Be sure that the radio button of the section “Strategy for Metamodel-based Optimization” is switched to "Single Stage"

Solver

Define Solver and Input File

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

Variables

Define the Variables

Select the Variables tab. The variables are already defined in the input file main.k using *PARAMETER (see below) and therefore cannot be deleted.
For Type of tbumper switch the menu to Variable.
Enter 1 for the Minimum of the variable.
Enter 5 for the Maximum of the variable.
For Type of thood switch the menu to Variable.
Enter 1 for the Minimum of the variable.
Enter 5 for the Maximum of the variable.

Sampling

Choose the sampling

Select the Sampling tab.
For METAMODEL select from the list Polynomial.
For Order of the Polynomial model we take Linear.
Make sure that the Point Selection is set to D-Optimal, which is recommended.

Responses

Define the Responses

Define x-displacement of node 432

Select the Responses tab.
From the possible response types select: NODOUT.
For Node ID enter 432.
For Component select from the list Displacement.
For Direction select X Component.
For Response Name enter Disp2.
Push the Add button.

Define x-displacement of node 167

Stay in the Responses tab.
From the possible response types select: NODOUT.
For Node ID enter 167.
For Component select Displacement from the list.
For direction select X Component.
For Response Name enter Disp1.
Push the Add button.

Define x-acceleration of node 167

From the possible response types select: NODOUT.
For Node ID enter 167.
For Component select Acceleration from the list.
Select the X Component.
From Select choose Maximum Value.
Enter 0.0 in the From time field (this will choose the max. value of acceleration in x-direction during the crash).
For Filtering choose SAE Filter.
Enter 60.0 for Frequency.
For Response Name enter MaxAccel.
Push the Add button.

Define head injury coefficient of node 432

From the possible response types select: Injury Criteria.
For Node ID enter 432.
For Component select from the list Head Injury Coef.
For Time interval select 15ms.
For Time unit select s.
For Length unit select mm.
For Response Name enter HIC.
Push the Add button.

Define mass responses for structural components

From the possible response types select: MASS.
In the List of Parts enter 2.
Push the (Add) > button.
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).
For Response Name enter MASS.
Push the Add button.

Define composite response intrusion of Disp1 and Disp2

From the possible response types select: Composite.
For Composite Components select Responses.
From Response select Disp2.
For Weight enter -1.0.
From Response select Disp1.
For Weight enter 1.0.
For Composite Function Type select Weighted.
For Response Name enter Intrusion.
Push the Add button.

Objective

Select the Objective tab.
From Response select HIC as the objective.
For Weight leave the default 1. If you have several objective functions, you may assign weight to each one according to their importance.

Constraints

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

Run

Run LS-OPT

Select the Run tab.
Push the Run button. (Save the project as com.linear.single)

Com-file

The created command file may look like this:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.linear.single"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Optimization Problem"
$
$ Created on Wed Dec  8 10:17:55 2010
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 "ls971_R4_2"
  solver input file "main.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 ------
  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 60.0000"
 response 'HIC' 1 0 "BinoutResponse -res_type Nodout  
  -cmp HIC15  -units S -lengthunits MM -id 432"
 response 'MASS' 1 0 "DynaMass 2 3 4 5 MASS"

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
$
$ PARAMETERS FOR METAMODEL OPTIMIZATION
$
 Metamodel Optimization Strategy SINGLESTAGE
$
  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 0
STOP

Results

Accuracy

What is the approximation error of the result?

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

LS-OPT Viewer

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

Select under Metamodel the item Accuracy
From Entity select Responses → HIC.
We can find RMS Error and R² (R-sq) above the plot.

→ The coefficient of determination (R²) is high (=0.922), but the RMS Error may need further improvement, e.g. more iterations or selection of a more suitable metamodel (e.g. Feedforward Neural Network or Radial Basis Function Network). Nevertheless for a raw estimate the result may be considered as acceptable.

lsopt_output File

Open the lsopt_output file with a text editor.
Search in the file for "Approximating".
Find the appropriate values for root mean square error (RMS Error) and R².

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

	Mean Response Value	RMS Error	R²
MASS	0.7742	0	1
Disp1	-159.3846	2.0286 (1.27%)	0.4790
Disp2	-694.5753	5.5459 (0.80%)	0.9896
HIC	275.72	76.5620 (27.77%)	0.9224

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), e.g for the response HIC you may find:

LS-OPT Viewer

ANOVA

Restart the LS-OPT Viewer and select under Metamodel the item Sensitivity
Select Linear ANOVA in the new window.
From Response select HIC.
Sort the variables according to their significance for HIC

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

GSA/Sobol

Select GSA/Sobol.
From Response select HIC.
Sort the variables according to their significance for HIC.

→ We come to the same conclusion by using GSA. The influence of thood on HIC is 84.9%, larger than that of tbumper (15.1%).

lsopt_output File

Open the lsopt_output file with a text editor.
Search in the file for "Ranking".
Find out the importance of each of the variables for the response.

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:

LS-OPT Viewer

Restart the LS-OPT Viewer and select under Optimization the item History.
From the left side of the window select Responses → HIC.
For Value to Plot select Value.
If you want to see the accurate values, simply click nearby the red points. There appears a table, which states all the computed and predicted data, e.g. computed HIC vs. predicted HIC.

→ 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_view1.png

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

comp.vs.pred_view2.png

lsopt_output File

Open the lsopt_output file with a text editor.
Search in the file for "Evaluating Starting Design" and scroll a bit more forward.
You may find both the initial values of HIC, computed vs. predicted.
Search now in the file for "F I N A L".
The final values of HIC (computed and predicted) after one iteration are available.

comp.vs.pred_file1.png

comp.vs.pred_file2.png

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

	Start		First Iteration
	Predicted	Computed	Predicted	Computed
thood		1		1.548
tbumper		3		5
MASS	0.4103	0.4103	0.6569	0.6569
Intrusion	577.3	575.7	550	550.5
HIC	74.57	68.02	38.63	126.5
Max. Constr. Violation	27.27	25.68	1.162e-4	0.4658

Sections

Personal tools

Linear Response Surface with Strategy Single Stage

Solution with LS-OPT

Solution with LS-OPT

Strategy

Strategy

Select a Strategy for Metamodel-based Optimization

Solver

Solver

Define Solver and Input File

Variables

Variables

Define the Variables

Sampling

Sampling

Choose the sampling

Responses

Responses

Define the Responses

Objective

Objective

Objective

Constraints

Constraints

Constraints

Run

Run

Run LS-OPT

Com-file

Com-file

Results

Results

Accuracy

Accuracy

What is the approximation error of the result?

LS-OPT Viewer

lsopt_output File

Sensitivities

Sensitivities

Which variable appears to be the most important?

LS-OPT Viewer

lsopt_output File

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.

LS-OPT Viewer

lsopt_output File

Download

Download