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Linear RS: ten iteration

Automated iterative process using a linear (response surface) approximation.

Solution with LS-OPTui

Solution with LS-OPTui

Run

Run

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

 

Setup

  1. Select the Run panel.
  2. Select a tolerance of 1% to be satisfied by both the design and objective changes.
  3. For Number of iterations enter 10.
  4. Push the Run button.

 

run_10-lin3.png

Com-file

Com-file

The created command file may look like this:

"Optimization Problem"
$ Created on Fri Dec 21 08:58:41 2007
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_10iterations/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 10
STOP

Results

Results

Convergence

Convergence

Variables

 Fig. 1(a) shows:
  • The optimization history of the variable thood.
  • The development of the variable value (red line)
  • How the range of thood (set to 1...5 at the beginning) decreases after every iteration (blue lines).
  • This variable is important (see ANOVA) to reach the bounds of objective and constraint and seems to be converged.

history_thood1.png

Fig. 1(a)

Fig. 1(b)  shows:
  • The optimization history of the variable tbumper.
  • The development of the variable value (red line)
  • How the range of tbumper (set to 1...5 at the beginning) decreases after every iteration (blue lines).
  • This variable is rather insignificant (see ANOVA) and therefor differs between the iteration without affecting the objective.

history_tbumper1.png

Fig. 1(b)

As you can see in the figure the value of thood doesn't change a lot between iteration 3 and 4. The tolerance for termination of 1% is reached and this will make LS-OPT stop the optimization process after 4 iterations although 10 iterations were specified in the Run panel.

 

 

Responses

Fig. 2(a) shows:
  • The predicted result (black line) of the HIC response for every iteration.
  • The computed result (red points) of the HIC response for every iteration.
  • The convergence trend of the HIC response.

history_hic1.png

Fig. 2(a)

Fig. 2(b) shows:
  • The predicted result (black line) of the Intrusion constraint for every iteration.
  • The computed result (red points) of the Intrusion constraint for every iteration.
  • The constraint upper bound is reached (blue line).

history_intrusion1.png

Fig. 2(b)

 

Accuracy

Accuracy

HIC

 

RMS Error

The root mean square error of the HIC response can be found at Type of Plot → Opt History in the LS-Opt Viewer. Note the range to find the appropriate values.

 

 

rms_hic1.png

R2 Indicator

The R2 Indicator of the HIC response for every iteration.

 

→ A small RMS error and a coefficient of determination (R2) ~1 indicates good fit (see table below).

r2_hic1.png

 

 

 RMS Error R2 Indicator Description
Small~1High variable detection: low noise, good fit.
Small~0Low noise/good fit, small gradient.
Large~1High variable detection with noise.
Large~0Lack of fit, perhaps accompanied by noise. Must shrink the move limits.

 

 

Download

Download

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