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Linear Response Surface with Strategy Sequential with Domain Reduction (SRSM)

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

Solution with LS-OPTui

Solution with LS-OPTui

Strategy

Strategy

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

 

  1. Select the Strategy panel. strategy_srsm.png
  2. Switch the radio button of the section Strategy for Metamodel-based Optimization to "Sequential with Domain Reduction (SRSM)".
  3. Select a tolerance of 1% to be satisfied by both the design and objective changes.

 

 

 

 

 

 

 

 

 

 

Solvers

Solvers

  1. Select the Solvers panel. solvers_srsm.png
  2. Make sure that the LS-DYNA command matches the one on your computer.
  3. Click the Replace button, if you've made a change.

 

 

 

 

 

 

 

 

 

 

 

Run

Run

  1. Select the Run panel.
  2. For Number of iterations enter 10.
  3. Push the Run button.

 

run_srsm.png

 

Com-file

Com-file

The created command file may look like this:

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.iterate"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
$
"Small car crash optimization problem: LINEAR"
$
$ Created on Wed Dec 15 13:41:30 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 'Acc_max' 1 0 "BinoutResponse -res_type Nodout  
  -cmp x_acceleration -id 167  -select MAX -filter SAE  -filter_freq 60"
 response 'Mass' 1 0 "DynaMass 2 3 4 5 MASS"
 response 'HIC' 1 0 "BinoutResponse -res_type Nodout  
  -cmp HIC15 -gravity 9810.00000  -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
$
$ PARAMETERS FOR METAMODEL OPTIMIZATION
$
 Metamodel Optimization Strategy DOMAINREDUCTION
$
  iterate param design 0.01
  iterate param objective 0.01
  iterate param stoppingtype or
$
$ OPTIMIZATION ALGORITHM
$
 Optimization Algorithm hybrid simulated annealing
$
$ JOB INFO
$
 iterate 10
STOP

 

Results

Results

Convergence

Convergence

  1. Select the Viewer tab to the LS-OPT Viewer.
  2. Choose History under the category Optimization.

viewer.png

new_plot1.png

We can choose from the left side the objects we want to observe.

 

Select Variables → thood

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 from 1 to 5 at the beginning) decreases after every iteration (blue lines).
  • This variable is important (see Sensitivities) to reach the bounds of objective and constraint and seems to be converged.

history_thood1.png

Fig. 1(a)

Select Variable → tbumper

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.

 

Select Response → HIC

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)

Select Constraint → Intrusion

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 (red line).

history_intrusion1.png

Fig. 2(b)

 

Accuracy

Accuracy

HIC

  1. Restart the LS-OPT Viewer. menubar1.png
  2. Select under Optimization the item History.new_plot2.png

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RMS Error and R2 Indicatoraccuary_hic1.png

  1. From the left side of the window select Responses → HIC.
  2. RMS Error and R2 (R-sq) can be found above the plot.
  3. We can slide to observe the accuary of the result at each iteration.

 

 

 

 

 

 

 

 

  • accuary_hic2.pngAt the last iteration we obtain a result with RMS Error = 4.85 (3.74%) and R2 = 0.823.
  • A small RMS error and a coefficient of determination (R2) ~1 indicates good fit (see table below).

 

 

 

 

 

 

 

 

 

 

 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.

 

 We can find the development of RMS Error and R2 in Optimazation History.

  1. Restart the LS-OPT Viewer. menubar1.png
  2. new_plot1.pngChoose History under the category Optimization.
  3. rms_hic1.pngSelect from the left of the window Response → HIC 
  4. r2_hic1.pngSelect RMS Error. We see that the RMS error is large at the first iterations and falls to a low level since the 5th iteration.
  5. Select R2 Error. The R2 error reaches its maximum near 1 at the 5th iteration, and then decreases again.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Surface

Surface

We can plot the response surface of the metamodel we've built. For example, we want to see the response surface of HIC with respect to the variables thood and tbumper, do it as following:

 

  1. menubar1.pngRestart the LS-OPT Viewer.
  2. new_plot3.pngSelect under Metamodel the item Surface.
  3. Slide to the last iteration.
  4. Select the Setup tab.
  5. Set the response HIC as the z-coordinate, the variables tbumper and thood as the x-coordinate and y-coordinate, respectively.
  6. Pick Constraints to show the constraints.  The feasible region is drawn in green while the infeasible region is drawn in red.
  7. Choose Predicted value. A purple cross will appear somewhere on the surface. You can move it by changing the values of the variables tbumper and thood.
  8. Click Optimum to locate the cross at the optimal point.
  9. Select the Points tab.
  10. Pick Predicted Optimum and Computed Optimum.

plot_panel.png

  • We zoom up the plot and rotate it with mouse by pressing Ctrl at the meantime. The purple cube shows the predicted optimum value, while the red cube above denotes the computed optimum value, which is computed directly through the simulation model.


















surface.png
























 

 

Download

Download

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

For Linux

For Windows