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.
- Select the Strategy panel.
- Switch the radio button of the section “Strategy for Metamodel-based Optimization” to "Sequential with Domain Reduction (SRSM)".
- Select a tolerance of 1% to be satisfied by both the design and objective changes.
Solvers
Solvers
- Select the Solvers panel.
- Make sure that the LS-DYNA command matches the one on your computer.
- Click the Replace button, if you've made a change.
Run
Run
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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
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We can choose from the left side the objects we want to observe.
Select Variables → thood Fig. 1(a) shows:
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Fig. 1(a) |
Select Variable → tbumper Fig. 1(b) shows:
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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:
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Fig. 2(a) |
Select Constraint → Intrusion Fig. 2(b) shows:
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Fig. 2(b) |
Accuracy
Accuracy
HIC
- Restart the LS-OPT Viewer.
- Select under Optimization the item History.
RMS Error and R2 Indicator
- From the left side of the window select Responses → HIC.
- RMS Error and R2 (R-sq) can be found above the plot.
- We can slide to observe the accuary of the result at each iteration.
At 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 | ~1 | High variable detection: low noise, good fit. |
| Small | ~0 | Low noise/good fit, small gradient. |
| Large | ~1 | High variable detection with noise. |
| Large | ~0 | Lack of fit, perhaps accompanied by noise. Must shrink the move limits. |
We can find the development of RMS Error and R2 in Optimazation History.
- Restart the LS-OPT Viewer.
Choose History under the category Optimization.
Select from the left of the window Response → HIC 
Select RMS Error. We see that the RMS error is large at the first iterations and falls to a low level since the 5th iteration.- 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:
Restart the LS-OPT Viewer.
Select under Metamodel the item Surface.
- Slide to the last iteration.
- Select the Setup tab.
- Set the response HIC as the z-coordinate, the variables tbumper and thood as the x-coordinate and y-coordinate, respectively.
- Pick Constraints to show the constraints. The feasible region is drawn in green while the infeasible region is drawn in red.
- 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.
- Click Optimum to locate the cross at the optimal point.
- Select the Points tab.
- Pick Predicted Optimum and Computed Optimum.
- 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.
Download
Download
The complete data set (input and command files) is available for download:
For Linux
For Windows
