Point MSE
A composite MSE (Mean Square Error) function is used in order to apply parameter identification with simple target values.
Solution with LS-OPTui
Solution with LS-OPTui
Strategy
Strategy
Choose a Strategy
Select the Strategy panel.- Switch the radio button of the section “Strategy for Metamodel-based Optimization” to "Sequential with Domain Reduction (SRSM)".
Solvers
Solvers
Solvers Panel
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Variables
Variables
Define the Variables
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Histories
Histories
Extract History
Define z-slave-force on interface 1
This will extract the Z-slave history Force from the binary LS-DYNA output database RCFORC. |
Responses
Responses
Define the Responses
Define force response at 2 ms
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Define force response at 4 ms
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Define force response at 6 ms
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Define force response at 8 ms
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Define composite function
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Objective
Objective
Objective
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Run
Run
Run the Optimization
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Com-file
Com-file
The created command file may look like this:
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Command file "com.mse_point"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Generated using LS-OPT Version 4.1
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"Optimization Problem"
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$ Created on Fri Jan 7 16:21:49 2011
solvers 1
responses 4
histories 1
$
$ DESIGN VARIABLES
$
variables 2
Variable 'YMod' 7.e5
Lower bound variable 'YMod' 5.e5
Upper bound variable 'YMod' 2.e6
Variable 'Yield' 1500.
Lower bound variable 'Yield' 500.
Upper bound variable 'Yield' 2.e3
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ OPTIMIZATION METHOD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
Optimization Method SRSM
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ SOLVER "Case1"
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
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$ DEFINITION OF SOLVER "Case1"
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solver dyna960 'Case1'
solver command "ls971_R4_2"
solver input file "foam1.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 ------
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$ WARNING - NO RESPONSES DEFINED FOR SOLVER "Case1"
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$
$ HISTORIES FOR SOLVER "Case1"
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history 'Force' "BinoutHistory -res_type RCForc -cmp z_force -id 1 -side SLAVE"
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$ RESPONSE EXPRESSIONS FOR SOLVER "Case1"
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response 'F1_1' expression {Force(0.002)}
response 'F2_1' expression {Force(0.004)}
response 'F3_1' expression {Force(0.006)}
response 'F4_1' expression {Force(0.008)}
composites 1
$
$ COMPOSITE RESPONSES
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composite 'MSE' type standardMSE
composite 'MSE' response 'F1_1' 10000
composite 'MSE' response 'F2_1' 13000
composite 'MSE' response 'F3_1' 15000
composite 'MSE' response 'F4_1' 17000
$
$ OBJECTIVE FUNCTIONS
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objectives 1
objective 'MSE' 1
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$ THERE ARE NO CONSTRAINTS!!!
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constraints 0
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$ PARAMETERS FOR METAMODEL OPTIMIZATION
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Metamodel Optimization Strategy DOMAINREDUCTION
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iterate param design 0.01
iterate param objective 0.01
iterate param stoppingtype and
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$ OPTIMIZATION ALGORITHM
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Optimization Algorithm hybrid simulated annealing
Use GSA
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$ JOB INFO
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iterate 5
STOP
Results
Results
Accuracy
Accuracy
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Start the LS-OPT Viewer by selecting the View tab and
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→ Good approximation: low distance between predicted (black line) and computed (green points) values. The RMS Err, Sqrt PRESS and R-sq coincide with the plot. |
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→The predicted (black line) values deviate from the computed (green points) values slightly, but they can still be considered as good approximation. |
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Computed vs Predicted in Opt History plot:
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→ Good approximation of optima: The computed values (red points) coincide with the predicted values (black line). |
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→ Asymptotical approximation of optima: It shows only a little difference between computed values (red points) and predicted values (black line) at the last two iterations. |
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Convergence
Convergence
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Convergence of the Variable YMod
→ Since we have applied the strategy Sequential with Domain Reduction, the optimal values of the variable (red line) at each iteration varies within the reduced ranges of the domain (blue lines). → The variable is rather insignificant (see ANOVA) and therefore isn't converged. | ![]() |
Convergence of the Variable Yield
→ The variable is important for the optimization (see ANOVA) and appears to be converged.
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Confidence Intervals
Confidence Intervals
The Confidence Intervals can be found in the lsopt_report file.
The Confidence Intervals are located at the end of the file.
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Alternatively, we can directly open the lsopt_report file from the main directory with an editor and scroll to the end to find the Confidence Intervals of YMod and Yield. | ![]() |
Sensitivities
Sensitivities
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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). |
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ANOVA
The ANOVA (analysis of variance) result can be displayed as follows in the LS-OPT Viewer:
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→ For response F1_1 the variable YMod is rather insignificant and the variable Yield is important. |
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→ For response F2_2 the variable YMod is rather insignificant and the variable Yield is more important. |
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GSA/Sobol
→ We get the same result by using GSA/Sobol. The variable YMod has hardly influence on F1_1 and the variable Yield affects F1_1 exclusively. |
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→ The variable YMod has only a little influence on F1_1 and the variable Yield affects F1_1 in a great measure. |
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Download
Download
The complete data set (input and command files) is available for download:
For Linux
For Windows










