Post on 02-Apr-2015
Tutorial 1: Sensitivity analysis of an
analytical function
2 Tutorial 1: Sensitivity Analysis
Example: Analytical nonlinear function
• Additive linear and nonlinear terms and one coupling term
• Contribution to the output variance (reference values):X1: 18.0%, X2: 30.6%, X3: 64.3%, X4: 0.7%, X5: 0.2%
3 Tutorial 1: Sensitivity Analysis
Task description
• Parameterization of the problem
• Defining DOE scheme
• Evaluation of DOE designs
• Statistical post-processing of DOE
• Approximation post-processing of DOE
• Defining MOP search algorithm
• Evaluation of MOP workflow
• Statistical post-processing of MOP
• Approximation post-processing of MOP
• Reload results in Result Monitoring
• Use Matlab as solver
• Use Excel as solver
• Use Excel plug-in to export data in optiSLang format
4 Tutorial 1: Sensitivity Analysis
Project manager
1. Open the project manager2. Define project name3. Create a new project directory4. Copy optiSLang examples/Coupled_Function
into project directory
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5 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Start a new parametrize workflow (double click)
2. Define workflow name
3. Create a new problem specification
4. Enter problem file name
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6 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Click “open file” icon in parametrize editor2. Browse for the SLang input file coupled_function.s 3. Choose file type as INPUT
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7 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Mark value of X1 in the input file
2. Define X1 as input parameter
3. Enter parameter name
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8 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Open parameter in parameter three2. Enter lower and upper bounds3. Set as default for other variables
and repeat for X2 … X5
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9 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
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1. Click “open file” icon in parametrize editor2. Browse for the SLang output file coupled_solution.s 3. Choose file type as OUTPUT
10 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Mark output value in editor2. Define Y as output parameter3. Enter parameter name 4. Close parametrize editor
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11 Tutorial 1: Sensitivity Analysis
Parameterization of the problem
1. Check parameter overview for inputs2. Check parameter overview for outputs3. Close overview
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12 Tutorial 1: Sensitivity Analysis
Define Design Of Experiments (DOE)
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1. Start a new DOE workflow (double click)2. Define workflow name3. Define workflow identifier (working directory)4. Enter problem file name
13 Tutorial 1: Sensitivity Analysis
Define Design Of Experiments (DOE)
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1. Enter solver call (slang –b coupled_function.s)2. Enter number of parallel runs3. Choose if design directories should be deleted 4. Start DOE workflow
14 Tutorial 1: Sensitivity Analysis
Generate DOE scheme
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1. Choose Latin hypercube sampling2. Enter number of samples (50…100)3. Generate samples4. Close dialog and show samples
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15 Tutorial 1: Sensitivity Analysis
Generate DOE scheme
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1. Start evaluation of samples
16 Tutorial 1: Sensitivity Analysis
Statistics post-processing
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1. Linear correlation matrix (In-In, In-Out, Out-In and Out-Out)2. Quadratic correlation matrix (total values or difference to linear)3. Histogram of input/output (select variable in 1.)4. Anthill plot (select variables in 1.)5. CoD/CoI values (linear: select in 1., quadratic: select in 2.)6. Ranked linear or quadratic correlations of single response
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17 Tutorial 1: Sensitivity Analysis
Statistics post-processing
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1. Switch between CoD/CoI visualization2. Extended correlation matrix (optiSLang 3.2)
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18 Tutorial 1: Sensitivity Analysis
Statistics post-processing
1. Statistical properties of single variable2. Traffic light plot of response for given
safety & failure limit (optiSLang 3.2)
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19 Tutorial 1: Sensitivity Analysis
Statistics post-processing
1. Show development of correlation coefficients
2. Show design table
3. Export DOE to Excel
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20 Tutorial 1: Sensitivity Analysis
Statistics post-processing
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1. Principal Component Analysis (PCA) of linear correlations2. Parallel coordinates plot to show designs having an input/output within certain
lower and upper bounds
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21 Tutorial 1: Sensitivity Analysis
Statistics post-processing
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1. Significance filter for CoD/CoI2. Manual filter for CoD/CoI
22 Tutorial 1: Sensitivity Analysis
Approximation post-processing
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1. Anthill plot of parameter 1 and the response2. Contour plot of approximation function in terms of parameter 1 and 2
(remaining are set to their mean) vs. the response3. Surface plot of approximation function4. Details about approximation settings and properties
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23 Tutorial 1: Sensitivity Analysis
Approximation post-processing
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• Manual approximation settings:• Parameter subspace• Polynomial or MLS (exponential or regularized)• Basis polynomial, constant or density dependent influence• Transformation settings
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24 Tutorial 1: Sensitivity Analysis
Meta-Model of Optimal Prognosis (MOP)
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1. Start a new MOP workflow (double click)2. Define workflow name3. Define workflow identifier (working directory)4. Choose DOE result file5. Choose optional problem file
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25 Tutorial 1: Sensitivity Analysis
Meta-Model of Optimal Prognosis (MOP)
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1. CoP settings (sample splitting or cross validation)2. Investigated approximation models3. CoP - accepted reduction in prediction quality to simplify model4. Filter settings5. Selection of inputs and outputs
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26 Tutorial 1: Sensitivity Analysis
Meta-Model of Optimal Prognosis (MOP)
• optiSLang console gives detailed information about the investigated models and obtained optimal CoP values
27 Tutorial 1: Sensitivity Analysis
Meta-Model of Optimal Prognosis (MOP)
• Approximation post-processing automatically shows surface and contour plot of the two most important variables vs. the response
• CoP values for single variables are shown
28 Tutorial 1: Sensitivity Analysis
Overview of different significance values
CoD, k=5 (all inputs)
CoI, k=5 (all inputs)
CoI, k=3 (manual)
CoP, k=3 (automatic)
Reference
Full model 75% 75% 74% 97% 100%
X1 2% 14% 14% 18% 18%
X2 18% 30% 28% 31% 31%
X3 41% 34% 39% 62% 64%
X4 0% 0% - - 0.7%
X5 0% 1% - - 0.2%
• MOP/CoP close to reference values (detects optimal subspace automatically, represents nonlinear and coupling terms)
29 Tutorial 1: Sensitivity Analysis
Reload DOE or MOP in Result Monitoring
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1. Start a new Results Monitoring workflow (double click)2. Define workflow name3. Choose DOE or MOP result file4. Start Post-Processing
Tutorial 1: Use Matlab as solver
31 Tutorial 1: Sensitivity Analysis
Use Matlab as solver
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Matlab input file: coupled_function.m1. Input parameter definition2. Function evaluation3. Writing the result file4. Exit Matlab execution!
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32 Tutorial 1: Sensitivity Analysis
Use Matlab as solver
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Call Matlab from Windows: matlab_windows.bat1. Disable splash2. Disable desktop3. Disable java virtual machine4. Minimize remaining command window5. Wait until Matlab is terminated
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33 Tutorial 1: Sensitivity Analysis
Use Matlab as solver
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Call Matlab from Linux: matlab_linux.sh1. Set empty display2. Disable splash3. Disable desktop4. Disable java virtual machine5. Wait until Matlab is finished
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34 Tutorial 1: Sensitivity Analysis
Use Matlab as solver
1. Parameterize inputs in optiSLang from coupled_function.m2. Parameterize output from coupled_solution.txt
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35 Tutorial 1: Sensitivity Analysis
Use Matlab as solver
1. Open new DOE workflow and select “Run a script file”2. Choose the batch script and start DOE process
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Tutorial 1: Use Excel as solver
37 Tutorial 1: Sensitivity Analysis
Use Excel as solver
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1. Generate Excel file with all inputs in one row and all outputs in one column
2. Mark first input as inputParams3. Mark first output as outputParams
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38 Tutorial 1: Sensitivity Analysis
Use Excel as solver
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1. Show Macros2. Enter Macro name3. Create Macro
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39 Tutorial 1: Sensitivity Analysis
Use Excel as solver
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1. In Visual Basic environment use import file feature 2. Import predefined macro file inout.bas
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40 Tutorial 1: Sensitivity Analysis
Use Excel as solver
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1. inout module should be shown in the module list2. Delete the empty default module
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41 Tutorial 1: Sensitivity Analysis
Use Excel as solver
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The visual basic macro1. Input file name2. Output file name
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42 Tutorial 1: Sensitivity Analysis
Use Excel as solver
Java script to run Excel in batch mode1. Excel file name
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43 Tutorial 1: Sensitivity Analysis
Use Excel as solver
Batch script to run Excel java script1. Call of java script with full path,
modify path if necessary!
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44 Tutorial 1: Sensitivity Analysis
Use Excel as solver
1. Parameterize inputs in optiSLang from input.txt2. Parameterize output from output.txt
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45 Tutorial 1: Sensitivity Analysis
Use Excel as solver
1. Open new DOE workflow and select “Run a script file”2. Choose the batch script and start DOE process
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Tutorial 1: Use Excel plug-in
47 Tutorial 1: Sensitivity Analysis
Use Excel plug-in
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1. Start the plug-in in Excel 2. Mark input data including parameter names3. Check parameter names and data array
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48 Tutorial 1: Sensitivity Analysis
Use Excel plug-in
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1. Mark output data including parameter names2. Check parameter names and data array
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49 Tutorial 1: Sensitivity Analysis
Use Excel plug-in
1. Choose design numbers2. Finish and save data in optiSLang *.bin file3. Open *.bin in result monitoring workflow
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