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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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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