Sensitivity Analysis of a Coupled Function

This tutorial allows you to complete a sensitivity analysis of the following analytical nonlinear function:

The function has 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%

 

Task Description

This tutorial demonstrates how to do the following:

  • Generate a solver chain using text parametrization and solver call by Windows script

  • Define the parameters and responses

  • Specify parameter properties

  • Define the Design of Experiment (DOE) scheme

  • Perform a sensitivity analysis including Metamodel of Optimal Prognosis (MOP)

  • Extend the data base by the adaptive MOP

  • Remove outliers and rebuild the MOP

 

Preparation

Before you start the tutorial, download the coupled_function_sensitivity zip file from here , and extract it to your working directory.

 

Tutorial Steps

To set up and run the tutorial, perform the following steps:

 

Creating a New Project

  1. Start optiSLang.

  2. Create a new empty project.

 

Starting the Solver Wizard

  1. From the Wizards pane, drag the Solver wizard to the Scenery pane and let it drop.

  2. From the solver list, click Common text based.

 

Selecting the Input File

  1. In the Select input file dialog box, browse to the coupled_function_sensitivity folder and select coupled_function.s.

  2. Click Open.

 

Defining the Input Parameters

  1. In the text editor, highlight lines 20-24.

  2. Click AutoParametrize.

    All possible values are marked.

  3. Change the base parameter name to X%01d.

    Parameter names are automatically defined (the first being X1 and so on).

  4. To move to the first value, click  .

  5. To register the parameter, click Add.

  6. Repeat this procedure for parameters X2 to X5.

  7. Click Next.

 

Editing the Parameter Properties

  1. To highlight all of the parameters in the table, do one of the following:

    • Click the name of the first parameter, press Shift, and then click the name of the parameter the last row.

    • Click the name of the first parameter, then with the mouse key pressed, pull down to the last parameter and release the mouse key.

  2. While still pressing the Shift key, double-click the range numbers in row 5.

  3. Change the lower bound to -3.14 and the upper bound to 3.14.

  4. Press Enter.

    The range of all of the parameters changes to -3.14 and 3.14.

  5. Click Next.

 

Selecting the Output File

  1. In the Choose a file to open dialog box, browse to the coupled_function_sensitivity folder and select coupled_solution.txt.

  2. Click Open.

 

Defining the Response

  1. From the File format list, ensure Plain text file is selected and click OK.

  2. Highlight the response value.

  3. In the Variable Name field, type Y.

  4. To register the value as a response, click Use as response.

  5. Click Next.

 

Defining the Optimization Criteria

  1. Do not adjust or add to the currently displayed values for parameters, responses, and criteria.

  2. Click Next.

 

Importing the Solver Call File

  1. To the right of the Absolute path field, click the orange folder.

  2. Browse to the coupled_function_sensitivity folder and select coupled_function.bat for Windows systems or coupled_function.sh for Linux systems.

  3. Click Open.

  4. Click Next.

 

Creating the Solver Chain Template

  1. Select the Create a template from solver chain check box.

  2. Click Finish.

    The template is displayed in the Templates pane and the system is added to the Scenery pane.

 

Saving and Running the Project

  1. To save the project, click  .

  2. Browse to the location to save the project and type a project name in the File name field.

  3. Click Save.

  4. To run the project, click  .

  5. To review the result, double-click the coupled function system and switch to the Result designs tab.

 

Completing the Sensitivity Wizard

  1. From the Wizards pane, drag the Sensitivity wizard to the head of the solver chain and let it drop.

  2. Do not adjust the values in the Parametrize Inputs table.

  3. Click Next.

  4. Do not adjust or add to the currently displayed values for parameters, responses, and criteria.

  5. Click Next.

  6. Select the Space filling Latin Hypercube Sampling method.

  7. Click Next.

  8. Do not adjust the current postprocessing settings.

  9. Click Finish.

    The sensitivity workflow is displayed on the Scenery pane.

 

Running the Sensitivity Analysis

  1. To save the project, click  .

  2. To start the sensitivity analysis, click  .

    The bar on top of the sensitivity system displays the progress of the analysis. The message log displays the sequence of events.

 

Viewing the MOP Results

  • If the MOP results are not automatically displayed, right-click the MOP node and select Show Postprocessing from the context menu.

    The results show a 3D-subspace-plot of the approximation function depending on the two most important parameters X2and X3.

    The approximation quality in terms of the Coefficient of Prognosis is shown together with the variance contribution of the single variables and indicates, that only X1, X2, and X3are important in this example.

 

Adding an Adaptive Metamodel of Optimal Prognosis System

  1. To increase the data set, drag and drop the Sensitivity wizard onto the head of the Sensitivity system.

  2. Leave the sampling method settings at the default and click Next.

  3. Leave the additional optional settings at the default and click Finish.

    An AMOP system is displayed on the Scenery pane.

    The designs of the first sensitivity system are automatically considered as start designs for the following AMOP using a slot connection.

 

Configuring AMOP Settings

  1. Double-click the AMOP system to open the settings.

  2. On the Adaption tab, select the Show advanced settings check box.

  3. In the Target CoP field, enter 0.99 (set target to 99%).

  4. To save and close the settings, click OK.

 

Running the Project and Viewing AMOP Postprocessing

  1. To save the project, click  .

  2. To run the project, click  .

    The AMOP postprocessing is displayed. You can observe:

    • The Coefficient of Prognosis was increased to 99% in 3 iterations

    • The influence of the individual parameters was changed slightly

    • The AMOP stopped by reaching the maximum number of iterations

 

Deactivating Outliers

The residual plot shows the predicted values (from cross validation) versus the original data values by indicating lower and upper error bounds. Error bounds are obtained from the standard deviation of the error values multiplied with the user defined sigma level. Samples outside the error bounds may be possible outliers.

To deactivate outliers:

  1. Select outliers in the residual plot.

  2. Right-click and select Deactivate from the context menu.

  3. To update the MOP directly in the postprocessing, click   Create and update database.