Creating a User-Defined Approximation Using the Response Surface Model (RSM) Technique

You can create a user-defined approximation using the Response Surface Models (RSM) technique, which uses polynomials of low order (from 1 to 4) to approximate the response of an actual analysis code.

Important: If you are selecting a component that is in a Task Plan, you must select the component using the model explorer.

Related Topics
Response Surface Models
About the Term Selection Methods

  1. Do one of the following:

    • From the Design Gateway,

      1. Select the component for which you want to create an approximation:
        • Select a component on the Sim-flow tab or in the model explorer, and click the Approximations button on the component title bar.
        • Right-click the component on the Sim-flow tab or in the model explorer, and select Approximations.

        The Approximations dialog box appears.

      2. On the right side of the dialog box, click New.

        The Approximation Wizard appears.

    • From the Runtime Gateway,

      1. Select a component on the Sim-flow tab or in the model explorer.
      2. Click the Visual Design tab, and click the button on the component title bar.

        The Approximation Wizard appears.

  2. In the Name of approximation text box, enter a name for the approximation.

  3. Click User Defined, and click Next.

    The Approximation Technique screen appears.

  4. In the Approximation technique list, select Response Surface Model.

  5. Click Next.

    The Input and Output Parameters screen appears.

  6. Determine which parameters you want to use for your approximation by selecting the corresponding check boxes in the first column. Alternatively, you can click Check to add all the selected parameters. To clear all the parameters, click Uncheck.

    If your parameters contains arrays, click the check box next to the array root to select all members of the array.

  7. Click Next.

    The RSM Technique Options screen appears.

  8. In the Polynomial Order list, select an option. This option controls the order of the polynomials used by the Response Surface Model approximation technique. If you selected an array, the number of input parameters shown next to the list includes all the members of the array.

    Option Description
    Linear This option is the recommended value when the outputs are known to be linear with respect to the inputs. This option requires the smallest number of design points for initialization, but it produces larger errors for nonlinear output functions
    Quadratic This option is the recommended value for most cases and provides the best approximation performance to cost ratio. Quadratic RSM provides the best optimization performance for smooth exact functions.
    Cubic If this option is selected, the model polynomial will have all quadratic terms and only pure cubic terms (i.e., no mixed interaction terms of third order are included).

    This option is recommended when the outputs are highly nonlinear functions of the inputs. This option requires more design points for initialization than Quadratic RSM.
    Quartic If this option is selected, the model polynomials will have all quadratic terms, only pure cubic terms, and only pure fourth-order terms (i.e., no interaction terms of third and fourth order are included).

    The same recommendations listed under Cubic apply to Quartic approximations. Using quartic polynomials in optimization may create undesired local minima.

  9. Click Use term selection to select the most significant terms from the polynomial if you want to remove some polynomial terms with low significance, which can improve reliability for your approximation and reduce the number of required design points. For more information about the term selection methods, see About the Term Selection Methods.

    1. From the Term selection method list, select one of the following options:

      Option Description
      Sequential Replacement This method starts with the constant and adds polynomial terms one at a time so that the fitting errors of the Response Surface Model are minimized at every step.
      Stepwise (Efroymson) This method starts with the constant and adds polynomial terms one at a time so that the fitting errors of the RSM are minimized at every step. These terms can be controlled using the text boxes that appear under the Term selection method list when Stepwise (Efroymson) is selected:
      • F-ratio to drop term. The maximum value of the F-ratio to drop a polynomial term from the RSM.
      • F-ratio to add term. The minimum value of the F-ratio to add a new polynomial term to the RSM.
      Two-At-A-Time Replacement This method starts with the constant and adds polynomial terms one at a time so that the fitting errors of the RSM are minimized at every step.
      Exhaustive Search This method generates all possible combinations of polynomial terms and finds the best combination that produces the minimum fitting errors.

    2. Perform one of the following actions, based on your term selection method:

      • Click Specify number of selected terms, and enter the number you want selected in the corresponding text box.
      • For Stepwise (Efroymson) only, click Specify maximum number of selected terms, and enter the maximum number you want selected in the corresponding text box.

      Note: The reason for the different option names specified above is that the Stepwise (Efroymson) algorithm may not select the maximum number of terms and instead stops after selecting a smaller number of terms.

  10. Click Next.

    The Sampling Options screen appears.

  11. Select the desired sampling method (Random Points, Data File, or DOE Matrix), and configure the corresponding options as described in Configuring the Random Points Sampling Method, Configuring the Data File Sampling Method, or Configuring the DOE Matrix Sampling Method.

    If the model has already executed and you had already created an approximation for the selected component, you can select Component History Data. Isight uses the history data of the selected component for the approximation and bypasses the sampling range option.

  12. Click Next.

    The Sampling Range screen appears

  13. Select one of the following:

    • Absolute Values. This option defines the region by using absolute bounds for each inputs parameter. You need to specify the Lower and Upper values for each parameter in the corresponding columns.

    • Relative to Baseline. This option defines the region by applying relative move limits to the baseline values in both directions. You need to specify the baseline, move limit percentage, and minimum move limit for each parameter in the corresponding columns.

  14. Click Next.

    The Error Analysis Method screen appears.

  15. Select the desired error analysis method for the approximation:

    • Separate data set. This method compares exact and approximate output values for each data point of the second (additional) set.

      1. Click Next.
      2. Select the desired sampling method (Random Points, Data File, or DOE Matrix), and configure the corresponding options as described in Configuring the Random Points Sampling Method, Configuring the Data File Sampling Method, or Configuring the DOE Matrix Sampling Method.

    • Cross-validation. This method selects a subset of points from the main data set, removes each point one at a time, recalculates coefficients, and compares exact and approximate output values at each removed point.

      1. In the first text box, type the number of points from the total number of sampling points that you want to use for cross-validation error analysis.
      2. Click Use a fixed random seed for selecting points and specify a seed value to use for the random number generator when determining the set of sample points selected for cross-validation. This option allows you to reproduce the approximation with the same set of points later, if desired.

      For more information about cross-validation, see About Cross-Validation.

    • No error analysis.

  16. Click Next.

    If you are performing an error analysis, the Approximation Improvement Options screen appears; if you choose to skip the error analysis, the Runtime Options screen appears.

  17. If you are performing an error analysis, you can configure the approximation improvement options.

    For more information, see Improving Approximations using Sequential Sampling.

    You can choose to improve the approximation by allowing Isight to add sample points. Isight will use a sequential sampling technique that is appropriate for the approximation technique selected.

    1. Enter a target for the average prediction error of the approximation. Isight will add sample points sequentially until the average error falls below the value that you enter. Valid values are 0.0–1.0.
    2. Enter the maximum number of additional points that you want to use for improving the approximation.
    3. Enter the maximum number of iterations to improve the approximation. Dividing the maximum number of additional points by the maximum number of iterations results in the number of points that are added during each iteration of sequential sampling. Although it is desirable to add one point during each iteration, choosing fewer iterations reduces the time taken to fit the approximation model.
    4. Click Next.

      The Runtime Options screens appears.

  18. Set the Store coefficient data in file parameter named option. When activated, this option creates a file parameter that stores the approximation’s coefficient data. This option is useful if the approximation is initialized or updated (re-initialized) during execution and the coefficient data are needed for custom postprocessing. It is also useful if you want the coefficient data preserved in your database. For more information on file parameters, see Using File Parameters.

  19. Click Finish.

    A message appears prompting you to initialize the approximation.

  20. Perform one of the following actions: