Creating a User-Defined Approximation Using the Orthogonal Polynomial Technique

You can create a user-defined approximation using the Orthogonal polynomial technique, which is a regression technique. Orthogonal polynomials minimize the autocorrelation between the response values that exist because of the sampling location. An advantage of using orthogonal functions as the basis for fitting is that the inputs can be decoupled in the analysis of variance (ANOVA).

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

Related Topics
Chebyshev/Orthogonal Polynomial Model

  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 Orthogonal Polynomial Model.

  5. Click Next.

    The Input and Output Parameters screen appears.

    1. 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.

    2. Click Next.

      The Orthogonal Polynomial Approximation Technique Options screen appears.

  6. In the Type of fit-polynomial list, select Chebyshev or Successive orthogonal polynomial.

    • Chebyshev. If the data points are generated using an equally spaced orthogonal array, Isight uses the quadrature method to calculate the coefficients of the model. If the levels are not equally spaced or if the data are not from an orthogonal array, Isight processes Chebyshev polynomials as transformations and uses a linear regression approach to compute the coefficients.

    • Successive Orthogonal Polynomial. The successive orthogonal polynomial technique generates a series of polynomials that are orthogonal with respect to the data provided. These polynomials are used as basis functions to obtain an approximation for the responses. Basis functions depend only on the sample locations and not the response values.

  7. In the Degree of fit-polynomial text box, enter the value to which this model is limited.

  8. Click Include cross terms to use cross terms in the model.

  9. Click Next.

    The Sampling Options screen appears.

  10. Select the desired sampling method (Component History Data, 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.

  11. Click Next.

    The Sampling Range screen appears

  12. 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.

  13. Click Next.

    The Error Analysis Method screen appears.

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

    • 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.

  15. Click Next.

    The Runtime Options screens appears.

  16. 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.

  17. Click Finish.

    A message appears prompting you to initialize the approximation.

  18. Perform one of the following actions: