Creating a User-Defined Approximation Using the Radial Basis Functions (RBF) Technique

You can create a user-defined approximation based on Radial Basis Functions (RBF), which are a type of neural network employing a hidden layer of radial units and an output layer of linear units.

Elliptical Basis Functions (EBF) are similar to Radial Basis Functions but use elliptical units in place of radial units. Compared to RBF networks where all inputs are handled equally, EBF networks treat each input separately using individual weights.

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

Related Topics
RBF and EBF Models
About the Smoothing Filter

  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 RBF 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 RBF Technique Options screen appears.

  8. From the RBF Technique Options screen, do the following, as desired:

    1. Enter the Smoothing Filter value.

      You can use the smoothing filter to relax the requirement that the RBF approximation pass through every single data point. The smoothing filter’s primary purpose is to smooth out noisy data. For more information about the smoothing filter, see About the Smoothing Filter.

    2. In the Type of Basis Function list, select Radial or Elliptical.

      RBF networks are characterized by reasonably fast training and reasonably compact networks, whereas EBF networks require several iterations to learn individual input weights. EBF networks are often more accurate than RBF networks but can increase initialization time.

    3. If you are using EBF networks, enter the Maximum Iterations to Fit value.

      Isight uses an iterative procedure to learn the weights for individual inputs in the EBF model. Isight limits the maximum number of iterations used to fit a model for each response based on this value.

  9. Click Next.

    The Sampling Options screen appears.

  10. 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.

  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:

    • 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.

  15. 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.

  16. 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.

  17. 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.

  18. Click Finish.

    A message appears prompting you to initialize the approximation.

  19. Perform one of the following actions: