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Estimate Nonlinear ARX Models in the App

You can estimate nonlinear ARX models in the System Identification app after you perform the following tasks:

To estimate a nonlinear ARX model using the imported estimation data and chosen nonlinearity estimators:

  1. In the System Identification app, select Estimate > Nonlinear ARX Models to open the Estimate Nonlinear ARX Models dialog box.

  2. (Optional) Edit Model name by deleting the default model name and entering a new name. The name of the model should be unique to all nonlinear ARX models in the System Identification app.

  3. (Optional) If you want to refine the parameters of a previously estimated model or configure the model structure to match that of an existing model:

    1. Click Initialize. A Initial Model Specification dialog box opens.

    2. In the Initial Model drop-down list, select a nonlinear ARX model.

      The model must be in the Model Board of the System Identification app and the input/output dimensions of this initial model must match that of the estimation data, selected as Working Data in the app.

    3. Click OK.

      The model structure as well as the parameter values are updated to match that of the selected model.

    Clicking Estimate causes the estimation to use the parameters of the initial model as the starting point.


    When you select an initial model, you can optionally update the estimation algorithm settings to match those used for the initial model by selecting the Inherit the model’s algorithm properties option.

  4. Keep the default settings in the Nonlinear Models dialog box that specify the model structure and the algorithm, or modify these settings:


    For more information about available options, click Help in the Nonlinear Models dialog box to open the app help.

    What to ConfigureOptions in Nonlinear Models GUIComment
    Model orderIn the Regressors tab, edit the No. of Terms corresponding to each input and output channel.Model order na is the output number of terms and nb is the input number of terms.
    Input delayIn the Regressors tab, edit the Delay corresponding to an input channel.If you do not know the input delay value, click Infer Input Delay. This action opens the Infer Input Delay dialog box to suggest possible delay values.
    RegressorsIn the Regressors tab, click Edit Regressors.This action opens the Model Regressors dialog box. Use this dialog box to create custom regressors or to include specific regressors in the nonlinear block.
    Nonlinearity estimatorIn the Model Properties tab.To use all standard and custom regressors in the linear block only, you can exclude the nonlinear block by setting Nonlinearity to None.
    Estimation algorithmIn the Estimate tab, click Algorithm Options. 
  5. To obtain regularized estimates of model parameters, in the Estimate tab, click Estimation Options. Specify the regularization constants in the Regularization_Tradeoff_Constant and Regularization_Weighting fields. To learn more, see Regularized Estimates of Model Parameters.

  6. Click Estimate to add this model to the System Identification app.

    The Estimate tab displays the estimation progress and results.

  7. Validate the model response by selecting the desired plot in the Model Views area of the System Identification app. For more information about validating models, see Validate Nonlinear ARX Models.

    If you get a poor fit, try changing the model structure or algorithm configuration in step 5.

You can export the model to the MATLAB® workspace by dragging it to To Workspace in the System Identification app.

See Also


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