System Identification Toolbox™ software provides several scalar nonlinearity estimators, for Hammerstein-Wiener models. The nonlinearity estimators are available for both the input and output nonlinearities f and h, respectively. For more information about f and h, see Structure of Hammerstein-Wiener Models.
Each nonlinearity estimator corresponds to an object class in this toolbox. When you estimate Hammerstein-Wiener models in the System Identification app, the toolbox creates and configures objects based on these classes. You can also create and configure nonlinearity estimators at the command line. For a detailed description of each estimator, see the references page of the corresponding nonlinearity class.
Nonlinearity | Class | Structure | Comments |
---|---|---|---|
Piecewise linear (default) | pwlinear | A piecewise linear function parameterized by breakpoint locations. | By default, the number of breakpoints is 10. |
One layer sigmoid network | sigmoidnet |
is the sigmoid function . is a row vector such that is a scalar. | Default number of units n is 10. |
Wavelet network | wavenet |
where is the wavelet function. | By default, the estimation algorithm determines the number of units n automatically. |
Saturation | saturation | Parameterize hard limits on the signal value as upper and lower saturation limits. | Use to model known saturation effects on signal amplitudes. |
Dead zone | deadzone | Parameterize dead zones in signals as the duration of zero response. | Use to model known dead zones in signal amplitudes. |
One- dimensional polynomial | poly1d | Single-variable polynomial of a degree that you specify. | By default, the polynomial degree is 1. |
Unit gain | unitgain |
Excludes the input or output nonlinearity from the model structure to achieve a Wiener or Hammerstein configuration, respectively. Note Excluding both the input and output nonlinearities reduces the Hammerstein-Wiener structure to a linear transfer function. | Useful for configuring multi-input, multi-output (MIMO) models to exclude nonlinearities from specific input and output channels. |
Custom network (user-defined) | customnet |
Similar to sigmoid network but you specify . |
(For advanced use) Uses the unit function that you specify. |