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## Available Nonlinearity Estimators for Hammerstein-Wiener Models

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.

NonlinearityClassStructureComments
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`

`$g\left(x\right)=\sum _{k=1}^{n}{\alpha }_{k}\kappa \left({\beta }_{k}\left(x-{\gamma }_{k}\right)\right)$`

$\kappa \left(s\right)$ is the sigmoid function $\kappa \left(s\right)={\left({e}^{s}+1\right)}^{-1}$. ${\beta }_{k}$ is a row vector such that ${\beta }_{k}\left(x-{\gamma }_{k}\right)$ is a scalar.

Default number of units n is 10.
Wavelet network`wavenet`

`$g\left(x\right)=\sum _{k=1}^{n}{\alpha }_{k}\kappa \left({\beta }_{k}\left(x-{\gamma }_{k}\right)\right)$`

where $\kappa \left(s\right)$ 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 $\kappa \left(s\right)$.

(For advanced use)

Uses the unit function that you specify.

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