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.

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	$$g(x)={\displaystyle \sum _{k=1}^n{\alpha }_k}\kappa \left({\beta }_k\left(x-{\gamma }_k\right)\right)$$ $$\kappa (s)$$ is the sigmoid function $$\kappa (s)={\left(e^s+1\right)}^{-1}$$. $${\beta }_k$$ is a row vector such that $${\beta }_k(x-{\gamma }_k)$$ is a scalar.	Default number of units n is 10.
Wavelet network	wavenet	$$g(x)={\displaystyle \sum _{k=1}^n{\alpha }_k}\kappa \left({\beta }_k\left(x-{\gamma }_k\right)\right)$$ where $$\kappa (s)$$ 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 $$\kappa (s)$$.	(For advanced use) Uses the unit function that you specify.

Related Topics

• What are Hammerstein-Wiener Models?
• Identifying Hammerstein-Wiener Models