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 nonlinearitiesfandh, respectively. For more information aboutfandh, seeStructure of Hammerstein-Wiener Models.

Each nonlinearity estimator corresponds to an object class in this toolbox. When you estimate Hammerstein-Wiener models in theSystem Identificationapp, 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)	`idPiecewiseLinear`	A piecewise linear function parameterized by breakpoint locations.	By default, the number of breakpoints is 10.
One layer sigmoid network	`idSigmoidNetwork`	$g (x) = \sum_{k = 1}^{n} α_{k} κ (β_{k} (x - γ_{k}))$ $κ (s)$ is the sigmoid function $κ (s) = {(e^{s} + 1)}^{- 1}$ . $β_{k}$ is a row vector such that $β_{k} (x - γ_{k})$ is a scalar.	Default number of unitsnis 10.
Wavelet network	`idWaveletNetwork`	$g (x) = \sum_{k = 1}^{n} α_{k} κ (β_{k} (x - γ_{k}))$ where $κ (s)$ is the wavelet function.	By default, the estimation algorithm determines the number of unitsnautomatically.
Saturation	`idSaturation`	Parameterize hard limits on the signal value as upper and lower saturation limits.	Use to model known saturation effects on signal amplitudes.
Dead zone	`idDeadZone`	Parameterize dead zones in signals as the duration of zero response.	Use to model known dead zones in signal amplitudes.
One- dimensional polynomial	`idPolynomial1D`	Single-variable polynomial of a degree that you specify.	By default, the polynomial degree is 1.
Unit gain	`idUnitGain`	从模型结构中排除输入或输出非线性，以实现维纳或Hammerstein配置。 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)	`idCustomNetwork`	类似于SIGMOID网络，但您指定 $κ (s)$ .	(For advanced use) Uses the unit function that you specify.

Available Nonlinearity Estimators for Hammerstein-Wiener Models

Related Topics

System Identification Toolbox Documentation

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