主要内容

What are Hammerstein-Wiener Models?

当系统的输出非线性取决于其输入时，有时可以将输入输出关系分解为两个或多个互连元素。在这种情况下，您可以通过线性传输函数来表示动力学，并使用线性系统的输入和输出的非线性函数捕获非线性。Hammerstein-Wiener模型将这种配置作为具有动态线性块的静态非线性块的串联连接。Hammerstein-Wiener模型应用程序跨越了几个区域，例如建模机电系统和射频组件，音频和语音处理以及化学过程的预测控制。这些模型具有方便的块表示，与线性系统的透明关系，并且比重型非线性模型（例如神经网络和Volterra模型）更容易实现。

You can use a Hammerstein-Wiener model as a black-box model structure because it provides a flexible parameterization for nonlinear models. For example, you can estimate a linear model and try to improve its fidelity by adding an input or output nonlinearity to this model. You can also use a Hammerstein-Wiener model as a grey-box structure to capture physical knowledge about process characteristics. For example, the input nonlinearity can represent typical physical transformations in actuators and the output nonlinearity can describe common sensor characteristics. For more information about when to fit nonlinear models, seeAbout Identified Nonlinear Models.

Structure of Hammerstein-Wiener Models

Hammerstein-Wiener模型使用一个或两个线性块串联使用一个或两个静态非线性块来描述动态系统。线性块是代表模型动态组件的离散传输函数。

该框图表示Hammerstein-Wiener模型的结构：

Where,

  • fis a nonlinear function that transforms input datau(t） 作为w(t) =f(u(t)).

    w(t), an internal variable, is the output of the Input Nonlinearity block and has the same dimension asu(t).

  • b/fis a linear transfer function that transformsw(t） 作为x(t) =(b/f)w(t).

    x(t), an internal variable, is the output of the Linear block and has the same dimension asy(t).

    B和Fare similar to polynomials in a linear Output-Error model. For more information about Output-Error models, seeWhat Are Polynomial Models?.

    For纽约输出和nuinputs, the linear block is a transfer function matrix containing entries:

    B j , i ( q ) F j , i ( q )

    wherej=1,2，...，纽约和i=1,2，...，nu.

  • his a nonlinear function that maps the output of the linear blockx(t) to the system outputy(t） 作为y(t) =h(x(t)).

Becausefacts on the input port of the linear block, this function is called theinput nonlinearity. Similarly, becauseh作用于线性块的输出端口，此功能称为output nonlinearity. If your system contains several inputs and outputs, you must define the functionsf和h对于每个输入和输出信号。您不必在模型结构中包括输入和输出非线性。当模型仅包含输入非线性时f, it is called aHammerstein模型。同样，当模型仅包含输出非线性时h, it is called aWiener模型。

The software computes the Hammerstein-Wiener model outputyin three stages:

  1. 计算w(t) =f(u(t)) from the input data.

    w(t）是线性传输函数的输入b/f.

    输入非线性是静态的（memoryless) function, where the value of the output a given timetdepends only on the input value at timet.

    You can configure the input nonlinearity as a sigmoid network, wavelet network, saturation, dead zone, piecewise linear function, one-dimensional polynomial, or a custom network. You can also remove the input nonlinearity.

  2. 计算the output of the linear block usingw(t）和初始条件：x(t) =(b/f)w(t).

    您可以通过指定分子的订单来配置线性块B和denominatorF.

  3. 通过转换线性块的输出来计算模型输出x(t）使用非线性功能hasy(t) =h(x(t)).

    与输入非线性类似，输出非线性是静态函数。您可以以与输入非线性相同的方式配置输出非线性。您还可以删除输出非线性，以便y(t) =x(t).

最终的模型是idnlhwobjects that store all model data, including model parameters and nonlinearity estimators. For more information about these objects, see非线性模型结构.

You can estimate Hammerstein-Wiener models in the系统标识app or at the command line using theNLHWcommand. You can use uniformly sampled time-domain input-output data for estimating Hammerstein-Wiener models. Your data can have one or more input and output channels. You cannot use time series data (output only) or frequency-domain data for estimation. If you have time series data, to fit a nonlinear model, identify nonlinear ARX models or nonlinear grey-box models. For more information about these models, see识别非线性ARX模型和Estimate Nonlinear Grey-Box Models.

See Also

|

相关话题