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| R2012a Documentation → System Identification Toolbox | |
Learn more about System Identification Toolbox |
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s=wavenet('NumberOfUnits',N)
s=wavenet(Property1,Value1,...PropertyN,ValueN)
wavenet is an object that stores the wavelet network nonlinear estimator for estimating nonlinear ARX and Hammerstein-Wiener models.
You can use the constructor to create the nonlinearity object, as follows:
s=wavenet('NumberOfUnits',N) creates a wavelet nonlinearity estimator object with N terms in the wavelet expansion.
s=wavenet(Property1,Value1,...PropertyN,ValueN) creates a wavelet nonlinearity estimator object specified by properties in wavenet Properties.
Use evaluate(s,x) to compute the value of the function defined by the wavenet object s at x.
Use wavenet to define a nonlinear function
, where y is
scalar and x is an m-dimensional
row vector. The wavelet network function is based on the following
function expansion:
where:
f is a scaling function.
g is the wavelet function.
P and Q are m-by-p and m-by-q projection matrices, respectively.
The projection matrices P and Q are determined by principal component analysis of estimation data. Usually, p=m. If the components of x in the estimation data are linearly dependent, then p<m. The number of columns of Q, q, corresponds to the number of components of x used in the scaling and wavelet function.
When used in a nonlinear ARX model, q is equal to the size of the NonlinearRegressors property of the idnlarx object. When used in a Hammerstein-Wiener model, m=q=1 and Q is a scalar.
r is a 1-by-m vector and represents the mean value of the regressor vector computed from estimation data.
d, as, bs, aw, and bw are scalars. Parameters with the s subscript are scaling parameters, and parameters with the w subscript are wavelet parameters.
L is a p-by-1 vector.
cs and cw are 1-by-q vectors.
The scaling function f and the wavelet function g are both radial functions, as follows:
where Nr is the length of x (number of regressors).
You can include property-value pairs in the constructor to specify the object.
After creating the object, you can use get or dot notation to access the object property values. For example:
% List all property values get(w) % Get value of NumberOfUnits property w.NumberOfUnits
You can also use the set function to set the value of particular properties. For example:
h set(w, 'LinearTerm', 'on')
The first argument to set must be the name of a MATLAB variable.
| Property Name | Description |
|---|---|
| NumberOfUnits | Integer specifies the number of nonlinearity units in
the expansion. For example: wavenet('NumberOfUnits',5) |
| LinearTerm | Can have the following values:
For example: wavenet(H,'LinearTerm','on') |
| Parameters | Structure containing the parameters in the nonlinear expansion, as follows:
|
| Options | Structure containing the following fields that affect the initial model:
|
When the idnlarx property Focus is 'Prediction', wavenet uses a fast, noniterative technique for estimating parameters. Successive refinements after the first estimation use an iterative algorithm.
When the idnlarx property Focus='Simulation', wavenet uses an iterative technique for estimating parameters.
To always use noniterative or iterative algorithm, specify the IterWavenet algorithm property of the idnlarx class.
Use wavenet to specify the nonlinear estimator in nonlinear ARX and Hammerstein-Wiener models. For example:
m=nlarx(Data,Orders,wavenet);
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