Class representing wavelet network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
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.
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.
Integer specifies the number of nonlinearity units in
Can have the following values:
Structure containing the parameters in the nonlinear expansion, as follows:
Structure containing the following fields that affect the initial model:
Use wavenet to specify the nonlinear estimator in nonlinear ARX and Hammerstein-Wiener models. For example:
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:
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).
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.