neuralnet
Class representing neural network nonlinearity estimator for nonlinear ARX models
Syntax
net_estimator = neuralnet(Network)
Description
neuralnet is the class that encapsulates
the neural network nonlinearity estimator. A neuralnet object
lets you use networks, created using Deep Learning Toolbox™ software,
in nonlinear ARX models.
The neural network nonlinearity estimator defines a nonlinear
function , where F is
a multilayer feed-forward (static) neural network, as defined in the Deep Learning Toolbox software. y is
a scalar and x is an m-dimensional
row vector.
You create multi-layer feed-forward neural networks using Deep Learning Toolbox commands
such as feedforwardnet (Deep Learning Toolbox), cascadeforwardnet (Deep Learning Toolbox) and linearlayer (Deep Learning Toolbox). When you create the network:
Designate the input and output sizes to be unknown by leaving them at the default value of zero (recommended method). When estimating a nonlinear ARX model using the
nlarxcommand, the software automatically determines the input-output sizes of the network.Initialize the sizes manually by setting input and output ranges to
m-by-2 and 1-by-2 matrices, respectively, wheremis the number of nonlinear ARX model regressors and the range values are minimum and maximum values of regressors and output data, respectively.
See Examples for more information.
Use evaluate(net_estimator,x) to compute
the value of the function defined by the neuralnet object net_estimator at
input value x. When used for nonlinear ARX model
estimation, x represents the model regressors for
the output for which the neuralnet object is
assigned as the nonlinearity estimator.
You cannot use neuralnet when the Focus option
in nlarxOptions is 'simulation' because
this nonlinearity estimator is considered to be nondifferentiable
for estimation. Minimization of simulation error requires differentiable
nonlinear functions.
Construction
net_estimator = neuralnet(Network)Network created using Deep Learning Toolbox commands feedforwardnet, cascadeforwardnet,
and linearlayer. Network must
represent a static mapping between the inputs and output without I/O
delays or feedback. The number of outputs of the network, if assigned,
must be one. For a multiple-output nonlinear ARX models, create a
separate neuralnet object for each output—that
is, each estimator must represent a single-output network object.
Properties
Network | Neural network object, typically created using the Deep Learning Toolbox commands feedforwardnet, cascadeforwardnet,
and linearlayer. |
After creating the object, you can use get or
dot notation to access the object property values. For example:
% List Network property value get(n) n.Network
You can also use the set function to set
the value of particular properties. For example:
set(d, 'Network', net_obj)
set must be the name of a MATLAB® variable.Examples
Create a Nonlinearity Estimator Using Feed-Forward Neural Network
Create a neural network nonlinearity estimator using a feed-forward neural network with three hidden layers; transfer functions of types logsig, radbas,and purelin; and unknown input and output sizes.
Create a neural network.
net = feedforwardnet([4 6 1]);
net.layers{1}.transferFcn = 'logsig';
net.layers{2}.transferFcn = 'radbas';
net.layers{3}.transferFcn = 'purelin';
View the network diagram.
view(net)
Create a neural network estimator.
net_estimator = neuralnet(net);
Estimate Nonlinear ARX Model Using a Neural Network Nonlinearity Estimator
Create a single-layer, cascade-forward network with unknown input and output sizes and use this network for nonlinear ARX model estimation.
Create a cascade-forward neural network with 20 neurons and unknown input-output sizes.
net = cascadeforwardnet(20);
Create a neural network nonlinearity estimator.
net_estimator = neuralnet(net);
Load estimation data.
load twotankdata
Data = iddata(y,u,0.2);Estimate nonlinear ARX model.
Model = nlarx(Data,[2 2 1],net_estimator);
Compare model response to measured output signal.
compare(Data,Model)
Initialize Input-Output Sizes of Neural Network Nonlinearity Estimator
Initialize the input-output sizes of a two-layer feed-forward neural network based on estimation data, and use this network for nonlinear ARX estimation.
Load estimation data.
load iddata7 z7 z7 = z7(1:200);
Create a template nonlinear ARX model with no nonlinearity.
model = idnlarx([4 4 4 1 1],[]);
This model has six regressors and is used to define the regressors. The range of regressor values for input-output data in z7 is then used to set the input ranges in the neural network object, as shown in the next steps.
Obtain the model regressor values.
R = getreg(model,'all',z7);Create a two-layer, feed-forward neural network and initialize the network input and output dimensions to 2 and 1, respectively. Use 5 neurons for first layer and 7 for second layer.
net = feedforwardnet([5 7]);
Determine input range.
InputRange = [min(R);max(R)].';
Initialize input dimensions of estimator.
net.inputs{1}.range = InputRange;Determine output range.
OutputRange = [min(z7.OutputData),max(z7.OutputData)];
Initialize output dimensions of estimator.
net.outputs{net.outputConnect}.range = OutputRange;Create a neural network nonlinearity estimator.
net_estimator = neuralnet(net);
Specify the nonlinearity estimator in the model.
model.Nonlinearity = net_estimator;
Estimate the parameters of the network to minimize the prediction error between data and model. Estimate model.
model = nlarx(z7,model);
Compare model's predicted response to measured output signal.
compare(z7(1:100),model,1)
Algorithms
The nlarx command uses
the train method of the network object,
defined in the Deep Learning Toolbox software, to compute the
network parameter values.
See Also
customnet | nlarx | sigmoidnet | treepartition | wavenet | cascadeforwardnet (Deep Learning Toolbox) | feedforwardnet (Deep Learning Toolbox) | linearlayer (Deep Learning Toolbox)