idFeedforwardNetwork

(Not recommended) Multilayer feedforward neural network mapping function for nonlinear ARX models (requires Deep Learning Toolbox)

idFeedforwardNetwork is not recommended. Use idNeuralNetwork instead to create mapping objects based on neural networks. For more information, see Version History.

Description

An idFeedforwardNetwork object implements a neural network function, and is a nonlinear mapping object for estimating nonlinear ARX models. This mapping object lets you use network (Deep Learning Toolbox) objects that are created using Deep Learning Toolbox™ in nonlinear ARX models.

Mathematically, idFeedforwardNetwork is a function that maps m inputs X(t) = [x(t₁),x₂(t),…,x_m(t)]^T to a scalar output y(t), using a multilayer feedforward (static) neural network, as defined in Deep Learning Toolbox.

You create multi-layer feedforward neural networks by using 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 nlarx command, the software automatically determines the input and 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, where m is 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 idFeedforwardNetwork 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 idFeedforwardNetwork object is assigned as the nonlinearity estimator.

You cannot use idFeedforwardNetwork when the Focus option in nlarxOptions is 'simulation' because the underlying network object is considered to be nondifferentiable for estimation. Minimization of simulation error requires differentiable nonlinear functions.

Use idFeedforwardNetwork as the value of the OutputFcn property of an idnlarx model. For example, specify idFeedforwardNetwork when you estimate an idnlarx model with the following command.

sys = nlarx(data,regressors,idFeedforwardNetwork)

When nlarx estimates the model, it essentially estimates the parameters of the idFeedforwardNetwork function.

Creation

Syntax

net_estimator = idFeedforwardNetwork(Network)

Description

net_estimator = idFeedforwardNetwork(Network) creates a feedforward neural network mapping object that is based on the feedforward (static) network object Network that has been created using one of the neural network commands feedforwardnet, cascadeforwardnet, or 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 set to one. For a multiple-output nonlinear ARX models, create a separate idFeedforwardNetwork object for each output—that is, each element of the output function must represent a single-output network object.

Properties

Network — Feedforward neural network

Network object

Feedforward neural network object, typically created using feedforwardnet (Deep Learning Toolbox), cascadeforwardnet (Deep Learning Toolbox) or linearlayer (Deep Learning Toolbox).

Inputs — Input signal names

cell array

Input signal names for the inputs to the mapping object, specified as a 1-by-m cell array, where m is the number of input signals. This property is determined during estimation.

Outputs — Output signal name

cell array

Output signal name for the output of the mapping object, specified as a 1-by-1 cell array. This property is determined during estimation.

Free — Option to train the network

true (default) | false

Option to train the neural network, specified as true or false. Set Free to false when the neural network you are using has already been trained and is known to provide good fit results. The Free property is especially useful when your idnlarx model has multiple outputs that each use a neural network. Setting Free to false for well trained networks allows processing time to be focused on the networks that do need training.

Examples

Create Nonlinear Mapping Object Using Feedforward Neural Network

Create a neural network mapping object that uses a feedforward 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 mapping object.

net_estimator = idFeedforwardNetwork(net);

Estimate Nonlinear ARX Model Using Feedforward Neural Network Mapping Object

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 feedforward neural network mapping object.

net_estimator = idFeedforwardNetwork(net);

Load the estimation data.

load twotankdata
data = iddata(y,u,0.2);

Estimate a nonlinear ARX model sys.

sys = nlarx(data,[2 2 1],net_estimator);

Compare the model response to the measured output signal.

compare(data,sys)

The plot shows good agreement between the measured signal and the simulated model output signal.

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);
R = R.Variables;

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 and the choice of training function.

net.outputs{net.outputConnect}.range = OutputRange;
net.trainFcn = 'trainbfg';

Create a neural network nonlinearity estimator.

net_estimator = idFeedforwardNetwork(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.

Version History

Introduced in R2007a

R2023b: idFeedforwardNetwork is not recommended

Use idNeuralNetwork instead to create mapping objects based on neural networks.

R2022a: Previous idnlarx data normalization information moved from mapping object properties to idnlarx Normalization property

Information related to data normalization was moved from the idFeedforwardNetwork mapping object level to the model level. The Normalization property of the idnlarx model contains the data centering and scaling information that the estimation process computes. In addition, the regressor-selection process for the mapping objects has also moved to the model level. The model now passes the actual regressor names rather than the selection indices to the mapping object, eliminating the need for an index property at the mapping object level.

The following table summarizes the mapping object subproperties that were eliminated. For more information, see the Normalization property of idnlarx.

Main Properties / Subproperties	Input	Output	LinearMdl	Offset	NonlinearMdl
Mean	X	X
Range	X	X
Minimum			X	X	X
Maximum			X	X	X
SelectedInputIndex			X		X

R2021b: Use of previous idnlarx and idnlhw mapping object names is not recommended.

Starting in R2021b, the mapping objects (also known as nonlinearities) used in the nonlinear components of the idnlarx and idnlhw objects have been renamed. The following table lists the name changes.

Pre-R2021b Name	R2021b Name
wavenet	idWaveletNetwork
sigmoidnet	idSigmoidNetwork
treepartition	idTreePartition
customnet	idCustomNetwork
saturation	idSaturation
deadzone	idDeadZone
pwlinear	idPiecewiseLinear
poly1d	idPolynomial1D
unitgain	idUnitGain
linear	idLinear
neuralnet	idFeedforwardNetwork

Scripts with the old names still run normally, although they will produce a warning. Consider using the new names for continuing compatibility with newly developed features and algorithms. There are no plans to exclude the use of these object names at this time.