Identification Window

On the basis of a data set and a predictor model, either a full network, a subnetwork or a single module/link can be identified.

The Identification Window contains the following panels:

Data and Predictor Models panels

A Data panel where selected/imported data sets can be loaded, stored and selected. A loaded data set is typically a nwdata object.

A Predictor model panel where predictor models can be loaded or newly created. A loaded predictor model should be a nwpredmodel or nwmodel object that was previously saved either at the command line or in the predictor model window. Any predictor models that were added to the identification window in the predictor model window are shown in this panel. When creating a new predictor model (), it is created for either full network identification or for a particular subnetwork, which first needs to be specified in the "Target" panel. Creating a new single module predictor model for directed networks in this window is not supported.

The selected data set and predictor model are tested on their compatibility, e.g. by verifying if the appropriate nodes in the predictor model are indeed available in the selected data set.

Data sets and predictor models can be created (), viewed/edited (), saved to workspace (), saved to a file () and deleted (). The full list can be cleared through the button.

Signals in data sets can be viewed by selecting the view button in the View/Edit window; Node signals of multiple data sets can also be viewed by right clicking nodes in the network plot.

Main network graph

On the main canvas a network plot shows the interconnection structure of the network, including the nodes and links.

When a single module/subnetwork predictor model is selected, one can toggle the network view, between the original (full) network, and the immersed network, composed of the signals that appear in the predictor model.

Node signals can be made visible by a right-click on the nodes in the network plot. After identification, when an identified model is selected:

• A right mouse click on a node shows options to visualize the measured and simulated node signals, and
• A right mouse click on a link, shows the dynamic properties (pulse response) of the concerned model.

Predictor model graph

In the predictor model graph, the predictor model mapping between inputs (w,r,e) and outputs (w) are shown.

A predictor model has the structure:

• For directed (module) networks:
  $w_{Y}(t) = G(q,\theta) w_{D}(t) + H(q,\theta) \varepsilon(t,\theta) + T(q,\theta)r_{P}(t)$

• For undirected networks:
  $(X(q,\theta)+Y(q,\theta)) w_{Y}(t) = B(q,\theta) r_{P}(t) + F(q,\theta) \varepsilon(t,\theta)$

where:

• For full network identification, the node sets $w_Y$ and $w_D$ are equal, and determined by all nodes in the network.
• For single module identification, the node sets $w_Y$ and $w_D$ are typically different, and constructed as subsets of all nodes present in the network.
• For subnetwork identification, the node sets $w_Y$ and $w_D$ are equal, and constructed as subsets of all nodes present in the network.

Identification panels

In the Target panel, it can be selected whether the full network or a subnetwork (single target) are going to be estimated.

The Identification panel, provides the choice of Identification method, and a selected estimation method.
Domain is Discrete-time (DT) and/or Continuous-time (CT).

Target object	Identification method	Domain	Estimation method	Description
Full directed network	Direct	DT	PEM	Direct minization of quadratic predictor error of possible MIMO model
	Multistep	DT	SLS	Sequential least squares algorithm
Single module in directed network	Direct	DT	PEM	Direct minization of quadratic predictor error
	Multistep	DT	OE	Output error approach for MISO model
		DT	Kernel-based	Kernel-based approach for MISO model
DCN full/subnetwork	Multistep	DT	ARMAX	Sequential algorithm based on weighted nullspace-fitting
		CT/DT	FDE	F-domain continuous time subnetwork identification

The Settings button () after the Estimation Method selection, provides access to particular parameter settings for the estimation, dependent on the selected estimation method.

After running the identification, the identified model is added to the list in the Identified models panel.

Model evaluation panel

In the current implementation a preliminary set of model evaluation tools is available.

• Model output shows the simulated model output together with the measured output, for a selected output node. The legend of this plot also shows the
  Model fit = $[1- \frac{\sqrt{\sum_t (w_{measured}(t) - w_{simulated}(t))^2}}{\sqrt{\sum_t (w_{measured}(t)-w_{mean})^2}}]*100\%$

• Residual tests shows the autocorrelation function of the output residual, and the cross-correlation between the output residual and any selected node or excitation signal.

• Transient response shows the pulse or step response of a selected module/link.

• Frequency response shows the frequency response of a selected module/link.

When right mouse-clicking an output node in the network graph, one can select:

• the autocorrelation function of the residual related to the selected output, and
• the simulated output compared to the measured output.