In a dynamic network of interconnected transfer functions, it is not necessary to use all the node signals for estimating a local transfer function. Given the network topology, detailed conditions are available for selecting inputs and outputs in a (MIMO) predictor model that warrants consistent and minimum variance estimation of a target module through the so-called local direct method. Motivated by the existing minimum-input signal selection approach that gradually incorporates additional signals, an alternative graphical algorithm for signal selection is developed in this work by directly exploiting the complete network graph. Then, as a straightforward application of existing analytical results, graphical conditions for consistent identification are derived for the novel signal selection approach. We show by an example that in some cases, for the consistent estimation of the target module, the developed method leads to fewer selected signals than the original minimum-input method.

Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this article introduces a novel network model structure such that excitation from unmeasured noise signals is included, which leads to less conservative identifiability conditions than relying on measured excitation signals only. More importantly, graphical conditions are developed to verify global and generic identifiability of a single module based on the topology of the dynamic network. Depending on whether the input or the output of the module can be measured, we present four identifiability conditions which cover all possible situations in single module identification. These conditions further lead to synthesis approaches for allocating excitation signals and selecting measured signals, to warrant single module identifiability. In addition, if the identifiability conditions are satisfied for a sufficient number of external excitation signals only, indirect identification methods are developed to provide a consistent estimate of the module. All the obtained results are also extended to identifiability of multiple modules in the network.

Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion.