  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 work 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, 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.
