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Register a new userAllocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks
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A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question addressed in this paper is where to allocate external excitation signals such that a network model set becomes generically identifiable when measuring all vertex signals. To tackle this synthesis problem, a novel graph structure, referred to as textit{directed pseudotree}, is introduced, and the generic identifiability of a network model set can be featured by a set of disjoint directed pseudotrees that cover all the parameterized edges of an textit{extended graph}, which includes the correlation structure of the process noises. Thereby, an algorithmic procedure is devised, aiming to decompose the extended graph into a minimal number of disjoint pseudotrees, whose roots then provide the appropriate locations for excitation signals. Furthermore, the proposed approach can be adapted using the notion of textit{anti-pseudotrees} to solve a dual problem, that is to select a minimal number of measurement signals for generic identifiability of the overall network, under the assumption that all the vertices are excited.
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Identifiability of a single module in a network of transfer functions is determined by the question 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.
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