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.
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 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 signal…
Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. refl…
This paper deals with the design of Excitation and Measurement Patterns (EMP) for the identification of a class of dynamical networks whose topology has the structure of a Directed Acyclic Graph (DAG). In addition to the by now well known condition that the identifiabiltiy of any dynamical network requires that the sources be excited, the sinks be measured, and all other nodes be either excited or measured, we show that for DAGs two other types of nodes have special excitation and measurement requirements. Armed with this result, we propose a systematic procedure for the design of EMPs that gu…
The paper [1] presented the first results on generic identifiability of dynamic networks with partial excitation and partial measurements, i.e. networks where not all nodes are excited or not all nodes are measured. One key contribution of that paper was to establish a set of necessary conditions on the excitation and measurement pattern (EMP) that guarantee generic identifiability. In a nutshell, these conditions established that all sources must be excited and all sinks measured, and that all other nodes must be either excited or measured. In the present paper, we show that two other types o…
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the capacity to generate extremely large datasets. We seek to develop generalized identifiability conditions for informing the design of automated experiments to discover predictive nonlinear biological models. For linear systems, identifiability is characterized by persistence of excitation conditions. For nonlinear systems, no such persistence of excitation con…
In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation,which we show is equivalent to interval excitation of the regressor vector. Continuous and discrete-time versions of the estimators are given. An extension to--separable and monotonic--non-linear parameterizations is also given. The estimators are shown to be robust to additive measurement noise and--not necessarily slow--parameter variations. Moreover, a version of the continuous-time es…
Identifiability of dynamical networks: which nodes need be measured?
Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Univsersité catholique de Louvain（天主教鲁汶大学）；Universidade Estadual do Rio Grande do Sul（南里奥格兰德州立大学）
Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations
Shiv Nadar University（希夫纳德大学）；Université de Lorraine, CNRS, CRAN（洛林大学、法国国家科学研究中心、CRAN）；UCLouvain（鲁汶天主教大学）；University of Namur（纳慕尔大学）；ICTEAM institute, UCLouvain（UCLouvain ICTEAM研究所）；Department of Mathematics, Namur Research Institute for Complex Systems, University of Namur（纳慕尔大学数学系、纳慕尔复杂系统研究所）
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University（湍流与复杂系统国家重点实验室，力学与工程科学系，工程学院，北京大学）；Massachusetts Institute of Technology（麻省理工学院）；Queen’s University（皇后大学）；KIOS Research and Innovation Center of Excellence and the Department of Electrical and Computer Engineering, University of Cyprus（科斯卓越研究中心与创新中心，塞浦路斯大学电气与计算机工程系）
