In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes combined, for which the accuracy obtained, in terms of the trace of the asymptotic covariance matrix, is optimal. We introduce the concept of partial information matrix as a means to systematically obtain the information matrix for any dynamic network. For a specific tree class, called cross, we show that the accuracy of a particular module depends on the magnitude of the parameters to be estimated. Furthermore, when all factors are equal, it is best to excite. We extend a topological condition for branches under which the accuracy of a particular module of the network is independent of the other parameters from the tree. We provide a numerical analysis showing that our guidelines could be used as a selection tool for minimal EMPs for tree networks.

This paper deals with the identification of dynamical networks with partial excitation and measurement. Most of the work of the last few years on this topic has dealt with the design of valid Excitation and Measurement Patterns (EMP) (i.e. a selection of excited nodes and measured nodes that guarantee the generic identifiability of the network) while at the same time being sparse. Thus the objective was to identify the network with an EMP of small or even minimal cardinality, where the cardinality is the sum of the number of excited and measured nodes. In [5] a novel approach was taken, where the objective is no longer to design an EMP with small cardinality, but one that minimizes an experimental cost. A solution was proposed, but only for the case where all nodes are excited. In this paper, we extend the objective of designing a valid EMP with minimal experimental cost to the case where not all nodes are excited and not all nodes are measured. The resulting constrained optimization problem is considerably more complex. We propose two greedy algorithms with low computational cost and present a case study in which the optimal solution is obtained, though in general this can not be guaranteed. We also discuss the solution of the optimization for networks with particular topologies, for which customized algorithms can be conceived, and illustrate this idea for networks with a tree topology.

The paper [1] presented the first results on generic identifiability of dynamic networks with partial excitation and partial measurements. All previous papers assumed that either all nodes are excited or 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: all sources must be excited and all sinks measured, and all other nodes must be either excited or measured. In this paper, we show that two other types of nodes, which are defined by the local topology of the network, play an essential rôle in the search for a valid EMP, i.e. one that guarantees generic identifiability. We have called these nodes dources and dinks. We show that a network is generically identifiable only if, in addition to the above mentioned conditions, all dources are excited and all dinks are measured. We also show that sources and dources are the only nodes in a network that always need to be excited, and that sinks and dinks are the only nodes that need to be measured for an EMP to be valid.

This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamic networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to construct EMPs that guarantee identifiability for a range of networks with specific graph topologies, such as trees, loops, parallel networks, or Directed Acyclic Graphs (DAGs). However, an EMP that is valid for the identification of a subnetwork taken in isolation may no longer be valid when that subnetwork is embedded in a larger network. Our main contribution is to exhibit conditions under which it does remain valid, and to propose ways to enhance such EMP when these conditions are not satisfied.

This work deals with the selection of the experimental setting that yields most accurate estimates for a cascade network. There is a number of excitation and measurement patterns in which all modules in a cascade network can be identified. We consider that the optimal experiment is the one that achieves the least trace of the asymptotic covariance matrix of the prediction error method using the minimal number of excitations and measurements combined. We develop theoretical results under the assumptions that all modules are equal and with equal signal-to-noise ratio throughout the network. Under these assumptions, we demonstrate that there is an excitation and measurement pattern that results in more accurate estimates than others. Moreover, we show that some excitation and measurement patterns yield equal overall precision. From these results, guidelines based on the topology of the network emerge for the choice of the experimental setting. We provide numerical results which attest that the principles behind these guidelines are also valid for more general situations.

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 guarantees identifiability of a network with DAG topology.

This Letter provides necessary and sufficient conditions on the excitation and measurement pattern (EMP) that guarantee identifiability of a dynamical network that has the structure of a loop. The conditions are extremely simple in their formulation, and they can be checked by visual inspection. They allow one to easily characterize all EMPs that make the loop network identifiable.

In this paper we determine under which additional requirements a dynamic network is generically identifiable when some structures within it are known to be generically identifiable. We derive a set of necessary or sufficient conditions to determine generic identifiability of the whole network. The conditions take form as rank conditions of these specific structures and also in the topology of the network. Necessary and sufficient conditions for generic identifiability are given for classes of networks with parallel paths among the nodes. For the quite general case of networks whose graph is acyclic, we present necessary and sufficient conditions to determine whether a particular node needs to be excited and/or measured.

The problem of choosing the best allocation of excitations and measurements for the identification of a dynamic network is formally stated and analyzed. The best choice will be one that achieves the most accurate identification with the least costly experiment. Accuracy is assessed by the trace of the asymptotic covariance matrix of the parameters estimates, whereas the cost criterion is the number of excitations and measurements. Analytical and numerical results are presented for two classes of dynamic networks in state space form: branches and cycles. From these results, a number of guidelines for the choice emerge, which are based either on the topology of the network or on the relative magnitude of the modules being identified.

In this paper were evaluated identification methods for linear parameter-varying systems (LPV) based on least squares (LS) and support vector machines (LS-SVM). Both strategies are compared by using a collected data set from a real 350MVA generating unit. In this application is used a local approach identification of LPV models in regression forms and it is compared to a local LTI model in order to show the advantages in modelling nonlinear systems by using an LPV representation. Resumen— En este trabajo se evalúan los métodos de identificación de sistemas de parámetros lineales (LPV) sobre la base de los mı́nimos cuadrados (LS) y máquinas de vectores de soporte (SVM-LS). Ambas estrategias son comparados usando un conjunto de datos recogidos con ayuda de una verdadera unidad de generación de 350 MVA. En esta aplicación se utiliza un enfoque local identificación de modelos de LPV en formas de regresión y se compara con un modelo local LTI con el fin de mostrar las ventajas en el modelado de sistemas no lineales con una representación LPV.