7 research outputs found
Prediction error identification of linear dynamic networks with rank-reduced noise
Dynamic networks are interconnected dynamic systems with measured node
signals and dynamic modules reflecting the links between the nodes. We address
the problem of \red{identifying a dynamic network with known topology, on the
basis of measured signals}, for the situation of additive process noise on the
node signals that is spatially correlated and that is allowed to have a
spectral density that is singular. A prediction error approach is followed in
which all node signals in the network are jointly predicted. The resulting
joint-direct identification method, generalizes the classical direct method for
closed-loop identification to handle situations of mutually correlated noise on
inputs and outputs. When applied to general dynamic networks with rank-reduced
noise, it appears that the natural identification criterion becomes a weighted
LS criterion that is subject to a constraint. This constrained criterion is
shown to lead to maximum likelihood estimates of the dynamic network and
therefore to minimum variance properties, reaching the Cramer-Rao lower bound
in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in
Automatica, 4 April 201
Local module identification in dynamic networks with correlated noise: the full input case
The identification of local modules in dynamic networks with known topology
has recently been addressed by formulating conditions for arriving at
consistent estimates of the module dynamics, typically under the assumption of
having disturbances that are uncorrelated over the different nodes. The
conditions typically reflect the selection of a set of node signals that are
taken as predictor inputs in a MISO identification setup. In this paper an
extension is made to arrive at an identification setup for the situation that
process noises on the different node signals can be correlated with each other.
In this situation the local module may need to be embedded in a MIMO
identification setup for arriving at a consistent estimate with maximum
likelihood properties. This requires the proper treatment of confounding
variables. The result is an algorithm that, based on the given network topology
and disturbance correlation structure, selects an appropriate set of node
signals as predictor inputs and outputs in a MISO or MIMO identification setup.
As a first step in the analysis, we restrict attention to the (slightly
conservative) situation where the selected output node signals are predicted
based on all of their in-neighbor node signals in the network.Comment: Extended version of paper submitted to the 58th IEEE Conf. Decision
and Control, Nice, 201
Identifiability of dynamic networks with part of the nodes noise-free
In dynamic network identification a major goal is to uniquely identify the topology and dynamic links between the measured node variables. It is common practice to assume that process noises affect every output in multivariable system identification, and every node in dynamic networks with a full rank noise process. For many practical situations this assumption might be overly strong. This leads to the question of how to handle situations where the process noise is not full rank, i.e. when the number of white noise processes driving the network is strictly smaller than the number of nodes. In this paper a first step towards answering this question is taken by addressing the case of a dynamic network where some nodes are noise-free, and others are disturbed with a (correlated) process noise. In this situation the predictor filters that generate the one-step-ahead prediction of the node signals are non-unique, and the appropriate identification criterion leads to a constrained optimization problem. It is assessed when it is possible to distinguish between models on the basis of this criterion, leading to new notions of network identifiability. It appears that a sufficient condition for network identifiability is that every node signal in the network is excited by an external excitation signal or a process noise signal that is uncorrelated with other node excitations
Generalized sensing and actuation schemes for local module identification in dynamic networks
For the problem of identifying a target module that is embedded in a dynamic network with known interconnection structure, different sets of conditions are available for the set of node signals to be measured and the set of excitation signals to be applied at particular node locations. In previous work these conditions have typically been derived from either an indirect identification approach, considering external excitation signals as inputs, or from a direct identification approach, considering measured node signals as inputs. While both approaches lead to different sets of (sufficient) conditions, in this paper we extend the flexibility in the sufficient conditions for selection of excitation and measured node signals, by combining both direct and indirect approaches. As a result we will show the benefits of using both external excitation signals and node signals as predictor inputs. The provided conditions allow us to design sensor selection and actuation schemes with considerable freedom for consistent identification of a target module
From closed-loop identification to dynamic networks: Generalization of the direct method
Identification methods for identifying (modules in) dynamic cyclic networks, are typically based on the standard methods that are available for identification of dynamic systems in closed-loop. The commonly used direct method for closed-loop prediction error identification is one of the available tools. In this paper we are going to show the consequences when the direct method is used under conditions that are more general than the classical closed-loop case. We will do so by focusing on a simple two-node (feedback) network where we add additional disturbances, excitation signals and sensor noise. The direct method loses consistency when correlated disturbances are present on node signals, or when sensor noises are present. A generalization of the direct method, the joint-direct method, is explored, that is based on a vector predictor and includes a conditioning on external excitation signals. It is shown to be able to cope with the above situations, and to retain consistency of the module estimates
Local module identification in dynamic networks with correlated noise: The full input case
The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, typically under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is an algorithm that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. As a first step in the analysis, we consider the situation where the selected output node signals are predicted based on all of their in-neighbor node signals in the network