12 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
Bayesian topology identification of linear dynamic networks
In networks of dynamic systems, one challenge is to identify the
interconnection structure on the basis of measured signals. Inspired by a
Bayesian approach in [1], in this paper, we explore a Bayesian model selection
method for identifying the connectivity of networks of transfer functions,
without the need to estimate the dynamics. The algorithm employs a Bayesian
measure and a forward-backward search algorithm. To obtain the Bayesian
measure, the impulse responses of network modules are modeled as Gaussian
processes and the hyperparameters are estimated by marginal likelihood
maximization using the expectation-maximization algorithm. Numerical results
demonstrate the effectiveness of this method
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
Learning linear modules in a dynamic network using regularized kernel-based methods
In order to identify one system (module) in an interconnected dynamic
network, one typically has to solve a Multi-Input-Single-Output (MISO)
identification problem that requires identification of all modules in the MISO
setup. For application of a parametric identification method this would require
estimating a large number of parameters, as well as an appropriate model order
selection step for a possibly large scale MISO problem, thereby increasing the
computational complexity of the identification algorithm to levels that are
beyond feasibility. An alternative identification approach is presented
employing regularized kernel-based methods. Keeping a parametric model for the
module of interest, we model the impulse response of the remaining modules in
the MISO structure as zero mean Gaussian processes (GP) with a covariance
matrix (kernel) given by the first-order stable spline kernel, accounting for
the noise model affecting the output of the target module and also for possible
instability of systems in the MISO setup. Using an Empirical Bayes (EB)
approach the target module parameters are estimated through an
Expectation-Maximization (EM) algorithm with a substantially reduced
computational complexity, while avoiding extensive model structure selection.
Numerical simulations illustrate the potentials of the introduced method in
comparison with the state-of-the-art techniques for local module
identification.Comment: 15 pages, 7 figures, Submitted for publication in Automatica, 12 May
2020. Final version of paper submitted on 06 January 2021 (To appear in
Automatica
Prediction error identification of linear dynamic networks with rank-reduced noise
\u3cp\u3eDynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of 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 Cramér–Rao lower bound in the case of Gaussian noise. In order to reduce technical complexity, the analysis is restricted to dynamic networks with strictly proper modules.\u3c/p\u3