| 1. |
- Everitt, Niklas, et al.
(författare)
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An empirical Bayes approach to identification of modules in dynamic networks
- 2018
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Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 91, s. 144-151
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Tidskriftsartikel (refereegranskat)abstract
- We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods.
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| 2. |
- Everitt, Niklas, et al.
(författare)
-
Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method
- 2018
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 221-234
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Tidskriftsartikel (refereegranskat)abstract
- In system identification, it is often difficult to use a physical intuition when choosing a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the model orders must be chosen according to the true system. However, if only the plant estimates are of interest and the experiment is performed in open loop, the noise model can be over-parameterized without affecting the asymptotic properties of the plant. The limitation is that, as PEM suffers in general from non-convexity, estimating an unnecessarily large number of parameters will increase the risk of getting trapped in local minima. Here, we consider the following alternative approach. First, estimate a high-order ARX model with least squares, providing non-parametric estimates of the plant and noise model. Second, reduce the high-order model to obtain a parametric model of the plant only. We review existing methods to do this, pointing out limitations and connections between them. Then, we propose a method that connects favorable properties from the previously reviewed approaches. We show that the proposed method provides asymptotically efficient estimates of the plant with open-loop data. Finally, we perform a simulation study suggesting that the proposed method is competitive with state-of-the-art methods.
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