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A Nonparametric Approach to Model Error Modeling
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2000 (English)In: Proceedings of the 12th IFAC Symposium on System Identification, 2000, 157-162 p.Conference paper (Refereed)
Abstract [en]

To validate an estimated model and evaluate its reliability is an important part of the system identification process. Recent work on model validation has shown that the use of explicit model error models provide a better way of visualizing the possible deficiencies of the nominal model. Previous contributions have mainly focused on parametric black-box models for estimating the error model. However, this requires that a correct model order for the error model has to be selected. Here we suggest an adaptive and nonparametric frequency-domain method that estimates the frequency response of the model error by an automatic procedure. A benefit with this approach is that the tuning can be done locally, i.e., that different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and utilize a statistical criterion for selecting the optimal resolution.

Place, publisher, year, edition, pages
2000. 157-162 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2230
Keyword [en]
Model error modeling, Non-parametric regression, Frequency-response methods
National Category
Engineering and Technology Control Engineering
URN: urn:nbn:se:liu:diva-91126ISBN: 978-0080435459OAI: diva2:618444
12th IFAC Symposium on System Identification, Santa Barbara, CA, USA, June, 2000
Available from: 2013-04-28 Created: 2013-04-17 Last updated: 2014-12-11
In thesis
1. Variance Expressions and Model Reduction in System Identification
Open this publication in new window or tab >>Variance Expressions and Model Reduction in System Identification
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Although system identification is now a mature research field, some problems remain unsolved. Examples of unsolved or partly unsolved problems are; accuracy of subspace identification algorithms, identification via model reduction, identification for control, and identification of non-linear systems. Some problems that fall into these categories are studied in this thesis.

This thesis discusses variance expressions in system identification. In particular, variance expressions for reduced models are analyzed.

The topic of model reduction via system identification has received little attention during the years. To understand how the variance of a high order model affects the reduced model, a general expression for the variance of the low order model as a function of the reduction method used is derived. This allows the analysis of all model reduction methods that can be written as a minimization criterion, where the function to be minimized is twice continuously differentiable. Many methods can be studied using this approach. However, the popular method of model reduction by balanced truncation of states does not immediately fit into this framework.

Many unsolved problems in system identification may be studied with the use of bootstrap methods. This statistical tool, used to assess accuracy in estimation problems, may be adopted to a series of problems in system identification and signal processing. The thesis presents how bootstrap can be adopted in the prediction error framework. In addition, we demonstrate how bootstrap can be applied to problems of constructing condence regions with a simultaneous confidence degree and calculating the variance of undermodeled models.

The thesis briefly discusses how set membership identification and prediction error identification can be combined into a more robust estimate. Finally, insights into how model validation can be performed in a more user informative way are also given.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2002. 192 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 730
National Category
Control Engineering
urn:nbn:se:liu:diva-98162 (URN)91-7373-253-2 (ISBN)
Public defence
2002-02-22, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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