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Nonlinear Black-Box Modeling in System Identification: a Unified Overview
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.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
IRISA/INRIA, Campus de Beaulieu, Rennes Cedex, France.
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1995 (English)Report (Other academic)
Abstract [en]

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of ‘used’ parameters considerably less than the number of ‘offered’ parameters, by regularization, shrinking, pruning or regressor selection.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1995. , 55 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1742
Keyword [en]
Nonlinear systems, Model structures, Parameter estimation, Wavelets, Neural networks, Fuzzy modeling
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55254ISRN: LiTH-ISY-R-1742OAI: oai:DiVA.org:liu-55254DiVA: diva2:315882
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2014-10-06Bibliographically approved

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Ljung, Lennart

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CiteExportLink to record
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