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Model Reduction and Parameter Estimation for Diffusion Systems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Diffusion is a phenomenon in which particles move from regions of higher density to regions of lower density. Many physical systems, in fields as diverse as plant biology and finance, are known to involve diffusion phenomena. Typically, diffusion systems are modeled by partial differential equations (PDEs), which include certain parameters. These parameters characterize a given diffusion system. Therefore, for both modeling and simulation of a diffusion system, one has to either know or determine these parameters. Moreover, as PDEs are infinite order dynamic systems, for computational purposes one has to approximate them by a finite order model. In this thesis, we investigate these two issues of model reduction and parameter estimation by considering certain specific cases of heat diffusion systems.

We first address model reduction by considering two specific cases of heat diffusion systems. The first case is a one-dimensional heat diffusion across a homogeneous wall, and the second case is a two-dimensional heat diffusion across a homogeneous rectangular plate. In the one-dimensional case we construct finite order approximations by using some well known PDE solvers and evaluate their effectiveness in approximating the true system. We also construct certain other alternative approximations for the one-dimensional diffusion system by exploiting the different modal structures inherently present in it. For the two-dimensional heat diffusion system, we construct finite order approximations first using the standard finite difference approximation (FD) scheme, and then refine the FD approximation by using its asymptotic limit.

As for parameter estimation, we consider the same one-dimensional heat diffusion system, as in model reduction. We estimate the parameters involved, first using the standard batch estimation technique. The convergence of the estimates are investigated both numerically and theoretically. We also estimate the parameters of the one-dimensional heat diffusion system recursively, initially by adopting the standard recursive prediction error method (RPEM), and later by using two different recursive algorithms devised in the frequency domain. The convergence of the frequency domain recursive estimates is also investigated.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2004. , p. 125
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 974
Keywords [en]
Diffusion system, Partial differential equations (PDEs), Model reduction, PDE solvers, Finite difference approximation, Chebyshev polynomials, System identification, Parameter estimation, Recursive estimation, Frequency domain estimation
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:uu:diva-4252ISBN: 91-554-5958-7 (print)OAI: oai:DiVA.org:uu-4252DiVA, id: diva2:164555
Public defence
2004-06-03, Room 2146, Building 2, Center for Mathematics and Information Technology, Uppsala, 10:15
Opponent
Supervisors
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2011-02-16Bibliographically approved
List of papers
1. Reduced order models for diffusion systems
Open this publication in new window or tab >>Reduced order models for diffusion systems
2001 In: International Journal of Control, Vol. 75, no 15, p. 1543-1557Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-91720 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
2. Reduced order models for diffusion systems using singular perturbations
Open this publication in new window or tab >>Reduced order models for diffusion systems using singular perturbations
2001 In: Energy and Buildings, Vol. 33, no 8, p. 769-781Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-91721 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
3. Reduced order model for a two-dimensional diffusion system
Open this publication in new window or tab >>Reduced order model for a two-dimensional diffusion system
In: International Journal of ControlArticle in journal (Refereed) Submitted
Identifiers
urn:nbn:se:uu:diva-91722 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
4. Reduced order models for diffusion systems via Collocation methods
Open this publication in new window or tab >>Reduced order models for diffusion systems via Collocation methods
2000 In: Proc of 12th IFAC Symposium on System Identification, Santa Barbara, CA, USA, JuneArticle in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-91723 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
5. Bias and variance of parameter estimates of a one-dimensional heat diffusion system
Open this publication in new window or tab >>Bias and variance of parameter estimates of a one-dimensional heat diffusion system
2002 In: Proc of 15th IFAC Congress, Barcelona, Spain, JulyArticle in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-91724 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
6. Recursive algorithm for estimating parameters in a one-dimensional heat diffusion system
Open this publication in new window or tab >>Recursive algorithm for estimating parameters in a one-dimensional heat diffusion system
2002 In: Proc of Reglermöte, Linköping, SwedenArticle in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-91725 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
7. Recursive algorithms for estimating parameters in a one-dimensional diffusion system: derivation and implementation
Open this publication in new window or tab >>Recursive algorithms for estimating parameters in a one-dimensional diffusion system: derivation and implementation
In: International Journal of Adaptive Control and Signal ProcessingArticle in journal (Refereed) Submitted
Identifiers
urn:nbn:se:uu:diva-91726 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
8. Recursive algorithms for estimating parameters in a one-dimensional diffusion system: analysis
Open this publication in new window or tab >>Recursive algorithms for estimating parameters in a one-dimensional diffusion system: analysis
In: International Journal of ControlArticle in journal (Refereed) Submitted
Identifiers
urn:nbn:se:uu:diva-91727 (URN)
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved

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