Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs

Matthijs van Berkel; Gerd Vandersteen; Egon Geerardyn; Rik Pintelon; Heiko J. Zwart; Marco de Baar

doi:10.1016/j.automatica.2014.05.027

Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs

Matthijs van Berkel, Gerd Vandersteen, Egon Geerardyn, Rik Pintelon, Heiko J. Zwart, Marco de Baar

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.

Original language	Undefined
Pages (from-to)	2113-2119
Number of pages	7
Journal	Automatica
Volume	50
Issue number	8
DOIs	https://doi.org/10.1016/j.automatica.2014.05.027
Publication status	Published - Aug 2014

Keywords

EWI-25236
Maximum likelihood estimators
Heat flows
IR-92442
Systems transfer functions
METIS-309627
Partial differential equations

Access to Document

10.1016/j.automatica.2014.05.027

http://eprints.eemcs.utwente.nl/secure2/25236/01/1-s2.0-S0005109814002179-main.pdf

Cite this

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title = "Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs",

abstract = "The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.",

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T1 - Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs

AU - van Berkel, Matthijs

AU - Vandersteen, Gerd

AU - Geerardyn, Egon

AU - Pintelon, Rik

AU - Zwart, Heiko J.

AU - de Baar, Marco

N1 - eemcs-eprint-25236

PY - 2014/8

Y1 - 2014/8

N2 - The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.

AB - The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.

KW - EWI-25236

KW - Maximum likelihood estimators

KW - Heat flows

KW - IR-92442

KW - Systems transfer functions

KW - METIS-309627

KW - Partial differential equations

U2 - 10.1016/j.automatica.2014.05.027

DO - 10.1016/j.automatica.2014.05.027

M3 - Article

SN - 0005-1098

VL - 50

SP - 2113

EP - 2119

JO - Automatica

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