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

M. Van Berkel, G. Vandersteen, E. Geerardyn, R. Pintelon, H.J. Zwart, M. de Baar

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
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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 languageEnglish
Pages (from-to)2113-2119
Number of pages7
JournalAutomatica
Volume50
Issue number8
DOIs
Publication statusPublished - 2014

Keywords

  • Heat flows
  • Maximum likelihood estimators
  • Partial differential equations
  • Systems transfer functions

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