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Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs |
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| Authors: | Matthijs van Berkel Gerd Vandersteen Egon Geerardyn Rik Pintelon Hans Zwart Marco de Baar |
| Affiliation: | 1. Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology group, PO Box 513, 5600 MB Eindhoven, The Netherlands;2. Vrije Universiteit Brussel, Department of Fundamental Electricity and Instrumentation, Pleinlaan 2, 1050 Brussels, Belgium;3. FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM–FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein, The Netherlands;4. Eindhoven University of Technology, Department of Mechanical Engineering, Dynamics and Control group, PO Box 513, 5600 MB Eindhoven, The Netherlands |
| 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. |
| Keywords: | Partial differential equations Maximum likelihood estimators Systems transfer functions Heat flows |
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