Estimating parameters with pre-specified accuracies in distributed parameter systems using optimal experiment design |
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Authors: | M G Potters X Bombois M Mansoori Paul M J Van den Hof |
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Affiliation: | 1. Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands;2. Laboratoire Ampère UMR CNRS 5005, Ecole Centrale de Lyon, Ecully Cedex, France;3. Department of Chemical and Petroleum Engineering, Sharif University of TechnologyTehran, Iran;4. Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands |
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Abstract: | Estimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results. |
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Keywords: | Distributed systems optimal experiment design physical systems identification accurate simulation optimal actuator and sensor locations |
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