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International Society for Industrial Process Tomography

3rd World Congress on Industrial Process Tomography

The Mathematical Formulation of the State Evolution Equation in Electrical Process Tomography


Hanna Katriina Pikkarainen


Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, FINLAND, hanna.pikkarainen@hut.fi


ABSTRACT


We consider the process tomography problem of imaging the concentration distribution of a given substance in a fluid moving in a pipeline based on electromagnetic measurements on the surface of the pipe. We view the problem as a state estimation problem. The concentration distribution is treated as a stochastic process satisfying a stochastic differential equation referred to as the state evolution equation. The measurements are described in terms of an observation equation containing the measurement noise. Our main interest is in the mathematical formulation of the state evolution equation. The time evolution is modelled by a stochastic convection-diffusion equation. We derive a discrete evolution equation for the concentration distribution by using the stochastic integration theory and the semigroup technique.


Keywords process tomography, electrical impedance tomography, state estimation, stochastic differential equations

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