Abstract
In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters is approximated with stochastic convection diffusion and fluid dynamics models. The actual time-varying reconstruction is carried out as a state estimation problem. As the boundary observations we use the voltage data of electrical impedance tomography. We have previously shown that state estimation works well in process tomography in the cases in which the fluid dynamics of the system are modeled correctly. In the real case, however, the velocity field cannot usually be determined accurately. This may be caused, for example, by complex nature of the flow, the turbulence, discretization, etc. In adopting the first proposed approach, it is essential to know how much the inaccuracies in the fluid dynamical model affect the state estimates in process tomography. In this paper we consider the tolerance of the approach with respect to these inaccuracies. We show that the estimation scheme is relatively tolerant to modeling errors in the flow field. Thus relatively reliable estimates can be obtained, for example, in a case in which a laminar flow model is used in turbulent flow conditions. However, the degradation that is due to incorrect flow fields is not insignificant and it is also conjectured that it could be possible that an extension of the proposed method could be used to estimate some flow field parameters.
