Statistical estimation of phase boundaries and material parameters in industrial process tomography

Process tomography (PT) is a noninvasive process imaging technique that aims at extracting process parameters like volume fractions in order to control industrial processes. In electrical capacitance tomography (ECT), one specific sensing modality in PT, the physical parameters of interest are the involved permittivities. Many different finite element model based deterministic and stochastic methods have been carried out to determine the spatial material distribution given indirect observations from the boundary of the closed object. In this contribution a novel boundary element method (BEM) based approach to solve the underlying inverse ECT problem in case of two-phase flow fields even in the presence of measurement noise and fluid dynamics is proposed. The occurring phase boundaries, i. e. the interfaces between liquid and gaseous states, are modeled by truncated Fourier descriptors. Both the Fourier coefficients and the absolute material values are estimated with the extended Kalman filter (EKF). Furthermore, the maximum probability method is introduced to assure that the material values are within a physically reasonable range. The proposed approach which is applicable for real-time monitoring is validated by means of real measurements acquired from our ECT prototype sensor