Direct process estimation from tomographic data using artificial neural systems Junita Mohamad-Saleh Brian S. Hoyle Frank J. W. Podd D. Mark Spink Institute of Integrated Information Systems School of Electronic and Electrical Engineering University of Leeds Leeds LS2 9JT, United Kingdom E-mail: b.s.hoyle@leeds.ac.uk Abstract. The paper deals with the goal of component fraction es- timation in multicomponent flows, a critical measurement in many processes. Electrical capacitance tomography (ECT) is a well- researched sensing technique for this task, due to its low-cost, non- intrusion, and fast response. However, typical systems, which in- clude practicable real-time reconstruction algorithms, give inaccurate results, and existing approaches to direct component fraction measurement are flow-regime dependent. In the investiga- tion described, an artificial neural network approach is used to di- rectly estimate the component fractions in gas – oil, gas – water, and gas – oil – water flows from ECT measurements. A two-dimensional finite-element electric field model of a 12-electrode ECT sensor is used to simulate ECT measurements of various flow conditions. The raw measurements are reduced to a mutually independent set using principal components analysis and used with their corresponding component fractions to train multilayer feed-forward neural networks (MLFFNNs). The trained MLFFNNs are tested with patterns consist- ing of unlearned ECT simulated and plant measurements. Results included in the paper have a mean absolute error of less than 1% for the estimation of various multicomponent fractions of the permittivity distribution. They are also shown to give improved component frac- tion estimation compared to a well known direct ECT method. © 2001 SPIE and IS&T. [DOI: 10.1117/1.1379570] 1 Introduction Many different tomographic measurement techniques such as ultrasonic, optical, and electrical impedance can be used for determining component measurements. Among these, the impedance methods have been very popular due to their design simplicity, high speed, and low costs. An electrical impedance system can be designed to predominantly sense conductance or capacitance, or both. Generally, measure- ments based on capacitance provide better reproducibility than conductance because of its typical dependence of on ion concentration. Capacitance-based methods have thus been more widely explored for process measurements in- volving multicomponent flows. Such systems may be un- suited to flows in which the continuous component is highly conductive, for example salt water. However, in this work we concentrate upon the processing of the sensor data, rather than its acquisition. In electrical capacitance tomography ECT, a number of electrodes are mounted around the periphery of a pipe at a point of interest. It is based on the principle that different materials with differing dielectric constants produce a change in the capacitance measurements between pairs of electrodes. All possible combinations of pairs of electrodes are used to provide capacitance measurements. As dis- cussed below, computation on the measurements can be performed to obtain the fraction of individual components in a multicomponent flow. This paper describes the use of artificial neural systems ANSs for the purpose of estimating component fractions of material in two-component and three-component flows based on capacitance-sensed tomographic data. The net- work can ‘learn’ the required nonlinear transformations needed to extract component fractions from ECT data by using a set of examples. The following section presents the simulation procedure performed in generating a set of simulated data. It also describes the ECT sensor model used. Following this, the application of artificial neural network ANN methods for determining component fraction of materials is described. Results of an experiment based on the simulated data are then presented. The final section describes the application of the method to actual plant data. 2 Finite Element Simulation of an ECT System An ECT system is characterized by Poisson’s equation div   x , y  grad   x , y  =0 1 where  ( x , y ) is the spatial permittivity distribution,  ( x , y ) is the spatial distribution of the electrical potential, div is the divergence operator, and grad is the gradient Paper IP-08 received Jan. 3, 2001; revised manuscript received Mar. 26, 2001; ac- cepted for publication Mar. 29, 2001. This paper is a revision of a paper presented at the SPIE conference on Process Imaging for Automatic Control, Nov. 2000, Boston, MA. The paper presented there appears unrefereed in Proceedings of SPIE Vol. 4188. 1017-9909/2001/$15.00 © 2001 SPIE and IS&T. Journal of Electronic Imaging 10(3), 646– 652 (July 2001). 646 / Journal of Electronic Imaging / July 2001 / Vol. 10(3)