A boundary element approach for real-time monitoring and control from electrical resistance tomographic data

Electrical tomography techniques provide the potential for a cheap and non-invasive approach to the monitoring and control of dynamic industrial processes. The predominant approach to the analysis of tomographic data is based on domain discretisation, leading to ill-posed inverse problems. Stable solution then requires substantial regularization which can mask features of interest. Although image reconstruction is useful for process visualization, for automatic control such an image is unnecessary, and will require further post-processing to allow control parameters to be obtained. However, reliable information cannot be obtained by post-processing poor images. For process monitoring, estimation of geometric parameters is more appropriate than visualization. These parameters can then be directly used for process control and thus avoiding the need for post-processing. This motivates the move to high-level geometric models which also make computational algorithms much more efficient. In addition, the boundary element method (BEM) proves to be an excellent alternative to the finite element method (FEM) for piecewise homogeneous examples, even making the real-time monitoring of processes feasible. This paper investigates the use of the BEM approach for monitoring and control in electrical resistance tomography. To illustrate the proposed methods a simple simulation study will be reported which considers real-time tracking of a single object in a circular section. This is motivated by water/oil separation in a hydrocyclone. A simple control strategy monitors oil core properties and adjusts input pressure.