Recent advances in statistical modelling and analysis for electrical tomography without image reconstruction

Robert G. Aykroyd, Stuart Barber, Brian A. Cattle, D. Alex Goodwin, & Robert M. West

The aim of industrial process control is to convert measurements, taken while the process is evolving, into parameters which can be used to control the process. That is to monitor an active process and predict unacceptable or sub-optimal behaviour. To be of practical use this must all be computationally efficient allowing real-time feedback. Electrical tomography measurements have the potential to provide useful data without intruding into the industrial process, but produce highly correlated and noisy data, and hence need sensitive analysis. Two recently developed approaches will be described. One approach is to work directly with the measurement data.Wavelets have proven to be highly effective at extracting information from noisy data. Their multiscale nature enables the efficient description of both transient and long-term signals. Furthermore, only a small number of wavelet coefficients are needed to describe complicated signals and the wavelet transform is computationally efficient. The resulting wavelet models can be used to classify flow into one of a set of regimes. Alternatively, estimation of geometric parameters describing the internal structure being imaged can be considered. These parameters can then be used directly for process control and thus avoiding the need for image post-processing. This motivates the move to high-level geometric models which also make computational algorithms much more efficient. In addition, for forward solution the boundary element method (BEM) is an excellent alternative to the finite element method (FEM) for piecewise homogeneous examples, even making the real-time monitoring of processes feasible. A simulation study will be reported which considers real-time tracking of objects.

Key Words: Boundary Element Method, Process Monitoring and Control, Wavelets