Hydrocyclones provide a simple and inexpensive method for removing solids from liquids, as well as separating two liquids according to their relative densities. They have widespread applications, including in areas such as environmental engineering and the petrochemical industry. Continual monitoring is essential in most industrial applications, since the input ﬂow rate is an important control parameter that can be adjusted to maximise the separation eﬃciency of the equipment. In addition, the high pressures that are often involved necessitate careful observation of the internal ﬂuid dynamics to ensure safety. However, direct observation of the internal ﬂow of the ﬂuids is diﬃcult or impossible due to, for example, the reinforced walls of the hydrocyclone and the opacity of the mixed component.
One possible technique for monitoring internal ﬂow in a hydrocyclone is electrical impedance tomography (EIT). This inherently statistical technique relates measurements of electrical potential taken on the exterior of the machine to the internal conductivity field of the liquid, via the repeated solution of a particular partial differential equation (PDE) model. Unfortunately, EIT methods are computationally intensive and are sensitive to numerical error in the solution of the PDE. It is therefore desirable to relax the statistical problem, in such a way that valid statistical inferences can be drawn at decreased computational cost.
This paper explores the role of probabilistic numerical methods in the monitoring of industrial equipment via EIT. As such, it represents one of the first serious industrial applications of probabilistic numerical methods. Results broadly supported the effectiveness of the statistical relaxation of PDE models that is provided by probabilistic numerical methods. On the other hand, this work highlighted a number of important issues that remain open, including the need to develop efficient alternatives to Markov chain Monte Carlo methods for posterior exploration and the need to address prior elicitation for models specified via a PDE.
Reference: Oates CJ, Cockayne J, Robert GA. Bayesian Probabilistic Numerical Methods for Industrial Process Monitoring, arXiv:1707.06107.