The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The task of monitoring the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods.
In this paper, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when numerical error is ignored. The method is cast with a sequential Monte Carlo framework and an optimised implementation is provided in Python.
Oates CJ, Cockayne J, Aykroyd RG. Bayesian Probabilistic Numerical Methods for Industrial Process Monitoring.