Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

TL;DR

This paper develops Bayesian probabilistic numerical methods for time-dependent state estimation in industrial hydrocyclone equipment, enabling uncertainty quantification in the numerical solution of physical models.

Contribution

It introduces a Bayesian approach that models numerical errors explicitly, improving the reliability of state estimation in complex industrial processes.

Findings

Provides a sequential Monte Carlo implementation in Python

Enables principled uncertainty quantification in physical model solutions

Improves inference accuracy over traditional methods

Abstract

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 fundamental task of state-estimation for 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 all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimised implementation is provided in Python.