Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment. Issue 528 (2nd October 2019)

• Record Type: Journal Article
• Authors: Oates, Chris J.; Cockayne, Jon; Aykroyd, Robert G.; Girolami, Mark
• Is Part Of: Journal of the American Statistical Association. Volume 114:Issue 528(2019)
• Page Start: 1518
• Page End: 1531
• Publication Date: 2019-10-02
• Subjects: Electrical tomography -- Inverse problems -- Partial differential equations -- Probabilistic meshless methods -- Sequential Monte Carlo; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2019.1574583
• Languages: English
• ISSNs: 0162-1459

Abstract

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 article, 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 optimized implementation is provided in Python.