Probabilistic Models for Process Monitoring and Causality Analysis with Industrial Applications

• Author / Creator

  Raveendran, Rahul

• Process monitoring involves ensuring that the process systems are run safely and operated in the most profitable manner. On the other hand, causal modelling involves studying the causal interactions among the variables in a process system. The knowledge of these interactions is useful in process monitoring, root cause analysis of process anomalies, and devising optimum operation strategies. Both these applications can greatly benefit from data-driven models when it is difficult to obtain models for the studied system based on the first principles.

  In this thesis, we develop and present probabilistic models for process monitoring and causal modelling applications. The models developed in thesis enjoy an important benefit of probabilistic modelling that it allows one to define very general models that subsume several special cases. This, in turn, has two advantages, (i) a result derived for the general model can be reduced to special cases if required, alleviating the need to study special cases in isolation and (ii) if the special cases turn out to be different competing hypotheses about the data generating process, the users can then leverage Bayesian analysis to select between the competing hypotheses.

  The probabilistic models developed for process monitoring address two extreme cases of monitoring problems, (i) monitoring unimodal systems and (ii) monitoring multi-modal systems. For monitoring unimodal systems, we define a general model that encompasses several linear Gaussian models as special cases. This allows us to develop a monitoring procedure based on the general model and reduce it to special cases if desired. In addition, we attempt to theoretically understand the connections between the linear Gaussian models and classical multivariate techniques such as principal component analysis in the context of process monitoring. For monitoring multi-modal systems, we propose a two-layer model that consists of a convex combination of linear Gaussian models in the layers stacked one above the other. This model scales well when compared to the probabilistic models used for process monitoring in the literature to approximate non-Gaussian distributions. Furthermore, we illustrate the two-layer model for process monitoring using a lab-scale and an industrial case study.

  In causal modelling, we address two important problems, (i) identification of time-lagged causal interactions in the presence of instantaneous/contemporaneous interactions among the variables and (ii) modelling long-term interactions for time-varying systems. Granger causality analysis is a most commonly used approach for studying time-lagged causal interactions. However, if the presence of contemporaneous interactions is not properly accounted for, the Granger causality analysis techniques tend to identify spurious time-lagged interactions. In this thesis, we propose a model for representing the time-lagged and contemporaneous interactions explicitly and perform Bayesian analysis to determine the presence and absence of both types of interactions. The approach is found to be more robust to the presence of contemporaneous interactions when compared to the traditional Granger causality analysis techniques. When studying the long-term effects of process variables on process performance indicators using the routine operation data from the process systems, time-varying nature of the process systems affects the correct identification of the effects. To address this problem, we propose a time-varying parameters model and a Bayesian analysis approach to recover the time-varying effects. We illustrate the causal modelling approaches developed in this thesis using industrial case studies.

• Subjects / Keywords

  • Causality analysis
  • Bayesian networks
  • Variational Bayes
  • Process data analysis
  • Process monitoring
  • Probabilistic modelling

• Graduation date

  Fall 2019

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-ay15-fk81

• License

  Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.