Bayesian uncertainty quantification in process modelling
File(s)
Author(s)
Gomoescu, Lucian
Type
Thesis
Abstract
This thesis promotes the Bayesian approach to uncertainty quantification. It allows the
consideration of a priori information about the estimated parameters and the estimation
result is an a posteriori distribution that captures all the effects of non-linear dependency
between observables and parameters. In contrast, the frequentist paradigm limits
itself to the exclusive use of data and its very popular method of confidence ellipsoids
assumes a linear dependency between observables and parameters. Despite these important
drawbacks, the frequentist method has the practical advantage of being much
less computationally demanding than the Bayesian counterpart. Even so, the improved
modelling tools and Monte Carlo sampling techniques combined with the speed, memory,
and parallel architecture of the present processors are sufficient ingredients for
solving real-life Bayesian parameter estimation problems. But the combination of these
ingredients is missing and it represents one of the main goals of this work. Another goal
is to apply the nested sampling technique in the context of set-membership estimation
and feasibility analysis in order to obtain an inner-approximation of a feasible set. The
resulting methods are applicable to any type of mathematical model because only the
value of the constraints is needed. Moreover, the methods consider both robustly and
probabilistically -satisfied constraints hence they are applicable to a variety of feasible
sets.
The first two chapters offer an introduction to the role of statistics in the mathematical
modelling exercise and recall the Bayesian paradigm advantages. Also, various
Monte Carlo techniques for posterior distribution sampling are presented briefly and
with a focus on the algorithms that are implemented in gPROMS.
Chapter 3 describes the work performed to integrate seamlessly within gPROMS a
Markov Chain Monte Carlo solver (BPEMC) and a Nested Sampling solver (BPENS) that
sample the parameter posterior distribution and provide summary information about the
marginal posterior distribution.
Chapter 4 demonstrates through case studies the capability of the solvers to tackle
practically relevant problems. The first case study – based on two datasets consisting of
tens of steady state experiments – estimates five to eleven parameters for four alternative
kinetic models of methanol and DME synthesis from syngas. The second case study
focuses on the issue of parameter non-identifiability in case of a Goodwin biological
oscillator, which is a challenging example of parameter estimation despite the small
model and dataset size.
Chapter 5 extends the nested sampling method applicability to characterization of
feasible sets defined by robustly or probabilistically -satisfied constraints. Set-membership
estimation is an example of problem with robustly-satisfied constraints. Stochastic flexibility
analysis is an example of problem with probabilistically-satisfied constraints. Illustrative
and more real-world cases are solved using our algorithms’ implementation in
the Python package DEUS.
The final chapter contains overall conclusions and future research directions.
consideration of a priori information about the estimated parameters and the estimation
result is an a posteriori distribution that captures all the effects of non-linear dependency
between observables and parameters. In contrast, the frequentist paradigm limits
itself to the exclusive use of data and its very popular method of confidence ellipsoids
assumes a linear dependency between observables and parameters. Despite these important
drawbacks, the frequentist method has the practical advantage of being much
less computationally demanding than the Bayesian counterpart. Even so, the improved
modelling tools and Monte Carlo sampling techniques combined with the speed, memory,
and parallel architecture of the present processors are sufficient ingredients for
solving real-life Bayesian parameter estimation problems. But the combination of these
ingredients is missing and it represents one of the main goals of this work. Another goal
is to apply the nested sampling technique in the context of set-membership estimation
and feasibility analysis in order to obtain an inner-approximation of a feasible set. The
resulting methods are applicable to any type of mathematical model because only the
value of the constraints is needed. Moreover, the methods consider both robustly and
probabilistically -satisfied constraints hence they are applicable to a variety of feasible
sets.
The first two chapters offer an introduction to the role of statistics in the mathematical
modelling exercise and recall the Bayesian paradigm advantages. Also, various
Monte Carlo techniques for posterior distribution sampling are presented briefly and
with a focus on the algorithms that are implemented in gPROMS.
Chapter 3 describes the work performed to integrate seamlessly within gPROMS a
Markov Chain Monte Carlo solver (BPEMC) and a Nested Sampling solver (BPENS) that
sample the parameter posterior distribution and provide summary information about the
marginal posterior distribution.
Chapter 4 demonstrates through case studies the capability of the solvers to tackle
practically relevant problems. The first case study – based on two datasets consisting of
tens of steady state experiments – estimates five to eleven parameters for four alternative
kinetic models of methanol and DME synthesis from syngas. The second case study
focuses on the issue of parameter non-identifiability in case of a Goodwin biological
oscillator, which is a challenging example of parameter estimation despite the small
model and dataset size.
Chapter 5 extends the nested sampling method applicability to characterization of
feasible sets defined by robustly or probabilistically -satisfied constraints. Set-membership
estimation is an example of problem with robustly-satisfied constraints. Stochastic flexibility
analysis is an example of problem with probabilistically-satisfied constraints. Illustrative
and more real-world cases are solved using our algorithms’ implementation in
the Python package DEUS.
The final chapter contains overall conclusions and future research directions.
Version
Open Access
Date Issued
2022-02
Date Awarded
2022-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
Advisor
Chachuat, Benoit
Pantelides, Constantinos Christou
Sponsor
European Commission
Grant Number
675585
Publisher Department
Chemical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)