Doctor of Philosophy
School of Mathematics and Applied Statistics
Understanding the uncertainty of model parameters is crucial for building predictive models. Within the field of spontaneous ignition a slight variation in the model parameters can cause a significant variation in our ability to determine if ignition occurs. We consider this problem through an application to the steel industry. A byproduct of the steelmaking process is stockpiled where oxidation can induce ignition. The resulting ignition process sinters the filter improving the durability. Understanding this process requires careful modelling and consideration of the uncertainty in the reaction kinetics. We examine some experimental data on the filter cake to determine these reaction kinetics. Due to the complex nature of the filter cake, standard estimation techniques are difficult to apply and the uncertainty in our parameters cannot be an input into the larger stockpiles. We apply a Bayesian framework for parameter estimation that considers a distribution for the parameters rather than a point estimation with an uncertainty. Using this approach we construct a Markov Chain Monte Carlo (MCMC) algorithm to sample this distribution and test this against simulated data; we capture the true values of the reaction kinetics within the target distribution. Our approach uses the experimental data, and we construct meaningful estimates for the reaction kinetics.
Once we consider multiple sets of experimental data it highlights some issues with our proposed reaction scheme and methodology. Our Sequential Monte Carlo approach identifies a discrepancy between the estimates for different experiments. We consider multiple different avenues to resolve this discrepancy. The most significant of these methods was to consider a different reaction scheme. In addition to this, the initial reactant concentrations were found to have a significant effect on the posterior distribution of parameter estimates; if we change these values then our distributions would not be overlapping. Additionally, we then consider a different approach to combining the multiple experiments; combining the parameter distributions from the MCMC method, we propose a new prior that contains this information and use this to combine the experimental data. This is effective at generating a new sample, though it does not address any of the issues that may arise from model mis-specification.
Berry, Matthew, Modelling the Self-Heating of Steel Stockpiles, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2023. https://ro.uow.edu.au/theses1/1612
FoR codes (2008)
0102 APPLIED MATHEMATICS, 0104 STATISTICS
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.