Browsing by Author "Basson, Marno"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- ItemBayesian parameter estimation for process monitoring(Stellenbosch : Stellenbosch University., 2020-03) Basson, Marno; Cripwell, Jamie T.; Auret, Lidia; Coetzer, R. L. J.; Kroon, R. S. (Steve); Stellenbosch University. Faculty of Engineering. Dept. of Process Engineering.ENGLISH ABSTRACT: The underlying mechanism of many physical systems studied in engineering can be described by algebraic, ordinary differential and auxiliary equations. While these equations stem from engineering expertise, the principles underpinning the model development phase do not always provide sufficient insight into selecting suitable values for all the model parameters. Furthermore, it might not be possible to directly measure all the model parameters (which can be related to several physicochemical system properties) from the system under consideration due to physical, economic and time constraints. As a result, the engineer often has to estimate the model parameters from noise-corrupted, time series data obtained from the physical system, while simultaneously quantifying how reliable these parameter estimates are. The purpose of the current study is to investigate model parameter estimation, from both the frequentist and Bayesian statistical inference perspectives, and to evaluate the merit of applying Bayesian probabilistic techniques in the chemical engineering setting. Two Bayesian parameter estimation methodologies were developed. The first methodology applies to estimating the parameters of lumped system algebraic dynamic models, while the second methodology is focused on lumped system ordinary differential equation model parameter estimation. Both proposed Bayesian methodologies were benchmarked against the Gauss-Newton nonlinear least squares implementation for which the resulting estimated model parameters have a (frequentist) maximum likelihood interpretation. The results obtained from the proposed Bayesian methodologies were compared to the benchmark approach results based on several performance criteria for a single data set manifestation as well as for multiple independently generated data sets. It was found that the proposed Bayesian methodologies, as well as the benchmark approaches, provide consistent parameter estimation results when compared to the simulation ground truth parameter values, across the multiple independent data sets. Based on the parameter inference results obtained from the different case studies considered in the current work, it was determined that, from a pragmatic engineering perspective, there is no reason to favour the use of the proposed Bayesian methodologies over the frequentist benchmark approaches and vice versa as both approaches provide comparable results. However, the benefit of the Bayesian approach (which explicitly expresses the model parameter uncertainty) was illustrated by considering a simple cost-benefit analysis for several of the case studies where it was possible to make more informed engineering decisions under uncertainty compared to the traditional frequentist benchmark approach. In conclusion, even though there is no noteworthy difference between the parameter inference results obtained from the benchmark and proposed Bayesian approaches, the value of the Bayesian approach shows up when one considers the subsequent application of the inferred parameters in day-to-day engineering tasks. Consequently, it is worth further exploring the benefit of applying probabilistic techniques and explicitly modeling with uncertainty, i.e. Bayesian statistical inference, in chemical engineering applications.