Estimation of Parameters and Selection of Models Applied to Population Balance Dynamics via Approximate Bayesian Computational

Document Type : Full Length Research Article

Authors

1 Graduate Program in Chemical Engineering, PPGEQ/ITEC/UFPA, Federal University of Pará, Belém, PA, Brazil

2 School of Biotechnology and Bioprocess Engineering, Federal University of Para, Belém, PA, Brazil

3 Graduate Program in Mathematics and Statistics, Federal University of Para, Belém, PA, Brazil

4 Natural Resources Engineering, Federal University of Para, Belém, PA, Brazil.

Abstract

Population balance models mathematically describe the particle size distribution based on modeling physical phenomena that influence the distribution, such as aggregation, growth, and breakage. Due to the wide range of mechanisms present, several models are presented in the literature since several hypotheses are considered. In the current work, the Approximate Bayesian Computational statistical technique was used to select four different models of population balance and estimate their parameters. Three strategies were applied to the drawing of parameters, evaluating the correlation between the parameters of the models. An adaptive tolerance in each population and a stopping criterion, based on Morozov's uncertainty principle, were used for the algorithm. The technique obtained reasonable estimates for the phenomenological rates of the models. The algorithm correctly selected the model used for generating measurements, and the three draw strategies demonstrated good applicability. The results obtained showed that the algorithm presented accuracy and precision in estimating the parameters and properly selected the models analyzed.

Keywords

Main Subjects

References

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  • Receive Date: 09 November 2021
  • Revise Date: 19 June 2022
  • Accept Date: 19 June 2022

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