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Statistical approximation of the iInverse problem in multivariate population balance modeling / Andreas Braumann in Industrial & engineering chemistry research, Vol. 49 N° 1 (Janvier 2010) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 49 N° 1 (Janvier 2010) . - pp. 428–438 Titre : Statistical approximation of the iInverse problem in multivariate population balance modeling Type de document : texte imprimé Auteurs : Andreas Braumann, Auteur ; Peter L. W. Man, Auteur ; Markus Kraft, Auteur Année de publication : 2010 Article en page(s) : pp. 428–438 Note générale : Industrial chemistry Langues : Anglais (eng) Mots-clés : Statistical--Approximation--Inverse--Problem--Multivariate--Population--Balance--Modeling Résumé : This paper deals with the estimation of model parameters and their uncertainties encountered in granulation modeling. The outcome of a multivariate, detailed population balance model of a high shear granulation process is locally approximated in the parameter space by first and second order response surfaces, allowing a fast computation of the model response. The response surfaces are used in three different objective functions—moment matching, expected least-squares, and expected weighted least-squares—in order to estimate ranges for the rate constants for particle coalescence, particle compaction, particle breakage, and reaction, which appear as free parameters in the granulation model. First, second-order response surfaces for the population balance model are constructed and used as approximations of the model in the objective functions for the numerical solution of the inverse problem. Second, the choice of objective function is investigated. It is found that the uncertainties of the model predictions differ for the three objective functions only slightly. The estimates for the intervals of the model parameters either overlap or are very close. However, the moment matching objective function is recommended because the number of estimated parameters and experimental data sets can be chosen independently. ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901230u [article] Statistical approximation of the iInverse problem in multivariate population balance modeling [texte imprimé] / Andreas Braumann, Auteur ; Peter L. W. Man, Auteur ; Markus Kraft, Auteur . - 2010 . - pp. 428–438. Industrial chemistry Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 49 N° 1 (Janvier 2010) . - pp. 428–438 Mots-clés : Statistical--Approximation--Inverse--Problem--Multivariate--Population--Balance--Modeling Résumé : This paper deals with the estimation of model parameters and their uncertainties encountered in granulation modeling. The outcome of a multivariate, detailed population balance model of a high shear granulation process is locally approximated in the parameter space by first and second order response surfaces, allowing a fast computation of the model response. The response surfaces are used in three different objective functions—moment matching, expected least-squares, and expected weighted least-squares—in order to estimate ranges for the rate constants for particle coalescence, particle compaction, particle breakage, and reaction, which appear as free parameters in the granulation model. First, second-order response surfaces for the population balance model are constructed and used as approximations of the model in the objective functions for the numerical solution of the inverse problem. Second, the choice of objective function is investigated. It is found that the uncertainties of the model predictions differ for the three objective functions only slightly. The estimates for the intervals of the model parameters either overlap or are very close. However, the moment matching objective function is recommended because the number of estimated parameters and experimental data sets can be chosen independently. ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie901230u