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Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization
Author(s) -
Du Yuncheng,
Budman Hector,
Duever Thomas
Publication year - 2017
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201600095
Subject(s) - inverse , monte carlo method , reactivity (psychology) , nonlinear system , mathematics , estimation theory , inverse problem , markov chain , polynomial chaos , markov chain monte carlo , mathematical optimization , computer science , algorithm , statistics , physics , mathematical analysis , medicine , alternative medicine , geometry , pathology , quantum mechanics
A generalized polynomial chaos (gPC)‐based methodology is developed to estimate the reactivity ratio in copolymerization, where the reactivity ratio is assumed to be stochastic unknown and determined by comparing model predictions with limited experimental data. The estimation step is formulated as a stochastic inverse problem of finding the distributional stochastic reactivity ratio parameters with a maximum likelihood function. The results show that the gPC‐based reactivity ratio estimation is efficient and powerful, since it simultaneously provides the best estimates and their corresponding variances. Beyond achieving accurate estimation results, it is shown that the computational cost of the gPC‐based methodology is significantly lower than Markov chain Monte Carlo simulations, thus demonstrating the potential of the gPC method for dealing with other more complicated nonlinear problems.