Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization. Issue 2 (1st March 2017)

• Record Type: Journal Article
• Authors: Du, Yuncheng; Budman, Hector; Duever, Thomas
• Is Part Of: Macromolecular theory and simulations. Volume 26:Issue 2(2017)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-03-01
• Subjects: maximum likelihood -- nonlinear parameter estimation -- polynomial chaos expansion -- uncertainty analysis; Macromolecules -- Periodicals; Polymers -- Periodicals; Polymerization -- Periodicals; Macromolécules -- Périodiques; 547.705
• DOI: 10.1002/mats.201600095
• Languages: English
• ISSNs: 1022-1344

Abstract

Abstract : Inverse problem is to estimate parameters from observed data through mathematical models. It is necessary to account for uncertainty resulting from variables of models and measurement noise to improve the accuracy of parameter estimation. An estimation methodology based on a generalized polynomial chaos and a maximum likelihood function to account for such uncertainty is presented. Abstract : 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.