International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 1998
Volume 8 - 1998

Issues in nonlinear parameter estimation and multivariate model discrimination: Applications in polymer reaction engineering

Thomas A. Duever, Alexander Penlidis

In this paper an overview is given of issues in parameter estimation, model discrimination, and optimal sensor selection as they relate to the modelling of copolymerization processes. The problems are discussed in the context of a comprehensive polymerization simulation package that is being developed, which includes an extensive database. A brief description of the modelling equations together with a listing of equations used to predict copolymer composition, triad fractions and polymerization rate, which are the primary responses used throughout this paper, is given. The problem of reactivity ratio estimation is reviewed and a method based on the Error-in-Variables model (EVM) is described which has the advantage that it properly accounts for all the errors in the measurements being used in the estimation. Two methods for describing the uncertainty in the estimates obtained are given. The first establishes approximate elliptical contours which are approximate in both shape and size. The other approach offers an improvement in that contours having the correct shape are calculated. The problem of discriminating between two models based on the terminal and penultimate mechanism using the method proposed by Buzzi-Ferraris and Forzatti (1983) is described. Simulations using copolymer composition, triad fractions and copolymerization rate are compared. An experimental verification for styrene/methyl methacrylate and triad fraction data is discussed and contrasted with previous experimental results. A comparison between experiments designed using the model discrimination criterion and those using equally-spaced points shows that in general the designed experiments are better able to correctly discriminate. Furthermore, even in those cases when the equally-spaced experiments lead to correct model discrimination, they usually lead to poor estimates of the model prediction error and the parameter uncertainty. Finally, the problem of optimally selecting sensors for a polymerization process is discussed. The approach shown uses a Kalman filter to optimally combine the polymerization model with process data. The different sensor scenarios are ranked using the determinant of the state covariance matrix.