Parameter Estimation for a Polymerization Reactor Model with a Composite-Step Trust-Region NLP Algorithm

Abstract

We consider an application of the trust-region SQP algorithm described by Arora and Biegler (Comput. Optim. Appl., in press) to the parameter estimation for a polymerization reactor. In particular, we are interested in the robustness of this algorithm in solving ill-conditioned optimization problems with differential algebraic (DAE) models. For this system, it is possible to measure a variety of states, such as production and concentrations. Some of these states contain more information and lead to more reliable parameter estimates than would be obtained if the states were not measured. To minimize sensor costs, it is thus beneficial to select the smallest combination of state measurements that contains the most information. Because the polymer process model is nonlinear, we decide to test the information content of measurements by analyzing properties of the reduced Hessian and constructing joint-confidence regions. This approach is related to the observability analysis (Albuquerque, J. S.; Biegler, L. T. AIChE J. 1996, 42, 2841. Narasimhan, S.; Jordache, C. Data Reconciliation and Gross Error Detection; Gulf Publishing Company: Houston, TX, 2000. Crowe, C. M. Chem. Eng. Sci. 1989, 44, 2909). However, for nonlinear problems, a reliable and efficient parameter estimation algorithm is essential for the measurement selection procedure. Finally, whereas inputs to the process are often held constant in parameter estimation problems, these inputs often contain noise. It is therefore necessary to reconcile inputs along with states in a simultaneous optimization framework. This problem becomes an errors in variables model (EVM) and can be considerably larger and more difficult to solve. In this study, we also consider the related EVM problem and compare results to the standard parameter estimation problem.