Approximate Maximum Likelihood Parameter Estimation for Nonlinear Dynamic Models: Application to a Laboratory-Scale Nylon Reactor Model

In this article, parameters and states of a laboratory-scale nylon 612 reactor model (Schaffer et al. Ind. Eng. Chem. Res. 2003, 42, 2946-2959; Zheng et al. Ind. Eng. Chem. Res. 2005, 44, 2675-2686; and Campbell, D. A. Ph.D. Thesis, Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada, 2007) are estimated using a novel approximate maximum likelihood estimation (AMLE) algorithm (Poyton et al. Comput. Chem. Eng. 2006, 30, 698-708; Varziri et al. Comput. Chem. Eng., published online, http:// dx.doi.org/10.1016/j.compchemeng.2008.04.005; Varziri et al. Ind. Eng. Chem. Res. 2008, 47, 380-393; and Varziri et al. Can. J. Chem. Eng., accepted for publication). AMLE is a method for estimating the states and parameters in differential equation models with possible modeling imperfections. The nylon reactor model equations are represented by stochastic differential equations (SDEs) to account for any modeling errors or unknown process disturbances that enter the reactor system during experimental runs. In this article, we demonstrate that AMLE can address difficulties that frequently arise when estimating parameters in nonlinear continuous-time dynamic models of industrial processes. Among these difficulties are different types of measured responses with different levels of measurement noise, measurements taken at irregularly spaced sampling times, unknown initial conditions for some state variables, unmeasured state variables, and unknown disturbances that enter the process and influence its future behavior.