(88e) Parameter Estimation of Nonlinear Stochastic Models: Reactivity Ratio Studies in Copolymerization

Mathematical models provide new ways to understand and describe complex systems. There are two key steps in the model development and design, i.e., parameter estimation (or model calibration) and optimal experimental design. Parameter estimation identifies the unknown parameters of the model, which can provide the best fit to a set of available experimental data. In contrast, optimal experimental design aims to devise the dynamic experiments that can provide the maximum information content for model identification, discrimination, and estimation. In this work, we focus on parameter estimation of nonlinear polymerization models using two popular stochastic modelling techniques, i.e., Markov Chain Monte Carlo (MCMC) and generalized polynomial chaos (gPC).

Nonlinearity in models may affect the way that a model is being interpreted, and linearization-based parameter estimation may be biased sometimes. For example, Kalman filters-based methods usually exert a restrictive assumption about the distribution of parameters to obtain desirable estimates. In addition, uncertainty, originating from noisy data, is another main restrictive factor for accurate parameter estimation. It is useful to propagate uncertainty into the model and study its effect on model predictions.

To estimate parameters of a nonlinear model in the presence of uncertainty, the error in variable model (EVM) was recently proposed. This treats each measurement as an unknown true value plus an error term and can handle implicit models. The disadvantage of EVM is that it is only tractable when all the distributions describing variations in the measurement are normal distributed. Another issue with EVM is that it may converge to a local optimum rather than a global optimum for parameter estimation.

As an alternative, Markov Chain Monte Carlo (MCMC) and generalized polynomial chaos (gPC) can overcome the limitations of EVM-based method. Using these techniques, we present a robust and efficient way to calculate parameter estimates and determine parameter uncertainty. The estimation of reactivity ratios from composition data using the Mayo-Lewis and Meyer Lowry models will be used to illustrate the efficiency of the proposed methods. In addition, comparisons will be provided between the MCMC and gPC results and the results obtained from classical regression approaches.