My research projects are funded through the University Partnership Initiative with Dow Chemical Company. I use nonlinear programming (NLP) techniques, maximum likelihood principles, and collocation methods to solve large-scale, constrained, nonlinear parameter estimation problems comprised of differential and algebraic equations (DAEs). I am also working with my research group on an existing software package KIPET to incorporate extensions such mixed-effects modeling, deviations from Beer-Lambert’s Law, and decomposition techniques for chemical kinetics.
in situ optical spectroscopy techniques have a wide variety of applications in both academia and industry. Decoupling information from spectral data into concentration profiles and pure component absorbance profiles is a nontrivial problem which requires a large amount of research effort. Based on the work of Chen, Weifeng & Biegler, Lorenz & Garcia-Munoz, Salvador (2016), I will be investigating extensions of using a simultaneous approach for the deconvolution of Beer-Lambert’s Law with reaction kinetic information.
The work involves investigating the use of nonlinear mixed-effects models to take into account batch-to-batch variation for kinetic parameter estimation problems using data from multiple batch reactions. Multiple longitudinal batch experiments with time series data often exhibit correlated residuals, violating a common assumption that all batches are independent. Nonlinear mixed-effects models offer an alternative approach to account for the two types of random experimental variation resulting from longitudinal experiments: the measurement error for each data point and the random batch-to-batch variation between experiments. This paper by Hickman et al. was the first case study examined. The physical system was described by differential equations that model a trickle-bed batch reactor system in space and time and well-stirred pot. Using orthogonal collocation on finite elements, the differential equations that describe the physical system can be discretized into a system on nonlinear equations. Using nonlinear programming strategies, we can then formulate and solve a nonlinear mixed-effects model. By taking into account the batch-to-batch variation between experiments, which can be attributed to physical effects such as deactivation of a catalyst over time, we estimate chemical kinetic parameter values with 95% confidence intervals for each parameter. Further, we apply Bayesian inference techniques for model discrimination to identify the most likely candidate model given the data.