(433e) Large-Scale Nonlinear Parameter Estimation with Mixed Effect and Multiresponse Models
AIChE Annual Meeting
2021
2021 Annual Meeting
Catalysis and Reaction Engineering Division
Modeling and Analysis of Chemical Reactors I
Wednesday, November 10, 2021 - 9:40am to 10:05am
Researchers conducting experiments to determine reaction kinetics often replicate the experiment
under similar conditions to ensure they are achieving a repeatable result. During each experiment, there
are sources of error that occur which fall into one of two categories: fixed and random effects. Mixed
effects models are used for chemical kinetics because they account for both the random error within an
individual experiment as well as across a set of experiments, preventing bias in the estimation of the
fixed parameters (Hickman et al. 2019). For a given repeated set of experiments, there are parameters
that are unique to an individual data set and those which are shared among all data sets. These
represent local and global parameters, respectively.
This work focuses on using KIPET (Kinetic Parameter Estimation Toolbox) to estimate the parameters of
the mixed effects problem (Short et al., 2019). KIPET uses Pyomo (Hart et al. 2017) to formulate the
parameter estimation problem based on maximum likelihood principles and large-scale nonlinear
programming strategies. KIPET applies an orthogonal collocation strategy on finite elements to discretize
the nonlinear system (Short et al., 2019). While the resulting nonlinear system can be solved with a
direct nonlinear algebra solver, as the problem size grows, the time and memory requirements can make
this approach intractable (Zavala et al. 2006). This work seeks to exploit the mixed effects problem
structure and use a Schur complement decomposition and parallel solver solution technique across data
sets. Further, this work applies model discrimination techniques based on (Stewart, Shon, Box 1998) to
determine the most probable model given the data.
This work focuses on applying these techniques to a smaller case study with four kinetic parameters
(Hickman et al. 2019) and larger case study with 39 kinetic parameters (Bui, Bhan 2018).
under similar conditions to ensure they are achieving a repeatable result. During each experiment, there
are sources of error that occur which fall into one of two categories: fixed and random effects. Mixed
effects models are used for chemical kinetics because they account for both the random error within an
individual experiment as well as across a set of experiments, preventing bias in the estimation of the
fixed parameters (Hickman et al. 2019). For a given repeated set of experiments, there are parameters
that are unique to an individual data set and those which are shared among all data sets. These
represent local and global parameters, respectively.
This work focuses on using KIPET (Kinetic Parameter Estimation Toolbox) to estimate the parameters of
the mixed effects problem (Short et al., 2019). KIPET uses Pyomo (Hart et al. 2017) to formulate the
parameter estimation problem based on maximum likelihood principles and large-scale nonlinear
programming strategies. KIPET applies an orthogonal collocation strategy on finite elements to discretize
the nonlinear system (Short et al., 2019). While the resulting nonlinear system can be solved with a
direct nonlinear algebra solver, as the problem size grows, the time and memory requirements can make
this approach intractable (Zavala et al. 2006). This work seeks to exploit the mixed effects problem
structure and use a Schur complement decomposition and parallel solver solution technique across data
sets. Further, this work applies model discrimination techniques based on (Stewart, Shon, Box 1998) to
determine the most probable model given the data.
This work focuses on applying these techniques to a smaller case study with four kinetic parameters
(Hickman et al. 2019) and larger case study with 39 kinetic parameters (Bui, Bhan 2018).