Design of Dynamic Experiments in Modeling for Optimization of Batch Processes

Abstract

Finding optimal operating conditions fast with a scarce budget of experimental runs is a key problem to speeding up the development of innovative products and processes. Modeling for optimization is proposed as a systematic approach to bias data gathering for iterative policy improvement through experimental design using first-principles models. Designing dynamic experiments that are optimally informative in order to reduce the uncertainty about the optimal operating conditions is addressed by integrating policy iteration based on the Hamilton-Jacobi-Bellman optimality equation with global sensitivity analysis. A conceptual framework for run-to-run convergence of a model-based policy iteration algorithm is proposed. Results obtained in the fed-batch fermentation of penicillin G are presented. The well-known Bajpai and Reuss bioreactor model validated with industrial data is used to increase on a run-to-run basis the amount of penicillin obtained by input policy optimization and selective (re)estimation of relevant model parameters. A remarkable improvement in productivity can be gain using a simple policy structure after only two modeling runs despite initial modeling uncertainty.

Study of n-Butyl Acrylate Self-Initiation Reaction Experimentally and via Macroscopic Mechanistic Modeling

“…Models that are based on the method of moments can be used to estimate kinetic rate coefficients more accurately. Applications of both types of models can be found in the literature [42][43][44][45][46].…”

Run‐to‐Run Optimization of Biodiesel Production using Probabilistic Tendency Models: A Simulation Study

“…Using only these available measurement methods, tendency models are proposed to optimize productivity. A tendency model is a simplified nonlinear model of a process that combines data with fundamental knowledge of the process characteristics …”

Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning

“…The main problem in bioreactor modeling for optimization is that biological activity occurs in metabolic pathways which are controlled by switches through built-in regulatory networks (Geng & Yuan, 2010). Due to the complexity of metabolic regulation and limited measurements, first-principles models of bioreactor dynamics can only capture the qualitative tendency of sampled state variables such as biomass, substrate and product concentrations (Martínez, Cristaldi, & Grau, 2009;Tsobanakis, 1994). Hence, without biasing data gathering by increasingly improving the operating policy, bioreactor performance predictions are too uncertain and unreliable in quantitative terms to be useful for productivity optimization (Bonvin, 1998;Martínez & Wilson, 2003;Schenker & Agarwal, 1995).…”

“…This approach does not rely on expert knowledge, but requires to model available data carefully. For model-based policy optimization to be successful it is mandatory to re-estimate selectively the more sensitive model parameters using optimal experimental design techniques in data gathering (Martínez et al, 2009). An approach for model-based heuristic optimization of operating policies has been proposed in Maria (2004Maria ( , 2007 and successfully applied to d-glucose oxidation.…”

“…This model-based policy optimization approach consists of iteratively using new measurements to increasingly reduce parametric uncertainty in a tendency (imperfect) model and later resorting to the updated model for policy improvement (Martínez et al, 2009). A "tendency model" is a low order, nonlinear, dynamic model that approximates the stoichiometry and kinetic relationships of a bioprocess using the available plant data along with fundamental knowledge of the process characteristics (Bonvin & Rippin, 1990;Filippi, Bordet, Villermaux, Marchal-Brassey, & Georgakis, 1989;Fotopoulos, Georgakis, & Stenger, 1998;Georgakis, 1995;Uhlemann, Cabassud, LeLann, Borredon, & Cassamatta, 1994).…”