### Optimal experimental design for nonlinear systems: Application to microbial kinetics identification

**Van Impe, JFM ***(Katholieke Universiteit Leuven)*

Monday 18 July 2011, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

Dynamic biochemical processes are omnipresent in industry, e.g., brewing, production of enzymes and pharmaceuticals. However, since accurate models are required for model based optimisation and measurements are often labour and cost intensive, Optimal Experiment Design (OED) techniques for parameter estimation are valuable tools to limit the experimental burden while maximising the information content. To this end, often scalar measures of the Fisher information matrix (FIM) are exploited in the objective function. In this contribution, we focus on the parameter estimation of nonlinear microbial kinetics. More specifically, the following issues are addressed: (1) Nonlinear kinetics. Since microbial kinetics is most often nonlinear, the unknown parameters appear explicitly in the design equations. Therefore, selecting optimal initialization values for these parameters as well as setting up a convergent sequential design scheme is of great importance. (2) Biological kinetics. Since we deal with models for microbial kinetics, the design of dynamic experiments is facing additional constraints. For example, upon applying a step change in temperature, an (unmodelled) lag phase is induced in the microbial population's response. To avoid this, additional constraints need to be formulated on the admissible gradients of the input profiles thus safeguarding model validity under dynamically changing environmental conditions. (3) Not only do different scalar measures of the FIM exist, but they may also be competing. For instance, the E-criterion tries to minimise the largest error, while the modified E-criterion aims at obtaining a similar accuracy for all parameters. Given this competing nature, a multi-objective optimisation approach is adopted for tackling these OED problems. The aim is to produce the set of optimal solutions, i.e., the so-called Pareto set, in order to illustrate the trade-offs to be made. In addition, combinations of parameter estimation quality and productivity related objectives are explored in order to allow an accurate estimation during production runs, and decrease down-time and losses due to modelling efforts. To this end, ACADO Multi-Objective has been employed, which is a flexible toolkit for solving dynamic optimisation or optimal control problems with multiple and conflicting objectives. The results obtained are illustrated with both simulation studies and experimental data collected in our lab.

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