Getting the most out of it: optimal experiments for parameter estimation of microalgae growth models

Rafael Muñoz-Tamayo 1 Pierre Martinon 2, 3 Gaël Bougaran 4 Francis Mairet 1 Olivier Bernard 1
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, X - École polytechnique, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : Mathematical models are expected to play a pivotal role for driving microalgal production towards a profitable process of renewable energy generation. To render models of microalgae growth useful tools for prediction and process optimization, reliable parameters need to be provided. This reliability implies a careful design of experiments that can be exploited for parameter estimation. In this paper, we provide guidelines for the design of experiments with high informative content based on optimal experiment techniques to attain an accurate parameter estimation. We study a real experimental device devoted to evaluate the effect of temperature and light on microalgae growth. On the basis of a mathematical model of the experimental system, the optimal experiment design problem was formulated and solved with both static (constant light and temperature) and dynamic (time varying light and temperature) approaches. Simulation results indicated that the optimal experiment design allows for a more accurate parameter estimation than that provided by the existing experimental protocol. For its efficacy in terms of the maximum likelihood properties and its practical aspects of implementation, the dynamic approach is recommended over the static approach.
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Rafael Muñoz-Tamayo, Pierre Martinon, Gaël Bougaran, Francis Mairet, Olivier Bernard. Getting the most out of it: optimal experiments for parameter estimation of microalgae growth models. Journal of Process Control, Elsevier, 2014, 24 (6), pp.991-1001. 〈http://www.sciencedirect.com/science/article/pii/S095915241400122X〉. 〈10.1016/j.jprocont.2014.04.021〉. 〈hal-00998525〉

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