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

• We solved the optimal experiment design (OED) problem for a microalgae growth model.
• The performances of optimal dynamic inputs obtained via a control vector parameterization and inputs obtained via a complete discretization of states and controls are comparable.
• The dynamic approach is recommended over the static approach for designing optimal experiments.
• Partitioning the full OED problem into subproblems is an efficient approach.
• Small uncertainty on the model parameters leads to high discrepancies on model predictions.

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.