Optimal experimental design for practical identification of unstructured growth models

In this paper, optimal experimental design for parameter estimation of unstructured microbial growth models during growth of biomass on a single limiting substrate in a fed-batch bioreactor is considered. The ratio of the largest to the smallest eigenvalue of the Fisher information matrix (i.e., the modified E-criterion for optimal experimental design) is used to evaluate the information content of several simulation fed-batch experiments, each with a different volumetric feed rate profile. The construction of optimal feed rate profiles is based on the following Conjecture: A feed rate strategy which is optimal in the sense of process performance, is an excellent starting point for feed rate optimization with respect to estimation of those parameters with a large influence upon process performance. The optimal value of 1 for the modified E-criterion is obtained for several feed rate profiles with different structures, after optimization of their corresponding degrees of freedom with respect to the information content of the experiment. For each profile a criterion evaluating the violation of model validity is calculated.