(204c) Information Theory-Based Sequential Parameter Estimation of Bioreactor
Identification is an indispensable step in optimization and control of batch bioreactors. Bioreactor models of a practical scale system are usually nonlinear, complex, and are accompanied with a large number of parameters. Optimal Experimental Design (OED), which aims to find the most information-rich operation, is a statistical tool to guide engineers to efficiently identify a system. Despite its wide acceptance as a viable tool, current OED approaches often result in a huge optimization problem. This makes not only the computation prohibitive, but more importantly, makes the analysis of the solution infeasible.
In this work, we suggest a new scheme which estimates parameters in a sequential manner. Parameters are ‘lined up’ into an order and estimated by the sequence. Since the parameters are highly correlated in a typical bioreactor system, it is crucial to decide how to group and place parameters in a proper order. First, simulation is performed with a purposely inaccurate (~50%) set of parameters. The objective of this simulation is to observe qualitative behavior of the process state variables, not their exact values. Applying several criterion based on information theory such as sensitivity, we can 1) rule out unidentifiable parameters, 2) combine highly correlated parameters as a set, and 3) place those parameter sets into an order that maximizes the information gain. As a result, we can obtain the ‘estimation schedule’.
In the actual implementation, optimal input is calculated at each step in a similar manner to the model predictive control. The parameter identification schedule obtained a priori is used as guidance. Maximum information gain to a certain parameter set over a predefined prediction horizon is used as an objective function. When the information gain for a certain set of parameters exceeds some predefined level, the set is considered fully identified and the objective function switches to identify the next set of parameters.
The suggested approach is illustrated with two fed-batch bioreactor models. The first is a theoretical model with five parameters. The second is a practical scale microalgal bioreactor model with more than 10 parameters. Results from both models have shown improved performance and convergence property.
The advantages of our approach are twofold. First, unlike other ‘blind’ approach of OED, the suggested approach can make use of the prior knowledge on the system in a quantitative sense. Second, the suggested approach can also handle other issues related to the identification that are being solved by experience or ad hoc including the number of batches required to run for identification and the amount of information that can be obtained with economical constraints.