Model re-parameterization and output prediction for a bioreactor system

Microalgal bioprocesses are of increasing interest due to the possibility of producing fine chemicals, pharmaceuticals, and biofuels. In this work, the parameter estimability of a first principles ODE model of a microalgal bioreactor, containing 6 states and 12 unknown parameters, is investigated. For this purpose, the system input trajectories are computed using the D-optimality criterion. Even by using a D-optimal input, not all parameters were found to have a significant effect on model predictions. Linear and non-linear transformations are used to partition the parameter space into estimable and inestimable subspaces. For the linear re-parameterization, a set of four directions in the twelve dimensional parameter space, along which a significant change in the output occurs, is identified using singular value decomposition of the parameter covariance matrix. The non-linear re-parameterization utilizes the three system rate functions as pseudo-outputs in order to perform a non-linear transformation which reduces the dimension of the parameter space from twelve to three. Both the proposed re-parameterization methods achieve a good degree of output prediction at a greatly decreased computational cost.