Fermentation data analysis and state estimation in the presence of incomplete mass balance

A method is developed for identifying measurement errors and estimating fermentation states in the presence of unidentified reactant or product. Unlike conventional approaches using elemental balances, this method employs an empirically determined basis, which can tolerate unidentified reaction species. The essence of this approach is derived from the concept of reaction subspace and the technique of singular value decomposition. It is shown that the subspace determined via singular value decomposition of multiple experimental data provides an empirical basis for identifying measurement errors. The same approach is applied to fermentation state estimation. Via the formulation of the reaction subspace, the sensitivity of state estimates to measurement errors is quantified in terms of a dimensionless quantity, maximum error gain (MEG). It is shown that using the empirically determined subspace, one can circumvent the problem of unidentified reaction species, meanwhile reducing the sensitivity of the estimates.