Application of macroscopic balances to the identification of gross measurement errors

Abstract

A systematic method is presented which is capable of both detecting the presence of grossly biased measurement errors and locating the source of these errors in a bioreactor through statistical hypothesis testing. Equality constraints derived from material and energy balances are employed for the detection of data inconsistencies and for the subsequent identification of the suspect measurements by a process of data analysis and rectification. Maximum likelihood techniques are applied to the estimation of the states and parameters of the bioreactor after the suspect measurements have been eliminated. The level of significance is specified by the experimenter while the measurments are assumed to be randomly, normally distributed with zero mean and known variances. Two different approaches of data analysis, batchwise and sequential, that lead to a consistent set of adjustments on the experimental values, are discussed. Several examples based on the fermentation data taken from literature sources are presented to demonstrate the utility of the proposed method, and one set of data is solved numerically to illustrate the computational aspect of the algorithm.