• conservation equations;
  • linear constraints;
  • data reconciliation;
  • balancing technique;
  • gross error detection;
  • error diagnosis


Conservation equations derived from elemental balances, heat balances, and metabolic stoichiometry, can be used to constrain the values of conversion rates of relevant components. In the present work, their use will be discussed for detection and localization of significant errors of the following types:

  • 1.
    At least one of the primary measurements has a significant error (gross measurement error).
  • 2.
    The system definition is incorrect: a component
    • a.
      is not included in the system description.
    • b.
      has a composition different from that specified.
  • 3.
    The specified variances are too small, resulting in a too-sensitive test.

The error diagnosis technique presented here, is based on the following: given the conservation equations, for each set of measured rates, a vector of residuals of these equations can be constructed, of which the direction is related to the error source, as its length is a measure of the error size. The similarity of the directions of such a residual vector and certain compare vectors, each corresponding to a specific error source, is considered in a statistical test. If two compare vectors that result from different error sources have (almost) the same direction, errors of these types cannot be distinguished from each other. For each possible error in the primary measurements of flows and concentrations, the compare vector can be constructed a priori, thus allowing analysis beforehand, which errors can be observed. Therefore, the detectability of certain errors likely to occur can be insured by selecting a proper measurement set. The possibility of performing this analysis before experiments are carried out is an important advantage, providing a profound understanding of the detectability of errors. The characteristics of the method with respect to diagnosis of simultaneous errors and error size estimation are discussed and compared to those of the serial elimination method and the serial compensation strategy, published elsewhere. © 1994 John Wiley & Sons, Inc.