• error diagnosis;
  • filtering technique;
  • data reconciliation;
  • measurement error detection


This article presents a method to test the presence of relatively small systematic measurement errors; e.g., those caused by inaccurate calibration or sensor drift. To do this, primary measurements—flow rates and concentrations—are first translated into observed conversions, which should satisfy several constraints, like the laws of conservation of chemical elements. This study considers three objectives:

  • 1.
    Modification of the commonly used balancing technique to improve error sensitivity to be able to detect small systematic errors. To this end, the balancing technique is applied sequentially in time.
  • 2.
    Extension of the method to enable direct diagnosis of errors in the primary measurements instead of diagnosing errors in the observed conversions. This was achieved by analyzing how individual errors in the primary measurements are expressed in the residual vector.
  • 3.
    Derivation of a new systematic method to quantitatively determine the sensitivity of the error, is that error size at which the expected value of the chisquare test function equals its critical value.

The method is applied to industrial data demonstrating the effectiveness of the approach. It was shown that, for most possible error sources, a systematic errors of 2% to 5% could be detected. In given application, the variation of the N-content of biomass was appointed to be the cause of errors. © 1994 John Wiley & Sons, Inc.