Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates
作者:
R. T. J. M. van der Heijden,
J. J. Heijnen,
C. Hellinga,
B. Romein,
K. Ch. A. M. Luyben,
期刊:
Biotechnology and Bioengineering
(WILEY Available online 1994)
卷期:
Volume 43,
issue 1
页码: 3-10
ISSN:0006-3592
年代: 1994
DOI:10.1002/bit.260430103
出版商: Wiley Subscription Services, Inc., A Wiley Company
关键词: data reconciliation;balancing;classification;observability;redundancy
数据来源: WILEY
摘要:
AbstractMeasurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrixR. MatrixRplays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrixRfor an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph‐theoretical approach), and it is easily implemented into a computer program. © 1994 John Wiley&Sons, I
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