Some Issues Associated with a General Data Reconciliation Problem

A simplified diagram of the general procedure for data reconciliation in chemical plants is given in Fig. 4. 

SOME ISSUES ASSOCIATED WITH A GENERAL DATA RECONCILIATION PROBLEM 

A processing plant is a physical system containing a large number of units and streams. For example, counting the equipment in the processing section as well as in the service section (considering mixers and stream dividers) of a petrochemical plant reveals the existence of approximately 1000 interconnected units and about 2500 streams. If we also take into account that in each stream the variables of interest can be flowrate, composition, temperature, pressure, and enthalpy, it is evident that data treatment in a typical plant involves the solution of a large-scale problem. 

The adjustment of measurements to compensate for random errors involves the resolution of a constrained minimization problem, usually one of constrained least squares. Balance equations are included in the constraints these may be linear but are generally nonlinear. The objective function is usually quadratic with respect to the adjustment of measurements, and it has the covariance matrix of measurements errors as weights. Thus, this matrix is essential in the obtaining of reliable process knowledge. Some efforts have been made to estimate it from measurements (Almasy and Mah, 1984 Darouach et al., 1989 Keller et al., 1992 Chen et al., 1997). The difficulty in the estimation of this matrix is associated with the analysis of the serial and cross correlation of the data. 

The presence of gross errors invalidates the statistical basis of the common data reconciliation procedures, so they must be identified and removed. Gross error detection has received considerable attention in the past 20 years. Statistical tests in combination with an identification strategy have been used for this purpose. A good survey of the available methodologies can be found in Mah (1990) and Crowe (1996). 

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