Variable classification using graphs

In this chapter, the mathematical formulation of the variable classification problem is stated and some structural properties are discussed in terms of graphical techniques. Different strategies are available for carrying out process-variable classification. Both graph-oriented approaches and matrix-based techniques are briefly analyzed in the context of their usefulness for performing variable categorization. The use of output set assignment procedures for variable classification is described and illustrated. 

Having completed the classification according to steps (a) and (b) above, we can make use of the additional information obtained in the described manner. First, the reduced graph G determines, having selected a reference node, the reduced incidence matrix A. It is the matrix occurring in (3.2.4)2, thus in the constraint equation for the measured vector m (in fact, only for the subvector m of redundant variables). The equation is employed for adjusting the given values if the components of m"" have been actually measured then for reconciliation by statistical methods. 

The structure of the graph G along with the partition (3.6.1) allows one to classify all the variables (mass flowrates) with respect to the solvability see Section 3.3. According to the standard terminology, the variables mj, i J are called measured, the remaining (j J°) unmeasured. This classification will be used henceforth any a priori fixed variable of a model will be called measured , else unmeasured . The classification of the measured variables follows immediately from the partition (3.6.3) if i e J then m is redundant, else (i G J ) nonredundant. The nonredundant variables are also characterized by the property that i g J if and only if arc i closes a circuit in G with certain unmeasured streams (/ g J°). The nonredundant variables are unaffected by the solvability condition. 

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