Variable classification

The concepts of structural observability are the basic tools for developing variable classification strategies. Some approaches presented in Chapter 3 are based on the fact that the classification of process variables results from the topology of the system and the placement of instruments and has nothing to do with the functional form of the balance equations. Thus, the linearity restriction will be removed and efficient reduction of the large-scale problem will be accomplished. 

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. 

Variable classification is the essential tool for the design or revamp of monitoring systems. After fixing the degree of required knowledge of the process, that is to say, the subset of variables that must be known, this technique is repeated until the selected set of instruments allows us to obtain the desired information about the process. There is a great economic incentive for robust classification because a deficient procedure will require the installation of extra instrumentation. 

For measurement adjustment, a constrained optimization problem with model equations as constraints is resolved at a fixed interval. In this context, variable classification is applied to reduce the set of constraints, by eliminating the unmeasured variables and the nonredundant measurements. The dimensional reduction of the set of constraints allows an easier and quicker mathematical resolution of the problem. 

The idea of process variable classification was presented by Vaclavek (1969) with the purpose of reducing the size of the reconciliation problem for linear balances. In a later work Vaclavek and Loucka (1976) covered the case of multicomponent balances (bilinear systems). 

Another procedure for variable classification was presented by Madron (1992). The categorization is performed by converting the matrix associated with the linear or linearized model equations to its canonical form. 

The authors (Meyer et al., 1993) introduced a variant method derived from Kretsovalis and Mah (1987) that allows chemical reactions and splitters to be treated. It leads to a decrease in the size of the data reconciliation problem as well as a partitioning of the equations for unmeasured variable classification. 

The procedure was originally applied to variable classification for bilinear systems of equations. In the case of multicomponent balances, it was considered that the composition of a stream is either completely measured, or not measured at all. 

The strategies developed by Crowe are described further in the next chapter, where other matrix computations for variable classification are analyzed. 

Classification of the measured variables included in NA1 and NA2 as redundant. The other measurements are categorised as nonredundant. Measured variable classification results for this example are in Table 7. 

Various strategies are available for performing process variable classification. These have been briefly presented. Their application for different types of plant model... 

Furthermore, a variable classification strategy based on an output set assignment algorithm and the symbolic manipulation of process constraints is discussed. It manages any set of unmeasured variables and measurements, such as flowrates, compositions, temperatures, pure energy flows, specific enthalpies, and extents of reaction. Although it behaves successfully for any relationship between variables, it is well suited to nonlinear systems, which are the most common in process industries. 

Sanchez, M., Bandoni, A., and Romagnoli, J. (1992). PLADAT—A package for process variable classification and plant data reconciliation. Comput. Chem. Eng. S16,499-506. 

This chapter is devoted to the analysis of variable classification and the decomposition of the data reconciliation problem for linear and bilinear plant models, using the so-called matrix projection approach. The use of orthogonal factorizations, more precisely the Q-R factorization, to solve the aforementioned problems is discussed and its range of application is determined. Several illustrative examples are included to show the applicability of such techniques in practical applications. 

Remark 4. As indicated by Crowe et al. (1983), measured variable classification is performed by examining the matrix associated with the reconciliation equations. The zero columns of G or Gx correspond to variables that do not participate in the reconciliation, so they are nonredundant. The remaining columns correspond to redundant measurements. 

As was discussed in Chapters 3 and 4, variable classification allows us to obtain a reduced subsystem of redundant equations that contain only measured and redundant variables. These are used in the reconciliation procedure. 

The first case study consists of a section of an olefin plant located at the Orica Botany Site in Sydney, Australia. In this example, all the theoretical results discussed in Chapters 4,5,6, and 7 for linear systems are fully exploited for variable classification, system decomposition, and data reconciliation, as well as gross error detection and identification. 

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