Observability and Redundancy

Crowe, C. M. (1989). Observability and redundancy of process data for steady state reconciliation. Chem. Eng. Sci. 44, 2909-2917. 

Kretsovalis, A., and Mah, R. S. H. (1988a). Observability and redundancy classification in generalised process networks. I Theorems. Comput. Chem. Eng. 12, 671-687. 

Vaclavek (1969) first defined the concepts of observability and redundancy. He formulated two rules for achieving variable categorization for linear plant models ... 

The multicomponent chemical species and energy balances are mostly non-linear in the primary variables (mass flowrates, mass fractions, temperatures, possibly also pressures of the streams). The solvability analysis of non-linear systems in Chapter 8 begins with examples showing that even in simple cases, the terminology introduced for linear systems (in particular observability and redundancy) becomes somewhat vague certain problems can be not well-posed . We then first analyse the solvability of the whole system of balance equations without a priori fixed variables (Sections 8.2 and 8.3) and show that under certain plausible stractural hypotheses, the system is solvable. 

If the values of certain variables have been fixed a priori (for example measured), there is no mathematically precise general solution to the observability and redundancy classification problem. We did not attempt to arrive at a complete analysis. Still, we have shown that remitting somewhat the mathematical precision, a pragmatically plausible classification is possible if the problem is linearized. 

It is thus seen that the observability and redundancy are, in the case of mass balance equations, exact stmctural properties of the graph G of the system, and of the partition of the streams (arcs) into J° and corresponding to variables called respectively, by convention, unmeasured and measured . Let us add an observation concerning the redundancy. We call redundant each variable (arc) of J separately, this does not necessarily imply that also a subset of J can be regarded as redundant in the sense that the variables m of the subset would be... 

Kretsovalis, A. and R.S.H. Mah (1988), Observability and redundancy classification in generalized process networks I and II (Algorithms), Comput. Chem. Engng. 7, 671-703... 

If it happens that 7 = 0 (all variables measured) then z = x, fW = and X e iM means simply g(x) = 0 (with S g U). In practice, if 7 > 0 then the frequent assumption is that the unmeasured vector y is uniquely determined by the condition g(z) = 0 given x = x g the decomposition (10.1.29) then the unique y = y is the estimate of the unmeasured vector. More generally, we have admitted the case that y is not uniquely determined see then the observability (and redundancy) classification in Section 8.5. 

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