Bilinear balances reconciliation

In this chapter, the use of projection matrix techniques, more precisely the Q-R factorization, to analyze, decompose, and solve the linear and bilinear data reconciliation problem was discussed. This type of transformation is selected because it provides a very good balance of numerical accuracy, flexibility, and computational cost (Goodall, 1993). 

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). 

Orthogonal factorizations may be applied to resolve problem (5.3) if the system of equations cp(x, u) = 0 is made up of linear mass balances and bilinear component and energy balances. After replacing the bilinear terms of the original model by the corresponding mass and energy flows, a linear data reconciliation problem results. 

To do this, the product of the mass flowrate and the specific enthalpy was substituted by the corresponding enthalpy flow. Results of the reconciliation procedure using the Q-R factorization are given in Table 7. Table 8 compares the residuum of the balance equations, the value of the objective function, and the computing time of the MATLAB implementation for both approaches (Q-R factorization and use of SQP with the reduced set of balance equations). These results show the improvement and the efficiency achieved using Q-R decomposition when the system can be represented as bilinear. 

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See also in sourсe #XX -- [ , , ]

See also in sourсe #XX -- [ , , ]

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