| Evaluation and monitoring of a process depends on the accuracy as well as on the placement of the measuring instruments. For a given set of instruments, the observability of a variable and the redundancy of a measurement are basic information in determining their placement. In the present thesis we treat the observability and redundancy classification problems in a general process network operating under steady state. We allow overall and component balances, energy balances, chemical reactions, heat exchanges and stream splitting. Classification theorems are developed which exploit the measurement placement as well as the process structure by making use of the graph-theoretic properties of the process network. Two graph-oriented algorithms for observability classification (GENOBS) and redundancy classification (GENRED) are devised which check, in an efficient manner, the solvability of constraints. Both algorithms are illustrated with examples.; As an aid in rectifying the process data and estimating the unmeasured variables we develop a procedure for decoupling these two problems in generalized process networks. Algorithm GENOBS is utilized to determine the coaptation constraints. The reconciliation constraints are identified by constructing a complement set to the coaptation constraints, which contains no unobservable variable. The decoupling makes use of the graph-theoretic principles solely, and does not require linearization of the bilinear component and energy balances.; The estimation error in data reconciliation and coaptation, provides a basis for selecting instruments and specifying their placement. The accuracy of the estimates is measured by the trace of the estimation error covariance matrix. Quantitative relations are derived for the effect of adding and removing single measuements on the estimation accuracy. It is proved that redundancy will never adversely affect estimation accuracy. It will always enhance estimation accuracy, if the measurements relate the process variables in a different way from the constraints. These results are utilized to develop evolutionary strategies for selecting an optimal measurement structure. |
