Steady state data reconciliation linear

Chapter 5 deals with steady-state data reconciliation problem, from both a linear and a nonlinear point of view. Special consideration is given, in Chapter 6, to the problem of sequential processing of information. This has several advantages when compared with classical batch processing. 

In this chapter we concentrate on the statement and further solution of the general steady-state data reconciliation problem. Initially, we analyze its resolution for linear plant models, and then the nonlinear case is discussed. 

Historically, treatment of measurement noise has been addressed through two distinct avenues. For steady-state data and processes, Kuehn and Davidson (1961) presented the seminal paper describing the data reconciliation problem based on least squares optimization. For dynamic data and processes, Kalman filtering (Gelb, 1974) has been successfully used to recursively smooth measurement data and estimate parameters. Both techniques were developed for linear systems and weighted least squares objective functions. 

The steady-state linear model data reconciliation problem can be stated as... 

Several researchers [e.g., Tjoa and Biegler (1992) and Robertson et al. (1996)] have demonstrated advantages of using nonlinear programming (NLP) techniques over such traditional data reconciliation methods as successive linearization for steady-state or dynamic processes. Through the inclusion of variable bounds and a more robust treatment of the nonlinear algebraic constraints, improved reconciliation performance can be realized. 

The operation of a plant under steady-state conditions is commonly represented by a non-linear system of algebraic equations. It is made up of energy and mass balances and may include thermodynamic relationships and some physical behavior of the system. In this case, data reconciliation is based on the solution of a nonlinear constrained optimization problem. 

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