Steady state data reconciliation

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. 

As in the classical steady-state data reconciliation formulation, the optimal estimates are those that are as close as possible (in the least squares sense) to the measurements, such that the model equations are satisfied exactly. 

This chapter discusses some recent approaches for dealing with different aspects of the data reconciliation problem. A more general formulation in terms of a probabilistic framework is first introduced, and its use in dealing with gross error is discussed in particular. Robust estimation approaches are then considered, in which the estimators are designed so that they are insensitive to outliers. Finally, a strategy that combines principal component analysis and steady-state data reconciliation will be discussed. 

Correlations are inherent in chemical processes even where it can be assumed that there is no correlation among the data. Principal component analysis (PCA) transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components, and is an effective tool in multivariate data analysis. In the last section we describe a method that combines PCA and the steady-state data reconciliation model to provide sharper, and less confounding, statistical tests for gross errors. 

The key idea of this section is to combine PCA and the steady-state data reconciliation model to provide sharper and less confounding statistical tests for gross errors, through exploiting the correlation. 

The main assumption in data reconciliation is that measurement values correspond to the steady state. However, process plants are rarely at steady state. Data reconciliation is used to manipulate the measured plant data to satisfy the steady-state assumption. Data reconciliation is used to detect instrument errors and leaks and to get smoother data for design calculations. 

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