Simultaneous estimation of gross errors

This section briefly discusses an approach that combines statistical tests with simultaneous gross error identification and estimation. The strategy is called SEGE (Simultaneous Estimation of Gross Error Method). It was proposed by Sanchez and Romagnoli (1994). 

Test Method (Narasimhan and Mah, 1987), the Modified Iterative Measurement Test (MIMT), and the Simultaneous Estimation of Gross Error Method (SEGE). In order to compare results on the same basis, the level of significance of each method is chosen such that it gives an AVTI, under null hypothesis, equal to 0.1. 

The simultaneous estimation of gross errors enhances identification performance and the accuracy of the estimation. This is a key characteristic when instruments cannot be repaired until the units are out of service. In these situations the corrected measurement data are used for control and optimization purposes. 

If H0 is rejected, a two-stage procedure is initiated. First, a list of candidate biases and leaks is constructed by means of the recursive search scheme outlined by Romagnoli (1983). All possible combinations of gross errors (measurement biases and/or process leaks) from this subset are analyzed in the second stage. Gross error magnitudes are estimated simultaneously for each combination and chi-square test statistic calculations are performed to identify the suspicious combinations. We will now explain the stages of the procedure. 

Tjoa and Biegler (1991) used this formulation within a simultaneous strategy for data reconciliation and gross error detection on nonlinear systems. Albuquerque and Biegler (1996) used the same approach within the context of solving an error-in-all-variable-parameter estimation problem constrained by differential and algebraic equations. 

As an alternative to a sequential approach (gross error detection followed by parameter estimation), simultaneous data reconciliation and parameter estimation (DRPE) has been espoused by a number of researchers and has been tested in industrial applica-tion. " " In the DRPE formulation, parameters are estimated by minimizing the difference between the measured and calculated values of process variables in a least-squares sense ... 

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