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. 

In this chapter we first presented a number of different, simple strategies for gross error identification. The serial elimination of measurements, the search along equations, and a combined procedure have been demonstrated to be simple and efficient ways for identifying gross errors. The estimation of gross errors due to both bias and... 

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. 

Rollins, D., and Davis, J. (1992). Unbiased estimation of gross errors in process measurements. AlChE J. 38,563-572. 

The adjusted mea.surements are not unique and may he no better than the actual mea.surements. Simulation studies testing reconciliation methods in the absence of gross error show that they arrive at a better estimate of the actual component and stream flows 60 percent of the time 40 percent of the time, the acdual measured values better represent the unit performance. 

Gro.s.s-error-detection methods detect errors when they are not pre.sent and fail to detect the gro.s.s errors when they are. Couphng the aforementioned difficulties of reconciliation with the hmitations of gross-error-detection methods, it is hkely that the adjusted measurements contain unrecognized gross error, further weakening the foundation of the parameter estimation. 

In Chapter 7 the problem of dealing with systematic gross biased errors is addressed. Systematic techniques are described for the identification of the source of gross errors and for their estimation. These techniques are computationally simple, they are well suited for on-line implementation, and they conform to the general process of variable monitoring in a chemical plant. 

In order to estimate the vector i in the presence of gross errors, we need to invert the covariance matrix, < , as Eq. (7.22) indicates. It is possible, though, to relate to balance residuals in the absence of gross errors) through the simple recursive formula (6.32), which was presented in the previous chapter. In this case we obtain the following relation ... 

Once the existence of systematic errors is ascertained, their effect is modeled functionally. In the following, three cases of gross error estimation are discussed ... 

Recall that, in the absence of gross errors, the measurement and linear constraint models are given by Eqs. (7.1) and (7.4), respectively. Furthermore, the solution of the least square estimation problem of x variables is... 

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. 

The preceding results are applied to develop a strategy that allows us to isolate the source of gross errors from a set of constraints and measurements. Different least squares estimation problems are resolved by adding one equation at a time to the set of process constraints. After each incorporation, the least square objective function value is calculated and compared with the critical value. 

As was shown, the conventional method for data reconciliation is that of weighted least squares, in which the adjustments to the data are weighted by the inverse of the measurement noise covariance matrix so that the model constraints are satisfied. The main assumption of the conventional approach is that the errors follow a normal Gaussian distribution. When this assumption is satisfied, conventional approaches provide unbiased estimates of the plant states. The presence of gross errors violates the assumptions in the conventional approach and makes the results invalid. 

We have discussed, in Chapter 7, a number of auxiliary gross error detection/ identification/estimation schemes, for identifying and removing the gross errors from the measurements, such that the normality assumption holds. Another approach is to take into account the presence of gross errors from the beginning, using, for example,... 

This work presents a comparative performance analysis among some robust estimators (all estimators reported by Ozyurt and Pike, 2004, and Welsch estimator) for nonlinear dynamic data reconciliation (NDDR in the presence of gross errors. 

In this work a comparative analysis of the capacity of robust estimators to reduce the negative effect of gross errors on nonlinear dynamic data reconciliation was accomplished. The results obtained have shown that among the studied cases the Welsch and Lorentzian robust estimators produced better reconciled values, but they also have shown that, although the robust estimators were more efficient in reducing the effect of biases, this problem still deserves more investigation. 

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