Gross error detection

As was shown before, the measurement vector in the absence of gross errors can be written as 

Furthermore, the balance (constraint) equations for the linear or linearized case are 

In Chapters 3 and 4 we have shown that the vector of process variables can be partitioned into four different subsets (1) overmeasured, (2) just-measured, (3) determinable, and (4) indeterminable. It is clear from the previous developments that only the overmeasured (or overdetermined) process variables provide a spatial redundancy that can be exploited for the correction of their values. It was also shown that the general data reconciliation problem for the whole plant can be replaced by an equivalent two-problem formulation. This partitioning allows a significant reduction in the size of the constrained least squares problem. Accordingly, in order to identify the presence of gross (bias) errors in the measurements and to locate their sources, we need only to concentrate on the largely reduced set of balances 

Introducing the measurements within the balances, we obtain the vector of the residua in the balances, r  

The most common techniques for detecting the presence of gross errors are based on so-called statistical hypothesis testing. This is based on the idea of testing the data set against alternative hypotheses (1) the null hypothesis. Ho, that no gross error is present, and (2) the alternative hypothesis. Hi, that gross errors are present. 

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To determine if a process unit is at steady state, a program monitors key plant measurements (e.g., compositions, product rates, feed rates, and so on) and determines if the plant is steady enough to start the sequence. Only when all of the key measurements are within the allowable tolerances is the plant considered steady and the optimization sequence started. Tolerances for each measurement can be tuned separately. Measured data are then collec ted by the optimization computer. The optimization system runs a program to screen the measurements for unreasonable data (gross error detection). This validity checkiug automatically modifies tne model updating calculation to reflec t any bad data or when equipment is taken out of service. Data vahdation and reconciliation (on-line or off-line) is an extremely critical part of any optimization system. 

Serth, R.W, B. Srikanth, and S.J. Maronga, Gross Error Detection and Stage Efficiency Estimation in a Separation Process, AlChE Journal, 39(10), 1993, 1726-1731. (Physical model development, parameter estimation)... 

Phillips, A.G. and D.P. Harrison, Gross Error Detection and Data Reconciliation in Experimental Kinetics, Indushial and Engineeiing Chemistiy Reseaieh, 32, 1993,2530-2536. (Measurement test)... 

Rollins, D.K. and J.F. Davis, Gross Error Detection when Variance-Covariance Matrices are Unknown, AlChE Journal, 39(8), 1993, 13.35-1341. (Unknown statistics)... 

Serth, R.W. and W.A. Heenan, Gross Error Detection and Data Reconciliation in Steam-Metering Systems, AlChE Journal, 32(5), 1986, 7.3.3-742. 

Verneuil, VS. Jr., P. Yang, and F. Madron, Banish Bad Plant Data, Chemical Engineeiing Piogiess, October 1992, 45-51. (Gross-error detection overview)... 

Intended Use The intended use of the model sets the sophistication required. Relational models are adequate for control within narrow bands of setpoints. Physical models are reqiiired for fault detection and design. Even when relational models are used, they are frequently developed bv repeated simulations using physical models. Further, artificial neural-network models used in analysis of plant performance including gross error detection are in their infancy. Readers are referred to the work of Himmelblau for these developments. [For example, see Terry and Himmelblau (1993) cited in the reference list.] Process simulators are in wide use and readily available to engineers. Consequently, the emphasis of this section is to develop a pre-liminaiy physical model representing the unit. 

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. 

Consider the process flowsheet shown in Figure El6.4, which was used by Rollins and Davis (1993) in investigations of gross error detection. The seven stream numbers are identified in Figure El6.4. The overall material balance can be expressed using the constraint matrix Ay = 0, where A is given by... 

The presence of gross errors invalidates the statistical basis of the common data reconciliation procedures, so they must be identified and removed. Gross error detection has received considerable attention in the past 20 years. Statistical tests in combination with an identification strategy have been used for this purpose. A good survey of the available methodologies can be found in Mah (1990) and Crowe (1996). 

Tamhane, A. C., and Mah, R. S. H. (1985). Data reconciliation and gross error detection in chemical process networks. Technometrics, 27, 409-422. 

Tjoa, I., and Biegler, L. (1991), Simultaneous strategies for data reconciliation and gross error detection of nonlinear systems. Comput. Chem. Eng. 15,679. 

The sequential procedure can be implemented on-line, in real time, for any processing plant without much computational effort. Furthermore, by sequentially deleting one measurement at a time, it is possible to quantify the effect of that measurement on the reconciliation procedure, making this approach very suitable for gross error detection/identification, as discussed in the next chapter. 

Serth, R., and Heenan, W. (1986). Gross error detection and data reconciliation in steam metering systems. AIChE J. 32,733-742. 

Alburquerque, J. S., and Biegler, L. T. (1996). Data reconciliation and gross error detection for dynamic systems. AIChE J 42,2841-2856. 

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,... 

As discussed before, in the conventional data reconciliation approach, auxiliary gross error detection techniques are required to remove any gross error before applying reconciliation techniques. Furthermore, the reconciled states are only the maximum likelihood states of the plant, if feasible plant states are equally likely. That is, P x = 1 if the constraints are satisfied and P x = 0 otherwise. This is the so-called binary assumption (Johnston and Kramer, 1995) or flat distribution. 

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. 

Within the context of data reconciliation and gross error detection, Alburquerque and Biegler (1996) used a p function given by... 

The first case study consists of a section of an olefin plant located at the Orica Botany Site in Sydney, Australia. In this example, all the theoretical results discussed in Chapters 4,5,6, and 7 for linear systems are fully exploited for variable classification, system decomposition, and data reconciliation, as well as gross error detection and identification. 

A data reconciliation procedure was applied to the subset of redundant equations. The results are displayed in Table 4. A global test for gross error detection was also applied and the x2 value was found to be equal to 17.58, indicating the presence of a gross error in the data set. Using the serial elimination procedure described in Chapter 7, a gross error was identified in the measurement of stream 26. The procedure for estimating the amount of bias was then applied and the amount of bias was found... 

Application of the Data Reconciliation and Gross Error Detection Procedure within a Supervisory Control Scheme for the Column... 

Table 9 presents a summary of the variables in a typical real-time run. The raw measurements are initially used to run the simulation with PROCESS (therefore, only the simulation switch is activated). The first column of the table shows the raw measurements, and the second indicates the results from PROCESS. It is clear that the results from the simulation are not in agreement with the measurements.1 It can be seen from Table 9 that the measurements of the condenser and reboiler duties are quite different from the simulation results. This suggests that there are gross errors in those measurements. The gross error detection and data reconciliation modules are then activated. The third, fourth, and fifth columns show the rectified and reconciled data. 

Terry, PA. and D.M. Himmelblau, Data Rectification and Gross Error Detection in a Steady-State Process via Artificial Neural Networks, Industrial and Engineering Chemistry Research, 32, 1993, 3020-3028. (Neural networks, measurement test)... 

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