Serial elimination

A serial elimination algorithm was first proposed by Ripps (1965) and extended later by Nogita (1972). This approach eliminates one measuring element at a time from the set of measurements and each time checks the value of a test function, subsequently choosing the consistent set of data with the minimum variance. In this case, after a new measurement has been deleted, the test function and the variance for the resulting system have to be recomputed when the number of suspect measurements is increased, this may become a laborious solution. 

Of the various available techniques, the most widely used are based on the Measurement Test (Mah and Tamhane, 1982). These are the Modified Iterative Measurement Test (MIMT) developed by Serth and Heenan (1986) and the Generalized Likelihood Ratio (GLR) method presented by Narasimhan and Mah (1987). The MIMT method uses a serial elimination strategy to detect and identify only biases in measuring instruments. The GLR method allows us to identify multiple gross errors of any type. It uses a serial compensation strategy. 

In the following a serial elimination procedure (Romagnoli and Stephanopoulos, 1981 Romagnoli, 1983) is described. This scheme isolates the sources of gross errors by a systematic treatment of the measurements. 

Let us consider again the system defined in Example 5.1. From the application of the global statistical test, gross errors were detected among the data set as indicated in Example 7.1. Now the serial elimination strategy will be applied to isolate the source of gross error, that is to identify which set of measurements contains gross error. 

More than one measurement is suspected then the serial elimination of the measurements is initiated until a new reliable estimate is obtained... 

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... 

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... 

The serial elimination strategy was implemented to identify the source of the bias, and the results are displayed in Figs. 3 and 4. As can be seen, a significant improvement in the value is obtained when one of the measurements associated with coil number... 

Try to cut the number of suspect flows by method of serial elimination of measured variables. Set flows 1,3 and 6 successively as nonmeasured (use menu DATA -MODIFY, item Streams and Parameters) and watch the value of. If gross error is no longer detected (low value of fiinin ) this flow is suspect. 

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