QMC MIMT PROGRAM for Windows MIMT BACKGROUND Accurate and reliable energy accounting in chemical plants is important for process monitoring as well as for decision-making regarding the implementation and effectiveness of energy conservation measures. Most energy accounting is based on steam-metering systems in various plant operating units. Measured steam flow rates are subject to random measurement errors and to systematic errors that result from instrument bias or failure. As a result of these errors, the measurements will generally be inconsistent with material balance requirements. Furthermore, the data may present a confusing or misleading picture of energy use patterns in the plant. Of particular concern are large (gross) errors, which may greatly distort the energy use pattern. Such errors will usually be systematic errors resulting from instrument malfunctions. What is needed, then, is a method that will identify faulty steam meters by detecting gross errors in a set of data, and that furthermore will generate an adjusted data set that satisfies the material balance requirements. This problem is a special case of the general problem of error detection and process data reconciliation, a topic that has received considerable attention in the recent literature. Reconciliation of process data subject to linear material balance constraints and containing only random errors can be achieved by means of a constrained least-squares procedure. This technique was first employed by Kuehn and Davidson (1961) and has since been utilized by numerous workers in the field. However, as pointed out by Ripps (1965), the presence of gross errors in the data can vitiate the least-squares procedure. Hence, it is necessary to identify and eliminate measurements containing gross errors before proceeding with data reconciliation. A number of methods for gross error detection have been developed, most of which involve the use of statistical tests based on the assumption that the random errors in the data are normally distributed. In one of the simplest methods, the set of residuals from the least-squares procedure is tested for outliers. Any measurement for which the residual fails the test is considered to contain a gross error. This method has been advocated by several investigators, including Mah and Tamhane (1982), Crowe et al. (1983) and Stephenson and Shewchuck (1984). A related method, in which the largest residual is used to identify a single gross error in a data set containing only one gross error, was developed by Almasy and Sztano (1975). A chi-square test to detect the presence of gross error in a data set was established by Reilly and Carpani (1963) and was used by Madron et al (1977), Crowe et al. (1983), and Romagnoli and Stephanopoulos (1980, 1981). The latter authors incorporated the test into a sequential analysis of the material balance equations that identifies the measurements containing the gross errors. This method was subsequently employed by Wang and Stephanopoulos (1983). Ripps (1965) used a gross error identification scheme in which each measurement is in turn deleted from the data set. The deletion that minimizes the least-squares objective function is identified with the gross error. It was shown by Crowe et al. (1983) that this serial elimination procedure is equivalent to minimizing a chi-square statistic. This method was extended to data sets containing more than one gross error by Nogita (1972). However, his iterative method is based on a test statistic that permits cancellation of errors, as shown by Mah et al. (1976). The latter authors also developed a gross error identification scheme based on a graph-theoretical analysis of material balance networks. Their method utilizes a statistical test for the imbalance in individual material balance equations and combinations of balance equations. System Requirements Available for: Win95/98/NT
|
|
* * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * |