Detecting persistent gross errors by sequential analysis of principal components

Abstract

Measurements such as flow rates from a chemical process violate conservation laws and other process constraints because they are contaminated by random errors and possibly gross errors such as process disturbances, leaks, departures from steady state, and biased instrumentation. Data reconcilation is aimed at estimating the true values of measured variables that are consistent with the constraints, at detecting gross errors, and at solving for unmeasured variables. An approach to constructing sequential principal‐component tests for detecting and identifying persistent gross errors during data reconciliation by combining principal‐component analysis and sequential analysis is presented. The tests detect gross errors as early as possible with fewer measuremennts. They were sharper in detecting and have a substantially greater power in correctly identifying gross errors than the currently used statistical tests in data reconciliation.

On the definition of software accuracy in redundant measurement systems

“…Narasimhan and Mah (1987) and Crowe (1988) showed that these two are equivalent and have maximum power for the case of one gross error. Later, principal‐component tests (PCT) were proposed by Tong and Crowe (1995,1996) as an alternative for multiple bias and leak identification. Industrial applications of PCMT were reported by Tong and Bluck (1998), who indicated that tests based on principal‐component analysis (PCA) are more sensitive to subtle gross errors than others, and have greater power to correctly identify the variables in error than the conventional nodal, measurement, and global tests.…”

Dynamic data rectification using particle filters

“…This task is termed dynamic data rectification (or dynamic data reconciliation) (Darouach & Zasadzinski, 1991;Liebman, Edgar & Lasdon, 1992;Singhal & Seborg, 2000), and differs to the "steady" rectification techniques reported in the literature (Morad, Young & Svrcek, 2005;Tong & Crowe, 1997) which are designed around the steady state operation of processes and thus do not need to take into account the process dynamics. Dynamic data rectification is especially challenging when the state and/or measurement functions are highly non-linear, and the posterior distribution of the process states, is not Gaussian.…”

Use of a novel autoassociative neural network for nonlinear steady‐state data reconciliation

“…The key process variables are normally used for closed-loop control, whereas the great majority of measured variables remain unused or merely serve for monitoring the states of the process. A lot of research is now being conducted to find ways to make better use of this wealth of information that characterizes the real behavior of the process: development of softsensors (Aynsley et al, 1993), fault diagnosis (Dunia et al, 1996;Hoskins et al, 1991;MacGregor, 1995;Tong and Crowe, 1996;Wise and Ricker, 1991), statistical process monitoring (Chen et al, 1996;Nomikos et al, 1994;Piovoso and Kosanovich, 19941, and data reconciliation (Crowe et al, 1983;Crowe, 1986Crowe, ,1996Hodouin and Everell, 1980;Karjala and Himmelblau, 1994;Liebman et al, 1992;Mah, 1990;Romagnoli and Stephanopoulos, 1981;Schraa and Crowe, 1996;Smith and Ichiyen, 1973). The latter topic is the subject of this article.…”

“…Nonrandom measurement errors, such as persistent gross errors, must first be detected and then removed or corrected. Indeed, meaningful data adjustments can be achieved if and only if there is no gross error present in the data (Tong and Crowe, 1996). Gross-error detection has been the subject of a significant amount of research (Mah, 1990;Rollins and Davis, 1992;Tjoa and Biegler, 1991;Tong and Crowe, 1996).…”

“…Indeed, meaningful data adjustments can be achieved if and only if there is no gross error present in the data (Tong and Crowe, 1996). Gross-error detection has been the subject of a significant amount of research (Mah, 1990;Rollins and Davis, 1992;Tjoa and Biegler, 1991;Tong and Crowe, 1996). The second step, usually referred to as data reconciliation per se, generally satisfies the following three objectives: (1) the random errors in measurement are filtered out in order to reduce the variance of the data; (2) the measured data are corrected to render them as coherent as reasonable with the process model and/or process constraints; (3) the values of unmeasured process variables are estimated.…”