Detection of Gross Errors in Nonlinearly Constrained Data: A Case Study

Serth, Robert W.; Valero, Carlos; Heenan, W. A.

doi:10.1080/00986448708911836

Cited by 28 publications

(15 citation statements)

References 11 publications

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“…In both cases, the MIMT method was used for gross error detection. Details of the method as applied to nonlinear systems have been given by Serth et al (1987b). It is clear from the results of our own work, as well as that of others (Narasimhan and Mah, 1987;Crowe, 1988), that the iterative procedure used to identify gross errors in the MIMT algorithm will not yield correct results in all instances.…”

Section: Simulation Proceduresmentioning

confidence: 81%

“…The measures of performance listed in Table III are the same as those used by Serth et al (1987b). In particular, the error reduction refers to the change in length of the error vector achieved by the algorithm based on an L 2 norm.…”

Section: Resultsmentioning

confidence: 99%

“…(1976), which was used previously as a test example by Crowe (1986) and Serth et al (1987b). A complete description of the system was given by the latter authors.…”

Section: Problem Definitionmentioning

confidence: 99%

“…The overall simulation procedure was similar to that used in our previous study (Serth et al, 1987b) and the same parameters were used as in the base case of that study. For each simulation run, a measurement vector was constructed by using pseudo random number generators to introduce random and systematic errors into the set of balanced data (true values).…”

Section: Simulation Proceduresmentioning

confidence: 99%

“…(1987a) was used to avoid loss of significant figures and the associated numerical problems encountered in previous work (Serth et al, 1987b).…”

Section: Simulation Proceduresmentioning

confidence: 99%

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On the Choice of Regression Variables in Nonlinear Data Reconciliation

Serth

Weart

Heenan

1989

Chemical Engineering Communications

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Reconciliation of process data constrained by multicomponent material balance equations can be accomplished by a regression calculation in which either total flow rates and compositions (primary variables) or total and component flow rates (secondary variables) are used as the regression variables. It is shown by means of computer simulation experiments that the choice of secondary variables for regression can adversely affect the performance of an associated gross error detection algorithm. The principal effect is an increased tendency of the algorithm to make Type I errors.

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Section: Simulation Proceduresmentioning

confidence: 81%

Section: Resultsmentioning

confidence: 99%

“…(1976), which was used previously as a test example by Crowe (1986) and Serth et al (1987b). A complete description of the system was given by the latter authors.…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

“…(1987a) was used to avoid loss of significant figures and the associated numerical problems encountered in previous work (Serth et al, 1987b).…”

Section: Simulation Proceduresmentioning

confidence: 99%

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On the Choice of Regression Variables in Nonlinear Data Reconciliation

Serth

Weart

Heenan

1989

Chemical Engineering Communications

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Application of broyden's method to reconciliation of nonlinearly constrained data

Pai

Fisher

1988

AIChE Journal

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Process data reconciliation and gross error detection have been the subject of many recent publications, for which Tamhane and Mah (1985) and Mah (1987) have provided a thorough review. Analytical solutions to linear data reconciliation problems can be obtained efficiently, for instance, by matrix projection (Crowe et al., 1983). However, solving general data reconciliation problems with nonlinear constraints invariably requires some type of iterative procedure. In this note, an iterative procedure is developed that makes use of Crowe's matrix projection and for the first time combines a quasi-Newton update with the Gauss-Newton scheme for solving nonlinear data reconciliation problems.Using the Lagrange method, Britt and Leucke (1973) developed the normal equations for nonlinear parameter estimation. More recently, Stephenson and Shewchuk (1986) and Serth et al. (1 987) also based their data reconciliation problems on the normal equations. Although straightforward, the approaches based on solving the system of normal equations suffer from two drawbacks. First, the size of the problem may be unduly large due to the Lagrange multipliers; second, first-order derivatives of the constraints appear in the normal equations and have to be calculated for every iteration.Crowe (1986) extended his method of matrix projection to bilinear constraints with an iterative procedure for determining one of the variables in the bilinear terms. Unfortunately, this procedure is too specific to be useful for more general cases.Knepper and Gorman (1980) proposed a Gauss-Newton iterative algorithm and, in order to reduce computational effort, suggested using old derivatives of constraints until the constraints are satisfied (i.e., the constant-direction approach). HLowever, their algorithm is limited to problems with no more constraints than measured variables and the constant-direction approach is characterized by slow convergence. Knepper and Glorman applied the theory of generalized inverses to solve the linearized subproblem. Crowe (private communication, 1987) presented a more general method based on matrix projection (Crowe et al., f983). The latter not only effectively reduces the problem size but also removes the restriction that no more constraints than measured variables be handled. In this note, a Broyden-type update (Broyden, 1965) is proposed to replace the old derivatives so that the rate of convergence can be improved without repeatedly evaluating the derivatives. Crowe's Iterative SchemeA general data reconciliation problem is defined aswhere f is an m vector of functions, x is an n vector of measured variables, u is an r vector of unmeasured variables, and Z is the variance-covariance matrix of measurements 2, or some weighting matrix. The sizes of these vectors are related by n + r 2 m > r z 0. Linearizing the constraint functions f around Xk and v k gives where Bk and Pk denote, respectively, the ( m x n) and ( m x r ) matrices of the derivatives offwith respect to x and v evaluated a t xk and v k .Following Crowe ...

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