Studies on system engineering. II. On the application of the calculus of observations in calculations of chemical engineering balances

Václavek, V.

doi:10.1135/cccc19690364

Cited by 12 publications

(4 citation statements)

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“…Kuehn and Davidson [2] were the first to work on this problem for all variables being measured. Between 1968 and 1976, [3,4] several ideas arose, especially for linear systems, e.g. concepts of observability and redundancy.…”

Section: Introductionmentioning

confidence: 99%

Diagnosis of the Doubly-Fed Induction Generator of a Wind Turbine

et al. 2005

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This paper presents a method of identifying and estimating gross errors for linear dynamic systems. The method is applied to wind power, in particular the doubly-fed induction generator. Measurements have errors, but it is possible to reduce the effect of such errors on control by exploiting relationships between the different variables of the system. Such analysis is called ‘data validation’. Data validation uses a mathematical model, based on equations, to simulate the real dynamic system. An analysis of systematic errors is made using a measurement test. The method has the potential to support the on-line multiparameter data analysis, and hence maintenance, of complex systems, such as wind turbines.

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Section: Introductionmentioning

confidence: 99%

Diagnosis of the Doubly-Fed Induction Generator of a Wind Turbine

et al. 2005

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“…Indeed, the use of matrix Yhere is a direct extension of the work of Mah et al (1976) on partitioning the incidence matrix for the single-component flow rate problem. It will be seen that the exact choice of the matrix Y does not affect a, but that one possible choice of Yfor the case of no reactions is equivalent to deleting and merging nodes as suggested by Vaclavek (1969a), but for each component separately. Stanley and Mah (1981) have recently presented a general method of decomposition, which differs from the present one in finding a suitable transformation of the variables rather than of the constraint equations.…”

Section: P-[b2 I S T ]mentioning

confidence: 99%

“…They also considered.energy balances where the product of total flow rate and specific enthalpy makes the equations nonlinear (more specifically, bilinear). Much more work has subsequently been done, notably by Ripps (1962Ripps ( , 1965, Reilly and Carpani (1963), Swenker (1964), Vaclavek (1969aVaclavek ( ,b,c, 1975, Mah et al (1976), Romagnoli and Stephanopoulos (1981), Stanley and Mah (1981a,b), and Mah and Tamhane (1982). Excellent reviews of the published work have been presented by Hlavacek (1977) and Mah (1981).…”

Section: Introductionmentioning

confidence: 99%

Reconciliation of process flow rates by matrix projection. Part I: Linear case

1983

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Flow rate measurements in a steady-state process are reconciled by weighted least squares so that the conservation laws are obeyed. A projection matrix is constructed which can be used to decompose the linear problem into the solution of two subproblems, by first removing each balance around process units with an unmeasured component flow rate. The remaining measured flow rates are reconciled, and the unmeasured flow rates can then be obtained from the solution of the conservation equations. The basic case contains constraints which are linear in the component and the total flow rates. The method is extended to cases with bilinear constraints, involving unknown parameters such as split fractions.Chi-square and normal statistics are used to test for overall gross measurement errors, for gross error in each node imbalance which is fully measured, and for each measurement adjustment. C. M. CROWE SCOPETo monitor the performance of a chemical process, we require balanced component and total flow rates in the process streams. These flows can be calculated from judiciously chosen measurements of concentrations, temperatures and total flow rates; but since these measurements are subject to random error, the conservation laws will in general be violated.The basic case considered here is linear in that it is assumed that whenever a concentration or temperature in a stream is measured, so is the total flow rate. Then the component or enthalpy flow can be calculated and used as the raw measurement data. These data are adjusted (reconciled), and the unmeasured flow rates are estimated so that the weighted sum of squares of the adjustments is a minimum and the conservation laws are obeyed. This restriction is then relaxed to allow the inclusion of bilinear constraints, which contain unknown parameters, multiplied by measured quantities.The computational effort can be minimized if a reduced set of balance equations can be obtained from the original balances, such that the reduced set involves no unmeasured flow rate but a maximum number of measured flow rates. This was accomplished originally by Vaclavek (1969b), and later by Mah et al. (1976) and Romagnoli and Stephanopoulos (1981) by algorithms which iteratively eliminate balances involving unmeasured feed or product flow rates and merge two balances with a common unmeasured flow rate. These workers assumed that a stream was either unmeasured or completely measured, an assumption not made here.The approach here is to define a projection matrix which can be directly constructed and which effectively blanks out the unmeasured quantities in producing this reduced set of balances.

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“…Data Reconciliation (DR) is such a data processing strategy that achieves random error reduction by forcing the measurements to satisfy the interrelationships among the variables on which the measurements are made, called the process constraint model (Kuehn and Davidson, 1961;Narasimhan and Jordache, 2000). In this process, DR also gives scope for the estimation of the unmeasured and faulty variables as presented in Vaclavek (1969); Crowe et al (1983) with the concept of projection matrix based on Q-R factorization (Noble and Daniel, 1977). In spite of the availability of the DR technique in linear, non-linear, steadystate, and dynamic versions (Narasimhan and Jordache, 2000), it can be stated from the results obtained in Yellapu et al (2015b) and Yellapu et al (2017) that a linear steady-state DR is sufficient for random error reduction for the cases in which the process is almost steady.…”

Section: Introductionmentioning

confidence: 99%