A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Hill, William J.; Hunter, William G.; Wichern, Dean W.

doi:10.1080/00401706.1968.10490542

Cited by 91 publications

(43 citation statements)

References 9 publications

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“…Then the joint design criterion proposed by Hill et al (1968), and discussed by Tan et al (1989), was used to select the conditions for each successive run. Then the joint design criterion proposed by Hill et al (1968), and discussed by Tan et al (1989), was used to select the conditions for each successive run.…”

Section: Modelmentioning

confidence: 99%

The reaction network for the oxidation of propylene over a bismuth molybdate catalyst

1989

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An initial-rate study was conducted to determine the kinetics of the oxidation of acrolein over a bismuth molybdate catalyst. The results were combined with results from a previous initial-rate study of propylene oxidation on the same catalyst to develop a quantitative description of the reaction network for propylene oxidation.The redox steady-state model with half-order in oxygen which provided the best fit to the propylene oxidation data also provided the best fit to the acrolein oxidation data. The disappearance of propylene occurs through parallel reactions to acrolein, carbon oxides, and acetaldehyde, with subsequent oxidation of the acrolein to carbon oxides.Une Ctude de vitesse initiale a it6 effectuCe afin de determiner la cinktique de I'oxydation de I'acrolCine sur un catalyseur de rnolybdate de bismuth. Les rksultats ont CtC combinks h des donnCes antCrieures sur I'Ctude de vitesse initiale de I'oxydation du propyltne sur le rn&rne catalyseur pour rnettre au point une description quantitative du rCseau de rtaction pour I'oxydation du propyltne.Le modtle permanent d'oxydo-rCduction d'un demi-ordre en oxygtne qui concorde le mieux avec les donntes d'oxydation du propykne, est celui qui prCsente Cgalernent la rneiUeure concordance avec les donnks d'oxydation de I'acroltine. Le propyltne disparait lors de rCactions paralleles produisant I'acroltine, les oxydes de carbone et I'acCtaldChyde, suivies de I'oxydation de I'acrolCine en oxydes de carbone.he overall objective of this research was to develop a T quantitative description of the reaction network for the oxidation of propylene over a bismuth molybdate catalyst. An initial-rate study of propylene oxidation was completed first (Tan et al., 1988), using a joint criterion design for model discrimination and parameter estimation (Tan et al., 1989). The present paper reports the results of the final two stages of the work, namely, an initial-rate study of the oxidation of the intermediate acrolein, and the combination of propylene and acrolein results to develop a quantitative description of the reaction network.The first point to be resolved when modelling a reaction network is whether the individual steps can be adequately described by the same kinetic model form. Different model forms can be used for each step but the network model is simpler if this is not necessary. In the case of propylene and acrolein there are reports of different models being required for each (Cartlidge et al., 1975, using bismuth molybdate, and Forissier et al., 1979, using iron molybdate).

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Section: Modelmentioning

confidence: 99%

The reaction network for the oxidation of propylene over a bismuth molybdate catalyst

1989

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“…Hill, Hunter and Wichern (1968) have combined model discrimination and parameter estimation design procedures which gradually switch from the first to the second task as experiments are being performed.…”

Section: Sequential Design Procedures For Optimal Parameter Estimationmentioning

confidence: 99%

Model discrimination and parameter estimation in heterogeneous catalysis

Froment¹

1975

AIChE Journal

116

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After a brief discussion of the experimental aspects of a kinetic investigation, the paper reviews the methodology of kinetic analysis, for both single and complex reactions. The necessity of statistical testing of the results is emphasized. Special attention is given to methods for estimating parameters in algebraic and differential equations. Sequential methods for the design of an experimental program aiming at optimal discrimination between rival models and optimal parameter estimation are reviewed and illustrated by means of practical examples.

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“…A joint design criterion (Hill et al, 1968) which combines the model discrimination and parameter precision criteria was used for this purpose. A joint design criterion (Hill et al, 1968) which combines the model discrimination and parameter precision criteria was used for this purpose.…”

Section: Modelmentioning

confidence: 99%

“…Le premier est un critbre combin6 pour le problbme double de la discrimination du mdele et de l'estimation des parambtres qui a CtC purpost par Hill et al (1968), mais qui au mieux de nos connaissances, n'a pas CtC test6 dans un programme experimental. Deux crittres statistiques ont CtC utilists pour concevoir les expkriences.…”

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“…In this study we have used a sequential joint design strategy (Hill et al, 1968) which takes both objectives into account simultaneously. However, precise parameter estimates for each of the candidate models are needed to discriminate effectively between models, but an experimental design strategy for obtaining precise estimates of the parameters in a model depends on the assumption that the model is valid.…”

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Sequential statistical design strategy in a kinetic study of propylene oxidation

1989

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A sequential design strategy was used to direct an experimental kinetic study of propylene oxidation over bismuth molybdate. Two statistical criteria were used to design experiments. The first is a joint criterion for the dual problem of model discrimination and parameter estimation which was proposed by Hill et al. (1968), but which to the best of our knowledge has not been tested in an experimental program. Using this joint criterion design, it was demonstrated that both the objectives of model discrimination and precise parameter estimation were effectively accomplished. After model discrimination had been achieved, a design strategy for further improvement in parameter precision was found, as expected, to be effective for that purpose.

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A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Cited by 91 publications

References 9 publications

The reaction network for the oxidation of propylene over a bismuth molybdate catalyst

The reaction network for the oxidation of propylene over a bismuth molybdate catalyst

Model discrimination and parameter estimation in heterogeneous catalysis

Sequential statistical design strategy in a kinetic study of propylene oxidation

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