Preliminaries in (Mpdx) method associated with Cohen equations

Sas, Diana Monica; Kovendi, Zoltan

doi:10.1109/aqtr.2016.7501386

Cited by 7 publications

(4 citation statements)

References 2 publications

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“…The tabular method may be considered an ideal method whenever experimentally can be completed tables such as the one below, both from to and from to , either for a real process or for an approximating solution, which corresponds, for example, with the relation (23) Table I, for the line the following curve could be represented [4], [5]: (24) Also, for column the following curve could be represented [4], [5]: (25) where and Thus, it can be observed that from the relations (24) and (25) days to days, and from to meters, both and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space.…”

Section: Approximation Of Structure Parameters By Tabular Methodsmentioning

confidence: 99%

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Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Mureșan¹,

D.²,

Clitan³

et al. 2017

IJMO

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Abstract-Theisotope separation column process presented in this article represents a space propagation process modeled by second-order quasi-linear equations with two independent variables. The new approach of Cohen's equation using a second-order differential equation in relation to time variable t and spatial variable s is presented. For this stage of development, for variables and there is a limitation of two time constants ( ), or space constants ( ). Also, and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space. In this case, results a family of curves of the concentration.Index Terms-Isotopic separation process, cohen's equation, transcendent equations, structural parameters approximation. I. INTRODUCTIONThe space propagation process presented in this article represents an isotope separation column process which is modeled by second-order quasi-linear equations with two independent variables.Using a second-order differential equation in relation with both time and space variables, a new approach of Cohen's equation is presented.In the following equation, it is considered the overdamped version of approximating solutions associated with the isotopic separation phenomena [1]-[3]:(1) For this stage of development, for variables and there is a limitation of two time constants ( ), or space constants ( ). The evolution of and is represented in the following figure:Also, and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space. In this case, results a family of curves of the concentration.Considering the final values and In addition, it can also be shown that for the decreasing evolutions of and defined by the relations (7) and (8) and exemplified in figure 2, where and , the inflection abscises respectively correspond to those defined in the relations (5) and (6) [1-2].(7) (8) Further, in this paper it will be presented only the case for increasing evolution of the and .Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an Isotope Separation Column Muresan V., Sas D., Clitan I., and Unguresan M.-L.International Journal of Modeling and Optimization, Vol. 7, No. 5, October 2017 305 DOI: 10.7763/IJMO.2017.V7.603 Based on knowing the abscises ( , and ordinate , but also the abscises , and ordinate the aproximating parameters noted above determine the aproximation of both and , respectively and . It will be considered the following transcendentwhere:Calculations start with for providing iterative increasing for until the difference (DIF) changes its mark and fulfills to the solution of the transcendent equation.The following relations corresponds to the approximation of space constants ( ) and ( with an error, as low as the step (At the same time, it can be shown that there is only one value ( for which the curve represented in the following figure passes simultaneously through t...

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Section: Approximation Of Structure Parameters By Tabular Methodsmentioning

confidence: 99%

“…Considering the final values and The approximating solution represented in relation (1) may be rewritten considering relations (2) and (3) such as [1]- [5]: (4) The inflection abscises correspond to the following relations [1]- [3], [5]- [7]:…”

Section: Introductionmentioning

confidence: 99%

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Mureșan¹,

D.²,

Clitan³

et al. 2017

IJMO

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“…In this case, the usage of AI is not necessarily due to the absence of the necessity to learn variable parameters. In [45,46], the authors propose distributed parameter processes for separation processes, based on the Cohen equation [47]. The usage of these type of models has the disadvantage that they cannot be used for highlighting the effects of the parametric disturbances that occur in the separation plant operation.…”

Section: Introductionmentioning

confidence: 99%

AI versus Classic Methods in Modelling Isotopic Separation Processes: Efficiency Comparison

et al. 2021

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In the paper, the comparison between the efficiency of using artificial intelligence methods and the efficiency of using classical methods in modelling the industrial processes is made, considering as a case study the separation process of the 18O isotope. Firstly, the behavior of the considered isotopic separation process is learned using neural networks. The comparison between the efficiency of these methods is highlighted by the simulations of the process model, using the mentioned modelling techniques. In this context, the final part of the paper presents the proposed model being simulated in different scenarios that can occur in practice, thus resulting in some interesting interpretations and conclusions. The paper proves the feasibility of using artificial intelligence methods for industrial processes modeling; the obtained models being intended for use in designing automatic control systems.

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“…With and are noted the initial and final moments of the isotopic separation process. (1), the partial derivatives expressed in relation (6) lead to much more unitary and systematized expressions than those resulting in , presented in [3], directly associated with Cohen's equation. (6) As a result, the following relations will be presented as follows [1], [2], [4]: (7) ) (…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of an 15N Isotope Separation Column by Second-Order Quasi-Linear Equations with Two Independent Variable

Sas¹,

Clitan²,

M-L.³

et al. 2017

IJMO

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Abstract-The presented process is an isotope separation column for , which represents a space propagation process modeled by the proposed method. Cohen's equation was approached by a second-order differential equation in relation to time t and also second-order in relation to the spatial variable s. This second order partial derivative equation was developed at an initial stage for which the variables and have been limited to two time constants ( ), or space ( ), resulting a family of curves of the concentration.

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Preliminaries in (Mpdx) method associated with Cohen equations

Cited by 7 publications

References 2 publications

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

AI versus Classic Methods in Modelling Isotopic Separation Processes: Efficiency Comparison

Analytical Modeling of an 15N Isotope Separation Column by Second-Order Quasi-Linear Equations with Two Independent Variable

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