A regularization method for the inverse design of solidification processes with natural convection

Okamoto, Kei; Li, B.Q.

doi:10.1016/j.ijheatmasstransfer.2006.10.019

Cited by 28 publications

(6 citation statements)

References 16 publications

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“…The back-propagation of the training data can be one of the methods for training the deep network. More examples of inverse problems in mathematical modeling and simulations can be found in [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

Brociek

Wajda²,

Słota

2023

Sensors

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In recent times, fractional calculus has gained popularity in various types of engineering applications. Very often, the mathematical model describing a given phenomenon consists of a differential equation with a fractional derivative. As numerous studies present, the use of the fractional derivative instead of the classical derivative allows for more accurate modeling of some processes. A numerical solution of anomalous heat conduction equation with Riemann-Liouville fractional derivative over space is presented in this paper. First, a differential scheme is provided to solve the direct problem. Then, the inverse problem is considered, which consists in identifying model parameters such as: thermal conductivity, order of derivative and heat transfer. Data on the basis of which the inverse problem is solved are the temperature values on the right boundary of the considered space. To solve the problem a functional describing the error of the solution is created. By determining the minimum of this functional, unknown parameters of the model are identified. In order to find a solution, selected heuristic algorithms are presented and compared. The following meta-heuristic algorithms are described and used in the paper: Ant Colony Optimization (ACO) for continous function, Butterfly Optimization Algorithm (BOA), Dynamic Butterfly Optimization Algorithm (DBOA) and Aquila Optimize (AO). The accuracy of the presented algorithms is illustrated by examples.

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Section: Introductionmentioning

confidence: 99%

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

Brociek

Wajda²,

Słota

2023

Sensors

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“…Solving the inverse problem is obviously much more difficult than solving the direct problem in which all the initial data and conditions are known. However, in literature one can find several proposed approaches for solving the inverse problems concerning the heat transfer and solidification (see for example Zabaras et al [3], Momose et al [4], Nejad et al [5] and Okamoto et al [6]). In particular, in the work by Du et al [7] an inverse algorithm is applied to calculate the heat flux between the ingot and the crystallizer on the basis of temperatures measured by using the thermocouples buried in the mould.…”

Section: Introductionmentioning

confidence: 99%

Application of the Swarm Intelligence Algorithm for Reconstructing the Cooling Conditions of Steel Ingot Continuous Casting

2020

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This paper presents a proposal to apply one of the swarm intelligence algorithms, the artificial bee colony (ABC) algorithm, to solve the inverse problem of steel ingot continuous casting. The discussed task consists of retrieving the cooling conditions of the process on the basis of temperature measurements and by taking into account the macrosegregation phenomenon. The examined process was modeled by using the mathematical model of solidification within the temperature interval. The solution method was based on the implicit scheme of the finite difference method supplemented by the procedure of correcting the field of temperature in the vicinity of liquidus and solidus curves, which was then used for solving the appropriate direct problem. The computational example, illustrating the stability and accuracy of the proposed method, is also presented in the paper.

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“…Most of the published works about the inverse Stefan problem concern the one-dimensional version of this problem (see [2][3][4][5][6][7][8][9][10][11][12][13], and references therein), whereas studies referring to the two-dimensional inverse Stefan problem are minor. In the first study related to the two-dimensional inverse design Stefan problem [14] the temperature at boundary of the domain was determined in form of a series of integrals based on the known interface position.…”

Section: Introductionmentioning

confidence: 99%

Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem

Hetmaniok

Słota

Zielonka

2015

Computers & Mathematics with Applications

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a b s t r a c tIn the paper a procedure for solving the two-dimensional inverse Stefan problem is presented. In considered problem the heat transfer coefficient is identified with the aid of known measurements of temperature in selected points of the region as the additional information. Direct Stefan problem is solved by using the alternating phase truncation method. Goal of the paper is to compare two swarm intelligence algorithms -the Ant Colony Optimization algorithm and the Artificial Bee Colony algorithm -applied for minimizing a functional expressing the error of approximate solution.

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A regularization method for the inverse design of solidification processes with natural convection

Cited by 28 publications

References 16 publications

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

Application of the Swarm Intelligence Algorithm for Reconstructing the Cooling Conditions of Steel Ingot Continuous Casting

Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem

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