Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

Hetmaniok, Edyta�; Hristov, Jordan; Słota, Damian; Zielonka, Adam�

doi:10.1007/s00231-016-1923-1

Cited by 10 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mathematical fundaments and results concerning the convergence of the different versions of the ACO algorithm are included in [ 24 , 25 , 26 , 27 ]. Based on the analysis of the papers of various authors, see for example [ 28 , 29 , 30 , 31 , 32 ], as well as on the computation carried out by us (for example [ 7 , 17 , 20 , 22 , 31 ]) we come to the conclusion that using the artificial intelligence algorithms (ACO, RACO, RACO, IRM, etc.) in most cases does not require the application of the explicit regulatory procedures.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Brociek

Chmielowska

Słota

2020

Entropy

Self Cite

View full text Add to dashboard Cite

This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

show abstract

Section: Methods Of Solutionmentioning

confidence: 99%

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Brociek

Chmielowska

Słota

2020

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…The previous Lemma guarantees that each local solution ū ∈ U ad can be approximated by a sequence of local solutions of the discretized problems (28). Due to ūε h ∈ B ε (ū) and ūε h → ū for h 0 (i. e., the constraint ūε h ∈ B ε (ū) is never active), the functions ūε h are local solutions of the discrete problems (21) provided that h > 0 is small enough. Hence, we neglect the superscript ε in the following and denote by ūh the sequence of discrete local solutions converging to the local solution ū.…”

Section: Convergence Of the Fully Discrete Solutionsmentioning

confidence: 98%

“…For further applications, u can be interpreted as a heat-exchange coefficient in thermodynamics or as a quantity for corrosion damage in electrostatics. There are many publications dealing with the identification of the Robin coefficient, see for instance [11,21,27,30]. Only a few papers use an optimal control approach similar to the one considered in the present article.…”

Section: Introductionmentioning

confidence: 99%

Error estimates for the finite element approximation of bilinear boundary control problems

Winkler

2020

Comput Optim Appl

View full text Add to dashboard Cite

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin coefficient from a given measurement of the state, or when the Robin coefficient can be controlled in order to reach a desired state. To this end, necessary and sufficient optimality conditions are derived and several discretization approaches for the numerical solution the optimal control problem are investigated. Considered are both a full discretization and the postprocessing approach meaning that we compute an improved control by a pointwise evaluation of the first-order optimality condition. For both approaches finite element error estimates are shown and the validity of these results is confirmed by numerical experiments.

show abstract

“…Simplified modeling can include linearization techniques (Bazán and Bedin, 2017), reducing model dimension (Hetmaniok et al , 2017), decomposition in a series of subproblems, (Karalashvili et al , 2011) or steady state analysis (Marques et al , 2016). The main challenge is to find a satisfying level of simplification as a tradeoff between performance and accuracy.…”

Section: Introductionmentioning

confidence: 99%

Identification of temperature-dependent boundary conditions using MOR

Frank

Wieting

Wielitzka

et al. 2019

HFF

View full text Add to dashboard Cite

Purpose A mathematical description of temperature-dependent boundary conditions is crucial in manifold model-based control or prototyping applications, where accurate thermal simulation results are required. Estimation of boundary condition coefficients for complex geometries in complicated or unknown environments is a challenging task and often does not fulfill given accuracy limits without multiple manual adaptions and experiments. This paper aims to describe an efficient method to identify thermal boundary conditions from measurement data using model order reduction. Design/methodology/approach An optimization problem is formulated to minimize temperature deviation over time between simulation data and available temperature sensors. Convection and radiation effects are expressed as a combined heat flux per surface, resulting in multiple temperature-dependent film coefficient functions. These functions are approximated by a polynomial function or splines, to generate identifiable parameters. A formulated reduced order system description preserves these parameters to perform an identification. Experiments are conducted with a test-bench to verify identification results with radiation, natural and forced convection. Findings The generated model can approximate a nonlinear transient finite element analysis (FEA) simulation with a maximum deviation of 0.3 K. For the simulation of a 500 min cyclic cooling and heating process, FEA takes a computation time of up to 13 h whereas the reduced model takes only 7-11 s, using time steps of 2 s. These low computation times allow for an identification, which is verified with an error below 3 K. When film coefficient estimation from literature is difficult due to complex geometries or turbulent air flows, identification is a promising approach to still achieve accurate results. Originality/value A well parametrized model can be further used for model-based control approaches or in observer structures. To the knowledge of the authors, no other methodology enables model-based identification of thermal parameters by physically preserving them through model order reduction and therefore derive it from a FEA description. This method can be applied to much more complex geometries and has been used in an industrial environment to increase product quality, due to accurate monitoring of cooling processes.

show abstract

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

Cited by 10 publications

References 26 publications

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Error estimates for the finite element approximation of bilinear boundary control problems

Identification of temperature-dependent boundary conditions using MOR

Contact Info

Product

Resources

About