Application of iterative regularization for the solution of incorrect inverse problems

Alifanov, O. M.; Rumyantsev, S. A.

doi:10.1007/bf00871098

Cited by 19 publications

(5 citation statements)

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“…520 E.P. DEL BARRIO Introducing the stationarity condition (14) in the direct problem (12) yields to the following two-point boundary-value problem:…”

Section: The Ichp Solutionmentioning

confidence: 99%

“…Two advantages of these methods are that they have had rigorous mathematical investigation and that they can be applied very generally. They are clearly very important methods that have been used to solve a great variety of inverse problems [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], including IHCP, as well as problems of parameters determination and shape identification. However, the generality comes at the expense of greater computational and programming burdens.…”

Section: Introductionmentioning

confidence: 99%

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Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Barrio

2003

Inverse Problems in Engineering

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This article is concerned with inverse heat conduction problems (IHCP) involving large-scale linear systems (i.e. multidimensional systems) with unknown sources or boundary conditions. The inverse problem is stated as an optimisation problem with a regularised quadratic objective functional, and it is solved using Lagrange theory. We demonstrate that the IHCP solution is obtained by simple time integration of a state-variable model: the inverse model, which is analytically derived from the so called direct and adjoint problems. In addition, we show that the number of differential equations in the inverse model can be strongly reduced without a significant loss of precision. The inversion is then carried out in three main steps: calculation of the full-order inverse model, size reduction, and time integration of the resulting reduced-order inverse model. A numerical example of heat sources identification in a 2D diffusion problem shows the performances and the accuracy of the proposed approach.

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“…520 E.P. DEL BARRIO Introducing the stationarity condition (14) in the direct problem (12) yields to the following two-point boundary-value problem:…”

Section: The Ichp Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Barrio

2003

Inverse Problems in Engineering

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“…The inverse heat conduction problem (IHCP) involves the determination of the heat flux at the surface of a solid using one or more measured internal temperature histories. A number of methods have been proposed including function specification [1,2], Tikhonov regularization (TR) [1,3,4,5], conjugate gradient (CG) [6,7,8,9,10] and singular value decomposition (SVD) methods [11,12,13,14]. The problem is challenging because it is ill-posed which is, in part, caused by the internal measurements being delayed and damped compared to the heated surface.…”

Section: Introductionmentioning

confidence: 99%

“…By applying CG method for each successive time, the full filter matrix for CGM can be computed. The number of iterations required is determined by minimizing the E(Rq) for a known heat flux input, as outlined previously (Eqs (9)(10)(11)(12)…”

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confidence: 99%

Inverse heat conduction problem: Sensitivity coefficient insights, filter coefficients, and intrinsic verification

Beck

Woodbury

2016

International Journal of Heat and Mass Transfer

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The inverse heat conduction problem is the estimation of the time and/or space dependence of the surface heat flux or temperature utilizing interior temperature measurements at discrete times and/or locations. This problem is ill-posed since it is very sensitive to omnipresent measurement errors. Many solution methods have been proposed including exact-matching, function specification, Tikhonov regularization, iterative regularization, conjugate gradient, steepest descent and singular value decomposition. In this paper, the tools provided by the scaled sensitivity coefficients, digital filter coefficients and intrinsic verification are used to investigate and compare several of these methods. The utility of digital filters designed for on-line instrumentation for "continuous" measurements of the surface heat flux and temperature in manufacturing settings is also demonstrated.

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“…However, many such problems are reduced to a task of the minimization of the discrepancies (T i,calc -T i,meas ); these are 332 Solid Phase Transformations then governed by the properties of "correct problems" as proposed by Hadamard, i.e. requirements of solvability, unambiguity, and stability of the solution [8,9]. The problem's solvability is assured by existence of the minimum and of the algorithm of its finding.…”

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confidence: 99%

Calculation of Some Thermodynamic Parameters of Non-Ideal Solutions

Asadov

Akhmedly

2008

SSP

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A computational method has been proposed for calculating the correct interaction parameters from experimental phase diagrams, despite reports that this problem was believed to be a "thermodynamically incorrect” one. It has been shown that the presumed difficulties are not of fundamental importance. An original computer program has been applied to two well-known systems Bi – Sb (1) and Bi2Te3 – Sb2Te3 (2), and a good agreement between calculated and observed values has been achieved. The values of interaction parameters s= 7.1 ± 0.4, l= 1.56 ± 0.09 kJ mol-1 for (1) and s = 5.9 ± 2.5, l = 3.9 ± 2.5 kJ mol-1 for (2) have been found. The results have been analyzed and their statistical reliability has been established. In addition, the possibilities of calculating the liquidus curve from only the solidus experimental data the solidus from the liquidus experimental data have been demonstrated. It has been found that the prediction of liquidus from solidus is much more successful than predicting the solidus from the liquidus. The results allow one to determine with reliance that the backward problem of modeling regular solutions for finding thermodynamic interaction parameters can be solved correctly. The calculated parameters can be used for both the computational restoration of missing pieces of the experimental phase equilibrium diagrams of binary and multinary systems and for the recognition of the physical nature of regular solutions.

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Application of iterative regularization for the solution of incorrect inverse problems

Cited by 19 publications

References 0 publications

Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Inverse heat conduction problem: Sensitivity coefficient insights, filter coefficients, and intrinsic verification

Calculation of Some Thermodynamic Parameters of Non-Ideal Solutions

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