One method of solving incorrectly stated problems

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

doi:10.1007/bf00861246

Cited by 15 publications

(18 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As seen above, an extra regularization term in the functional (18) resulted in an extra term on the main diagonal of the matrix on the left-hand side of Equation (19). Changing the value of the regularization parameter, one can influence the diagonal dominance of the left-hand side matrix.…”

Section: Parameter Regularization Approachmentioning

confidence: 93%

“…Also some hybrid methods were reported in the literature, e.g. Alifanov proposed the procedure in which the Tikhonov functional was minimized with steepest descent method [19]. As mentioned above, in this article the coupled initial and parameter estimation inverse problem is considered, which arises in the technology of the vacuum drying in electrical industry.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Retrieving of the initial moisture field in porous material based on temperature measurements during drying

Buliński

Nowak

Kasza

et al. 2012

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

In this article, a simultaneous initial inverse problem and parameter estimation inverse problem in context of the vacuum paper drying process is presented. In this problem an evaporation constant and initial distribution of the water content are retrieved indirectly based on the temperature measurements at selected sampling points during vacuum phase of the process. As such, a problem is illposed and two different Tikhonov-type regularization techniques are proposed. The L-curve method was used to establish the value of the regularization parameter for both techniques. Results obtained with both regularization techniques are compared.

show abstract

Section: Parameter Regularization Approachmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 98%

Retrieving of the initial moisture field in porous material based on temperature measurements during drying

Buliński

Nowak

Kasza

et al. 2012

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

show abstract

“…The matrix J [n Â q] is formed by zeros and ones; as the Dirac distribution in Eq. (10), it serves to select the points within the system where the temperature is measured. 520 E.P.…”

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%

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

Barrio

2003

Inverse Problems in Engineering

View full text Add to dashboard Cite

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.

show abstract

“…Currently, the most widely used criterion for stopping the iterative process is an error cutoff, where an error functional to be minimized reaches a value corresponding to the total errors in the experimental data [2,4,5]. Rigorous results on the stability conditions for the approximations in the gradient method using this approach can be found in [5,6].…”

mentioning

confidence: 99%