Regularization using truncated singular value decomposition for estimating the Fourier spectrum of a noised space distribution over an extended support

• Autorzy: Al Hadad W. , Maillet D. , André S. , Rémy B.
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are not precisely known. This happens in different characterization problems where infrared camera is used for temperature measurements. In order to overcome this difficulty, the interval where the Fourier transform (its support) is supposed to be larger than the measurement domain is defined. Thus, this virtual interval larger than the measurement interval is used. We show that regularization by truncated singular value decomposition is able to yield good estimates to this very ill-posed inverse problem.

Słowa kluczowe

EN

integral transforms; thermal quadrupoles; heat transfer in mini-channel; inverse heat conduction and convection

PL

integralne transformacje; termalne kwadrupole; wymiana ciepła w kanale; odwrotne przewodzenie ciepła i konwekcji

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2014
• Tom: Vol. 21, no. 3-4
• Strony: 211--222
• Opis fizyczny: Bibliogr. 8 poz., tab., wykr.

Twórcy

autor

Al Hadad W.

• LEMTA, University of Lorraine and CNRS ENSEM – 2 avenue de la Forêt de Haye – TSA60604 54518 Vandœuvre-lès-Nancy cedex, France

autor

Maillet D.

• LEMTA, University of Lorraine and CNRS ENSEM – 2 avenue de la Forêt de Haye – TSA60604 54518 Vandœuvre-lès-Nancy cedex, France

autor

André S.

• LEMTA, University of Lorraine and CNRS ENSEM – 2 avenue de la Forêt de Haye – TSA60604 54518 Vandœuvre-lès-Nancy cedex, France

autor

Rémy B.

• LEMTA, University of Lorraine and CNRS ENSEM – 2 avenue de la Forêt de Haye – TSA60604 54518 Vandœuvre-lès-Nancy cedex, France

Bibliografia

• [1] Y. Souhar, B. Rémy, A. Degiovanni. Thermal characterization of anisotropic materials at high temperature through integral methods and localized pulsed technique. International Journal of Thermophysics, 34: 322–340, 2013.
• [2] Y. Rouizi, D. Maillet, Y. Jannot. Fluid temperature distribution inside a flat mini-channel: semi-analytical wall transfer functions and estimation from temperatures of external faces. International Journal of Heat and Mass Transfer, 64: 331–342, 2013.
• [3] Y. Rouizi, W. Al Hadad, D. Maillet, Y. Jannot. Experimental assessment of the fluid bulk temperature profile in a mini-channel through inversion of external surface temperature measurements. International Journal of Heat and Mass Transfer, 83: 522–535, 2015.
• [4] W. Al Hadad, Y. Rouizi, Y. Jannot, B. Rémy, D. Maillet. Estimation of the heat transferred to a fluid minichannel by an inverse technique. Proceedings of the 15th International Heat Transfer Conference, IHTC-15, Kyoto, Begell House, August, 2014. doi: 10.1615/IHTC15.inv.009190
• [5] D. Maillet, S. André, J.C. Batsale, A. Degiovanni, C. Moyne. Thermal quadrupoles – solving the heat equation through integral transforms. Wiley, Chichester, England, 2000.
• [6] A. Bendada, F. Erchiqui, M. Lamontagne. Pulsed thermography in the evaluation of an aircraft composite using 3D thermal quadrupoles and mathematical perturbations. Inverse Problems, 21: 857–877, 2005.
• [7] R.C. Aster, B. Borchers, C.H. Thurber. Parameter Estimation and Inverse Problems, Second edition, Elsevier Edition, Academic Press, Amsterdam, The Netherlands, 2012.
• [8] Y. Boukari, H. Haddar. A convergent data completion algorithm using surface integral equations. Inverse Problems, Institute of Physics: Hybrid Open Access, 21 pages, 2015.