On the inverse point-source problem of the Poisson equation

YILMAZ, Melek; ŞENGÜL, Metin; GEÇKİNLİ, Melih

On the inverse point-source problem of the Poisson equation

Melek YILMAZ, (Kadir Has Üniversitesi, Mühendislik Fakültesi, Elektronik Bölümü, İstanbul, Türkiye)

Metin ŞENGÜL, (Kadir Has Üniversitesi, Mühendislik Fakültesi, Elektronik Bölümü, İstanbul, Türkiye)

Melih GEÇKİNLİ (İstanbul Teknik Üniversitesi, İstanbul)

Istanbul University Journal of Electrical and Electronics Engineering

1 0

Yıl: 2005 Cilt: 5 Sayı: 2 Sayfa Aralığı: 1395 - 1401 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On the inverse point-source problem of the Poisson equation

Öz:

In this work, a basic inverse heat conduction problem of a simple 2-D model with steady state heat source is taken into view. The physical problem is for a square region with uniform thermophysical properties and a point heat source of unit magnitude. To obtain boundary data , temperature probes are placed at the midpoints of the sides of the square domain. The objective of the inverse problem is to estimate the coordinates of the point source with the least amount of data. Initially, the inverse problem is analyzed to determine the main causes that render the problem ill conditioned. As for the solution, among the methods that has been tried so far, the best results are obtained from a backpropagating ANN with four-probe data. When white Gaussian noise is added to the measurements, no catastrophic failure has been observed.

Anahtar Kelime:

Konular: Mühendislik, Elektrik ve Elektronik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Özışık M.N., Orlande H.R.B., Inverse Heat Transfer:Fundamentals and Applications, Taylor & Francis, 2000. [2] Kurpisz K., Nowak A.J., Inverse Thermal Problems, Computational Mechanics Publications, Southhampton, UK, 1995. [3] Hensel E., Inverse Theory and Applications for Engineers, Prentice-Hall, 1992 [4] Engl H.W., Hanke M., Neubauer A., Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 2000. [5] Alifanov O.M., Inverse Heat Transfer Problems,Springer-Verlag, 1994. [6] Hensel E., Inverse Theory and Applications for Engineers, Prentice Hall, 1991. [7] Gencer N.G., Tanzer I.O.,”Forward Problem Solution of Electromagnetic Source Imaging Using a New BEM Formulation with High-Order Elements”,Phys. Med. Biol.,Vol. 44 ,pp. 2275–2287, 1999. [8] Kim S.K., Lee W.I., “Solution of Inverse Heat Conduction Problems Using Maximum Entropy Method”, Int. J. Heat Mass Transfer, Vol.45, pp.381-391, 2002. [9] Huang C.-H., Cheng S.-C., “A Three- Dimensional Inverse Problem of Estimating the Volumetric Heat Generation for a Composite Material”, Numerical Heat Tr. Part A, Vol. 39, pp. 383-403, 2001. [10] Huang C-H, Chin S-C, “A Two- Dimensional Inverse Problem in Imaging the Thermal Conductivity of a Non-Homogeneous Medium”, International Journal of Heat and Mass transfer, Vol. 43, 2000. [11] Chan H.-T., “Estimation of Surface Temperature in Two-Dimensional Inverse Heat Conduction Problems”, Int. J. HeatMass Tr. Vol. 44, pp. 1455-1463, 2001. [12] Reed R.D., Marks R.J., Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, The MIT Press, 1999. [13] Haykin S., Neural Networks: A Comprehensive Foundation, 2nd ed., Prentice Hall International, 1999.

APA	YILMAZ M, ŞENGÜL M, GEÇKİNLİ M (2005). On the inverse point-source problem of the Poisson equation. , 1395 - 1401.
Chicago	YILMAZ Melek,ŞENGÜL Metin,GEÇKİNLİ Melih On the inverse point-source problem of the Poisson equation. (2005): 1395 - 1401.
MLA	YILMAZ Melek,ŞENGÜL Metin,GEÇKİNLİ Melih On the inverse point-source problem of the Poisson equation. , 2005, ss.1395 - 1401.
AMA	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M On the inverse point-source problem of the Poisson equation. . 2005; 1395 - 1401.
Vancouver	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M On the inverse point-source problem of the Poisson equation. . 2005; 1395 - 1401.
IEEE	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M "On the inverse point-source problem of the Poisson equation." , ss.1395 - 1401, 2005.
ISNAD	YILMAZ, Melek vd. "On the inverse point-source problem of the Poisson equation". (2005), 1395-1401.

APA	YILMAZ M, ŞENGÜL M, GEÇKİNLİ M (2005). On the inverse point-source problem of the Poisson equation. Istanbul University Journal of Electrical and Electronics Engineering, 5(2), 1395 - 1401.
Chicago	YILMAZ Melek,ŞENGÜL Metin,GEÇKİNLİ Melih On the inverse point-source problem of the Poisson equation. Istanbul University Journal of Electrical and Electronics Engineering 5, no.2 (2005): 1395 - 1401.
MLA	YILMAZ Melek,ŞENGÜL Metin,GEÇKİNLİ Melih On the inverse point-source problem of the Poisson equation. Istanbul University Journal of Electrical and Electronics Engineering, vol.5, no.2, 2005, ss.1395 - 1401.
AMA	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M On the inverse point-source problem of the Poisson equation. Istanbul University Journal of Electrical and Electronics Engineering. 2005; 5(2): 1395 - 1401.
Vancouver	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M On the inverse point-source problem of the Poisson equation. Istanbul University Journal of Electrical and Electronics Engineering. 2005; 5(2): 1395 - 1401.
IEEE	YILMAZ M,ŞENGÜL M,GEÇKİNLİ M "On the inverse point-source problem of the Poisson equation." Istanbul University Journal of Electrical and Electronics Engineering, 5, ss.1395 - 1401, 2005.
ISNAD	YILMAZ, Melek vd. "On the inverse point-source problem of the Poisson equation". Istanbul University Journal of Electrical and Electronics Engineering 5/2 (2005), 1395-1401.