PSI - Issue 5

S. Sahnoun et al. / Procedia Structural Integrity 5 (2017) 1267–1274 A.Saifi et al/ StructuralIntegrity Procedia 00 (2017) 000 – 000

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figures below the values of the thicknesses obtained by the network (output) as a function of the desired thicknesses (Target) for the three datasets (Training, validation and test).

Fig 10: Result of the chosen neural model

The correlation coefficients obtained in the three data (R = 1 for training, R = 0.99999 for validation and R = 0.99997 for test) show perfect linearity; which translates a good correspondence between the thicknesses obtained (output) and the thicknesses desired (target) The error of the neural model calculated by relation (3) is equal to 0.001, which confirms the relevance of the neural model established in the prediction of limestone thickness in steel water pipes, using contrast Maximum absolute thermal input. 5. Conclusion In this work, we have demonstrated the ability of the 3D finite element method to simulate scale thickness detection by the infrared thermograph technique. We have studied the effects of geometric parameters on the thermal response of the conducts inspected. Indeed, we have found that the dimensions of pipe do not have a notable influence on the thermal response. We proposed a model that allows estimating the thickness of the scale from the maximum thermal contrast using the polynomial regression. Then, we were interested in the use of neural networks. The performance study of this method shows that it provides a good correlation with the polynomial regression. A.M. Bianchi, Y. Fautrelle & J. Etay. Transferts thermiques. Collection de l’Agenc e universitaire de la Francophonie. Presses polytechniques et universitaires romandes,2004 Angel Valentinov Valchev, Petko Hristov Mashkov, Tamara Grigorievna Pencheva, Berkant Sejdaly Gyoch "Thermal processes modeling during soldering of BGA components to PCB". 24 – 26 September(2008) A.Elballouti,S.Belattar”Three - dimensional thermal nondestructive caracterisation of defect of pipe the roadway” 4th Middle East NDT Conference and Exhibition, Kingdom of Bahrain, Dec 2007. Cybenko, G. (1989). ‘Approximation by superposition of a sygmoidal function’. Math.control systems signals, 2(4): 303 -314. Funahashi, K (1989). ‘On the approximate realisation of continous mapping by neural networks’. Neural networks, 2: 183 -192. Roussel MD, Guy AR, Shaw LG, et al. The Use Of Calcium Carbonate In Polyolefins Offers Significant Improvement In Productivity 2005, http://www.tappi.org/content/enewsletters/eplace/2006/06-3Rousselv1.pdf (accessed 14 December 2012). HS Carslaw & JC Jaeger. Conduction of Heat in Solids(paperback, ). 1959. Kang llLEE “Ultrasonic Technique for Measuring the Thickness of Scale on the Inner Surfaces of Pipes“ Journal of the Korean Physical Society,Vol.56, No. 2, February 2010, pp. 558_561 Moulay A. Akhloufi1 and Benjamin Verney ” Multimodal Registration and Fusion for 3D Thermal Imaging” Mathe matical Problems Engineering Volume 2015 (2015), Article ID 450101, 14 pages. O. C. Zienkiewicz et R. L. Taylor « La méthode des éléments finis : Formulation de base et problèmes linéaires » AFNOR, 1989. Ruiz, F.A., “Mineral Enhancement of Extrusion Coated Polyethylene”, TAPPI Polymers, Laminations & Coatings Conference Proceedings 2001. References