Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 27, No. 10 (October 2014) 1635-1644   

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  PREDICTION OF DEFORMATION OF CIRCULAR PLATES SUBJECTED TO IMPULSIVE LOADING USING GMDH-TYPE NEURAL NETWORK
 
H. Babaei
 
( Received: August 11, 2013 – Accepted: June 26, 2014 )
 
 

Abstract    In this paper, experimental responses of the clamped mild steel, copper, and aluminium circular plates are presented subjected to blast loading. The GMDH-type neural networks (Group Method of Data Handling) are then used for the modelling of the mid-point deflection thickness ratio of the circular plates using those experimental results. The aim of such modelling is to show how the mid-point deflection varies with the variations of the important parameters. Further, it is shown that the use of dimensionless input variables, rather than the actual physical parameters, in such GMDH-type network modelling leads to simpler polynomial expressions which can be used for modelling and prediction purposes. It is also demonstrated that Singular Value Decomposition (SVD) can be effectively used to find the vector of coefficients of quadratic sub-expressions embodied in such GMDH-type networks. Such application of SVD will highly improve the performance of GMDH-type networks to model of nonlinear dynamic behavior of circular plates.

 

Keywords    Neural network, Modelling, Circular plate, Impulsive load, Deformation

 

چکیده    در این مقاله پاسخ ورقهای گیردار دایروی از جنس فولاد نرم، مس و آلومینیوم تحت بار انفجاری بصورت تجربی بررسی و با استفاده از آن مدلی برای نسبت خیز مرکز به ضخامت ورقهای دایروی با استفاده از شبکه های عصبی از نوع GMDH ارائه شده است. چنین مدلی می تواند برای بررسی چگونگی تغییرات خیز مرکز ورق نسبت به سایر پارامترها به کار رود. علاوه بر این در این مقاله نشان داده شده است که با جایگزین کردن متغیرهای ورودی بدون بعد با پارامترهای واقعی فیزیکی در شبکه های عصبی از نوع GMDH می توان چند جمله ای درجه دوم ساده ای را برای مدلسازی و پیش بینی خیز مرکز ورق بدست آورد. همچنین ضرائب این چند جمله ای با استفاده از روش تجزیه مقادیر منفرد تعیین می شود بگونه ای که عملکرد و کارایی شبکه عصبی از نوع GMDH برای مدلسازی رفتار دینامیکی غیر خطی ورقهای مدور بهبود می یابد.

References   

 

1.     Kim, T., Kim, H., Bae, J., Lee, S. and Kang, C., "Semi-solid die forging of al6061 wrought aluminium alloy with electromagnetic stirring", Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture,  Vol. 222, No. 9, (2008), 1083-1095.

2.     Gerdooei, M. and Dariani, B., "Strain-rate-dependent forming limit diagrams for sheet metals", Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture,  Vol. 222, No. 12, (2008), 1651-1659.

3.     Tavakoli, H. and Kiakojouri, F., "Influence of sudden column loss on dynamic response of steel moment frames under blast loading", International Journal of Engineering-Transactions B: Applications,  Vol. 26, No. 2, (2012), 197-206.

4.     Nurick, G. and Martin, J., "Deformation of thin plates subjected to impulsive loading—a review: Part i: Theoretical considerations", International Journal of Impact Engineering,  Vol. 8, No. 2, (1989), 159-170.

5.     Nurick, G. and Martin, J., "Deformation of thin plates subjected to impulsive loading—a review part ii: Experimental studies", International Journal of Impact Engineering,  Vol. 8, No. 2, (1989), 171-186.

6.     Teeling-Smith, R. and Nurick, G., "The deformation and tearing of thin circular plates subjected to impulsive loads", International Journal of Impact Engineering,  Vol. 11, No. 1, (1991), 77-91.

7.     Kowsarnia, E., Alizadeh, Y. and Salavati Pour, H.S., "Experimental evaluation  of  blast wave parameters in under water explosion of hexogen charges", International Journal of Engineering-Transactions B: Applications,  Vol. 25, No. 1, (2012), 65-72.

8.     Mynors, D.J. and Zhang, B., "Applications and capabilities of explosive forming", Journal of materials processing technology,  Vol. 125, (2002), 1-25.

9.     Johnson, W., "Liberator on explosive forming", CME-Chartered Mech. Eng.,  Vol. 34, No. 12, (2011).

10.   Jones, N., "Impulsive loading of a simply supported circular rigid plastic plate", Journal of Applied Mechanics,  Vol. 35, No. 1, (1968), 59-65.

11.   Åström, K.J. and Eykhoff, P., "System identification—a survey", Automatica,  Vol. 7, No. 2, (1971), 123-162.

12.   Sanchez, E., Zadeh, L.A. and Shibata, T., "Genetic algorithms and fuzzy logic systems, World Scientific,  (1997).

13.   Austina, N., Kumarb, P.S. and Kanthavelkumaranc, N., "Artificial neural network involved in the action of optimum mixed refrigerant (domestic refrigerator)", International Journal of Engineering,  Vol. 26, No. 10, (2013)., 1025-2495

14.   Nariman-Zadeh, N. and Darvizeh, A., "Design of fuzzy systems for modelling of explosive cutting process of plates using singular value decomposition", Iranian Journal of Science and Technology,  Vol. 26, No. B3, (2002), 455-464.

15.   Kristinsson, K. and Dumont, G.A., "System identification and control using genetic algorithms", Systems, Man and Cybernetics, IEEE Transactions on,  Vol. 22, No. 5, (1992), 1033-1046.

16.   Bagheri , A., Narimanzadeh , N., Siavash, A.S. and Khoobkar, A.R., "Gmdh type neural networks and their application to the identification of the inverse kinematics equations of robotic manipulators (research note)", International Journal of Engineering,  Vol. 18, No. 2, (2005), 135-143.

17.   Iba, H. and Sato, T., "A numerical approach to genetic programming for system identification", Evolutionary Computation,  Vol. 3, No. 4, (1995), 417-452.

18.   Porter, B. and Nariman-Zadeh, N., "Genetic design of computed-torque fuzzy logic controllers for robotic manipulators", in Proc. IEEE Int. Symp. On Int. Control, USA. (1995).

19.   Ivakhnenko, A., "Polynomial theory of complex systems", Systems, Man and Cybernetics, IEEE Transactions on,  No. 4, (1971), 364-378.

20.   Farlow, S.J., "Self-organizing methods in modeling: Gmdh type algorithms, CrC Press,  Vol. 54,  (1984).

21.   Back, T., Fogel, D.B. and Michalewicz, Z., "Handbook of evolutionary computation, IOP Publishing Ltd.,  (1997).

22.   Darvizeh, A., Nariman-Zadeh, N. and Gharababaei, H., "Gmdh-type neural network modelling of explosive cutting process of plates using singular value decomposition", Systems Analysis Modelling Simulation,  Vol. 43, No. 10, (2003), 1383-1397.

23.   Gharababaei, H. and Darvizeh, A., "Experimental and analytical investigation of large deformation of thin circular plates subjected to localized and uniform impulsive loading", Mechanics Based Design of Structures and Machines,  Vol. 38, No. 2, (2010), 171-189.

24.   Golub, G.H. and Reinsch, C., "Singular value decomposition and least squares solutions", Numerische Mathematik,  Vol. 14, No. 5, (1970), 403-420.

25.   Mahmoodabadi, M., Taherkhorsandi, M. and Safikhani, H., "Modeling and hybrid pareto optimization of cyclone separators using group method of data handling (GMDH) and particle swarm optimization (pso)", International Journal of Engineering-Transactions C: Aspects,  Vol. 26, No. 9, (2012), 1089.

26.   Nariman-Zadeh, N., Darvizeh, A., Felezi, M. and Gharababaei, H., "Polynomial modelling of explosive compaction process of metallic powders using gmdh-type neural networks and singular value decomposition", Modelling and Simulation in Materials Science and Engineering,  Vol. 10, No. 6, (2002), 727.

27.   Press, W., Teukolsky, S., Vetterling, W. and Flannery, B., Numerical recipes in fortran 77: The art of scientific computing, , Cambridge Univ. Press, New York. (1992)

28.   Gharababaei, H., Nariman-Zadeh, N. and Darvizeh, A., "A simple modelling method for deflection of circular plates under impulsive loading using dimensionless analysis and singular value decomposition", Journal of Mechanics,  Vol. 26, No. 03, (2010), 355-361.

29.           Taylor, E.S., "Dimensional analysis for engineers",  (1974).





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