Using GMDH-type neural network model to predict the response of triangular plates under the hydrodynamic loading

Authors

1 universityof guilan

2 Faculty of Mechanical Engineering, University of Eyvanekey

3 Assistant Professor, Department of Chemistry, Faculty of Science, Islamic Azad University, Varamin-Pishva Branch ,Varamin, Iran

4 Faculty of Mechanical Engineering, University of Guilan

Abstract

The aim of this study is investigating the center of mass deflection to thickness ratio of triangular plates using the GMDH-type neural networks and comparing it with results of laboratory tests performed on a narrow triangular plate using water-hammer apparatus. Also, the study focuses on the overall deformation, strain and impact transmission. Dimensionless input variables are used to investigate the center of mass deflection of triangular plate with changing variables. A simpler polynomial expression is derived using GMDH-type neural network and dimensionless number. The vector of coefficients of quadratic sub-expressions involved in GMDH-type networks is obtained by Singular Value Decomposition (SVD) method. SVD can improve the proficiency of GMDH-type networks to model the intricate process of deformation of triangular plates. Obtaining results by applying a GMDH model and comparing them with actual data indicates good agreement between model output and experimental data. The advantages of this approach are in the simplification of computation and convenient application to parametric study for impact behavior.

Keywords


[1] Espinosa HD, Lee S, Moldovan N (2006) A novel fluid structure interaction experiment to investigate deformation of structural elements subjected to impulsive loading. Exp Mech 17(4): 805-824.
[2] Palumbo G, Zhang SH, Tricarico L, Xu C, Zhou LX (2006) Numerical/experimental investigations for enhancing the sheet hydroforming process. Int J Mach Tool Manu 46(11): 1212-1221.
[3] Gerdooei M, Dariani B. (2008) Strain-rate-dependent forming limit diagrams for sheet metals. Proc Inst Mech Eng B-J Eng 222(12): 1651-1659.
[4] Safikhani A, Hashemi R, Assempour A (2008) The strain gradient approach for determination of forming limit stress and strain diagrams. Proc Inst Mech Eng B-J Eng 222(4): 467-483.
[5] Gelin JC, Delassus P, Fontaine JF (1994) Experimental and numerical modelling of the effects of process parameters in the aquadraw deep drawing J Mater Process Tech 45(1): 329-334.
[6] Zampaloni M, Abedrabbo N, Pourboghrat F (2003) Experimental and numerical study of stamp hydroforming of sheet metals. Int J Mech Sci 45(11):1815-1848.
[7] Kosing O, Skews B (1998) An investigation of high-speed forming of circular plates in a liquid shock tube. Int J Imp Eng 21(9): 801-816.
[8] Babaei H, Darvizeh A, Alitavoli M, Mostofi TM (2015) Experimental and analytical investigation into plastic deformation of circular plates subjected to hydrodynamic loading. Journal of Modares Mechanical Engineering 15(2): 305-312. (In Persian)
[9] Babaei H, Mirzababaie Mostofi T, Alitavoli M (2017) Experimental and theoretical study of large deformation of rectangular plates subjected to water hammer shock loading. Proc Inst Mech Eng-Part E: J Process Mech Eng 231(3):490-496.
[10] Nariman-Zadeh N, Darvizeh A, Dadfarmai MH (2004) Design of ANFIS networks using hybrid genetic and SVD methods for the modelling of explosive cutting process. J Mater Proces Tech 155: 1415-1421.
[11] Besarati SM, Atashkari K, Jamali A, Hajiloo A, Nariman-Zadeh N (2010) Multi-objective thermodynamic optimization of combined Brayton and inverse Brayton cycles using genetic algorithms. Energ Convers Manage 51(1): 212-217.
[12] Ivakhnenko AG (1971) Polynomial theory of complex systems. IEEE Trans Syst Man Cybern Syst (4):364-78.
[13] Åström KJ, Eykhoff P (1971) System identification—a survey. Automatica 7(2):123-62.
[14] Lee DW, Seo SW, Sim KB (2008) Online evolution for cooperative behavior in group robot systems. Int J Control Autom 6(2):282-287.
[15] Farlow SJ (1984) Self-organizing methods in modeling: GMDH type algorithms. CrC Press.
[16] Nariman-Zadeh N, Darvizeh A, Jamali A, Moeini A (2005) Evolutionary design of generalized polynomial neural networks for modelling and prediction of explosive forming process. J Mater Proces Tech 164:1561-71.
[17] Nariman-Zadeh N, Atashkari K, Jamali A, Pilechi A, Yao X (2005) Inverse modelling of multi-objective thermodynamically optimized turbojet engines using GMDH-type neural networks and evolutionary algorithms. Eng Optimiz 37(5):437-62.
[18] Jamali A, Hajiloo A, Nariman-Zadeh N (2010) Reliability-based robust Pareto design of linear state feedback controllers using a multi-objective uniform-diversity genetic algorithm (MUGA). Expert Syst Appl 37(1): 401-413.
[19] Ahmadi M, Ahmadi MA, Mehrpooya M, Rosen M (2015) Using GMDH neural networks to model the power and torque of a stirling engine. Sustain 7(2): 2243-2255.
[20] Nariman-Zadeh N, Darvizeh A, Felezi M, Gharababaei H (2002) Polynomial modelling of explosive compaction process of metallic powders using GMDH-type neural networks and singular value decomposition. Model Simul Mater Sc 10(6): 727.
[21] Gharababaei H, Nariman-Zadeh N, Darvizeh A (2010) A simple modelling method for deflection of circular plates under impulsive loading using dimensionless analysis and singular value decomposition. J Mech 26(3): 355-361.
[22] Ahmadi MA, Golshadi M (2012) Neural network based swarm concept for prediction asphaltene precipitation due to natural depletion. J Petrol Sci Eng 98:40-49.
[23] Mostofi TM, Babaei H, Alitavoli M, Lu G, Ruan D (2019) Large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load. Int J Impact Eng 125: 93-106.
[24] Babaei H, Mostofi TM, Alitavoli M, Saeidinejad A (2017) Experimental investigation and dimensionless analysis of forming of rectangular plates subjected to hydrodynamic loading. J Appl Mech Tech Phys 58(1):139-47.
[25] Babaei H, Mirzababaie Mostofi T, Alitavoli M (2015) Experimental study and analytical modeling for inelastic response of rectangular plates under hydrodynamic loads. Journal of Modares Mechanical Engineering 15(4): 361-368. (In Persian)
[26] Babaei H, Mirzababaie Mostofi T, Alitavoli M
(2015) Study on the response of circular thin plate under low velocity impact. Geomech Eng 9(2): 207-218.
[27] Jamali A, Babaei H, Nariman-Zadeh N, Ashraf Talesh SH, Mirzababaie Mostofi T (2016) Multi-objective optimum design of ANFIS for modelling and prediction of deformation of thin plates subjected to hydrodynamic impact loading. Proc Inst Mech Eng-Part L J Mater Des Appl 1464420716660332.
[28] Babaei H, Mostofi T.M, Alitavoli M, Darvizeh A (2016) Empirical Modelling for Prediction of Large Deformation of Clamped Circular Plates in Gas Detonation Forming Process. Exp Tech 40(6): 1485-1494.
[29] Mostofi TM, Babaei H, Alitavoli M, Hosseinzadeh S (2017) On dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile. Thin-Walled Struc 112: 118-124.
 [30] Rezasefat M, Mostofi TM, Ozbakkaloglu T (2019) Repeated localized impulsive loading on monolithic and multi-layered metallic plates. Thin Wall Struc 144: 106332.
 [31] Babaei H, Mostofi TM, Alitavoli M (2017) Experimental and analytical investigation into large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile. Thin Walled Struct 107: 257-265.
 [32] Mostofi TM, Babaei H, Alitavoli M (2017) The influence of gas mixture detonation loads on large plastic deformation of thin quadrangular plates: Experimental investigation and empirical modelling. Thin Walled Struct 118: 1-11.
[33] Mirzababaie Mostofi T, Babaei H, Alitavoli M (2017) Experimental and theoretical study on large ductile transverse deformations of rectangular plates subjected to shock load due to gas mixture detonation. Strain 53(4): e12235.
[34] Babaei H, Mostofi TM, Namdari-Khalilabad M, Alitavoli M, Mohammadi K (2017) Gas mixture detonation method, a novel processing technique for metal powder compaction: Experimental investigation and empirical modeling. Powder Tech 315: 171-81.
[35] Babaei H, Mirzababaie Mostofi T, Armoudli E (2017) On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading. Proc Inst Mech Eng-Part E J Process Mech Eng 231(5): 939-950.
[36] Babaei H, Mirzababaie Mostofi T (2016) New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading. Proc Inst Mech Eng-Part L J Mater Des Appl 1464420716654195.
[37] Babaei H, Mirzababaie Mostofi T (2016) Modeling and prediction of fatigue life in composite materials by using singular value decomposition method. Proc Inst Mech Eng-Part L J Mater Des Appl 1464420716660875.
[38] Rezasefat M, Mirzababaie Mostofi T, Babaei H, Ziya-Shamami M, Alitavoli M (2019) Dynamic plastic response of double-layered circular metallic plates due to localized impulsive loading. Proc Inst Mech Eng-Part L J Mater Des Appl 233(7):1449-1471.
[39] Babaei H, Mostofi TM, Sadraei SH (2015) Effect of gas detonation on response of circular plate-experimental and theoretical. Struct Eng Mech 56(4): 535-548.
[40] Babaei H, Mostofi TM, Alitavoli M (2015) Experimental investigation and analytical modelling for forming of circular-clamped plates by using gases mixture detonation. Proc Inst Mech Eng-Part C J Mech Eng Sci 0954406215614336.
[41] Mostofi TM, Babaei H, Alitavoli M (2016) Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behavior of fully clamped thin quadrangular plates. Thin-Walled Struct 109: 367-376.
[42] Mostofi TM, Golbaf A, Mahmoudi A, Alitavoli M, Babaei H (2018) Closed-form analytical analysis on the effect of coupled membrane and bending strains on the dynamic plastic behaviour of fully clamped thin quadrangular plates due to uniform and localized impulsive loading. Thin-Walled Struct 123: 48-56.
[43] Mostofi TM, Badkhor MS, Ghasemi E (2019) Experimental investigation and optimal analysis of the high-velocity forming process of bilayer plates. Journal of Solid and Fluid Mechanics 9(3) 65-80.
[44] Mostofi TM, Babaei H (2019) Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part I: Experimental studies. Journal of Solid and Fluid Mechanics 9(1) 71-83.
[45] Mostofi TM, Babaei H (2019) Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part II: Analytical and empirical modelling. Journal of Solid and Fluid Mechanics 9(2) 15-29.