Abstract
Tube hydroforming process is widely used in various industrial applications which consists of combining internal pressure and axial displacement to manufacture tubular parts. Inappropriate choice as small changes in such variables may affect the process stability and, in some cases, lead to failure. Consequently, loading path should be optimised to better control the process and to guarantee hydroformed parts with desired specifications. However, optimisation procedure requires several evaluations of the real models which induces a huge computational time. To cope with this limitation, we propose to compare two metamodelling techniques to solve the problem efficiently: the response surface method and the least squares support vector regression. To enhance the metamodels precision, optimal latin hypercube design is used to generate sampled points. It is obtained through iterative optimisation procedure based on a modified version of the simulated annealing algorithm by minimising simultaneously two optimality criterions. Then, multi-objective optimisation problem is formulated to search for the Pareto optimal solutions. Fuzzy classification is then applied to rank the non-dominated solutions which helps designers in the decision-making phase. Before optimising the process, a global sensitivity analysis is carried out using the variance-based method by coupling metamodels and Monte Carlo simulations in order to identify the relative importance of the design variables in terms of internal pressure and axial displacement on the variance of the responses of interest defined to control the process.
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References
Oh SI, Jeon BH, Kim HY, Yang JB (2006) Applications of hydroforming processes to automobile parts. J Mater Proc Technol 174:42–55
Dohmann F, Hartl Ch (2004) Hydroforming-applications of coherent FE-simulations to the development of products and processes. J Mater Proc Technol 150:18–24
Palumbo G (2013) Hydroforming a small scale aluminum automotive component using a layered die. Mater Des 44:365–373
Ray P, Mac Donald BJ (2004) Determination of the optimal load path for tube hydroforming processes using a fuzzy load control algorithm and finite element analysis. Finite Elem Anal Des 41:173–192
An H, Green DE, Johrendt J (2010) Multi-objective optimization and sensitivity analysis of tube hydroforming. Int J Adv Manuf Technol 50:67–84
Ingarao G, Di Lorenzo R, Micari F (2009) Internal pressure counter punch action design in Y-shaped tube hydroforming processes: a multi-objective optimisation approach. Comput Struct 87:591–602
Lin FC, Kwan CT (2004) Application of abductive network and FEM to predict an acceptable product on T-shape tube hydroforming process. Comput Struct 82:1189–1200
Mirzaalia M, Liaghata GH, Moslemi Naeinia H, Seyedkashia SMH, Shojaeeb K (2011) Optimization of tube hydroforming process using simulated annealing algorithm. Procedia Eng 10:3012–3019
Xu X, Zhang W, Li S, Lin Z (2009) Study of tube hydroforming in a trapezoid-sectional die. Thin-Walled Struct 47:1397–1403
Zadeh HK, Mashhadi MM (2006) Finite element simulation and experiment in tube hydroforming of unequal T shapes. J Mater Proc Technol 177:684–687
Alaswad A, Benyounis KY, Olabi AG (2011) Employment of finite element analysis and response surface methodology to investigate the geometrical factors in T-type bi-layered tube hydroforming. Adv Eng Softw 42:917–926
Abedrabbo N, Worswicka M, Mayerb R, Van Riemsdijkc I (2009) Optimization methods for the tube hydroforming process applied to advanced high-strength steels with experimental verification. J Mater Proc Technol 209:110–123
Di Lorenzo R, Ingarao G, Chinesta F (2009) A gradient-based decomposition approach to optimize pressure path and counter punch action in Y-shaped tube hydroforming operations. Int J Adv Manuf Technol 44:49–60
Wei D, Cui Z, Chen J (2008) Optimization and tolerance prediction of sheet metal forming process using response surface model. Comput Mater Sci 42:228–233
Bahloul R, Ben-Elechi S, Potiron A (2006) Optimisation of springback predicted by experimental and numerical approach by using response surface methodology. J Mater Proc Technol 173:101–110
Hu W, Yao LG, Zhi-Hua Z (2008) Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Proc Technol 197:77–88
Azaouzi M, Lebaal N (2012) Tool path optimization for single point incremental sheet forming using response surface method. Simul Model Pract Theory 24:49–58
Tang B, Sun J, Zhao Z, Chen J, Ruan X (2006) Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology. Int J Adv Manuf Technol 31:225–234
Naceur H, Ben-Elechi S, Batoz JL, Knopf-Lenoir C (2008) Response surface methodology for the rapid design of aluminum sheet metal forming parameters. Mater Des 29:781–790
Ingarao G, Di Lorenzo R, Micari F (2009) Analysis of stamping performances of dual phase steels: a multi-objective approach to reduce springback and thinning failure. Mater Des 30:4421–4433
Alaswad A, Benyounis KY, Olabi AG (2011) Employment of finite element analysis and response surface methodology to investigate the geometrical factors in T-type bi-layered tube hydroforming. Adv Eng Softw 42:917–926
Di Lorenzo R, Ingarao G, Chinesta F (2010) Integration of gradient based and response surface methods to develop a cascade optimisation strategy for Y-shaped tube hydroforming process design. Adv Eng Softw 41:336–348
Alaswad A, Olabi AG, Benyounis KY (2011) Integration of finite element analysis and design of experiments to analyse the geometrical factors in bi-layered tube hydroforming. Mater Des 32:838–850
Hasanpour F, Ensafi AA, Khayamian T (2010) Simultaneous chemiluminescence determination of amoxicillin and clavulanic acid using least squares support vector regression. Anal Chim Acta 670:44–50
Hea K, Laib KK, Yenc J (2012) A hybrid slantlet denoising least squares support vector regression model for exchange rate prediction. Procedia Comput Sci 1:2397–2405
Lin KP, Pai PF, Lu YM, Chang PT (2013) Revenue forecasting using a least-squares support vector regression model in a fuzzy environment. Inf Sci 220:196–209
Farquad MAH, Ravi V, Bapi Raju S (2010) Support vector regression based hybrid rule extraction methods for forecasting. Expert Syst Appl 37:5577–5589
Morris MD, Mitchell TJ (1995) Exploratory designs for computational experiments. J Stat Plan Infer 43:381–402
MATLAB R (2008) The MathWorks Inc., Natick
Zhiwei G, Guangchen B (2008) Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut 22:160–166
Abaqus Manual (2010) Version 6.10. Dassault systèmes. http://www.simulia.com
Song WJ, Heo SC, Ku TW, Jeong K, Kang BS (2010) Evaluation of effect of flow stress characteristics of tubular material on forming limit in tube hydroforming process. Int J Mach Tool Manuf 50:753–764
Koç M, Altan T (2002) Prediction of forming limits and parameters in the tube hydroforming process. Int J Mach Tool Manuf 42:123–138
Yuan S, Yuan W, Wang X (2006) Effect of wrinkling behavior on formability and thickness distribution in tube hydroforming. J Mater Proc Technol 177:668–671
Ze-jun T, Gang L, Zhu-bin H, Shi-jian Y (2010) Wrinkling behavior of magnesium alloy tube in warm hydroforming. Trans Nonferrous Metals Soc China 20:1288–1293
Kim J, Kim SW, Song WJ, Kang BS (2004) Analytical approach to bursting in tube hydroforming using diffuse plastic instability. Int J Mech Sci 46:1535–1547
Kim J, Kang SJ, Kang BS (2003) A prediction of bursting failure in tube hydroforming processes based on ductile fracture criterion. Int J Adv Manuf Technol 22:357–362
Wei L, Yuying Y (2008) Multi-objective optimization of sheet metal forming process using Pareto-based genetic algorithm. J Mater Proc Technol 208:499–506
Sun G, Li G, Gong Z, Cui X, Yang X, Li Q (2010) Multiobjective robust optimization method for drawbead design in sheet metal forming. Mater Des 31:1917–1929
Stoughton TB (2000) A general forming limit criterion for sheet metal forming. Int J Mech Sci 42:1–27
Helton JC, Davis FJ (2000) Mathematical and statistical methods for sensitivity analysis of model output. Wiley, New York
Sobol’ IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280
Sobol’ IM (1990) On sensitivity estimation for nonlinear mathematical models. Matem Mod 2(1):112–118
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley Ltd, New York
Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181:259–270
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA–II. IEEE Trans Evol Comput 6:182–197
Schott JR (1995) Fault tolerant design using single and multi-criteria genetic algorithms. Master’s thesis
Pulido GT, Coello Coello CA (2004) The micro genetic algorithm 2: towards online adaptation in evolutionary multiobjective optimisation. Col. San Pedro Zacatenco, Mexico: CINVESTAV-IPN, Evolutionary Computing Group, Department of Electrical Engineering, Section of Computation
Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses and new innovations. PhD Thesis, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Ptterson, AFB, Ohio
Panigrahia BK, Pandia VR, Sharmab R, Dasc S, Dasd S (2011) Multiobjective bacteria foraging algorithm for electrical load dispatch problem. Energy Convers Manage 52:1334–1342
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Ben Abdessalem, A., El-Hami, A. Global sensitivity analysis and multi-objective optimisation of loading path in tube hydroforming process based on metamodelling techniques. Int J Adv Manuf Technol 71, 753–773 (2014). https://doi.org/10.1007/s00170-013-5518-4
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DOI: https://doi.org/10.1007/s00170-013-5518-4