Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method

Abstract In this study, the previously developed adaptive response surface method (ARSM) is suggested for construction of metamodel for highly non-linear responses. In order to develop the accuracy and efficiency of metamodel, the particle swarm optimization intelligent sampling (PSOIS) scheme is developed. This kind of intelligent method can guarantee the sampling search in right direction and constraint the bounds of design variables in feasible region. For validation of developed method, the Rosenbrock function is successfully approximated by proposed method; corresponding metamodel appropriateness can be well predicted by analysis of variance (ANOVA). Metamodel by ARSM with PSOIS are employed for optimization of initial blank shape and blank hold force (BHF) in sheet forming process, with validations by finite element simulations using LSDYNA970 commercial code. The results show that developed method is able to produce remarkable metamodels for highly non-linear problems with multi-parameter.

[1]  R. H. Wagoner,et al.  An algorithm for improved convergence in forming analysis , 1997 .

[2]  T. Krink,et al.  Particle swarm optimisation with spatial particle extension , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[3]  Sankaran Mahadevan,et al.  Reliability analysis of automotive body-door subsystem , 2002, Reliab. Eng. Syst. Saf..

[4]  Sankaran Mahadevan,et al.  An Indicator Response Surface-Based Monte Carlo Method for Efficient Component and System Reliability Analysis , 2003, DAC 2003.

[5]  Alf Samuelsson,et al.  Solution of quasi‐static, force‐driven problems by means of a dynamic‐explicit approach and an adaptive loading procedure , 1996 .

[6]  R. Haftka,et al.  Response surface approximations for structural optimization , 1996 .

[7]  Ted Belytschko,et al.  On the dynamic effects of explicit FEM in sheet metal forming analysis , 1998 .

[8]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[9]  Hakim Naceur,et al.  Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach , 2000 .

[10]  James Kennedy,et al.  Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[11]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[12]  Abdelkhalak El Hami,et al.  Reliability analysis of the metal forming process , 2007, Math. Comput. Model..

[13]  Yong Zhang,et al.  Uniform Design: Theory and Application , 2000, Technometrics.

[14]  Nielen Stander,et al.  The successive response surface method applied to sheet-metal forming , 2001 .

[15]  Urmila M. Diwekar,et al.  An efficient sampling technique for off-line quality control , 1997 .

[16]  Lih-Yuan Deng,et al.  Orthogonal Arrays: Theory and Applications , 1999, Technometrics.

[17]  Jerry I. Lin,et al.  Explicit algorithms for the nonlinear dynamics of shells , 1984 .

[18]  E. Doege,et al.  Design and application of pliable blank holder systems for the optimization of process conditions in sheet metal forming , 2001 .

[19]  T. Simpson,et al.  Computationally Inexpensive Metamodel Assessment Strategies , 2002 .

[20]  Ted Belytschko,et al.  Advances in one-point quadrature shell elements , 1992 .

[21]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[22]  Yohei Abe,et al.  Optimisation of the distribution of wall thickness in the multistage sheet metal forming of wheel disks , 2002 .

[23]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[24]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[25]  K. Kuzman,et al.  Optimization of sheet metal forming processes by the use of numerical simulations , 2002 .

[26]  Tomas Jansson,et al.  Optimization of Draw-In for an Automotive Sheet Metal Part An evaluation using surrogate models and response surfaces , 2005 .

[27]  Jeong‐Soo Park.  Optimal Latin-hypercube designs for computer experiments , 1994 .

[28]  G. Gary Wang,et al.  ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS , 2001 .

[29]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[30]  P. Villon,et al.  Moving least squares response surface approximation: Formulation and metal forming applications , 2005 .

[31]  Ronald L. Iman,et al.  Risk methodology for geologic disposal of radioactive waste: small sample sensitivity analysis techniques for computer models, with an application to risk assessment , 1980 .

[32]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[33]  Nielen Stander,et al.  Springback Compensation in Sheet Metal Forming Using a Successive Response Surface Method , 2002 .