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Sheet metal forming optimization by using surrogate modeling techniques

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Abstract

Surrogate assisted optimization has been widely applied in sheet metal forming design due to its efficiency. Therefore, to improve the efficiency of design and reduce the product development cycle, it is important for scholars and engineers to have some insight into the performance of each surrogate assisted optimization method and make them more flexible practically. For this purpose, the state-of-the-art surrogate assisted optimizations are investigated. Furthermore, in view of the bottleneck and development of the surrogate assisted optimization and sheet metal forming design, some important issues on the surrogate assisted optimization in support of the sheet metal forming design are analyzed and discussed, involving the description of the sheet metal forming design, off-line and online sampling strategies, space mapping algorithm, high dimensional problems, robust design, some challenges and potential feasible methods. Generally, this paper provides insightful observations into the performance and potential development of these methods in sheet metal forming design.

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References

  1. ZHANG Q, LIU Y, ZHANG Z. A new optimization method for sheet metal forming processes based on an iterative learning control model[J]. The International Journal of Advanced Manufacturing Technology, 2016, 85(5–8): 1063–1075.

    Article  Google Scholar 

  2. LUO Y, YANG W, LIU Z, et al. Numerical simulation and experimental study on cyclic multi-point incremental forming process[J]. The International Journal of Advanced Manufacturing Technology, 2016, 85(5–8): 1249–1159.

    Article  Google Scholar 

  3. YUAN B, FANG W, LI J, et al. A coupled finite element-element-free Galerkin method for simulating viscous pressure forming[J]. Engineering Analysis with Boundary Elements, 2016, 68: 86–102.

    Article  MathSciNet  Google Scholar 

  4. ESFAHANI R T, ZOJAJI Z. Optimization of finite element model of laser forming in circular path using genetic algorithms and ANFIS[J]. Soft Computing, 2016, 20(5): 2031–2045.

    Article  Google Scholar 

  5. PENG C Y, WU C F J. On the choice of nugget in kriging modeling for deterministic computer experiments[J]. Journal of Computational and Graphical Statistics, 2014, 23(1): 151–168.

    Article  MathSciNet  Google Scholar 

  6. DATTA R, REGIS R G. A surrogate-assisted evolution strategy for constrained multi-objective optimization[J]. Expert Systems with Applications, 2016, 57: 270–284.

    Article  Google Scholar 

  7. CHEN J, YAN J, YANG Z, et al. Flexible riser configuration design for extremely shallow water with surrogate-model-based optimization[J]. Journal of Offshore Mechanics and Arctic Engineering, 2016, 138(4): 041701.

    Article  Google Scholar 

  8. KOZIEL S, OGURTSOV S, BEKASIEWICZ A. Suppressing side-lobes of linear phased array of micro-strip antennas with simulation-based optimization[J]. Metrology and Measurement Systems, 2016, 23(2): 193–203.

    Article  Google Scholar 

  9. HAMDAOUI M, LE QUILLIEC G, BREITKOPF P, et al. POD surrogates for real-time multi-parametric sheet metal forming problems[J]. International journal of material forming, 2014, 7(3): 337–358.

    Article  Google Scholar 

  10. SUN G, LI G, LI Q. Variable fidelity design based surrogate and artificial bee colony algorithm for sheet metal forming process[J]. Finite Elements in Analysis and Design, 2012, 59: 76–90.

    Article  Google Scholar 

  11. SUN G, LI G, GONG Z, et al. Multiobjective robust optimization method for drawbead design in sheet metal forming[J]. Materials & Design, 2010, 31(4): 1917–1929.

    Article  Google Scholar 

  12. BOX G E P, WILSON K B. On the experimental attainment of optimum conditions[J]. Journal of the Royal Statistical Society Series, 1951, B13(1): 1–45.

    MathSciNet  MATH  Google Scholar 

  13. CHO H, BAE S, CHOI K K, et al. An efficient variable screening method for effective surrogate models for reliability-based design optimization[J]. Structural and Multidisciplinary Optimization, 2014, 50(5): 717–738.

    Article  Google Scholar 

  14. CAI X, QIU H, GAO L, et al. An enhanced RBF-HDMR integrated with an adaptive sampling method for approximating high dimensional problems in engineering design[J]. Structural and Multidisciplinary Optimization, 2016, 53(6): 1209–1229.

    Article  Google Scholar 

  15. DURBIN J, WATSON G S. Testing for serial correlation in least squares regression. II[J]. Biometrika, 1951, 38(1/2): 159–177.

    Article  MathSciNet  MATH  Google Scholar 

  16. LIU W K, LI S, BELYTSCHKO T. Moving least-square reproducing kernel methods(I) methodology and convergence[J]. Computer Methods in Applied Mechanics and Engineering, 1997, 143(1): 113–154.

    Article  MathSciNet  MATH  Google Scholar 

  17. SIMPSON T W, MAUERY T M, KORTE J J, et al. Kriging models for global approximation in simulation-based multidisciplinary design optimization[J]. AIAA journal, 2001, 39(12): 2233–2241.

    Article  Google Scholar 

  18. BUHMANN M D. Radial basis functions[J]. Acta Numerica 2000, 2000, 9: 1–38.

    Article  MathSciNet  MATH  Google Scholar 

  19. WOLFINGER R D, LIN X. Two Taylor-series approximation methods for nonlinear mixed models[J]. Computational Statistics & Data Analysis, 1997, 25(4): 465–490.

    Article  MATH  Google Scholar 

  20. HORNIK K. Some new results on neural network approximation[J]. Neural Networks, 1993, 6(8): 1069–1072.

    Article  Google Scholar 

  21. KEULEN F V A N, TOROPOV V V. New developments in structural optimization using adaptive mesh refinement and multipoint approximations[J]. Engineering Optimization, 1997, 29(1–4): 217–234.

    Article  Google Scholar 

  22. FRIEDMAN J H. Multivariate adaptive regression splines[J]. The Annals of Statistics, 1991: 1–67.

    Google Scholar 

  23. RAJASHEKHAR M R, ELLINGWOOD B R. A new look at the response surface approach for reliability analysis[J]. Structural safety, 1993, 12(3): 205–220.

    Article  Google Scholar 

  24. JAKUMEIT J, HERDY M, NITSCHE M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm[J]. Structural and Multidisciplinary Optimization, 2005, 29(6): 498–507.

    Article  Google Scholar 

  25. KOK S, STANDER N. Optimization of a sheet metal forming process using successive multipoint approximations[J]. Structural Optimization, 1999, 18(4): 277–295.

    Article  Google Scholar 

  26. BARLET O, BATOZ J L, GUO Y Q, et al. The inverse approach and mathematical programming techniques for optimum design of sheet forming parts[J]. IEEE/ASME Transactions on Mechatronics, 1996, 3(3):227–232.

    Google Scholar 

  27. HU J, MARCINIAK Z, DUNCAN J. Mechanics of sheet metal forming[M] London: Edward Arnold, 1992.

    Google Scholar 

  28. DONG G, ZHAO C, PENG Y, et al. Hot granules medium pressure forming process of AA7075 conical parts[J]. Chinese Journal of Mechanical Engineering, 2015, 28(3): 580–591.

    Article  Google Scholar 

  29. JANSSON T, NILSSON L, MOSHFEGH R. Reliability analysis of a sheet metal forming process using Monte Carlo analysis and metamodels[J]. Journal of Materials Processing Technology, 2008, 202(1): 255–268.

    Article  Google Scholar 

  30. BREITKOPF P, NACEUR H, RASSINEUX A, et al. Moving least squares response surface approximation: formulation and metal forming applications[J]. Computers & Structures, 2005, 83(17): 1411–1428.

    Article  Google Scholar 

  31. TENG F, ZHANG W, LIANG J, et al. Springback prediction and optimization of variable stretch force trajectory in three-dimensional stretch bending process[J]. Chinese Journal of Mechanical Engineering, 2015, 28(6): 1132–1140.

    Article  Google Scholar 

  32. WEI D, CUI Z, CHEN J. Optimization and tolerance prediction of sheet metal forming process using response surface model[J]. Computational Materials Science, 2008, 42(2): 228–233.

    Article  Google Scholar 

  33. NACEUR H, GUO Y Q, BEN-ELECHI S. Response surface methodology for design of sheet forming parameters to control springback effects[J]. Computers & Structures, 2006, 84(26): 1651–1663.

    Article  Google Scholar 

  34. LIU W, LIU Q, RUAN F, et al. Springback prediction for sheet metal forming based on GA-ANN technology[J]. Journal of Materials Processing Technology, 2007, 187: 227–231.

    Article  Google Scholar 

  35. KAZAN R, FIRAT M, TIRYAKI A E. Prediction of springback in wipe-bending process of sheet metal using neural network[J]. Materials & Design, 2009, 30(2): 418–423.

    Article  Google Scholar 

  36. BOX G E P, HUNTER J S, HUNTER W G. Statistics for experimenters: design, innovation, and discovery[M] New York: Wiley-Interscience, 2005.

    MATH  Google Scholar 

  37. SCHEIBER V. Experimental designs for stochastic optimization[J]. Computing, 1972, 9(4):383–399.

    Article  Google Scholar 

  38. SACKS J, WELCH W J, MITCHELL T J, et al. Design and analysis of computer experiments[J]. Statistical science, 1989: 409–423.

    Google Scholar 

  39. HEDAYAT A S, SLOANE N J A, STUFKEN J. Orthogonal arrays: theory and applications[J]. Technometrics, 2000, 42(4): 440–440.

    Google Scholar 

  40. TANG B. Orthogonal array-based Latin hypercubes[J]. Journal of the American Statistical Association, 1993, 88(424): 1392–1397.

    Article  MathSciNet  MATH  Google Scholar 

  41. KALAGNANAM J R, DIWEKAR U M. An efficient sampling technique for off-line quality control[J]. Technometrics, 1997, 39(3): 308–319.

    Article  MATH  Google Scholar 

  42. FANG K T, LIN D K J, WINKER P, et al. Uniform design: theory and application[J]. Technometrics, 2000, 42(3): 237–248.

    Article  MathSciNet  MATH  Google Scholar 

  43. WANG H, ZENG Y, LI E, et al. “Seen Is Solution” a CAD/CAE integrated parallel reanalysis design system[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 299: 187–214.

    Article  MathSciNet  Google Scholar 

  44. OHATA T, NAKAMURA Y, KATAYAMA T, et al. Development of optimum process design system for sheet fabrication using response surface method[J]. Journal of Materials Processing Technology, 2003, 143: 667–672.

    Article  Google Scholar 

  45. TANG B, SUN J, ZHAO Z, et al. Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology[J]. The International Journal of Advanced Manufacturing Technology, 2006, 31(3–4): 225–234.

    Article  Google Scholar 

  46. KAREN T, KAYA N, ÖZTÜ RK F. Intelligent die design optimization using enhanced differential evolution and response surface methodology[J]. Journal of Intelligent Manufacturing, 2015, 26(5):1027–1038.

    Article  Google Scholar 

  47. KLEIJNEN J P C. Design and analysis of simulation experiments [M] New York: Springer, 2008.

    MATH  Google Scholar 

  48. LI Y H, WU Y Z, HUANG Z D. An incremental kriging method for sequential optimal experimental design[J]. Cmes Computer Modeling in Engineering & Ences, 2014, 97(4):323–357.

    Google Scholar 

  49. JIN R, CHEN W, SUDJIANTO A. An efficient algorithm for constructing optimal design of computer experiments[J]. Journal of Statistical Planning and Inference, 2005, 134(1): 268–287.

    Article  MathSciNet  MATH  Google Scholar 

  50. SASENA M, PARKINSON M B, GOOVAERTS P, et al. Adaptive experimental design applied to an ergonomics testing procedure [C]//Asme International Design Engineering Technical Conferences & Computers & Information in Engineering Conference, Canada, September 29–October 2, 2002: 529–537.

    Google Scholar 

  51. WANG H, LI E, LI G Y, et al. Development of metamodeling based optimization system for high nonlinear engineering problems[J]. Advances in Engineering Software, 2008, 39(8): 629–645.

    Article  Google Scholar 

  52. WANG H, YAO L G, HUA Z Z. Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method[J]. Journal of Materials Processing Technology, 2008, 197(1): 77–88.

    Google Scholar 

  53. STANDER N, BURGER M, ZHU X, et al. Springback compensation in sheet metal forming using a successive response surface method[C]//Proceedings of the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, September 4–6, 2002: 2002–2039.

    Google Scholar 

  54. NACEUR H, BEN-ELECHI S, BATOZ J L, et al. Response surface methodology for the rapid design of aluminum sheet metal forming parameters[J]. Materials & Design, 2008, 29(4): 781–790.

    Article  Google Scholar 

  55. WANG G G. Adaptive Response surface method using inherited latin hypercube design points[J]. Journal of Mechanical Design, 2003, 125(2): 210–220.

    Article  Google Scholar 

  56. WANG H, LI E, LI G Y. Parallel boundary and best neighbor searching sampling algorithm for drawbead design optimization in sheet metal forming[J]. Structural and Multidisciplinary Optimization, 2010, 41(2): 309–324.

    Article  Google Scholar 

  57. SENER B, KURTARAN H. Optimization of process parameters for rectangular cup deep drawing by the Taguchi method and genetic algorithm[J]. Materials Testing, 2016, 58(3): 238–245.

    Article  Google Scholar 

  58. WEI L, YUYING Y. Multi-objective optimization of sheet metal forming process using Pareto-based genetic algorithm[J]. Journal of Materials Processing Technology, 2008, 208(1): 499–506.

    Article  Google Scholar 

  59. WEI L, YUYING Y, ZHONGWEN X, et al. Springback control of sheet metal forming based on the response-surface method and multi-objective genetic algorithm[J]. Materials Science and Engineering: A, 2009, 499(1): 325–328.

    Article  Google Scholar 

  60. LIAO M, LIU J, LIU Y, et al. Optimal stamping direction for an automotive part[J]. International Journal of Advanced Manufacturing Technology, 2015, 79(1–4): 285–297.

    Article  Google Scholar 

  61. INAMDAR M V, DATE P P, DESAI U B. Studies on the prediction of springback in air vee bending of metallic sheets using an artificial neural network[J]. Journal of Materials Processing Technology, 2000, 108(1): 45–54.

    Article  Google Scholar 

  62. LIU N, YANG H, LI H, et al. BP artificial neural network modeling for accurate radius prediction and application in incremental in-plane bending[J]. International Journal of Advanced Manufacturing Technology, 2015, 80(5–8):1–14.

    Google Scholar 

  63. CHENG P J, LIN S C. Using neural networks to predict bending angle of sheet metal formed by laser[J]. International Journal of Machine Tools and Manufacture, 2000, 40(8): 1185–1197.

    Article  Google Scholar 

  64. WANG J, WU X, THOMSON P F, et al. A neural networks approach to investigating the geometrical influence on wrinkling in sheet metal forming[J]. Journal of Materials Processing Technology, 2000, 105(3): 215–220.

    Article  Google Scholar 

  65. SIVASANKARAN S, NARAYANASAMY R, JEYAPAUL R, et al. Modelling of wrinkling in deep drawing of different grades of annealed commercially pure aluminium sheets when drawn through a conical die using artificial neural network[J]. Materials & Design, 2009, 30(8): 3193–3205.

    Article  Google Scholar 

  66. LIEW K M, TAN H, RAY T, et al. Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm[J]. Structural and Multidisciplinary Optimization, 2004, 26(3–4): 284–294.

    Article  Google Scholar 

  67. FU Z, MO J, CHEN L, et al. Using genetic algorithm-back propagation neural network prediction and finite-element model simulation to optimize the process of multiple-step incremental air-bending forming of sheet metal[J]. Materials & Design, 2010, 31(1): 267–277.

    Article  MathSciNet  Google Scholar 

  68. KITAYAMA S, KITA K, YAMAZAKI K. Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network[J]. International Journal of Advanced Manufacturing Technology, 2012, 61(61):1067–1083.

    Article  Google Scholar 

  69. SÓBESTER A, LEARY S J, KEANE A J. A parallel updating scheme for approximating and optimizing high fidelity computer simulations[J]. Structural & Multidisciplinary Optimization, 2004, 27(5): 371–383.

    Article  Google Scholar 

  70. REGIS R G, SHOEMAKER C A. Parallel radial basis function methods for the global optimization of expensive functions[J]. European Journal of Operational Research, 2007, 182(2): 514–535.

    Article  MathSciNet  MATH  Google Scholar 

  71. KERRY K E, HAWICK K A. Kriging interpolation on high-performance computers[C]//High-Performance Computing and Networking, Amsterdam, April 21–23, 1998:429–438.

    Chapter  Google Scholar 

  72. ONG Y S, NAIR P B, KEANE A J. Evolutionary optimization of computationally expensive problems via surrogate modeling[J]. Aiaa Journal, 2003, 41(4):687–696.

    Article  Google Scholar 

  73. ELDRED M S, AGARWAL H, PEREZ V M, et al. Investigation of reliability method formulations in DAKOTA/UQ[J]. Structure & Infrastructure Engineering, 2007, 3(3):199–213.

    Article  Google Scholar 

  74. JAKUMEIT J, HERDY M, NITSCHE M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm[J]. Structural and Multidisciplinary Optimization, 2005, 29(6): 498–507.

    Article  Google Scholar 

  75. WANG H, LI E, LI G Y. The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet forming optimization[J]. Materials & Design, 2009, 30(5): 1468–1479.

    Article  MathSciNet  Google Scholar 

  76. IVANOV M, KUHNT S. A parallel optimization algorithm based on FANOVA decomposition[J]. Quality & Reliability Engineering, 2014, 30(7): 961–974.

    Article  Google Scholar 

  77. ZHOU Z, ONG Y S, LIM M H, et al. Memetic algorithm using multi-surrogates for computationally expensive optimization problems[J]. Soft Computing, 2007, 11(10): 957–971.

    Article  Google Scholar 

  78. JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global optimization, 1998, 13(4): 455–492.

    Article  MathSciNet  MATH  Google Scholar 

  79. WANG L, SHAN S, WANG G G. Mode-pursuing sampling method for global optimization on expensive black-box functions[J]. Engineering Optimization, 2004, 36(4): 419–438.

    Article  Google Scholar 

  80. LI E, WANG H. Bi-direction multi-surrogate assisted global optimization[J]. Engineering Computations, 2016, 33(3): 646–666.

    Article  MathSciNet  Google Scholar 

  81. WANG H, YE F, LI E, et al. A comparative study of expected improvement-assisted global optimization with different surrogates[J]. Engineering Optimization, 2015: 1–27.

    Google Scholar 

  82. GOEL T, HAFTKA R T, SHYY W, et al. Ensemble of surrogates[J]. Structural and Multidisciplinary Optimization, 2007, 33(3): 199–216.

    Article  Google Scholar 

  83. BANDLER J W, BIERNACKI R M, CHEN S H, et al. Space mapping technique for electromagnetic optimization[J]. IEEE Transactions on Microwave Theory and Techniques, 1994, 42(12): 2536–2544.

    Article  Google Scholar 

  84. BANDLER J W, CHENG Q S, DAKROURY S A, et al. Space mapping: the state of the art[J]. IEEE Transactions on Microwave Theory and Techniques, 2004, 52(1): 337–361.

    Article  Google Scholar 

  85. JANSSON T, NILSSON L, REDHE M. Using surrogate models and response surfaces in structural optimization–with application to crashworthiness design and sheet metal forming[J]. Structural and Multidisciplinary Optimization, 2003, 25(2): 129–140.

    Article  Google Scholar 

  86. JANSSON T, ANDERSSON A, NILSSON L. Optimization of draw-in for an automotive sheet metal part: an evaluation using surrogate models and response surfaces[J]. Journal of Materials Processing Technology, 2005, 159(3): 426–434.

    Article  Google Scholar 

  87. WANG H, LI E Y, LI G Y, et al. Optimization of sheet metal forming processes by the use of space mapping based metamodeling method[J]. The International Journal of Advanced Manufacturing Technology, 2008, 39(7–8): 642–655.

    Google Scholar 

  88. SHAN S, WANG G G. Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions[J]. Structural and Multidisciplinary Optimization, 2010, 41(2): 219–241.

    Article  MathSciNet  MATH  Google Scholar 

  89. LI E, WANG H, YE F. Two-level multi-surrogate assisted optimization method for high dimensional nonlinear problems[J]. Applied Soft Computing, 2016, 46: 26–36.

    Article  Google Scholar 

  90. LI E, WANG H. An alternative adaptive differential evolutionary Algorithm assisted by Expected Improvement criterion and cut-HDMR expansion and its application in time-based sheet forming design[J]. Advances in Engineering Software, 2016, 97: 96–107.

    Article  Google Scholar 

  91. WANG H, TANG L, LI G Y. Adaptive MLS-HDMR metamodeling techniques for high dimensional problems[J]. Expert Systems with Applications, 2011, 38(11): 14117–14126.

    Google Scholar 

  92. WIEBENGA J H, BOOGAARD A H V D. On the effect of numerical noise in approximate optimization of forming processes using numerical simulations[J]. International Journal of Material Forming, 2014, 7(3): 317–335.

    Google Scholar 

  93. JU Y, ZHANG C. Robust design optimization method for centrifugal impellers under surface roughness uncertainties due to blade fouling[J]. Chinese Journal of Mechanical Engineering, 2016, 29(2): 301–314.

    Article  Google Scholar 

  94. TANG Y, CHEN J. Robust design of sheet metal forming process based on adaptive importance sampling[J]. Structural and Multidisciplinary Optimization, 2009, 39(5): 531–544.

    Article  MathSciNet  MATH  Google Scholar 

  95. KLEIBER M, ROJEK J, STOCKI R. Reliability assessment for sheet metal forming operations[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(39): 4511–4532.

    Article  MATH  Google Scholar 

  96. JANSSON T, NILSSON L, MOSHFEGH R. Reliability analysis of a sheet metal forming process using Monte Carlo analysis and metamodels[J]. Journal of Materials Processing Technology, 2008, 202(1): 255–268.

    Article  Google Scholar 

  97. ZHANG W, SHIVPURI R. Probabilistic design of aluminum sheet drawing for reduced risk of wrinkling and fracture[J]. Reliability Engineering & System Safety, 2009, 94(2): 152–161.

    Article  Google Scholar 

  98. NAJAFI A, ACAR E, RAISROHANI M. Multi-objective robust design of energy-absorbing components using coupled processperformance simulations[J]. Engineering Optimization, 2014, 46(46): 146–164.

    Article  Google Scholar 

  99. KIM K J, LIN D K J. Dual response surface optimization: a fuzzy modeling approach[J]. Journal of Quality Technology, 1998, 30(1): 1–10.

    MathSciNet  Google Scholar 

  100. VINING G, MYERS R. Combining Taguchi and response surface philosophies—A dual response approach[J]. Journal of Quality Technology, 1990, 22(1): 38–45.

    Google Scholar 

  101. SUN G, LI G, GONG Z, et al. Multiobjective robust optimization method for drawbead design in sheet metal forming[J]. Materials & Design, 2010, 31(4): 1917–1929.

    Article  Google Scholar 

  102. CAI Y, WANG G, LI G, et al. A high performance crashworthiness simulation system based on GPU[J]. Advances in Engineering Software, 2015, 86: 29–38.

    Article  Google Scholar 

  103. HE G, WANG H, LI E, et al. A multiple-GPU based parallel independent coefficient reanalysis method and applications for vehicle design[J]. Advances in Engineering Software, 2015, 85: 108–124.

    Article  Google Scholar 

  104. KAMPOLIS I C, TROMPOUKIS X S, ASOUTI V G, et al. CFD-based analysis and two-level aerodynamic optimization on graphics processing units[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(9): 712–722.

    Article  MathSciNet  MATH  Google Scholar 

  105. SUNARSO A, TSUJI T, CHONO S. GPU-accelerated molecular dynamics simulation for study of liquid crystalline flows[J]. Journal of Computational Physics, 2010, 229(15): 5486–5497.

    Article  MATH  Google Scholar 

  106. KOMATITSCH D, ERLEBACHER G, GÖDDEKE D, et al. High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster[J]. Journal of Computational Physics, 2010, 229(20): 7692–7714.

    Article  MathSciNet  MATH  Google Scholar 

  107. CAI Y, LI G, WANG H, et al. Development of parallel explicit finite element sheet forming simulation system based on GPU architecture[J]. Advances in Engineering Software, 2012, 45(1): 370–379.

    Article  Google Scholar 

  108. LI J, WAN D, CHI Z, et al. An efficient fine-grained parallel particle swarm optimization method based on GPU-acceleration[J]. International Journal of Innovative Computing, Information and Control, 2007, 3(6): 1707–1714.

    Google Scholar 

  109. ZHOU Y, TAN Y. GPU-based parallel particle swarm optimization[C]//2009 IEEE Congress on Evolutionary Computation, Trondheim, May 18–21, 2009: 1493–1500.

    Chapter  Google Scholar 

  110. POSPICHAL P, JAROS J, SCHWARZ J. Parallel genetic algorithm on the cuda architecture[C]//European Conference on the Applications of Evolutionary Computation, Turkey, April 7–9, 2010: 442–451.

    Google Scholar 

  111. POSPICHAL P, SCHWARZ J, JAROS J. Parallel genetic algorithm solving 0/1 knapsack problem running on the gpu[C]//16th International Conference on Soft Computing, Brno, Jun 23–25, 2010: 64–70.

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Hu Wang, Fan Ye & Lei Chen

  2. Joint Center for Intelligent New Energy Vehicle, Shanghai, China

    Hu Wang

  3. School of Logistics, Central South University of Forestry and Technology, Changsha, 41004, China

    Enying Li

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  1. Hu Wang
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  2. Fan Ye
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  4. Enying Li
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Correspondence to Hu Wang.

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Supported by National Natural Science Foundation of China(Grant Nos. 11572120, 11172097, 11302266)

WANG Hu, born in 1975, is currently a professor and a PhD candidate supervisor at State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, China. He received his PhD degree from Hunan Universtiy, China, in 2006. His research interests include mechanical design, engineering optimization, numerical computer method and parallel optimization.

YE Fan, born in 1991, is currently a PhD candidate at State Key Laboratory of Advance Design and Manufacturing for Vehicle Body, Hunan University, China. He received his bachelor degree from Yangzhou University, China, in 2013. His research interests include composite material and engineering optimization.

CHEN Lei, born in 1991, is currently a master candidate at State Key Laboratory of Advance Design and Manufacturing for Vehicle Body, Hunan University, China.

LI Enying, born in 1975, is currently a associate professor at Central South University of Forestry and Technology, China. Her main research interests include engineering optimization, mechanical design and nonlinear dynamic problem.

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Wang, H., Ye, F., Chen, L. et al. Sheet metal forming optimization by using surrogate modeling techniques. Chin. J. Mech. Eng. 30, 22–36 (2017). https://doi.org/10.3901/CJME.2016.1020.123

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