Time dependent sheet metal forming optimization by using Gaussian process assisted firefly algorithm
Source abstract
Abstract
For a sheet metal forming optimization problem, time related design variables are seldom considered in practice. The purpose of this work is to handle time dependent sheet metal forming problems. Because it is difficult to investigate all time points during the entire forming procedure, some key time points should be extracted. Therefore, the number of design variables should be significantly increased due to introduce auxiliary time design variables. However, curse of dimensionality is a formidable difficult issue to be solved. To solve such medium-scale problems, Gaussian Process Assisted Firefly Algorithm (GPFA) is suggested. The main idea of the suggested method is to construct a surrogate model-aware search mechanism with Firefly Algorithm (FA) for simulation-based optimization efficiently. Compared with other FAs, the distinctive characteristic of GPFA is to generate new sample points adaptively based on maximum Expected Improvement (EI) criterion, so that the local and global search can be well balanced, and a small promising area can be quickly focused on. Numerical studies on benchmark problems with 20 variables and a real-world application of time dependent sheet metal forming optimization reveal that the GPFA is capable to solve such similar problems.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Laser and Thermal Forming Techniques · Metal Forming Simulation Techniques · Advanced Numerical Analysis Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (60)
Show source-provided references
1. Ohata T, Nakamura Y, Katayama T, Nakamachi E, Nakano K (1996) Development of optimum process design system by numerical simulation. J Mater Process Technol 60(1–4):543–54810.1016/0924-0136(96)02384-9 ↗
2. Batoz JL, Guo YQ (1997) Analysis and design of sheet metal forming parts using a simplified inverse approach. COMPLAS V, Barcelona, p 178–185
3. Ghouati O, Joannic D, Gelin JC (1998) Optimization of process parameters for the control of springback in deep drawing. Proceedings of the NUMIFORM’98 on Simulation of Material Processing: Theory, Methods and Applications, Twente, p 819–824
4. Ghouati O, Lenoir H, Gelin JC (1999) Optimization techniques for the drawing of sheet metal parts. Proceedings of the Fourth International Conference on Numerical Simulation of 3D Sheet metal forming Processes. Numisheet’99, vol. 1, Besançon, p 293–298
5. Park SH, Yoon JW, Yang DY, Kim YH (1999) Optimum blank design in sheet metal forming by the deformation path iteration method. Int J Mech Sci 41(10):1217–123210.1016/S0020-7403(98)00084-8 ↗
6. Guo YQ, Batoz JL, Naceur H, Bouabdallah S, Mercier F, Barlet O (2000) Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach. Comput Struct 78:138–148
7. Naceur H, Guo YQ, Batoz JL, Knopf-Lenoir C (2001) Optimization of drawbead restraining forces and drawbead design in sheet metal forming process. Int J Mech Sci 43(10):2407–243410.1016/S0020-7403(01)00014-5 ↗
8. Azaouzi M, Naceur H, Delameziere A, Batoz JL, Belouettar S (2008) A heuristic optimization algorithm for the blank shape design of high precision metallic parts obtained by a particular stamping process. Finite Elem Anal Des 44(14):842–85010.1016/j.finel.2008.06.008 ↗
9. Naceur H, Guo YQ, Batoz JL (2004) Blank optimization in sheet metal forming using an evolutionary algorithm. J Mater Process Technol 151(1–3):183–19110.1016/j.jmatprotec.2004.04.036 ↗
10. Ohata T, Nakamura Y, Katayama T, Nakamachi E (2003) Development of optimum process design system for sheet fabrication using response surface method. J Mater Process Technol 143-144:667–67210.1016/S0924-0136(03)00314-5 ↗
11. Jansson T, Nilsson L, Redhe M (2003) Using surrogate models and response surfaces in structural optimization–with application to crashworthiness design and sheet metal forming. Struct Multidiscip Optim 25(2):129–14010.1007/s00158-002-0279-y ↗
12. Breitkopf P et al (2005) Moving least squares response surface approximation: formulation and metal forming applications. Comput Struct 83(17):1411–142810.1016/j.compstruc.2004.07.011 ↗
13. Jansson T, Andersson A, Nilsson L (2005) Optimization of draw-in for an automotive sheet metal part: an evaluation using surrogate models and response surfaces. J Mater Process Technol 159(3):426–43410.1016/j.jmatprotec.2004.06.011 ↗
14. Huang Y, Lo ZY, Du R (2006) Minimization of the thickness variation in multi-step sheet metal stamping. J Mater Process Technol 177(1–3):84–8610.1016/j.jmatprotec.2006.03.225 ↗
15. Bonte MHA, van den Boogaard AH, Huétink J (2007) A metamodel based optimisation algorithm for metal forming processes. Advanced Methods in Material Forming p 55–7210.1007/3-540-69845-0_4 ↗
16. Wang H, Li EY, Li GY (2008) Optimization of drawbead design in sheet metal forming based on intelligent sampling by using response surface methodology. J Mater Process Technol 206(1):45–55
17. Wang H, Li EY, Li GY (2009) The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet metal forming optimization. Mater Des 30(5):1468–147910.1016/j.matdes.2008.08.014 ↗
18. Wiebenga JH, Atzema EH, van den Boogaard AH (2015) Stretching the limits of forming processes by robust optimization: a numerical and experimental demonstrator. J Mater Process Technol 217:345–35510.1016/j.jmatprotec.2014.11.018 ↗
19. Jakumeit J, Herdy M, Nitsche M (2005) Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm. Struct Multidiscip Optim 29(6):498–50710.1007/s00158-004-0455-3 ↗
20. Goel A, Wang JW, Yang FC (2009) Blank optimization for sheet metal forming using multi-step finite element simulations. Int J Adv Manuf Technol 40(7–8):709–720
21. Zhou Z, Ong Y, Nair P, Keane A, Lum K (2007) Combining global and local surrogate models to accelerate evolutionary optimization. IEEE Trans Syst Man Cybern Part C- Cybern 37(1):66–7610.1109/TSMCC.2005.855506 ↗
22. Lim D, Jin Y, Ong Y, Sendhoff B (2010) Generalizing surrogate assisted evolutionary computation. IEEE Trans Evolut Comput 14(3):329–35510.1109/TEVC.2009.2027359 ↗
23. Bo L, Qingfu Z, Gielen G (2014) A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Trans Evolut Comput 18(2):180–19210.1109/TEVC.2013.2248012 ↗
24. Gary W, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–38010.1115/1.2429697 ↗
25. Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidiscip Optim 23(1):1–1310.1007/s00158-001-0160-4 ↗
26. Simpson TW, Booker AJ, Ghosh D et al (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidiscip Optim 27(5):302–31310.1007/s00158-004-0389-9 ↗
27. Ackermann ER, de Villiers JP, Cilliers PJ (2011) Nonlinear dynamic systems modeling using Gaussian processes: predicting ionospheric total electron content over South Africa. J Geophys Res 116(10):A10303.1–A1030313
28. Buche D, Schraudolph NN, Koumoutsakos P (2005) Accelerating evolutionary algorithms with Gaussian process fitness function models. IEEE Trans Syst Man Cybernet Part C-Cybernet 35(2):183–19410.1109/TSMCC.2004.841917 ↗
29. Jones DR, Schonlau M, Welch W (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–49210.1023/A:1008306431147 ↗
30. Emmerich M, Giannakoglou K, Naujoks B (2006) Single-and multiobjective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Trans Evolut Comput 10(4):421–43910.1109/TEVC.2005.859463 ↗
31. Rasmussen CE (2004) Gaussian processes in machine learning. Advanced lectures on machine learning. Springer, Berlin, pp 63–7110.1007/978-3-540-28650-9_4 ↗
32. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments (with discussion). Stat Sci 4:409–43510.1214/ss/1177012413 ↗
33. Dennis J, Torczon V (1997) Managing approximation models in optimization. Multidisciplinary Des Optim p 330–347
34. Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Glob Optim 21(4):345–38310.1023/A:1012771025575 ↗
35. Mockus J, Tiesis V, Zilinskas A (1978) The application of Bayesian methods for seeking the extremum. Towards Global Optimization 2(117–129):2
36. Viana AC, Felipe HT, Raphael WT (2013) Layne, efficient global optimization algorithm assisted by multiple surrogate techniques. J Glob Optim 56(2):669–68910.1007/s10898-012-9892-5 ↗
37. Yang XS (2008) Nature-inspired Metaheuristic algorithms. Luniver Press, UK
38. Yang XS (2009) Firefly algorithms for multimodal optimisation. Proc 5th Symposium on Stochastic Algorithms, Foundations and Applications. In: Watanabe O, Zeugmann T (eds) Lecture Notes in Computer Science, vol 5792, pp 169–178
39. Yang XS (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-Inspired Computation 2(2):78–8410.1504/IJBIC.2010.032124 ↗
40. Khadwilard A (2011) Application of firefly algorithm and its parameter setting for job shop scheduling. First Symposius on Hands-On Research and Development 8(1):89–97
41. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading
42. Kennedy J, Eberhart R (1995) Particle swarm optimization. Proc of the IEEE Int Conf on Neural Networks, vol. 1942–1948, Piscataway, p 45–5510.1109/ICNN.1995.488968 ↗
43. Price K, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, New York
44. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–47110.1007/s10898-007-9149-x ↗
45. Banati H, Bajaj M (2011) Firefly based feature selection approach. Int J Computer Science Issues 8(2):473–480
46. Basu B, Mahanti GK (2011) Firefly and artificial bees colony algorithm for synthesis of scanned and broadside linear array antenna. Progress in Electromagnetic Research B 32:169–19010.2528/PIERB11053108 ↗
47. Senthilnath J, Omkar SN, Mani V (2011) Clustering using firefly algorithm: performance study. Swarm Evolut Comput 1(3):164–17110.1016/j.swevo.2011.06.003 ↗
48. Zaman MA, Matin A (2012) Nonuniformly spaced linear antenna array design using firefly algorithm. Inter J Micro Sci Technol 2012(2012):1–9
49. Yang XS, Xingshi H (2013) Firefly algorithm: recent advances and applications. Inter J Swarm Intel 1(1):36–5010.1504/IJSI.2013.055801 ↗
50. Stein M (1987) Large sample properties of simulations using latin hypercube sampling. Technometrics 29(2):143–15110.1080/00401706.1987.10488205 ↗
51. McKay MD, Beckman RJ, William JC (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1):55–6110.1080/00401706.2000.10485979 ↗
52. Montgomery DC, Myers RH (1995) Response surface methodology: process and product optimization using designed experiments. J Raymond H. Meyers and Douglas C. Montgomery. A Wiley-Interscience Publications
53. Chengzhi S, Guanlong C, Zhongqin L (2005) Determining the optimum variable blank-holder forces using adaptive response surface methodology (ARSM). Int J Adv Manuf Technol 26(1–2):23–2910.1007/s00170-003-1979-1 ↗
54. Zhang W, Shivpuri R (2009) Probabilistic design of aluminum sheet drawing for reduced risk of wrinkling and fracture. Reliab Eng Syst Saf 94(2):152–16110.1016/j.ress.2008.02.024 ↗
55. John C, Xia C, Yang L, Xu S, Stoughton T, Hartfield-Wunsch S, Li J, Chen Z (2014) Benchmark 2. The 9th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes (NUMISHEET2014), Melbourne, http://www.numisheet2014.org/
56. Rabitz H, Aliş ÖF (1999) General foundations of high-dimensional model representations. J Math Chem 25(2–3):197–23310.1023/A:1019188517934 ↗
57. Wang H, Tang L, Li GY (2011) Adaptive MLS-HDMR metamodeling techniques for high dimensional problems. Expert Syst Appl 38(11):14117–1412610.1016/j.eswa.2011.04.222 ↗
58. Kleiber M, Rojek J, Stocki R, Kleiber M, Rojek J, Stocki R, (2002) Reliability assessment for sheet metal forming operations. Computer Methods in Applied Mechanics and Engineering 191 (39-40):4511–453210.1016/S0045-7825(02)00394-8 ↗
59. Wei Liu, Yuying Yang, Wei Liu, Yuying Yang, (2008) Multi-objective optimization of sheet metal forming process using Pareto-based genetic algorithm. Journal of Materials Processing Technology 208 (1-3):499–506
60. Hillmann M, Kubli W (1999) Optimization of sheet metal forming processes using simulation programs. In Numisheet 99(1): 287–292