On Applying Kriging Approximate Optimization to Sheet Metal Forming

Abstract:

This paper presents a methodology to effectively determine the optimal process parameters using finite element analysis (FEA) and design of experiments (DOE) based on Metamodels. The idea is to establish an approximation function relationship between quality objectives and process parameters to alleviate the expensive computational expense in the optimization iterations for the sheet metal forming process. This paper investigated the Kriging metamodel approach. In order to prove accuracy and efficiency of Kriging method, the nonlinear function as test functions is implemented. At the same time, the practical nonlinear engineering problems such as square drawing are also optimized successfully by proposed method. The results prove Kriging model is an effective method for nonlinear engineering problem in practice.

• Periodical: Applied Mechanics and Materials (Volumes 63-64)
• Pages: 3-7
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.63-64.3
• Online since: June 2011
• Authors: Yan Min Xie
• Keywords: Kriging Model, Optimization, Sheet Metal Forming

References

[1] G. Venter, R.T. Haftka, J.H. Starnes. Construction of response surfaces for design optimization applications. In: Proceedings of the 6th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization. Bellevue (Washington), September 4-6, 1996, Part 1. p.548–64.

DOI: 10.2514/6.1996-4040

[2] J. Sacks, S.B. Schiller, W.J. Welch. Design for computer experiment. Technometrics 1989; 31 (1):41–7.

[3] N. A.. C. Cressie, Statistics for Spatial Data, J. Wiley: New York, 1993.

[4] G. Matheron. Principles of geostatistics. Economic Geology, 1963, 58, 1246–1266.

DOI: 10.2113/gsecongeo.58.8.1246

[5] A.A. Giunta. Aircraft multidisciplinary optimization using design of experiments theory and response surface modeling methods. Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg (Virginia); 1997.

[6] A.J. Booker, J.E. Dennis, P.D. Frank, et al. A rigorous framework for optimization of expensive functions by surrogates. Struct Optimization 1999;17(1):1–13.

DOI: 10.1007/bf01197708

[7] A. Sakata, F. Ashida, M. Zako. Structural optimization using Kriging approximation. Comput Meth Appl Mech Eng 2003; 192(7–8):923–39.

DOI: 10.1016/s0045-7825(02)00617-5

[8] A.A. Giunta, L.T. Watson. A comparison of approximation modeling techniques: polynomial versus interpolating models, AIAA-98-4758. 1998, 36(1):275-286.

DOI: 10.2514/6.1998-4758

[9] K. Park, P.K. Oh, H.J. Lim. The application of the CFD and Kriging method to an optimization of heat sink. International Journal of Heat and Mass Transfer, 2006, 49:3439~3447

DOI: 10.1016/j.ijheatmasstransfer.2006.03.009

[10] Hu Wang, Enying Li, Guang Yao Li. Parallel boundary and best neighbor searching sampling algorithm for drawbead design optimization in sheet metal forming, Struct Multidisc Optim, 2010, 41:309–324.

DOI: 10.1007/s00158-009-0411-3

[11] J. J. M. Rijpkema, L. F. P. Etman, A. J. G. Schoofs. Use of design sensitivity information in response surface and Kriging metamodels [J]. Optimization and Engineering, 2001, 2(4): 469-484.

[12] Joachim Danckert. Experimental investigation of a square-cup deep-drawing process. Journal of Materials Processing Technology, 1995(50): 375~384.

DOI: 10.1016/0924-0136(94)01399-l