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Comparing sampling strategies for aerodynamic kriging surrogate models. (English) Zbl 1348.74101

Summary: In aerodynamic applications often evaluations of an expensive computer simulation like a CFD solver are needed for a whole range of input parameters. Dense computations to describe the global behavior of an objective function are out of reach due to limited computational resources. Surrogate models like the Kriging method allow an interpolation of collected data and a global approximation. Adaptive sampling strategies can reduce the number of required samples for accurate and efficient surrogate models by automatically identifying critical or too coarse sampled regions of the input domain. We compare different existing sampling strategies as well as new theoretical methods using a dense set of validation data in order to gain a deeper understanding of optimal sample distributions and lower error boundaries.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
62K10 Statistical block designs
90C15 Stochastic programming

Software:

DACE; EGO; TAU
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References:

[1] Baldi Antognini, J. Stat. Plan. Inference 140(9) pp 2607– (2010) · Zbl 1188.62214 · doi:10.1016/j.jspi.2010.03.027
[2] Busby, SIAM J. Sci. Comput. 29(1) pp 49– (2007) · Zbl 1129.62071 · doi:10.1137/050639983
[3] H.S. Chung J.J. Alonso
[4] N. Cressie
[5] K. Crombecq L. De Tommasi D. Gorissen T. Dhaene
[6] Currin, J. Am. Statist. Assoc. 86(416) pp 953– (1991) · doi:10.1080/01621459.1991.10475138
[7] R. Dwight Z.H. Han
[8] J. Ferziger M. Perić
[9] Forrester, Prog. Aerospace Sci. 45(1-3) pp 50– (2009) · doi:10.1016/j.paerosci.2008.11.001
[10] A.I.J. Forrester A. Sobester A.J. Keane
[11] Goel, Struct. Multidiscip. Optim. 38 pp 429– (2009) · Zbl 06227666 · doi:10.1007/s00158-008-0290-z
[12] Gramacy, Technometrics 51(2) pp 130– (2009) · doi:10.1198/TECH.2009.0015
[13] Iooss, Int. J. Adv. Syst. Meas. 3(1-2) (2010)
[14] R. Jin W. Chen A. Sudjianto
[15] Jones, J. Global Optim. 13 pp 455– (1998) · Zbl 0917.90270 · doi:10.1023/A:1008306431147
[16] J. Koehler A. Owen
[17] N. Kroll J. Fassbender
[18] Lam, J. Optim. Theor. Appl. 142 pp 533– (2009) · Zbl 1175.90360 · doi:10.1007/s10957-009-9520-9
[19] Laurenceau, AIAA J. 46(2) pp 498– (2008) · doi:10.2514/1.32308
[20] W. Liu
[21] S.N. Lophaven H.B. Nielsen J. Søndergaard
[22] Lovison, Math. Comput. Simul. 81(3) pp 681– (2010) · Zbl 1204.62136 · doi:10.1016/j.matcom.2010.03.007
[23] Mardia, Biometrika 71(1) pp 135– (1984) · Zbl 0542.62079 · doi:10.1093/biomet/71.1.135
[24] J. Martin T. Simpson
[25] McKay, Technometrics 21(2) pp 239– (1979)
[26] Meckesheimer, AIAA J. 40 pp 2053– (2002) · doi:10.2514/2.1538
[27] Morris, Technometrics 35(3) pp 243– (1993) · doi:10.1080/00401706.1993.10485320
[28] H.B. Nielsen S.N. Lophaven J. Søndergaard
[29] J. Nocedal S. Wright
[30] Owen, Stat. Sin. 2(2) pp 439– (1992)
[31] Sacks, Stat. Sci. 4(4) pp 409– (1989) · Zbl 0955.62619 · doi:10.1214/ss/1177012413
[32] T.J. Santner B.J. Williams W. Notz
[33] Sasena, Eng. Optim. 34 pp 263– (2002) · doi:10.1080/03052150211751
[34] O. Schabenberger C. Gotway
[35] D. Schwamborn T. Gerhold R. Heinrich
[36] Shan, Struct. Multidiscip. Optim. 41 pp 219– (2010) · Zbl 1274.74291 · doi:10.1007/s00158-009-0420-2
[37] Simpson, Int. J. Reliab. Safety (IJRS) 2(3) pp 209– (2001)
[38] Tang, J. Am. Stat. Assoc. 88(424) pp 1392– (1993) · doi:10.1080/01621459.1993.10476423
[39] Viana, AIAA J. 47(9) pp 2266– (2009) · doi:10.2514/1.42162
[40] H. Wackernagel
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