Support Vector enhanced Kriging for metamodeling with noisy data
- 288 Downloads
Sample data may be corrupted by noise in engineering problems. In order to make satisfactory approximations for the data with noise, some regression metamodels are adopted in current researches. The commonly used nugget-effect Kriging regards the variance of noise as a constant and ignores the difference of the noise influence, thus may not be effective enough in some cases. Therefore, a Kriging-based metamodel which combines the merits of Kriging and Support Vector Regression (SVR) is put forward for improving the performance in metamodeling with noisy data. The developed method, termed as SVEK, can capture the underlying trend of an unknown function efficiently by classifying the sample points and then regressing these classified points with different extents. Besides, a criterion for selecting the error margin ε in SVR training is proposed to facilitate the parameter setting process. Moreover, a one-variable test example is used to illustrate the modeling theory and construction procedures of SVEK. Eight numerical benchmark problems with different important characteristics are used to validate the proposed method. Then an overall comparison between the nugget-effect Kriging and the proposed method has been made. Results show that SVEK is promising in metamodeling with noisy data.
KeywordsMetamodeling Noisy observation Kriging Support Vector Regression (SVR)
This work was supported in part by National Natural Science Foundation of China under Grant No 51675198, the 973 National Basic Research Program of China under Grant No 2014CB046705, and the National Natural Science Foundation of China under Grant No 51421062.
- Binois M, Gramacy RB, Ludkovski M (2016) Practical heteroskedastic Gaussian process modeling for large simulation experiments. arXiv preprint arXiv:1611.05902Google Scholar
- Cressie NAC (1993) Statistics for Spatial Data, revised edition. Wiley, New YorkGoogle Scholar
- Forrester AIJ, Sóbester A, Keane AJ (2008) Engineering design via surrogate modelling: a practical guide. Wiley, ChichesterGoogle Scholar
- Goldberg PW, Williams CKI, Bishop CM (1998) Regression with input-dependent noise: A Gaussian process treatment. In: Advances in neural information processing systems. pp 493–499Google Scholar
- Kersting K, Plagemann C, Pfaff P, Burgard W (2007) Most likely heteroscedastic Gaussian process regression. In: Proceedings of the 24th international conference on Machine learning. ACM, pp 393–400Google Scholar
- Mattera D, Haykin S (1999) Support vector machines for dynamic reconstruction of a chaotic system. In: Schölkopf B., Burges C.J.C., and Smola A.J. (Eds.), Advances in Kernel Methods—Support Vector Learning. MIT Press, Cambridge, pp. 211–242.Google Scholar
- Molga M, Smutnicki C (2005) Test functions for optimization needs. Test functions for optimization needs. Retrieved in June 2017, from http://new.zsd.iiar.pwr.wroc.pl/files/docs/functions.pdf
- Picheny V, Wagner T, and Ginsbourger D (2013) A benchmark of kriging-based infill criteria for noisy optimization. Structural and multidisciplinary optimization 48.3:607–626Google Scholar
- Schölkopf B, Smola AJ (2002) Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT press, CambridgeGoogle Scholar
- Wiebenga JH, Van den Boogaard AH (2014) On the effect of numerical noise in approximate optimization of forming processes using numerical simulations. Int J Mater Form 7(3):317–335Google Scholar