Structural and Multidisciplinary Optimization

, Volume 50, Issue 3, pp 383–394 | Cite as

Pointwise ensemble of meta-models using v nearest points cross-validation



As the use of meta-models to replace computationally-intensive simulations for estimating real system behaviors increases, there is an increasing need to select appropriate meta-models that well represent real system behaviors. Since in most cases designers do not know the behavior of the real system a priori, however, they often have trouble selecting a suitable meta-model. In order to provide robust prediction performance, ensembles of meta-models have been developed which linearly combines stand-alone meta-models. In this study, we propose a new pointwise ensemble of meta-models whose weights vary according to the prediction point of interest. The suggested method can include all kinds of stand-alone meta-models for ensemble construction, and can interpolate real system response values at training points, even if regression models are included as stand-alone meta-models. To evaluate the effectiveness of the proposed method, its prediction performance is compared with those of existing ensembles of meta-models using well-known mathematical functions. The results show that our pointwise ensemble of meta-models provides more robust and accurate predictions than existing models for a majority of test problems.


Pointwise ensemble of meta-models v nearest points cross validation Meta-model 


  1. Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidiscip O 37:279–294CrossRefGoogle Scholar
  2. Balabanov V, Haftka RT, Grossman B, Mason WH, Watson LT (1998) Multifidelity response model for HSCT wing bending material weight. In: Proceedings of 7th AIAA/USAF/ NASA/ISSMO symposium on multidisciplinary analysis and optimization. St Louis, pp AIAA Paper 98–4804Google Scholar
  3. Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, OxfordGoogle Scholar
  4. Clarke SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. J Mech Design 127:1077–1087CrossRefGoogle Scholar
  5. Craig KJ, Stander N, Dooge DA, Varadappa S (2002) MDO of automotive vehicles for crashworthiness and NVH using response surface methods. In: Proceedings of 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization. Atlanta, pp AIAA Paper 2002–5607Google Scholar
  6. Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF (2005) A comparative study of metamodeling methods for multiobjective crashworthiness optimization. Comput Struct 83:2121–2136CrossRefGoogle Scholar
  7. Giunta AA, Balabanov V, Haim D, Grossman B, Mason WH, Watson LT, Haftka RT (1997) Multidisciplinary optimisation of a supersonic transport using design of experiments theory and response surface modeling. Aeronaut J 101:347–356Google Scholar
  8. Giunta AA, Watson LT (1998) A comparison of approximation modeling techniques: polynomial versus interpolating models. In: Proceedings of 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization. St. Louis, pp AIAA Paper 98-4758Google Scholar
  9. Goel T, Haftka RT, Shyy W, Queipo NV (2007) Ensemble of surrogates. Struct Multidiscip O 33:199–216CrossRefGoogle Scholar
  10. Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip O 23:1–13CrossRefGoogle Scholar
  11. Kurtaran H, Eskandarian A, Marzougui D, Bedewi NE (2002) Crashworthiness design optimization using successive response surface approximations. Comput Mech 29:409–421CrossRefMATHGoogle Scholar
  12. Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley, New YorkMATHGoogle Scholar
  13. Orr MJL (1996) Introduction to radial basis neural networks. Techncal report-Center for Cognitive Science, Edinburgh University, ScotlandGoogle Scholar
  14. Park JS (1994) Optimal latin-hypercube designs for computer experiments. J Stat Plan Infer 39:95–111CrossRefMATHGoogle Scholar
  15. Queipo NV, Goicochea JV, Pintos S (2002a) Surrogate modeling-based optimization of SAGD processes. J Petrol Sci Eng 35:83–93CrossRefGoogle Scholar
  16. Queipo NV, Verde AJ, Canelon J, Pintos S (2002b) Efficient global optimization for hydraulic fracturing treatment design. J Petrol Sci Eng 35:151–166CrossRefGoogle Scholar
  17. Sacks J, Welch W, Mitchell T, Wynn H (1989) Design and analysis of computer experiments. Stat Sci 4:409–435CrossRefMATHMathSciNetGoogle Scholar
  18. Sanchez E, Pintos S, Queipo NV (2008) Toward an optimal ensemble of kernel-based approximations with engineering applications. Struct Multidiscip O 36:247–261CrossRefGoogle Scholar
  19. Smola AJ, Scholkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222CrossRefMathSciNetGoogle Scholar
  20. Stander N, Roux W, Giger M, Redhe M, Fedorova N, Haarhoff J (2004) A comparison of meta-modeling techniques for crashworthiness optimization. In: Proceedings of the 10th AIAA/ISSMO multidisciplinary analysis and optimization conference. Albany, pp AIAA-2004-4489Google Scholar
  21. Vaidyanathan R, Tucker PK, Papila N, Shyy W (2004) Computational-fluid-dynamics-based design optimization for single-element rocket injector. J Propul Power 20:705–717CrossRefGoogle Scholar
  22. Wang L, Beeson D, Wiggs G, Rayasam M (2006) A comparison of metamodeling methods using practical industry requirements. In: Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Newport, pp AIAA Paper 06-1811Google Scholar
  23. Zerpa LE, Queipo NV, Pintos S, Salager J-L (2005) An optimization methodology of alkaline-surfactant-polymer flooding processes using field scale numerical simulation and multiple surrogates. J Petrol Sci Eng 47:197–208CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.PIDOTECHSeoulKorea
  2. 2.The Center of Innovative Design Optimization TechnologyHanyang UniversitySeoulKorea

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