Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Vision, Objectives and Research Activities Read chapter Read first chapter

2019 | OriginalPaper | Chapter

General Introduction to Surrogate Model-Based Approaches to UQ

Authors : Daigo Maruyama, Stefan Görtz, Dishi Liu

Published in: Uncertainty Management for Robust Industrial Design in Aeronautics

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter introduces two popular surrogate modeling methods which can be used to quantify uncertainties such as statistics of the aerodynamic coefficients from scattered data obtained by computational fluid dynamics (CFD) simulations. One is Kriging, which is able not only to interpolate predicted data but also to provide statistical information at unsampled locations in the parameter space based on Bayesian statistics. The other one is the radial basis function (RBF) method. The RBF method is also a powerful nonlinear interpolation method which exactly interpolates the samples, and its various radial basis function types support the interpolated values locally or globally when appropriately selected. Both methods can make use of gradient information, if available, to improve the model accuracy.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Screening Analysis and Adaptive Sparse Collocation Method
next chapter Comparing Surrogates for Estimating Aerodynamic Uncertainties of Airfoils
Literature
1.
Krige, D.G.: A statistical approach to some basic mine valuations problems on the Witwatersrand. J. Chem. Metall. Min. Eng. Soc. S. Afr. 52(6), 119–139 (1951)
2.
Hengl, T.: A practical guide to geostatistical mapping of environmental variables. European Comission, JRC Scientific and Technical Reports. EUR 22904 EN (2007)
3.
Chung, H.S., Alonso, J.J.: Using gradients to construct cokriging approximation models for high-dimensional design optimization problems. AIAA Paper 2002-0317 (2002)
4.
Han, Z.H., Görtz, S., Zimmermann, R.: Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function. J. Aerosp. Sci. Technol. 25(1) (2013)
5.
Dwight, R., Han, Z.H.: Efficient uncertainty quantification using gradient-enhanced Kriging. AIAA Paper 2009–2276 (2009)
6.
Lockwood, B.A., Anitescu, M.: Gradient-enhanced universal kriging for uncertainty propagation. Preprint ANL/MCS-P1808-1110 (2010)
7.
Yamazaki, W., Rumpfkeil, M.P., Mavriplis, D.J.: Design optimization utilizing Gradient/Hessian enhanced surrogate model. In: 28th AIAA Applied Aerodynamics Conference. AIAA paper 2010-4363 (2010)
8.
Rumpfkeil, M.P., Mavriplis, D.J.: Efficient Hessian calculations using automatic differentiation and the adjoint method. AIAA-2010-1268 (2010)
9.
Shimoyama, K., Kawai, S., Alonso, J.J.: Dynamic adaptive sampling based on kriging surrogate models for efficient uncertainty quantification. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA paper 2013-1470 (2013)
10.
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)MathSciNetCrossRef
11.
Emmerich, M.: Single- and multi-objective evolutionary design optimization using gaussian random field metamodels. Ph.D. Dissertation, TU Dortmund (2005)
12.
Shimoyama, K., Sato, K., Jeong, S., Obayashi, S.: Updating Kriging surrogate models based on the hyper volume indicator in multi-objective optimization. J. Mech. Des. 135(9). Article ID 094503 (2013)
13.
Łaniewski-Wołłk, L.: Relative expected improvement in kriging based optimization. In: EUROGEN 2009 Kwakow Conference (2009)
14.
de Boer, A., van der Schoot, M.S., Bijl, H.: Mesh deformation based on radial basis function interpolation. Comput. Struct. 85(11–14), 784–795 (2007)CrossRef
15.
Giannakoglou, K.C., Papadimitriou, D.I., Kampolis, I.C.: Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels. Comput. Methods Appl. Mech. Eng. 195(44–47), 6312–6329 (2006)CrossRef
16.
McDonald, D.B., Grantham, W.J., Tabor, W.L., Murphy, M.J.: Global and local optimization using radial basis function response surface models. Appl. Math. Model. 31(10) (2007)
17.
Liu, D.: A best practice guide: effcient quantification of aerodynamic uncertainties. Report of the Institute of Aerodynamics and Flow Technology, DLR, DLR-IB 124-2012/2. ISSN 1614-7790 (2012)
18.
Lazzaro, D., Montefusco, L.B.: Radial basis functions for the multivariate interpolation of large scattered data sets. J. Comput. Appl. Math. 140, 521–536 (2002)MathSciNetCrossRef
Metadata
Title
General Introduction to Surrogate Model-Based Approaches to UQ
Authors
Daigo Maruyama
Stefan Görtz
Dishi Liu
Copyright Year
2019
Book
Uncertainty Management for Robust Industrial Design in Aeronautics

Print ISBN: 978-3-319-77766-5

Electronic ISBN: 978-3-319-77767-2

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-77767-2_12

Premium Partners

    Image Credits