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Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling

Han, Zhong-Hua und Zimmermann, Ralf und Görtz, Stefan (2012) Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling. AIAA Journal, 50 (5), Seiten 1205-1210. DOI: 10.2514/1.58361.

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Kurzfassung

Surrogate modeling plays an increasingly important role in different areas of aerospace engineering, such as erodynamic shape optimization, aerodynamic data production, structural design, and multidisciplinary design optimization of aircraft or spacecraft. Cokriging provides an attractive alternative approach to conventional kriging to improve the efficiency of building a surrogate model. It was initially proposed and applied in the geostatistics community for the enhanced prediction of less intensively sampled primary variables of interest with the assistance of intensively sampled auxiliary variables. As the underlying theory of cokriging is that of two-variable or multivariable kriging, it can be regarded as a general extension of (one-variable) kriging to a model that is assisted by auxiliary variables or secondary information. In an attempt to apply cokriging to the surrogate modeling problems associated with deterministic computer experiments, this article is motivated by the development of an alternative cokriging method to address the challenge related to the construction of the covariance matrix of cokriging [7]. Earlier work done by other authors related to this study can be found in the statistical community. For example, Kennedy and O’Hagan (KOH) proposed an autoregressive model to calculate the covariances and crosscovariances in the covariance matrix and developed a Bayesian approach to predict the output from an expensive high-fidelity simulation code with the assistance of lower-fidelity simulation codes. This Bayesian approach is identical to a form of cokriging suitable for computer experiments. Later, Qian andWu proposed a similar method, in which a random function (Gaussian process model) was used to replace the constant multiplicative factor of KOH’s method to account for the nonlinear scale change. KOH’s method was applied to multifidelity analysis and design optimization in the context of aerospace engineering by Forrester et al. and Kuya et al. More recently, Zimmerman and Han proposed a cokriging method with simplified cross-correlation estimation. In this article, we propose an alternative approach for the construction of the cokriging covariance matrix and develop a more practical cokriging method in the context of surrogate-based analysis and optimization. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil.

Dokumentart:Zeitschriftenbeitrag
Titel:Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling
Autoren:
AutorenInstitution oder E-Mail-Adresse der Autoren
Han, Zhong-HuaNICHT SPEZIFIZIERT
Zimmermann, RalfNICHT SPEZIFIZIERT
Görtz, StefanNICHT SPEZIFIZIERT
Datum:Mai 2012
Erschienen in:AIAA Journal
Referierte Publikation:Ja
In Open Access:Nein
In SCOPUS:Ja
In ISI Web of Science:Ja
Band:50
DOI :10.2514/1.58361
Seitenbereich:Seiten 1205-1210
Status:veröffentlicht
Stichwörter:surrogate modeling, Kriging, Cokriging, CFD, aerodynamics, variable fidelity modeling
HGF - Forschungsbereich:Luftfahrt, Raumfahrt und Verkehr
HGF - Programm:Luftfahrt
HGF - Programmthema:Starrflügler
DLR - Schwerpunkt:Luftfahrt
DLR - Forschungsgebiet:L AR - Starrflüglerforschung
DLR - Teilgebiet (Projekt, Vorhaben):L - Simulation & Validierung
Standort: Braunschweig
Institute & Einrichtungen:Institut für Aerodynamik und Strömungstechnik > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Hinterlegt von: Stefan Görtz
Hinterlegt am:30 Aug 2012 14:26
Letzte Änderung:26 Mär 2013 13:41

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