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Cost-Aware Adaptive Design of Experiment with Nonstationary Surrogate Model for Wind Tunnel Testing

Abstract

This paper proposes a novel adaptive design of experiment (ADoE) framework with cost-aware sampling strategy and nonstationary surrogate model for efficient wind tunnel testing. The ADoE framework, which is based on the Gaussian process, can effectively reduce the required number of an experiment while maintaining its accuracy. The proposed cost-aware sampling strategy augments the framework by selecting cost-efficient experiment points and the nonstationary surrogate model effectively reflects the nonlinearity of the system on the response surface model. The efficacy of the proposed framework has been validated through a virtual experiment using an actual high angle-of-attack wind tunnel test dataset, which is highly nonlinear.

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Abbreviations

\( \chi \) :

Training input

\( {\mathbf{y}} \) :

Training output

\( {\mathbf{x}}_{\text{T}} \) :

Test input

\( \chi_{\text{T}} \) :

Set of test points

N :

Number of training data

d :

Dimension of input

D :

Training dataset

\( f_{*} \) :

Posterior output with zero mean function

\( \bar{f}_{*} \) :

Posterior output mean \( {\mathbb{E}}\left[ {f_{*} } \right] \)

\( \sigma_{*} \) :

Posterior output standard deviation

\( \theta ,\hat{\theta } \) :

Gaussian process hyperparameters and their estimation

\( L \) :

Number of clusters

\( l \) :

Cluster index

\(\chi^{(l)} \) :

Cluster l

\( \varepsilon_{l} \) :

Index set of given training data partitioned to cluster l

\( P(l|{\mathbf{x}}) \) :

Posterior probability that the input x belongs to the cluster l

\( \tilde{\chi}^{(l)} \) :

Overlapped cluster l

\( \tilde{\varepsilon }_{l} \) :

Index set of overlapped cluster l

References

  1. 1.

    Yondo R, Andrés E, Valero E (2018) A review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses. Prog Aerosp Sci 96:23–61

  2. 2.

    DeLoach R (2000) The modern design of experiments—a technical and marketing framework. In: 21st aerodynamic measurement technology and ground testing conference, Denver, CO, USA

  3. 3.

    Lee D, Jin H, Shim H, Ahn J, Choi HL (2016) Two-phase experimental design with adaptive subspacing for wind tunnel testing based aerodynamic modeling. J Mech Sci Technol 30(11):5041–5050

  4. 4.

    Choi H-L, Ahn J, Cho D-H (2014) Information-maximizing adaptive design of experiments for wind tunnel testing. In: 4th international conference on engineering optimization (EngOpt 2014), Lisbon, Portugal

  5. 5.

    Kaminsky AL, Wang Y, Pant K, Hashii WN, Atachbarian A (2018) Adaptive sampling techniques for surrogate modeling to create high-dimension aerodynamic loading response surfaces. In: 2018 applied aerodynamics conference, Atlanta, Georgia, USA

  6. 6.

    Shimoyama K, Kawai S, Alonso JJ (2013) 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, Boston, Massachusetts, USA

  7. 7.

    Crombecq K, Gorissen D, Deschrijver D, Dhaene T (2011) A novel hybrid sequential design strategy for global surrogate modeling of computer experiments. SIAM J Sci Comput 33(4):1948–1974

  8. 8.

    Liu H, Cai J, Ong Y-S (2017) An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error. Comput Chem Eng 106(2):171–182

  9. 9.

    Mackman TJ, Allen CB (2010) Multidimensional adaptive sampling for global metamodelling. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, USA

  10. 10.

    Jiang P, Zhang Y, Zhou Q, Shao X, Hu J, Shu L (2018) An adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS. Appl Intell 48(6):1644–1656

  11. 11.

    Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT Press, Cambridge

  12. 12.

    Tresp V (2001) Mixtures of Gaussian processes. Proc Adv Neural Inf Process Syst 13:654–660

  13. 13.

    Jin H, Lee D, Lee J, Ahn J (2016) Hyperparameters optimization for adaptive design of experiment applied to wind tunnel testing. In: 30th congress of the international council of the aeronautical sciences, Daejeon, Republic of Korea

  14. 14.

    Clark DL, Bae H-R, Gobal K, Penmetsa R (2016) Engineering design exploration using locally optimized covariance kriging. AIAA J 54(10):3160–3175

  15. 15.

    Liem RP, Mader CA, Martins JRRA (2015) Surrogate models and mixtures of experts in aerodynamic performance prediction for aircraft mission analysis. Aerosp Sci Technol 43:126–151

  16. 16.

    Kaufman L, Rousseeuw PJ (2009) Finding groups in data: an introduction to cluster analysis, vol 344. Wiley, Hoboken

  17. 17.

    Jeong B et al (2015) Yaw-control spoiler design using design of experiments based wind tunnel testing. J Aircr 52(2):713–718

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Acknowledgements

This work was conducted at High-Speed Vehicle Research Center of KAIST with the support of the Defense Acquisition Program Administration and the Agency for Defense Development under Contract UD170018CD.

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Correspondence to Jaemyung Ahn.

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Choi, U., Kim, J. & Ahn, J. Cost-Aware Adaptive Design of Experiment with Nonstationary Surrogate Model for Wind Tunnel Testing. Int. J. Aeronaut. Space Sci. (2020). https://doi.org/10.1007/s42405-020-00250-1

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Keywords

  • Adaptive design of experiment
  • Gaussian process
  • Mixture of expert
  • Cost-aware sampling