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
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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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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. 21, 670–680 (2020). https://doi.org/10.1007/s42405-020-00250-1
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DOI: https://doi.org/10.1007/s42405-020-00250-1