TY - JOUR
T1 - A kriging-based dynamic adaptive sampling method for uncertainty quantification
AU - Shimoyama, Koji
AU - Kawai, Soshi
N1 - Funding Information:
The authors would like to thank Juan J. Alonso of Stanford University for his valuable comments, which helped to improve the dynamic adaptive sampling method, and the Sandia National Laboratories for Dakota. In addition, the authors were supported in part by the Grant-in-Aid for Scientific Research (B) No. H1503600 and the Grant-in-Aid for Scientific Research (B) No. 18H01620 administered by the Japan Society for the Promotion of Science (JSPS).
Publisher Copyright:
© 2019 The Japan Society for Aeronautical and Space Sciences.
PY - 2019
Y1 - 2019
N2 - A new method for dynamic sampling of Kriging surrogate models for uncertainty quantification is developed and presented. The criterion for the dynamic adaptive sampling proposed is based on combining the expected uncertainty of the fit and the gradient information resulting from the Kriging predictors, and an error-estimate term (based on the difference in the Kriging predictors with different correlation length scales). The Kriging-based dynamic adaptive sampling method proposed is tested on two-dimensional analytic functions with smoothly and steeply varied responses in the quantities of interest under normal uncertainty distributions. Compared with a classical polynomial chaos expansion method based on the Gauss quadrature rule and a dynamic adaptive sampling method based only on the uncertainty of the Kriging predictor fit, this new method shows superior performance for estimating the statistics of the quantity of interest in terms of both accuracy and robustness, and regardless of either the choice of the initial set of samples or the smoothness of the stochastic space.
AB - A new method for dynamic sampling of Kriging surrogate models for uncertainty quantification is developed and presented. The criterion for the dynamic adaptive sampling proposed is based on combining the expected uncertainty of the fit and the gradient information resulting from the Kriging predictors, and an error-estimate term (based on the difference in the Kriging predictors with different correlation length scales). The Kriging-based dynamic adaptive sampling method proposed is tested on two-dimensional analytic functions with smoothly and steeply varied responses in the quantities of interest under normal uncertainty distributions. Compared with a classical polynomial chaos expansion method based on the Gauss quadrature rule and a dynamic adaptive sampling method based only on the uncertainty of the Kriging predictor fit, this new method shows superior performance for estimating the statistics of the quantity of interest in terms of both accuracy and robustness, and regardless of either the choice of the initial set of samples or the smoothness of the stochastic space.
KW - Adaptive sampling
KW - Kriging surrogate model
KW - Uncertainty quantification
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U2 - 10.2322/tjsass.62.137
DO - 10.2322/tjsass.62.137
M3 - Article
AN - SCOPUS:85069042296
VL - 62
SP - 137
EP - 150
JO - Transactions of the Japan Society for Aeronautical and Space Sciences
JF - Transactions of the Japan Society for Aeronautical and Space Sciences
SN - 0549-3811
IS - 3
ER -