A Nonstationary Covariance Based Kriging Method for Metamodeling in Engineering Design

Xiong, Ying; Chen, Wei; Apley, Daniel W.; Ding, Xuru

doi:10.2514/6.2006-7050

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…The Treed Gaussian process approach of Gramacy and Lee (2008) can also improve the coverage, because the space can be partitioned into different regions with the response in each region having different variance. Yet another approach to improve the coverage in kriging is to use a nonstationary covariance function (Xiong et al 2007). In a recent work, Gramacy and Lee (2011) showed that the coverage of kriging CIs can be significantly improved by adding a nugget term to the predictor.…”

Section: Confidence Interval For Idwmentioning

confidence: 99%

Regression-Based Inverse Distance Weighting With Applications to Computer Experiments

Joseph

Kang

2011

Technometrics

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Inverse distance weighting (IDW) is a simple method for multivariate interpolation but has poor prediction accuracy. In this article we show that the prediction accuracy of IDW can be substantially improved by integrating it with a linear regression model. This new predictor is quite flexible, computationally efficient, and works well in problems having high dimensions and/or large datasets. We also develop a heuristic method for constructing confidence intervals for prediction. This article has supplementary material online.

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Section: Confidence Interval For Idwmentioning

confidence: 99%

Regression-Based Inverse Distance Weighting With Applications to Computer Experiments

Joseph

Kang

2011

Technometrics

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“…Although a non-stationary correlation function is expected to be more effective for non-linear function approximation (e.g., Ref. 28), it is out of the scope in this study on dynamic adaptive sampling for UQ. Next, consider that the real value of f (ξ) is given at N sample points ξ (1) , ξ (2) , · · · , ξ (N ) .…”

Section: A Fundamentalsmentioning

confidence: 99%

Dynamic Adaptive Sampling Based on Kriging Surrogate Models for Efficient Uncertainty Quantification

Shimoyama

Kawai

Alonso

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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New Kriging-surrogate-model-based dynamic adaptive sampling methods are proposed for an accurate and efficient uncertainty quantification (UQ). The criteria for the proposed dynamic adaptive sampling are based on the combination of both the uncertainty and the gradient information of the Kriging predictors. The polynomial errors (related to Runge's phenomenon) appeared near the endpoints in the stochastic space are reduced by adding an extra error-estimate term (based on the difference of the Kriging predictors with different correlation functions) in the adaptive sampling criteria. The proposed Kriging-based dynamic adaptive sampling methods are tested on one-dimensional and two-dimensional analytic functions with smooth and non-smooth response surfaces. The method shows a superior performance to estimate the statistics of output solution in terms of efficiency, accuracy, and robustness regardless of the choice of initial samples and the smoothness and dimensionality of stochastic space compared to the existing criterion based on only the Kriging predictor uncertainty.

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“…Although a non-stationary correlation function is expected to be more effective for non-linear function approximation (e.g., Ref. 11 ), here we focus on the stationary correlation function. Next, consider that the real value of f (ξ) is given at N sample points ξ (1) , ξ (2) , • • • , ξ (N ) .…”

Section: Iia Fundamentalsmentioning

confidence: 99%

Kriging-model-based uncertainty quantification in computational fluid dynamics

Kawai

Shimoyama

2014

32nd AIAA Applied Aerodynamics Conference

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This paper proposes an efficient and accurate non-intrusive uncertainty quantification (UQ) method in computational fluid dynamics (CFD). Emphasis is placed on developing an UQ method that can accurately predict stochastic behaviors of output solution with small number of sampling simulations, and is also accurate for non-smooth output uncertainty responses. The proposed method is based on Kriging surrogate model, and the Kriging function values are used to evaluate output uncertainties robustly even with non-smooth responses, while using both the fit uncertainty and the gradient information of the Kriging predictors for dynamic adaptive sampling. The proposed Kriging-model-based UQ method shows a superior performance in estimating the non-smooth responses of output solution in terms of accuracy and robustness compared to the existing polynomial chaos expansion and the adaptive sampling method based on only the Kriging predictor fit uncertainty. The proposed method is first tested on analytical non-smooth functions under uniform uncertainties, and then applied to the transonic RAE 2822 airfoil flow under normal uncertainties in freestream Mach number by coupling the proposed UQ method with CFD.

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A Nonstationary Covariance Based Kriging Method for Metamodeling in Engineering Design

Cited by 3 publications

References 24 publications

Regression-Based Inverse Distance Weighting With Applications to Computer Experiments

Regression-Based Inverse Distance Weighting With Applications to Computer Experiments

Dynamic Adaptive Sampling Based on Kriging Surrogate Models for Efficient Uncertainty Quantification

Kriging-model-based uncertainty quantification in computational fluid dynamics

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