Designs for Computer Experiments

Sacks, Jerome; Schiller, Susannah B.; Welch, William J.

doi:10.2307/1270363

Cited by 241 publications

(213 citation statements)

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“…A surrogate model can be formulated in a number of different ways, though the most common methods are by a polynomial [43], radial basis functions (RBFs) [44,45] or Kriging [46][47][48]. Reviews of surrogate modelling and surrogate-based optimization have been presented [26][27][28], which the reader is guided to for more in-depth discussions on the formulations and common uses for each method.…”

Section: Surrogate Modellingmentioning

confidence: 99%

Adaptive Surrogate-Based Optimization of Vortex Generators for Tiltrotor Geometry

Bevan

Poole

Allen

et al. 2017

Journal of Aircraft

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Design of vortex generators (VGs) on a tiltrotor aircraft infinite wing is presented using an adaptive surrogate modelling approach. Particular design issues in tiltrotors produce wings that are thick and highly loaded, so separation and early onset buffet can be problematic and VGs are commonly used to alleviate these issues. In this work, the design of VGs for elimination of separation is considered using a viscous flowfield simulations. A large design space of rectangular vane-type vortex generators is sampled and simulated, and a radial basis function surrogate model is implemented to model the full design space. An efficient adaptive sampling approach for improved design space sampling has also been developed that balances the properties of space-filling, curvature capture and optimum locating. This approach has been tested on the design of a VG on a highly loaded infinite wing, with a representative tiltrotor airfoil section, using a five-dimensional design space. Design of the VGs using this approach shows that elimination of the separation is possible whilst simultaneously reducing the drag of the wing with optimized the VGs, compared to the clean wing.

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Section: Surrogate Modellingmentioning

confidence: 99%

Adaptive Surrogate-Based Optimization of Vortex Generators for Tiltrotor Geometry

Bevan

Poole

Allen

et al. 2017

Journal of Aircraft

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“…There are many kinds of uniformity metrics, such as discrepancy (Weyl, 1916;Hickernell, 1998), integrated mean squared error (IMSE) (Sacks et al, 1989), entropy (Shewry et al, 1987) and maxmin or minimax distance (Johnson et al, 1990). These metrics describe different aspects of the representation ability of a sample set.…”

Section: Uniformity Metricsmentioning

confidence: 99%

An Intercomparison of Sampling Methods for Uncertainty Quantification of Environmental Dynamic Models

Gong

Duan²,

Li³

et al. 2015

J ENV INFORM

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ABSTRACT. Uncertainty quantification (UQ) of environmental dynamic models requires an efficient way to extract the information about the relationship between input parameter and model output. A uniformly scattered sample set is generally preferred over crude Monte Carlo sampling for its ability to explore the parameter space more effectively and efficiently. This paper compares eight commonly used uniform sampling methods along with the crude Monte Carlo sampling. The efficiency is measured by six uniformity metrics, while the effectiveness is measured by the goodness-of-fit of the surrogate models, and the sensitivity analysis and optimization results. We used two test problems: the Sobol' g-function and the SAC-SMA hydrological model. The results show that among the sampling methods evaluated, the Good Lattice Points (GLP) and Symmetric Latin hypercube (SLH) have the highest uniformity scores, and the Ranked Gram-Schmidt (RGS) de-correlation algorithm can further improve the uniformity of the lattice sample sets. On the other hand, the Quasi-Monte-Carlo (QMC) methods, such as Halton and Sobol' sequences, are not as uniform as their theoretical potential suggests when the number of sample points is low. Further, we found no clear relationship between the sampling methods used and their effectiveness, as the latter is affected by many factors other than the sampling methods, such as the choice of the surrogate modeling methods, sensitivity analysis and optimization methods, and the intrinsic properties of the dynamic models.

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“…The trend function can usually be a simple low-order polynomial, and even a constant value over the entire input space may be sufficient [8]. The GP is typically assumed to be stationary with zero mean, which implies that the correlation between prediction point and training point is only a function of the distance between them.…”

Section: Appendix Gaussian Process (Gp) Modelingmentioning

confidence: 99%

“…Cheaper models (in terms of CPU time per evaluation) which may be in the form of mathematical surrogate models (also referred to as response surfaces or metamodels), reduced order models, or reduced physics models have been pursued in this regard. Common surrogate models include simple regression models, Gaussian process (GP) or Kriging models [7,8], polynomial chaos expansion models [9], support vector machines [10], and neural networks [11]. However, additional error is introduced to the system prediction by these surrogates, so it is preferable to make selective use of the high-fidelity model at some sample points as allowed by the computational budget.…”

Section: Introductionmentioning

confidence: 99%