Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling

Han, Zhonghua; Zimmermann, Ralf; Görtz, Stefan

doi:10.2514/1.j051243

Cited by 164 publications

(44 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has built-in modern DOE methods suited for deterministic computer experiments, such as LHS, UD, and Monte Carlo design. A variety of surrogate models, such as PRSM, kriging and its variants (GEK [47], cokriging [33], HK [34]), RBFs, ANN, SVR [22], etc., were implemented. A couple of infill-sampling criteria and dedicated constraint handling methods were implemented, such as minimizing surrogate predictor (MSP) [76], expected improvement [77,78], probability of improvement [5], mean-squared error (MSE) [79,80], lower-confidence bounding [51,81], target searching [74], and parallel infilling [30].…”

Section: A Integration Into a Surrogate-based Optimization Codementioning

confidence: 99%

“…One is the variable-fidelity model or multifidelity model. With assistance of the data obtained by simplified, lower-fidelity physical model or the same physical model on coarser computational grid, the accuracy of a surrogate model for high-fidelity and expensive function can be significantly enhanced [33,34]. In turn, the efficiency for solving an optimization problem can be remarkably improved [35][36][37][38][39].…”

mentioning

confidence: 99%

“…Gradient-enhanced kriging (GEK) denotes the extension of kriging to models in which inexpensive gradient information is incorporated [47]. Note that GEK was also viewed as one kind of cokriging (e.g., [44,45]), although the terminology "cokriging" generally means the kriging incorporating lower-fidelity auxiliary data (see [5] or [33]). There are two ways of incorporating gradients into the construction of a kriging, which leads to indirect GEK and direct GEK [47].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

Self Cite

View full text Add to dashboard Cite

A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.

show abstract

Section: A Integration Into a Surrogate-based Optimization Codementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…As the performance of any surrogate based optimization is determined by the accuracy of the model a more accurate model can significantly reduce the total number of simulations required for an optimization. Such multi-fidelity approaches have been successfully employed throughout the literature in the design optimization of airfoils [17,24,26], wings [3], compressor rotors [2], combustors [25] and the creation of aerodynamic models [7,[9][10][11]26]. 1 An example of single and multi-fidelity Kriging [5] Figure 1 is a simple example, recreated from Forrester et al [5], of the advantages that multi-fidelity Kriging can offer if used to create a surrogate model.…”

Section: Introductionmentioning

confidence: 99%

Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

Toal

2014

Struct Multidisc Optim

112

View full text Add to dashboard Cite

Surrogate models or metamodels are commonly used to exploit expensive computational simulations within a design optimization framework. The application of multi-fidelity surrogate modeling approaches has recently been gaining ground due to the potential for further reductions in simulation effort over single fidelity approaches. However, given a black box problem when exactly should a designer select a multi-fidelity approach over a single fidelity approach and vice versa? Using a series of analytical test functions and engineering design examples from the literature, the following paper illustrates the potential pitfalls of choosing one technique over the other without a careful consideration of the optimization problem at hand. These examples are then used to define and validate a set of guidelines for the creation of a multi-fidelity Kriging model. The resulting guidelines state that the different fidelity functions should be well correlated, that the amount of low fidelity data in the model should be greater than the amount of high fidelity data and that more than 10% and less than 80% of the total simulation budget should be spent on low fidelity simulations in order for the resulting multi-fidelity model to perform better than the equivalent costing high fidelity model.

show abstract

“…Its capability to predict multidimensional and non−linear responses from scattered data gives it growing popularity. For example, in [16,17], efficient and robust Kr schemes suitable to various realistic engineering problems have been presented.…”

Section: Introductionmentioning

confidence: 99%

A Kriging and Stochastic Collocation ensemble for uncertainty quantification in engineering applications

Kaintura

Spina

Couckuyt

et al. 2017

Engineering with Computers

View full text Add to dashboard Cite

We propose a new surrogate modeling approach by combining two non-intrusive techniques: Kriging and Stochastic Collocation. The proposed method relies on building a sufficiently accurate Stochastic Collocation model which acts as a basis to construct a Kriging model on the residuals, in order to combine the accuracy and efficiency of Stochastic Collocation methods in describing stochastic quantities with the flexibility and modeling power of Kriging-based approaches. We investigate and compare performance of the proposed approach with state-of-art techniques over benchmark problems and practical engineering examples on various experimental designs.

show abstract

Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling

Cited by 164 publications

References 16 publications

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

A Kriging and Stochastic Collocation ensemble for uncertainty quantification in engineering applications

Contact Info

Product

Resources

About