Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling

Han, Zhonghua; Görtz, Stefan

doi:10.2514/1.j051354

Cited by 338 publications

(113 citation statements)

References 32 publications

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“…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: 93%

“…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%

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

et al. 2017

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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.

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mentioning

confidence: 93%

Section: A Integration Into a Surrogate-based Optimization Codementioning

confidence: 99%

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

et al. 2017

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“…The literature contains a number of examples of the effectiveness of this technique on problems including airfoil design [23][24][25], the creation of aerodynamic models [25][26][27][28][29], compressor blade design [3] and even whole engine optimization [10].…”

Section: Krigingmentioning

confidence: 99%

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

Zhang

Toal

Keane

et al. 2015

Journal of Engineering for Gas Turbines and Power

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The prometheus combustor design system aims to reduce the complexity of evaluating combustor designs by automatically defining preprocessing, simulation, and postprocessing tasks based on the automatic identification of combustor features within the computer-aided design (CAD) environment. This system enables best practice to be codified and topological changes to a combustor's design to be more easily considered within an automated design process. The following paper presents the prometheus combustor design system and its application to the multiobjective isothermal optimization of a combustor prediffuser and the multifidelity isothermal optimization of a fuel injector feed arm in combination with a surrogate modeling strategy accelerated via a high-performance graphical processing unit (GPU).

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“…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

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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.

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Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling

Cited by 338 publications

References 32 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

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

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

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