Recursive Co-Kriging Model for Design of Computer Experiments With Multiple Levels of Fidelity

Gratiet, Loïc Le; Garnier, Josselin

doi:10.1615/int.j.uncertaintyquantification.2014006914

Cited by 260 publications

(218 citation statements)

References 26 publications

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“…The surrogate model part contains models such as Kriging [12] and its variant Co-Kriging [13] and Support Vector Regression [14]. The implementation of the Co-Kriging model was based on the work of Le Gratiet et al [15] as it was implemented originally at the Open Multidisciplinary Design Analysis and Optimization (OpenMDAO) [16] framework in Python. The use of Co-Kriging requires the definition of variable levels of fidelity.…”

Section: Modulesmentioning

confidence: 99%

Heat Transfer Optimization of a Ribbed Surface Using Surrogate-Assisted Genetic Algorithms

Tsirikoglou

Ghorbaniasl

Abraham³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Over the last years, complex design and optimization engineering problems became more and more demanding in computational time. Despite the advances made in computer science, these demands are prohibitive in some cases, in many engineering fields such as fluid mechanics and heat transfer. Aiming to alleviate this, surrogate response models are introduced and coupled with optimization drivers to deliver cheaper and accurate optimization results. The present paper investigates the performance of various surrogate-assisted optimization schemes applied to a heat transfer modeling problem of a ribbed surface. In this study, performance of different surrogate models such as Kriging, Co-Kriging and Support Vector Regression in different evolutionary optimization schemes are assessed. These schemes employ the aforementioned surrogate models coupled with different infill strategies depending on the availability of an uncertainty measure for the prediction. The results show that Co-Kriging model provides accurate results in comparison with the other metamodels while the computational time is reduced by more than 50%. It is illustrated that the combination of multi-fidelity approaches and sophisticated infill strategies can provide accurate predictions at a reduced computational cost.

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Section: Modulesmentioning

confidence: 99%

Heat Transfer Optimization of a Ribbed Surface Using Surrogate-Assisted Genetic Algorithms

Tsirikoglou

Ghorbaniasl

Abraham³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…GECoK exploits the relationship between low-fidelity and high-fidelity sample data to enhance the prediction accuracy. It is based on the recursive CoKriging model of Le Gratiet (2012). Additionally, it incorporates multi-fidelity gradient data along with multi-fidelity function data to enhance surrogate model accuracy.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…It is also possible to calculate ρ using a least squares formulation as shown by Le Gratiet (2012). The advantage of using this formulation is that ρ can be expressed as a function of X which may provide more accurate estimation for ρ as shown in Le Gratiet (2012).…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The advantage of using this formulation is that ρ can be expressed as a function of X which may provide more accurate estimation for ρ as shown in Le Gratiet (2012). This leads to an alternative formulation where the second GEK model is directly built with high-fidelity data (X e ,ẏ e ) and ρ is estimated from a least squares formulation as,…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The authors further stated that the advantage of finding global optima with gradient incorporated multifidelity Kriging model over the standard multi-fidelity Kriging model without gradients is still ambiguous and unclear. Recently, Le Gratiet (2012) proposed a recursive formulation based multi-fidelity Kriging modelling. This approach significantly reduces the modelling complexity associated with multi-fidelity Kriging models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Performance study of multi-fidelity gradient enhanced kriging

Ulaganathan

Couckuyt

Ferranti

et al. 2014

Struct Multidisc Optim

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Multi-fidelity surrogate modelling offers an efficient way to approximate computationally expensive simulations. In particular, Kriging-based surrogate models are popular for approximating deterministic data. In this work, the performance of Kriging is investigated when multi-fidelity gradient data is introduced along with multi-fidelity function data to approximate computationally expensive black-box simulations. To achieve this, the recursive CoKriging formulation is extended by incorporating multi-fidelity gradient information. This approach, denoted by Gradient-Enhanced recursive CoKriging (GECoK), is initially applied to two analytical problems. As expected, results from the analytical benchmark problems show that additional gradient information of different fidelities can significantly improve the accuracy of the Kriging model. Moreover, GECoK provides a better approximation even when the gradient information is only partially available. Further comparison between CoKriging, Gradient Enhanced

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Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

Gao,

Iyama,

Itoi

2024

Japan Architectural Review

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This study introduces an approach for probabilistic seismic performance estimation, which focuses on the probability of intensity measures exceeding a specified value based on engineering demand parameters. Conventional methods face challenges owing to the increase in computational costs associated with the uncertainties in earthquake scenarios. To address this, we use high‐fidelity (HF) and low‐fidelity (LF) model data to develop a multilevel hierarchy of surrogate models, which improves the simulation‐based probabilistic estimation. However, designing a reliable LF model and ensuring the accuracy of the surrogate model hierarchy remains challenging. Herein, we present a multi‐fidelity Monte Carlo (MFMC) predictor combined with a conventional surrogate model to improve probabilistic seismic performance estimation, thereby leveraging LF model efficiency and HF data accuracy for unbiased results. We addressed the challenge of constructing a suitable LF model by using a surrogate model trained from limited HF data. The MFMC predictor improves the accuracy of probabilistic analysis than the surrogate models trained from limited HF data. Further, the automatic relevance determination method is introduced to select the most appropriate inputs for the surrogate model. A case study featuring a special moment‐resistant frame, subject to uncertainties from both ground motion and structural properties, illustrates the efficiency of the method. A LF model is developed using the Kriging method, followed by the construction of the MFMC predictor for probabilistic analysis, thereby leveraging both limited HF and numerous LF data. Comparing the exceedance probability curves obtained from the MFMC predictor with those from direct Monte Carlo simulations and conventional Kriging showed that our proposed method offers a promising tool for probabilistic seismic performance estimation under uncertainty.

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Recursive Co-Kriging Model for Design of Computer Experiments With Multiple Levels of Fidelity

Cited by 260 publications

References 26 publications

Heat Transfer Optimization of a Ribbed Surface Using Surrogate-Assisted Genetic Algorithms

Heat Transfer Optimization of a Ribbed Surface Using Surrogate-Assisted Genetic Algorithms

Performance study of multi-fidelity gradient enhanced kriging

Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

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