A generalized hierarchical co-Kriging model for multi-fidelity data fusion
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RESEARCH PAPER
A generalized hierarchical co-Kriging model for multi-fidelity data fusion Qi Zhou 1 & Yuda Wu 1 & Zhendong Guo 2 & Jiexiang Hu 1 & Peng Jin 1 Received: 20 October 2019 / Revised: 10 February 2020 / Accepted: 26 March 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Multi-fidelity (MF) surrogate models have shown great potential in simulation-based design since they can make a trade-off between high prediction accuracy and low computational cost by augmenting the small number of expensive high-fidelity (HF) samples with a large number of cheap low-fidelity (LF) data. In this work, a generalized hierarchical co-Kriging (GCK) surrogate model is proposed for MF data fusion with both nested and non-nested sampling data. Specifically, a comprehensive Gaussian process (GP) Bayesian framework is developed by aggregating calibrated LF Kriging model and discrepancy stochastic Kriging model. The stochastic Kriging model enables the GCK model to consider the predictive uncertainty from the LF Kriging model at HF sampling points, making it possible to estimate the model parameter separately under both nested and non-nested sampling data. The performance of the GCK model is compared with three well-known Kriging-based MF surrogates, i.e., hybrid Kriging– scaling (HKS) model, KOH autoregressive (KOH) model, and hierarchical Kriging (HK) model, by testing them on two numerical examples and two real-life cases. The influence of correlations between LF and HF samples and the cost ratio between them are also analyzed. Comparison results on the illustrated cases demonstrate that the proposed GCK model shows great potential in MF modeling under non-nested sampling data, especially when the correlations between LF and HF samples are weak. Keywords Multi-fidelity surrogate model . Non-nested sampling data . Co-Kriging model . Black-box function
1 Introduction Surrogate models have been widely used in simulation-based design and optimization (SBDO) to replace the computational expensive simulation models for relieving the computational burden (Dong et al. 2018; Hou et al. 2019; Jiang et al. 2019; Qian et al. 2019; Yu et al. 2019). In SBDO, the quantity of interest (QOI) at the sampling points can always be obtained by different fidelity computational simulation models. For example, in the aerodynamic shape design of the airfoil, the available simulation models for aerodynamic analysis can
Responsible Editor: Nestor V Queipo * Peng Jin [email protected] 1
School of Aerospace Engineering, Huazhong University of Science & Technology, Wuhan, Hubei 430074, People’s Republic of China
2
School of Computer Science and Engineering, Nanyang Technological University, Jurong West 639798, Singapore
differ in terms of the mathematical models (e.g., using Reynolds-averaged Navier-Stokes equations versus Euler inviscid equations), levels of discretization (e.g., using coarse mesh versus fine mesh in computational fluid dynamics (CFD) simulations), levels of abstraction (e.g., using low dimensional
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