Year: 2020
Author: Yixiang Deng, Guang Lin, Xiu Yang
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1812–1837
Abstract
We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. Although GE-Cokriging requires slightly higher computational cost than Cokriging in some cases, the comparison of the accuracy shows that this cost is worthwhile.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0151
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1812–1837
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Gaussian process regression multifidelity Cokriging gradient-enhanced integral-enhanced.