SFB 1313 Publication "Mixed Covariance Function Kriging Model for Uncertainty Quantification"

March 25, 2022

Authors: Kai Cheng, Zhenzhou Lu, Sinan Xiao, Sergey Oladyshkin, and Wolfgang Nowak | Scientific Journal: International Journal for Uncertainty Quantification

New SFB 1313 publication, published in the International Journal for Uncertainty Quantification. The work has been developped within the SFB 1313 research projects B04 and D03.

“Mixed Covariance Function Kriging Model for Uncertainty Quantification”

Authors
Abstract

In this paper, we develop a mixed covariance function Kriging (MCF-Kriging) model for uncertainty quantification. The mixed covariance function is a linear combination of a traditional stationary covariance function and a nonsta-tionary covariance function constructed by the inner product of orthonormal polynomial basis functions. We use a weight matrix to control the contribution of each polynomial basis to the whole model representation, and a trade-off parameter is used to balance the contribution of the two different covariance functions. The optimal values of these model hyperparameters are obtained through an iterative algorithm derived by maximum likelihood estimation (MLE), and sparse representation is achieved automatically in the MLE step by removing the basis functions with small contribution. Additionally, the hyperparameters of stationary covariance function are tuned by minimizing the leave-one-out cross-validation error of the surrogate model. For validation, we investigate three benchmark test functions with different dimensionalities, and compare the accuracy and efficiency with the state-of-art sequential PC-Kriging and optimal PC-Kriging models. The results show that the MCF-Kriging model provides comparable performance compared to the two PC-Kriging models for nonlinear problems, that are moderate and even high-dimensional. Finally, we apply our model to a heat conduction problem to demonstrate its effectiveness in engineering application.

This image shows Sergey Oladyshkin

Sergey Oladyshkin

apl. Prof. Dr.-Ing.

Principal Investigator, Research Project D03

This image shows Wolfgang Nowak

Wolfgang Nowak

Prof. Dr.-Ing.

Principal Investigator, Research Projects B04 and B05

To the top of the page