Analytical uncertainty quantification approach based on adaptive generalized co‐Gaussian process model

Abstract

Gaussian process modeling (GPM) is widely used to replace physical models for uncertainty quantification (UQ). The fidelity of training samples has a major impact on the prediction performance of the GPM, and the computational time of obtaining high‐fidelity (HF) samples from simulations may be very prohibitively expensive. Therefore, this study proposes the use of the multi‐fidelity GPM for UQ to make a trade‐off between the computational cost and accuracy by combining a few HF samples with many computationally‐cheaper low‐fidelity (LF) ones. Currently, the co‐Gaussian process model (co‐GPM, also known as multi‐fidelity GPM) requires that the LF and HF samples be nested. A generalized co‐Gaussian process model (GC‐GPM) is developed that can mix LF and HF samples under both nested and un‐nested conditions. In addition, to further alleviate the computational cost, an adaptive sampling strategy is introduced into GC‐GPM to reduce the number of training samples using a new infill criterion. Within the adaptive GC‐GPM framework, the high dimensional integrals associated with the statistical moments (mean and variance) of structural response can be decomposed to single dimensional ones that are analytically tractable, which finally allows for analytical calculation of the mean and variance. Three full‐scale structures are adopted to verify the reliability and efficiency of the proposed adaptive GC‐GPM method, and traditional GC‐GPM and Monte Carlo simulation (MCS) are used for comparison purpose. The comparison results show that the UQ results of the adaptive GC‐GPM match well with those of the MCS and compared to the traditional GC‐GPM, the adaptive GC‐GPM owns higher computational accuracy and efficiency.