Multi-fidelity Kriging structural reliability analysis with the fusion of non-hierarchical low-fidelity models

Abstract

Adaptive Kriging is a common Bayesian statistical method and has founded wide application in structural reliability analysis. Multi-fidelity (MF) Kriging model can significantly reduce computational cost compared to single-fidelity Kriging model. However, research on MF Kriging reliability analysis remains relatively limited in the literature. Most existing MF Kriging approaches assume that reliability performance functions of varying fidelity levels follow a hierarchical nature, which is not applicable when the performance functions exhibit non-hierarchical fidelity levels across the input space. To handle this challenge, we develop a novel Bayesian adaptive MF Kriging method to integrate high-fidelity (HF) data with non-hierarchical low-fidelity (LF) Kriging models for reliability analysis. We first use the local correlation and variance-weighted fusion approach to fuse all the non-hierarchical LF models. Then, the hierarchical Kriging is employed for the construction of MF model based on HF data and the fused LF model. A new adaptive hierarchical refinement strategy is proposed. This strategy mainly involves a new hierarchical expected feasibility function (HEFF) for identifying the location and fidelity of the optimal sample simultaneously, and a low-fidelity-selection (LFS) algorithm based on Kriging-Believer approach to allocate simulations among non-hierarchical LF models. One numerical example and two engineering examples involving an aircraft tubing and an airfoil stiffener rib, are used to validate the performance of our method.