Efficient multi-fidelity Kriging simulation for structural reliability analysis with new learning function and stopping criterion

Abstract

Structural reliability analysis often entails significant computational costs. Active learning surrogate models address this challenge, yet the potential of multi-fidelity surrogate models to reduce computational costs is noteworthy, particularly due to the efficiency of low-fidelity samples. However, the traditional learning function and stopping criterion are aimed at the single-fidelity framework, so they are not suitable for the multi-fidelity framework. This study introduces a novel active learning approach, the Adaptive Multi-fidelity Co-Kriging Monte Carlo Simulation (AMCK-MCS), to overcome these limitations. First, this study proposes a novel learning function for multi-fidelity Kriging surrogate models, which enhance the modeling efficiency by actively identifying high-uncertainty regions through a balanced integration of correlation, sampling density, and computational cost. Second, this study introduces a novel stopping criterion based on the relative error estimation of failure probability, derived from confidence intervals and the uncertainty weighting. This approach effectively mitigates the premature and delayed convergence in surrogate models. The proposed method is evaluated against classical methods based on distinct principles and two established multi-fidelity Kriging surrogate models through two numerical examples and an engineering case study. Results demonstrate that the AMCK-MCS method accurately predicts the failure probability while substantially reducing the computational costs.