An efficient latent map multi-fidelity Kriging model and adaptive point-selected strategy for reliability analysis with time-consuming simulations

Reliability analysis can be particularly challenging when performance functions require time-consuming simulations. Such simulations often involve multiple fidelity sources. This paper aims to enhance the efficiency of reliability analysis by leveraging multiple sample datasets with varying sources of fidelity. Firstly, this paper extends the GP model to integrate multiple low fidelity data into high fidelity predictions. In order to consider the correlations among data from different fidelity sources, the latent space representation from LMGP is introduced into the correlation matrix of different fidelity data. This multi-fidelity GP model is referred to as a latent map multi-fidelity Kriging (LMmfK). The effectiveness of LMmfK is validated through 1-dimensional analytical test and 8-dimensional Borehole test. Secondly, based on LMmfK, this paper proposes an active learning point-selected strategy suitable for scenarios with multiple fidelity sources, referred to as mfUEFF. The mfUEFF strategy intelligently selects the best data points from multiple fidelity sources, leveraging the benefits of both global improvement and local uncertainty. This integration enhances the efficiency and accuracy of reliability analysis. Two classic cases demonstrate that the proposed reliability method demonstrates superior computational accuracy and efficiency compared to other reliability methods. Finally, this paper applies the proposed method to the static reliability analysis of gears, involving time-consuming finite element models. Engineering application demonstrates that this method significantly improves efficiency, especially in scenarios with multiple fidelity sources.