Machine learning-based system reliability analysis with Gaussian Process
  Regression
Lisang Zhou Ziqian Luo Xueting Pan
Machine learning-based reliability analysis methods have shown great
advancements for their computational efficiency and accuracy. Recently, many
efficient learning strategies have been proposed to enhance the computational
performance. However, few of them explores the theoretical optimal learning
strategy. In this article, we propose several theorems that facilitates such
exploration. Specifically, cases that considering and neglecting the
correlations among the candidate design samples are well elaborated. Moreover,
we prove that the well-known U learning function can be reformulated to the
optimal learning function for the case neglecting the Kriging correlation. In
addition, the theoretical optimal learning strategy for sequential multiple
training samples enrichment is also mathematically explored through the
Bayesian estimate with the corresponding lost functions. Simulation results
show that the optimal learning strategy considering the Kriging correlation
works better than that neglecting the Kriging correlation and other
state-of-the art learning functions from the literatures in terms of the
reduction of number of evaluations of performance function. However, the
implementation needs to investigate very large computational resource.