Machine learning-based system reliability analysis with Gaussian Process Regression
This work addresses a theoretical gap in reliability analysis for engineering systems, but it is incremental as it builds on existing methods with mathematical proofs and simulations.
The paper tackles the problem of identifying theoretical optimal learning strategies in machine learning-based reliability analysis, proving that the U learning function can be reformulated as optimal for cases neglecting Kriging correlation and showing that the optimal strategy considering correlation reduces the number of performance function evaluations compared to state-of-the-art methods, though it requires significant computational resources.
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.