An active-learning Kriging model for non-probabilistic reliability analysis

Traditional reliability analysis methods are generally based on probability theory, where parameter uncertainties are represented as random variables. which is often impractical, especially in the early stages of product design when limited data are available. To address this issue, a non-probabilistic reliability analysis method has been developed. Among these, the Interval variables method provides major advantages in addressing insufficient information. However, for systems with implicit and computationally expensive limit-state functions, determining the nonprobabilistic reliability index remains a major challenge. To resolve this challenge, the Efficient Global Optimization (EGO) approach offers a promising way. Constraints in non-probabilistic reliability analysis ensure that the optimization process yields solutions that are physically feasible and meet the practical requirements of engineering design. This paper proposes a new strategy to handle the constraints for non-probabilistic reliability analysis in the framework of Efficient Global Optimization. The inequality constraint is merged with the performance function, so both the constraint and the performance function are considered, ensuring that the resulting solutions satisfy practical engineering requirements. The Kriging model serves as a surrogate for the computationally demanding simulations, while the EGO process actively guides the search for optimal bounds of uncertainty parameters. The applicability and efficiency of the proposed method are verified through examples, demonstrating improved feasibility, reduced computational cost, and enhanced practicality in structural reliability analysis.

Keywords: Surrogate model, non-probabilistic reliability index, learning function, constraint, Kriging, efficient global optimization.