Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization

Reliability-based design optimization (RBDO) aims at minimizing general cost under the reliability constraints by considering the inherent uncertainties in engineering. In this work, we develop a decoupled RBDO approach named RIFA-ADK which aims at reliability index function (RIF) approximation by adaptive double-loop Kriging. The proposed RIFA-ADK contains three main blocks, namely reliability analysis (Block 1), reliability index function approximation (Block 2) and optimization (Block 3). In RIFA-ADK, RIF is approximated by the outer loop adaptive gradient-enhanced Kriging (GEK) model which takes into account reliability sensitivity in addition to reliability index. The required reliability analysis in GEK is based on the inner loop adaptive Kriging model which focuses on approximating the performance function, and the required reliability sensitivity analysis in GEK is a post-processing of reliability analysis. Then the optimization can be proceeded using the cheap GEK model of RIF. In addition, an adaptive learning strategy which involves two stages of enrichment is also developed to improve the surrogate precision in the region of interest. Finally, four mathematical and practical engineering examples for RBDO are presented to illustrate the accuracy and the efficiency of the proposed RIFA-ADK decoupled approach.