Enriching IRA for nonlinear and low-probability failure problems: The active learning Kriging-based inverse reliability analyses

Active learning Kriging-based Inverse reliability analyses (AK-IRs) is proposed to addresses nonlinear and low-probability failure issues in inverse reliability analysis (IRA). Departing from linear approximations and inverse most probable point (iMPP) calculations, AK-IRs utilizes an active learning Kriging approach with proposed learning functions and discrimination criteria for precise limit state identification. This method focuses training points near the limit state, ensuring precise approximations in complex nonlinear scenarios. By constructing high-precision Kriging models without relying on gradient information, AK-IRs significantly enhances solution efficiency in IRA challenges. Numerical assessments and a real-world engineering case study validate the effectiveness of AK-IRs.