A high-dimension structural reliability method based on active learning Kriging and dimension reduction technique

For efficiently and accurately estimating the failure probability and the further sensitivity index of the high-dimension structures, a novel AS-AK-MCS method is proposed in this work. This method fully employs the merits of the active subspace-based dimension reduction technique, the active learning (AL) Kriging surrogate model, and the Monte Carlo simulation. In the proposed method, the intractable gradient information needed by the active subspace method is obtained by a crude Kriging model with initial training sample points. In the construction of the crude Kriging model, the proposed trend model selection criterion reduces the man-made error. Then the active subspace method converts the reliability analysis from the original high-dimension space into the low-dimension subspace, which facilities constructing an AL-Kriging model and also avoids the tricky “curse of dimension” problem. The state-of-the-art U learning function is applied as the points adding criterion in the active subspace. In order to demonstrate the effectivity and versatility of the proposed method, three representative examples including the linear/nonlinear and the explicit/implicit performance functions are studied for estimating the failure probability and the failure probability-based sensitivity index. Finally, the proposed method is applied to the reliability and sensitivity analysis of a composite radome structure.