A variable and mode sensitivity analysis method for structural system using a novel active learning Kriging model

In the frame of structural system reliability, quantifying the impact degree of random variables and failure modes on system output is indispensable. A generalized variable sensitivity analysis (VSA) index is introduced for measuring the effect of each random variable. Then a mode sensitivity analysis (MSA) index is proposed for quantifying the effect of each failure mode on system failure probability. Additionally, to estimate the system failure probability, VSA and MSA indices efficiently, a novel active learning Kriging model combined with the system importance sampling (SIS) density function is proposed for structural systems. The SIS density function is obtained by kernel density estimation-based importance sampling and weighted coefficients of failure modes, which is employed for generating the candidate population to reduce the computational cost on predicting the enormous candidates. The proposed called ALK-SIS model can precisely and effectively deal with small failure probability events as well as multiple most probable point problems, and estimate the system failure probability and sensitivity indices without calling the performance functions additionally. Four case studies are investigated to demonstrate the significance of proposed VSA and MSA indices on system reliability as well as the efficiency and accuracy of the ALK-SIS.