Scarce data-oriented parameter global sensitivity and reliability analysis with multidimensional dependence

In practical engineering, it is difficult to obtain sufficient data, and available data are typically limited and exhibit complex dependencies. To address the challenge of scarce and correlated data, a framework, termed Scarce data-oriented Parameter global sensitivity and Reliability analysis combined with Adaptive Kriging and Importance Sampling (SPR-AK-IS), is proposed to estimate the parameter global reliability sensitivity index and failure probability bounds, which aim to evaluate structural safety as well as guide data collection on important variables that affect structural failure. At first, the most likely distribution type for each variable is inferred by maximum likelihood estimation and the Kolmogorov-Smirnov test. Bootstrap resampling is applied to infer the confidence interval of distribution parameters, while the vine copula is used to represent the multidimensional dependence among variables. Then, auxiliary standard normal variables are introduced to decouple the distribution parameters from the input variables, so that the most probable failure point can be searched in the augmented space. Finally, the parameter global reliability sensitivity index and failure probability bounds can be evaluated efficiently based on a group of importance sampling samples combined with adaptive Kriging model. The proposed framework gives guidance for collecting data on the variables that are sensitive to the failure probability to minimize the epistemic uncertainty. Several examples show that SPR-AK-IS achieves comparable accuracy while significantly reducing computational cost.