Data-driven reliability assessment with scarce samples considering multidimensional dependence

Abstract

This study proposes a data-driven method for assessing reliability, based on the scarce input dataset with multidimensional correlation. Since considering the distribution parameters estimated from the scarce dataset as those of the population may lead to epistemic uncertainty, the bootstrap resampling algorithm is adopted to infer the distribution parameters as interval parameters. To account for the variable dependence, vine copula theory is utilized to construct the joint probability density function (PDF) of input variables, and maximum likelihood estimation (MLE) and Akaike information criterion (AIC) analysis are employed to select optimal copulas based on the samples for the vine structure. Subsequently, the failure probability bounds of a response function are calculated based on the constructed joint PDF with interval distribution parameters by the active learning Kriging (AK) method combining the sparse grid integration (SGI) method. Finally, several examples are provided to demonstrate the feasibility and efficiency of the proposed method.