Structural reliability analysis using a copula-function-based evidence theory model

Evidence theory contains powerful features for uncertainty analysis and can be effectively employed to address the epistemic uncertainty, which is attributed to a lack of information in complex engineering problems. This paper presents an evidence theory model based on the copula function and the related structural reliability analysis method. It is an effective tool for uncertainty modeling and reliability analysis with dependent evidence variables. In the evidence theory model, a canonical maximum likelihood (CML) method was adopted to estimate the correlation parameter, and the Akaike information criterion (AIC) was utilized to select a reasonable Archimedean copula function and whereby construct the joint basic probability assignment (BPA) for the multidimensional evidence variables. Based on the joint BPA function, a procedure for reliability analysis was formulated to compute the reliability interval on the structure with evidence uncertainty. Four numerical examples were provided to verify the effectiveness of the proposed method.