A regular-vine copula-based evidence theory model for structural reliability analysis involving multidimensional parameter correlation

Abstract

The structural reliability analysis subject to epistemic uncertainty and multidimensional correlations among input variables signifies a crucial and demanding task. To address this challenge, a new evidence theory model capable of quantifying complex multidimensional correlations is proposed in this study; and further, an efficient reliability analysis method is developed. To start with, the multidimensional correlations are investigated through the proposed regular-vine copula-based evidence theory (VCET) model by leveraging finite number of samples and the marginal distributions of evidence variables. A joint basic probability assignment reconstruction method is then developed which integrates the copula function with multidimensional correlated evidence variables using a full-factorial numerical integration approach, thereby addressing parameter correlations. Further, the proposed model is employed in reliability analysis, and an enhanced focus element reduction (EFER) technique is developed. EFER synchronously constructs multiple auxiliary regions within the frame of discernment, where the classes of joint focus elements are directly determined, bypassing the high-cost extreme value analysis. Finally, the probability interval consisting of belief and plausibility measures is derived for structures affected by parameter correlations. In this study, three numerical benchmark problems and an engineering case study on the reliability analysis of the array antenna’s maximum gain are presented to demonstrate the effectiveness of the proposed method.