An evidence-theory model considering dependence among parameters and its application in structural reliability analysis

Due to its strong ability to deal with the epistemic uncertainty, evidence theory has been widely used to solve complex engineering problems with very limited information. This paper proposes a novel evidence-theory model for multidimensional problems, with consideration of the dependence among evidence variables. More specifically, a joint frame of discernment (FD) is created for multidimensional problem through an ellipsoidal model, where the correlativity between the parameters is well reflected by the shape of the ellipsoid. An approach to construct reasonable ellipsoids using the experimental samples is also provided. Combination of the ellipsoidal model and the marginal basic probability assignments (BPAs) of the parameters then generates a joint BPA structure. Based on the new evidence-theory model, a reliability analysis method is formulated to evaluate the safety degree of structures with dependent epistemic uncertainty. Four numerical examples are investigated to demonstrate the applicability of the proposed method.