Evidence-theory-based structural static and dynamic response analysis under epistemic uncertainties

Abstract

Evidence theory has a strong ability to deal with epistemic uncertainty, based on which the imprecise parameters with limited information can be conveniently treated. In this paper, a numerical method is developed to compute the linear elastic static and dynamic responses of structures with epistemic uncertainty based on evidence theory. Inspired by the moment concept in probability theory, the Raw Moments, Central Moments and Mixed Central Moments are proposed to describe the distribution characteristics of evidence variables, and the corresponding moments of functions with evidence variables are also defined. By integrating the moment concept and finite element method, a linear elastic static and dynamic response analysis technique is formulated to compute the moments of uncertain structural responses. To reduce the computational cost, the interval analysis technique is adopted to obtain the approximate response bounds for each focal element. Three numerical examples are investigated to demonstrate the effectiveness of the present method.