Uncertainty Quantification of Structures Using Belief Theory

Abstract

Uncertainties due to loading, material properties, lack of knowledge, and manufacturing defaults are typical among practical engineering problems.They affect the performance and safety aspects of the structures.The fundamental difficulty in reliability evaluation is quantifying the uncertainty of structural systems.There are two forms of uncertainties such as aleatory uncertainty and epistemic uncertainty.Both aleatory uncertainty and epistemic uncertainty affect structures in the real world: aleatory uncertainty (induced by innate randomness) and epistemic uncertainty (induced by deficiency of information).Aleatory uncertainties can be handled effectively using probability measures, but epistemic uncertainties are not justified precisely using probability-based theories.Many non-probabilistic reliability estimates have been proposed to account for the influence of epistemic uncertainty, including evidence theory, interval analysis, fuzzy analysis, and the posbist reliability approach.A new reliability metric, belief reliability, is created to solve the disadvantages of non-probability approaches.Belief reliability is defined as the degree of confidence in the belief dependability of a system that meets four key axioms: normalcy, duality, subadditivity, and the product axiom.The belief’s reliability combines the contribution of design margin, aleatory uncertainty, and epistemic uncertainty.Belief reliability is an effective tool to evaluate uncertainties caused due to inherent randomness of the system (irreducible uncertainties) and uncertainties caused due to lack of information (reducible uncertainties).This paper reviews the belief reliability approach adopted for uncertainty quantification in civil engineering structures. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.