Belief reliability of structures with hybrid uncertainties

Reliability of structures is evaluated by considering uncertainties present in the system, which can be characterized into aleatory and epistemic. Inherent randomness in the physical environment leads to aleatory, whereas insufficient knowledge about the system leads to epistemic uncertainty. For the reliability evaluation, ascertaining the sources of uncertainties poses a great challenge since both uncertainties coexist widely in structural systems. Aleatory uncertainties are quantified by probabilistic measures (such as first order reliability method, second order reliability method and Monte Carlo techniques), whereas epistemic uncertainties are quantified by various non-probabilistic approaches (such as interval analysis methods, evidence theory, possibility theory and fuzzy theory). However, major issues like interval extension problem and duality conditions that lead to overestimation hinder the versatility of application of such methods, thus uncertainty theory has been emerged to overcome these limitations. Given the existing uncertainties and limitations, a hybrid strategy has been constructed and referred to as “belief reliability”. A belief reliability metric is integration of three key factors: design margin, aleatory and epistemic uncertainty factor to evaluate the reliability of the structural system. In this paper, Monte Carlo simulation is adopted to account for aleatory uncertainty. On the other hand, epistemic uncertainty is quantified through adjustment factor approach using FMEA (failure mode effective analysis). Numerical examples are presented to substantiate the proposed methodology being applied to variety of problems both implicit and explicit nature in structural engineering.