Structural Reliability Assessment Based on Subjective Uncertainty

Abstract

In traditional structural reliability analysis, the uncertainties, such as loads and strengths, are considered as random variables with specific probability distributions. When the information is insufficient, it is difficult to obtain the distribution functions. Hence, experts are usually asked to estimate the belief degrees. Uncertainty theory is a branch of mathematics used to model the belief degrees of experts. In this paper, the factors influencing system structures are treated as independent uncertain variables. Based on that, the concepts of safety margin, structural reliability and failure belief degree are proposed, respectively. Then the general calculation methods of structural reliability and failure belief degree for monotonic safety margins are given, which are not restricted by the specific distributions of variables and the safety margin forms. Furthermore, the reliability index is given for the structure with linear safety margin and normal uncertain variables, and the relationship between structural reliability and reliability index is proposed. In addition, the geometric property of reliability index is investigated and used to define the reliability index in non-linear safety margin and normal uncertain variables case. Finally, several numerical examples are employed to demonstrate the effectiveness of the methods.