Abstract:
As engineering systems become increasingly complex, it is imperative to comprehend and mitigate the influence of uncertainty in reliability analysis. This is essential to ensure the safety and reliability of systems, underscoring the need for a thorough understanding and proactive management of uncertainty in the analysis process. Uncertainty in reliability analysis can be mainly of two types: aleatory uncertainty, which is the inherent randomness of the system, and epistemic uncertainty, which arises due to a lack of knowledge. Traditionally, reliability analysis has focused mostly on aleatory uncertainty, with little consideration given to approaches that successfully include both aleatory and epistemic uncertainties in reliability analysis. With the rapid development of reliability theory, there has been a growing volume of work on how to integrate both of these uncertainties into a reliability analysis framework. However, there have been very few works that have considered hybrid epistemic uncertainty in reliability analysis, and the computational burden of those methods is very high. To overcome these issues, this thesis presents a simultaneous application of interval variables and fuzzy variables to accurately depict epistemic uncertain parameters in reliability analysis. A dual-stage, first-order reliability analysis framework under random, interval, and fuzzy uncertainty has been proposed in this thesis by integrating probability theory and fuzzy set theory. In this thesis, probability distributions are used to model random variables, capturing the inherent stochastic nature of the system, while interval uncertainty is modeled using the worst-case maximum likelihood approach. In addition, fuzzy set theory is utilized to address ambiguity and vagueness, using fuzzy membership functions (FMF) to represent the related uncertainty. This proposed method is a two-stage reliability assessment procedure where, in the first stage, the most probable point is determined using the improved Hasofer-Lind-Rackwitz-Fiessler(iHLRF) method, while the second stage focuses on determining the optimum responses of the performance function. This computational model calculates the maximum and minimum probability of failure for performance functions in the second stage. The effectiveness and feasibility of this proposed approach are shown through the utilization of one mathematical and two engineering problems.