Vertex method for computing functions of fuzzy variables
Fuzzy Sets and Systems
Probabilistic arithmetic. I. numerical methods for calculating convolutions and dependency bounds
International Journal of Approximate Reasoning
Uncertainty-Based Information: Elements of Generalized Information Theory
Uncertainty-Based Information: Elements of Generalized Information Theory
Structural reliability assessment based on probability and convex set mixed model
Computers and Structures
Comparative study of metamodeling techniques for reliability analysis using evidence theory
Advances in Engineering Software
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Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the large computational cost caused by its discrete property severely influences the practicability of evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with epistemic uncertainty, and hence improve the applicability of evidence theory in engineering problems. A uniformity approach is used to deal with the evidence variables, through which the original reliability problem can be transformed to a traditional reliability problem with only random uncertainty. It is then solved by using a response-surface-based reliability analysis method, and a most probable point (MPP) is obtained. Based on the MPP, the most critical focal element which has the maximum contribution to failure can be identified. Then using an approximate model created based on this focal element, the reliability interval can be efficiently computed for the original epistemic uncertainty problem. Three numerical examples are investigated to demonstrate the effectiveness of the present method, which include two simple problems with explicit expressions and one engineering application.