A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty

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.