An Efficient Method for Structural Reliability Analysis Using Evidence Theory

Due to a lack of complete information, epistemic uncertainty widely exists in engineering structures and mechanical systems. Evidence theory, which has a general and flexible framework, has been used to quantify the epistemic uncertainty and conduct reliability analysis recently. However, the discontinuous nature of uncertainty quantification using evidence theory can cause expensive computational cost. In this work, an efficient method based on evidence theory is proposed for reliability analysis under epistemic uncertainty. In this method, evidence variables in an original reliability problem are transformed into random variables by a method based on equal areas. Then, the most probable point (MPP) of the problem with random variables is obtained by reliability analysis using probability theory. Based on the MPP, the most probable focal element (MPFE) of the original reliability problem with evidence variables is identified. Finally, the contribution of some focal elements to the reliability analysis is judged directly and the calculation of extreme values of the limit-state function is just conducted over the other focal elements. The computing efficiency of the proposed method is demonstrated by two numerical examples. Results indicate that the proposed method can reduce the computational cost on the reliability analysis using evidence theory.