An improved first order approximate reliability analysis method for uncertain structures based on evidence theory

In this paper, an improved first order approximate reliability analysis method based on evidence theory is developed to evaluate the uncertain structures reliability. Firstly, the uncertain variables are described by using frame of discernment (FD) and the basic probability assignment (BPA). Secondly, the improved HL-RF (iHL-RF) method and Newton method are used to solve the most possible point(MPP) and the bound points, respectively. Thirdly, the limit-state functions are approximated by first order Taylor series at all key points obtained by most possible point and bound points. Then, based on the above approximate limit-state functions, the extremum analysis of all focal element is performed to solve the reliability measure indexes: the belief measure (Bel) and plausibility measure (Pl). Finally, two numerical examples and two engineering applications are discussed to verify the effectivity of the presented method.