A new three-phase algorithm for computation of reliability index and its application in structural mechanics

Computation of reliability index or probability of failure in practical problems is still a challenge. In this paper, an efficient three-phase non-gradient-based algorithm is proposed to be used in structural reliability analysis. Like approximation methods, the purpose in the proposed algorithm is to locate the position of design point. However, for this purpose, at the iterations of the phases random samples are generated based on a moving sampling density function, like what is done in adaptive importance sampling. At each phase, by representing an updating criterion, the position of the candidate of design point is updated to approach the real design point. Two criteria of the first and second phase are to reduce the initial relatively large distance between the candidate of design point and the real one. In the third phase, after introducing a new effective fitness function, the third updating criterion is represented to take the final smaller steps of approaching design point. Through various numerical examples, the accuracy and efficiency of three aforementioned phases have been shown.