An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single-loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables.