A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms

It is very difficult to know the exact boundaries of the variable domain for problems with small sample size, and the traditional convex set model is no longer applicable. In view of this, a novel reliability model was proposed on the basis of the fuzzy convex set (FCS) model. This new reliability model can account for different relations between the structural failure region and variable domain. Key computational algorithms were studied in detail. First, the optimization strategy for robust reliability is improved. Second, Monte Carlo algorithms (i.e., uniform sampling method) for hyper-ellipsoidal convex sets were studied in detail, and errors in previous reports were corrected. Finally, the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index. Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.