Efficient fuzzy simulations for estimating the failure credibility of engineering structures under fuzzy environment

Efficiently and accurately solving the failure credibility of a structural system plays a significant role in the engineering field under fuzzy environment. A more precise failure credibility can help assess the safety degree of the system, and then reduce the occurrence of security accidents. At present, the extended fuzzy first-order and second-moment method (EFFOSM) is effective to analyze failure credibility for some occasions. However, when it comes to complicated performance functions and fuzzy inputs, the accuracy of EFFOSM is greatly reduced and its efficiency also needs to be improved. To overcome the above shortcomings, this paper proposes two types of novel fuzzy simulation algorithms, namely uniform discretization algorithm (UDA) and bisection simulation algorithm (BSA). For the system involving frequently-encountered continuous and strictly monotone performance functions of regular LR fuzzy interval inputs, these two algorithms are designed to estimate failure credibility with higher efficiency and accuracy. Subsequently, with the aid of the linearization and regularization procedures in EFFOSM, the application of UDA and BSA is extended to non-monotone performance functions of irregular LR fuzzy intervals. To evaluate and verify the performance of the proposed two algorithms, their comparisons with EFFOSM are conducted through some numerical examples and practical problems. The results show that the proposed two algorithms outperform EFFOSM in terms of accuracy and efficiency, and also have wider application range for estimating the failure credibility of strictly monotone performance functions involving regular LR fuzzy interval inputs. Meanwhile, BSA is slightly better than UDA for the less runtime.