Time-dependent safety and sensitivity analysis for structure involving both random and fuzzy inputs

The analyses of safety degree and sensitivity for structure are significant in engineering. For the time-dependent structure involving both random and fuzzy inputs, two indices named as the fuzzy time-dependent failure probability and the random time-dependent failure possibility are presented to measure safety degree of time-dependent structure from different aspects, i.e., the fuzzy time-dependent failure probability measures safety degree from the probabilistic view and the random time-dependent failure possibility measures safety degree from the non-probabilistic view. For efficiently estimating these two indices, Genetic Algorithms (GA) is employed. Furthermore, Sparse Grid (SG) technique combined with fourth-moment method is used to estimate the fuzzy time-dependent failure probability. Based on these two safety degree indices, two global sensitivity indices are established. By considering different aspects of the output, the importance ranking of the inputs can be obtained from these two established global sensitivity models. Some efficient procedures are proposed to estimate the global sensitivity indices by combining the three-point estimation method. Several examples containing the numerical and engineering ones are listed to illustrate the effectiveness of the proposed procedures for estimating the two safety degree indices and the two global sensitivity indices.