Dynamic Uncertainty Quantification and Risk Prediction Based on the Grey Mathematics and Outcrossing Theory

Embarked from the practical conditions of small samples in time-invariant and time-variant uncertainties, a complete non-probabilistic analysis procedure containing uncertainty quantification, uncertainty propagation, and reliability evaluation is presented in this paper. Firstly, the Grey systematic approach is proposed to determine the boundary laws of static intervals and dynamic interval processes. Through a combination of the policies of the second-order Taylor expansion and the smallest parametric interval set, the structural response histories via quantitative uncertainty results are further confirmed. Additionally, according to the first-passage idea from classical random process theory, the study on the time-dependent reliability measurement on the basis of the interval process model is carried out to achieve a more elaborate estimation for structural safety during its whole life cycle. A numerical example and one experimental application are eventually discussed for demonstration of the usage and reasonability of the methodology developed.