This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties. A notable benefit of this approach is its ability to determine the response bounds across all degrees of freedom with a small sample size, which means that it has high efficiency. Firstly, the spatially varying uncertain parameters are quantified using an interval field model, which is described by a series of standard interval variables within a truncated interval Karhunen-Loève (K-L) series expansion. Secondly, considering that the bound of structural response is a function of spatial position with the property of continuity, a surrogate model for the response bound is constructed, namely the first-level Kriging model. The training samples required for this surrogate model are obtained by establishing the second-level Kriging model. The second-level Kriging model is established to describe the structural responses at particular locations relative to the interval variables so as to facilitate the upper and lower bounds of the node response required by the first-level Kriging model. Finally, the accuracy and effectiveness of the method are verified through examples.

This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the cross-correlation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model, through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.