An interval finite element method based on bilevel Kriging model

• The spatially uncertain parameters are described by the interval field model with upper and lower bounds. • An interval finite element method based on the bilevel Kriging model is proposed for spatially uncertain structures. • The proposed method is a non-intrusive method that can be applied to complex problems and have high computational efficiency. 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.