Uncertainty propagation with B-spline based interval field decomposition method in boundary value problems

Abstract

In this paper, uncertainty propagation problems are addressed by modelling the non-deterministic parameters as an interval field to account for spatial dependency. The interval field is constructed using a recently proposed B-spline based interval field decomposition method, which is related to an explicit formulation composed of B-spline basis functions and corresponding interval field coordinates, which can be incorporated directly into the governing equation of the boundary value problems. The solution to the governing equation can be approximated by a B-spline basis expansion using the collocation method taking advantage of high-degree continuity of B-spline basis functions. In this way, the crisp bounds of the output can be effectively accounted for. Numerical cases are provided to illustrate the effectiveness of the proposed method. The impact of the influence radius, the results obtained using an interval variable model and the combined impact of multiple uncertain parameters are also studied. Furthermore, for discretised problems, the interval field finite element formulation is presented and the resulting bounds of the output are determined by the Neumann expansion method, by which the extreme values can be effectively approximated.